Solving Integrated Process Planning, Dynamic Scheduling

Research ArticleSolving Integrated Process Planning Dynamic Schedulingand Due Date Assignment Using Metaheuristic Algorithms

Caner Erden 12 Halil Ibrahim Demir 12 and Abdullah Hulusi Koumlkccedilam 12

1Sakarya University Department of Industrial Engineering Sakarya Turkey2Sakarya University Artificial Intelligence Systems Application and Research Center Turkey

Correspondence should be addressed to Caner Erden cerdensakaryaedutr

Received 5 March 2019 Revised 2 May 2019 Accepted 13 May 2019 Published 30 May 2019

Academic Editor Alessandro Palmeri

Copyright copy 2019 Caner Erden et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Because the alternative process plans have significant contributions to the production efficiency of a manufacturing systemresearchers have studied the integration of manufacturing functions which can be divided into two groups namely integratedprocess planning and scheduling (IPPS) and scheduling with due date assignment (SWDDA) Although IPPS and SWDDA arewell-known and solved problems in the literature there are limited works on integration of process planning scheduling anddue date assignment (IPPSDDA) In this study due date assignment function was added to IPPS in a dynamic manufacturingenvironment And the studied problem was introduced as dynamic integrated process planning scheduling and due dateassignment (DIPPSDDA) The objective function of DIPPSDDA is to minimize earliness and tardiness (ET) and determine duedates for each job Furthermore four different pure metaheuristic algorithms which are genetic algorithm (GA) tabu algorithm(TA) simulated annealing (SA) and their hybrid (combination) algorithms GASA and GATA have been developed to facilitateand optimize DIPPSDDA on the 8 different sized shop floors The performance comparisons of the algorithms for each shop floorhave been given to show the efficiency and effectiveness of the algorithms used In conclusion computational results show that theproposed combination algorithms are competitive give better results than pure metaheuristics and can effectively generate goodsolutions for DIPPSDDA problems

1 Introduction

Process planning scheduling and due date assignmentfunctions have an important role in modern manufacturingsystems During the process planning stage operations ofjobs are sequenced and the production information is trans-ferred to the scheduling stage In a production facility processplanning stage comprises processes such as determination ofthe manufacturing method for the product and selection ofappropriate machines for each part Besides in a job shopscheduling problem (JSSP) machines are assigned to oper-ations of jobs with the objective of optimizing determinedperformance measures Although process planning is usedas an input in scheduling process planning and schedulingfunctions are considered as two independent and separatefunctions in classic manufacturing models [1] In recentyears it has been observed by various researchers across theworld that these two functions are interrelated and needed

to be handled together [2] Integration of process planningand scheduling (IPPS) studies aim to improve schedulingperformance measures such as optimizing makespan jobflow times earliness and tardiness (ET) of each job andmachine utilization level using different metaheuristic algo-rithms Furthermore there are several review articles on IPPSwhich can be given as [3ndash6] On the other hand many studiesproposed to integrate scheduling with due date assignment(SWDDA) as well Although there are numerous works onIPPS and SWDDA limited works on integrated processplanning scheduling and due date assignment (IPPSDDA)have been conducted so far

Obviously integrating due date assignment function withIPPS problem can provide a significant improvement inthe objective function and the global performance of themanufacturing system The first study on IPPSDDA wasconducted by Demir and Taskin [7] Demir et al [8ndash12]also presented genetic algorithm (GA) simulated annealing

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 1572614 19 pageshttpsdoiorg10115520191572614

2 Mathematical Problems in Engineering

(SA) tabu algorithm (TA) evolutionary strategies (ES) andhybrid algorithms to improve the global performance of theIPPSDDA problem In this study in addition to the otherstudies on IPPSDDA we considered a dynamic schedulingmodel in which each job enters the system at a randomtime and we introduced the integration of process planningdynamic scheduling and due date assignment (DIPPSDDA)problem The main contribution and the point at whichthis study is separated from other studies is to build adiscrete event simulation model for IPPSDDA problem thatcan adapt to unexpected and sudden internal or externalchanges (dynamic events) in a manufacturing system Westudied new job arrivals that may occur in real shop floorsas dynamic event for this study Furthermore it is also aimedat solving the DIPPSDDA problem with different efficientmetaheuristic algorithms which are simulated annealing(SA) tabu algorithm (TA) genetic algorithm (GA) and thecombination of GASA GATA to improve the performanceof the solutions The proposed model has been built withthe advantages of object-oriented programming (OOP) anddiscrete event simulation (DES) to enhance the flexibility ofthe model

This paper is organized as follows Section 1 is theintroduction part of the study A review of related worksis presented in Section 2 The background and definitionof DIPPSDDA are given in Section 3 Section 4 discussessolution techniques for the DIPPSDDA Section 5 gives thecomputational results and analysis of the study Conclusionsand future researches are also summarized in Section 6

2 Related Works

Minimizing costs by eliminating wastes is a core principleof a just-in-time (JIT) production philosophy Thus deter-mining due dates as close as possible to their due dates isinseparable from this philosophy If companies can completetheir productions on given due dates they can make morerealistic plans and have optimum capacity usage for shopfloors In this way resources are used efficiently and thecompany increases customer satisfaction In most modernJIT companies a job is expected to be completed in its timeThe completion of jobs after their due dates could lead toan increase in costs and a decrease in customer satisfactionand worst customer loss On the other hand the completionof jobs before their due date can cause inventory holdingcosts Integrated systems were proposed by considering theprocess planning and scheduling or scheduling with due dateassignment together to avoid ineffective production Someof the earlier studies reported that it is possible to findthe optimal due dates and optimal sequences of jobs usingdifferent heuristic algorithms [13ndash20] The objective of thesestudies is to minimize the cost related to due date assignmentand scheduling functions

Besides some of the recent studies on SWDDA canbe given such as [21ndash30] There are 3 types of due dateassignment models in the literature as follows

(i) Common due date assignment (CON) a predefinedcommon due date for each job

(ii) Due date assignment considering process times slackdue dates (SLK) total-work-content (TWK) process-ing plus due dates (PPW) etc

(iii) Assignment of due dates according to given values

Scheduling problems with an optimized due date hasbeen the subject of considerable works over the last severaldecades Determining the due date is amatter that needs to beemphasized in terms of customer satisfaction for companiesIf the due dates are not met the companies may face variousproblems Some of the studies on scheduling together withthe due date covered both single machine scheduling andmultimachine problems Scheduling studies considering duedates for single machine problems can often be seen in theliterature such as [17 23 26 31ndash35] Panwalkar and Smith[36] have studied the problem of determining the commondue date for the scheduling problem consisting of 119899 jobs andone machine in the shop floor At the end of the study theproblem was solved using a polynomial bound schedulingalgorithm Cheng [37] has set common due dates for each jobto minimize delay for a single machine scheduling problemBiskup andCheng [38] have attempted to solve the problemofsinglemachine scheduling and the assignment of due dates inwhich job is done with cramped process times In Gupta andSenrsquos [39] study decisions about scheduling batching andthe due date assignment were combined for a single machinescheduling problem with 119899 groups of jobs Bank and Werner[40] determined the duration of release and the duration ofthe transaction time for each job and assigned a common duedate Cheng [41] has aimed to find the optimal due dates fora scheduling problem He has emphasized that the heuristicmethod finds effective solutions for the problem

An early study on the single machine scheduling prob-lem with early and late due date penalties was conductedby Sidney [42] In another study the same problem wasaddressed again by Seidmann et al [43] and an algorithmwas developed to improve the solution performances Otherstudies in which ET are penalized for single machineschedules can be given such as [32ndash34 44]

On the other hand there are still many studies in theliterature in which there is more than one machine Allthese studies have attempted to determine common due datesfor each job With the intuitive use of heuristic algorithmsmany machine scheduling problems such as job floor typeproduction can be solved There is also a published literaturereview for multimachine scheduling problems conducted byLauff and Werner [45] in which researchers used for solvingthe multimachine scheduling problem a specific due date Inanother review study Gordon et al [46] drew a frameworkfor the common due date and scheduling problems In theirliterature study the models in which single machine andparallel machines are included and the other studies in theliterature on this subject were reviewed A study list onSWDDAclassified based on subjects or objectives of the studyis given in Table 1 Other examples of studies on schedulingwith due date assignment can be found in [46ndash48]

In a classic manufacturing model process planning andscheduling functions are carried out separately where onlyfixed process plans are transferred to the scheduling stage

Mathematical Problems in Engineering 3

Table 1 Studies with different approaches to SWDDA

Studies Subjects or objectives[16 18 21ndash23 25ndash28 30 32 46 53ndash56] Scheduling and common due date assignment[13 17 19 20 24 26 31 57ndash59] Scheduling and separate due date assignment[16 20 23ndash30 54] Single machine scheduling with due date assignment[53] Two-machine flow shop scheduling with due date assignment[18 19 22 28 46 55 56] Parallel machine scheduling with due date assignment[13 45 59 60] Multi-machine scheduling with due date assignment[57 58] Job shop scheduling with due date assignment[20] Earliness Penalty[31] Maximum Lateness[31 58] Total tardiness[21 27 31 54] ET penalties[61] Tardiness and due date related cost[18 22 24 26 28 45 53 55 56 62] Due-date related ET[29] Due date ET delivery cost[30] Due date assignment earliness and weighted number of tardy jobs[60] Processing ET costs[32] Resource consumption ET costs[17 21 25 31 32] Weighted number of late jobs Number of tardy jobs[19] Minimize maximum absolute lateness[23] Due date absolute lateness and processing time reduction[19 57] PPW (Process Plus Wait)[20 30] SLK (Common Slack)[57] TWK (Total work content)[60] Different ready times

Fixed process plans may cause some inefficient schedulesbecause of the inflexible nature To overcome these problemsthe idea of integrating process planning with scheduling hasarisen from the fact that working with alternative processplans on scheduling has improved the efficiency in man-ufacturing systems Wilhelm and Shin [49] addressed theefficiency of ldquoalternative operationsrdquo in their study in 1985 forthe first time After that the studies on IPPS were conductedby several researchers Chryssolouris et al [50] tried tointegrate process planning and scheduling for the first time in1985 Other early IPPS studies were carried out by Sundaramand Fu [51]

Thebestway to integrate process planning and schedulingis to take two functions together The integration of processplanning and scheduling functions is NP-Hard problem andit is difficult to find their optimal results in a reasonable timeeven with small sized problems [52] There are many studiesin the literature on the integration of these two functionswhich can be classified based on their solution approaches asgiven in Table 2

At the beginning of 2000 a very early study on IPPSDDAwas a PhD thesis conducted by Demir and Taskin [7]Integration of these three functions is useful to avoid theproblems that may arise in process planning scheduling anddue date assignment The intent of working with integratedfunctions is based on more efficient flow times processingtimes and variations in machine capacities and manufactur-ing flexibility From a literary perspective the integration of

the three functions is less mentioned In studies of Demiret al the feasibility advantages solution methods andresults of the integrated operation of the three functionswere mentioned In addition to the models discussed in theIPPS problems preparation times were also considered inthese studies and the importance of considering preparationtimes was discussed They integrated three functions whichare process planning scheduling and due date assignmentusing genetic algorithms in their thesis [7] It is observedthat weighted due date assignment and weighted schedulingimproved the overall performance of the problem substan-tially

One of the current work areas related to the jobshop scheduling problem is dynamic scheduling Dynamicscheduling problems are frequently encountered in real jobfloors for example jobs arriving at the shop floor randomlyover time machine breakdowns urgent jobs or cancellationof existing jobs Zandieh and Adibi [72] have used a variableneighboring search (VNS) algorithm to solve dynamic eventssuch as random jobs and machine failures in their studyThe dynamic scheduling problem can show deterministicor stochastic properties according to the arrival time of thejobs Scheduling is deterministic if the arrival time of jobs isknown in advance conversely if arrival times are randomlydistributed according to a specific distribution scheduling isstochastic [73]

The first literature review related to dynamic schedulingproblems can be found in [98] Dominic et al [99] have


Table 2 Classification of IPPS studies based on solution approaches

Solution Approach IPPS StudiesMulti-Agent Systems [63ndash68]Evolutionary Algorithm [4 39 69ndash71]GameTheory [31ndash33]Genetic Algorithm [7 34ndash36 40 45ndash47 49ndash52 70 72ndash75]Honey Bee Optimization [76ndash78]Imperialist Competitive Algorithm [79ndash81]Particle Swarm Optimization [82ndash88]Simulated Annealing [74 89 90]Hybrid Approaches [76 78 83 91ndash96]Ant Colony Optimization [97]

developed two new dispatching rules that work in thedynamic production job floor Dispatching rules have beenrevealed to be better than the existing SPT LIFO and LPTrules Aydin and Oztemel [100] have found a solution forthe dynamic scheduling problem using reinforced learningfactors for proper dispatching rule selection Li et al [101]developed an artificial neural network (ANN) using a GAfor the problem Sha and Liu [102] have developed a datamining tool that adapts to the dynamic conditions of jobsZandieh and Adibi [72] used it to predict the appropriateparameters of scheduling methods for the shortest averageprocessing time Zhang et al [103] developed a hybrid andtaboo search algorithm for a dynamic flexible job shopscheduling problem

As mentioned before dynamic integrated process plan-ning and scheduling problems are limited in the literature Inthe study by Lin et al [104] an integrated process planningand scheduling problem has been addressed to avoid thedynamic events that may occur in the job floors Xia et al[92] conducted a study using alternative process plans withthe benefit of the machine breakdowns in the job floor andthe problem with the random arrival of jobs was solved usingthe neighbor search algorithm Wong et al [105] have solvedthe dynamic integrated process planning and scheduling(DIPPS) problem by suggesting a hybrid multifactor-basedsystem Recent papers including that of Yu et al [106]employed a discrete particle swarm optimization to solvedynamic IPPS problem They used discrete particle swarmoptimization (DPSO) algorithm to solve IPPS optimizationproblem Meissner and Aurich [107] applied a cyberphysicalsystem for IPPS Sustainable IPPS problem was solved by Leeand Ha [108] using a standard GA Yin et al [109] used twocompeting agents for the integrated production inventoryand batch delivery scheduling and due date assignment Mor[110] studied common SWDDA with the focus on minmaxobjective functions Teymourifar and Ozturk [111] developeda new dispatching rule for dynamic JSSP

3 Problem Definition

Job shop scheduling problem (JSSP) mainly consists of 3elements which are machine configuration process charac-teristics and objective function [112] The main objective of

JSSP is to find a feasible schedule and to optimize given per-formance measures such as optimizing makespan earlinessand tardiness time of each job and machine utilization level

Basically scheduling models can be divided into twogroups static and dynamic models If there are stochas-tic events occurring over time such as new job arrivalsmachine breakdowns and order cancellations then thiskind of scheduling problem is named ldquodynamic schedulingproblemrdquoMost of the studies on scheduling focused on staticjob shop scheduling Static job shop scheduling means thatall scheduling conditions are static and all job information isknown and ready at 119905 = 0 A static JSSP deals with the processof assigning 119899 jobs to119898machines with the aim of optimizingdeterminedperformancemeasures simultaneously Althoughworking on static job shop scheduling is a well-knownproblem in the literature dynamic events often occur whichneeds to be handled to increase the productivity andmachinebalance rates in a real manufacturing system [98] Actualmanufacturing scheduling models are naturally dynamicwhich are harder to solve than static models [90 91] becausewhen there is an interruption proposed plans and schedulesshould be revised to respond to such dynamic events

In fact JSSP belongs to the NP-Hard class without anyintegration That is why the integration problems are seen asthe hardest among scheduling problems [71] It can be saidthat the problem of DIPPSDDA has a huge solution spacewhich is difficult to solve in a reasonable time Thereforethe use of metaheuristic algorithms is essential for solvingDIPPSDDA In this study we consider that arrival of jobsto the shop floor varies over time which makes our modeldynamic [113 114] Jobs are stochastically arriving at thesystem and have different weights due dates routes andprecedence rules

The assumptions of the problem to be addressed are listedbelow

(i) There is no ready job at 119905 = 0 and the arrival timeof the job is distributed according to the exponentialdistribution

(ii) Due dates for jobs are not assigned at 119905 = 0(iii) Each machine can process a single operation at the

same time


(iv) The processing time of the jobs is distributed accord-ing to the normal distribution

(v) Machines are not broken down(vi) The preparation times of the machines are ignored(vii) Each job can only be delivered to the customer after

all its operations are finished

The notation used for the formulation of the problem isgiven in Table 3

31 Due Date Assignment Rules DIPPSDDA begins withthe determination of due dates which is the assignment ofthe due dates of the jobs In many cases negotiations withcustomers can be made to arrange due dates in this process[63 64] Inconsistent due dates can lead to unwanted pricediscounts customer dissatisfaction or even end-customerloss In classic manufacturing models a job is expectedto be completed before its due date In contrast just-in-time (JIT) manufacturing environment requires all jobs tobe completed exactly on their due dates In most casesearly due dates can lead to an increase in inventory costsSimilarly late due dates lead to customer dissatisfaction pricedisruption and worst customer lossThere are many studiesusing quadratic penalty functions to solve tardiness andlinear penalty functions to solve earliness and tardiness (ET)problems In this study linear penalty functions are utilized toovercome these problems and generatemore accurate processplans

Both dynamic and static due date assignment rules wereemployed in this study Dynamic due date assignment rulesuse information about the job route and operation time aswell as the shop floor and average processing times Static duedate assignment rules use the information relevant to the jobsuch as the arrival of jobs route information and operationsfor calculating due dates All due date assignment rules usedin the study are given in Table 4 with the explanations andequations

32 Dispatching Rules Dispatching rules are widely used forjob shop scheduling with simple implementation Generallydispatching rules are used for the selection of the operationsby machines in shop floor 8 different dispatching rules wereused in the study and the list of dispatching rules with thepriority index and the descriptions of the rules is given inTable 5 The 119904119897119886119888119896 is calculated as in (1)

119904119897119886119888119896 = 119889119894 minus 119901119894 minus 119905 (1)

33 Objective Function Theobjective of scheduling problemshas been often to minimize the makespan Sometimes theobjective function may also be to minimize the average flowtime balance the machine loads etc In this study we usea penalty function for both ET and due dates for eachjob If the value of lateness is positive this means that thejob is completed lately If the value of lateness is negativethis means that the job is completed early The penalty forearly completion is 0 as expected and in case of the earlycompletion time the tardiness penalty is given as 0 Earliness

tardiness and due date penalties are calculated as in (2) (3)and (4) respectively

119879119895 = max (119888119895 minus 119889119895 0) (2)

119864119895 = max (119889119895 minus 119888119895 0) (3)

119875119863 = 119908119895 times (8 times ( 119863119895480)) (4)

Weights are applied for a better objective function inthe model We considered a working day as one shift with8 working hours and that makes 480 minutes per day Allthe weighted ET and due date related costs are punishedaccording to (5) and (6) Meanwhile (7) shows the sum ofthe total penalty

119875119864 = 119908119895 times (5 + 4 times ( 119864119895480)) (5)

119875119879 = 119908119895 times (6 + 6 times ( 119879119895480)) (6)

119875119905119900119905119886119897 = 119875119863 + 119875119864 + 119875119879 (7)

The objective function of the model is to minimize thetotal penaltieswhich are penalties for ET anddue datesThenthe final objective function which is a fitness value of thesolution is calculated as shown in (8)

119891119898119894119899 =119899sum119895=1

119875119905119900119905119886119897 (8)

34 Data Studied The configurations for the 8 shop floorsare given in Table 6 There is also a mini-shop floor fortesting algorithm performances by hand For example thefirst shop floor includes 25 jobs 10 operations 5 differentroutes and 5 machines Also the number of iterations ofalgorithms for the shop floors is given in Table 3 Theprocessing times in the shop floor conform to the nor-mal distribution which has a 6 average and 12 standarddeviations

The data produced for the study were generatedspecifically for this study because there is no other similardata in the literature in which process planning schedulingand due date assignment rules are employed The databelonging to the shop floors produced by using NumPylibrary in the Python programming language wereseparated according to the shop floors and saved asldquotxtrdquo files Firstly the time of job arrivals is generatedaccording to the exponential distribution and savedin the file ldquoarrivals shop floor numbertxtrdquo Secondlythe machine sequences for each alternative processplan of the jobs are saved in the file ldquomachine numbersshop floor numbertxtrdquo and the processing times are savedin the file ldquooperation durations shop floor numbertxtrdquoFinally weights are given in the file ldquoweights shopfloor numbertxtrdquo The data files are provided asSupplementary Materials


Table 3 The notation used for the formulation

119899 the number of jobs 119864119895 the earliness time of 119895-th job119898 the number of machines 119889119894 due date time of 119895-th job119903 the number of routes 120572 the penalty coefficient of early completion 120572 gt 0119900 the number of operations 120573 the penalty coefficient of late completion 120573 gt 0119886119895 the arrival time of 119895-th job 119875119863 the penalty for due date119908119895 the weight of the 119895-th job 119875119864 the penalty for earliness119901119895 the total processing time of 119895-th job 119875119879 the penalty for tardiness119901119894119895 the processing time of i-th operation of 119895-th job 119875119895 the penalty for 119895-th job119901119886V the mean processing time of all jobs waiting 119875119905119900119905119886119897 the total penalty119888119895 the departure time the completion time of 119895-th job 119891119898119894119899 the performance function119871119895 the lateness time of 119895-th job 119863119863119904119894119911119890 the number of due date assignment rules119879119895 the tardiness time of 119895-th job 119863119877119904119894119911119890 the number of dispatching rules119868119895 Priority index of 119895-th job 119863119895 the difference between due date and arrival time of job 119895-th job

Table 4 Due date assignment rules

Rule No Name Explanation Equations012 SLK Slack 119889119894 = 119886119894 + 119901119894 + 119902119909345 WSLK Weighted slack 119889119894 = 119886119894 + 119901119894 + 1199081119909119902119909678 TWK Total work content 119889119894 = 119886119894 + 11989611990911990111989491011 WTWK Weighted total work content 119889119894 = 119886119894 + 1199081119909119896119909119901119894121314 NOPPT Number of operations plus processing time 119889119894 = 119886119894 + 119901119894 + 5119896119909119900119894151617 WNOPPT The weighted number of operations plus processing time 119889119894 = 119886119894 + 119901119894 + 5119908111990911989611990911990011989418 RDM Random-allowance due dates 119889119894 = 119886119894 + 119873 (3119875119886V 119875119886V)192021222324252627 PPW Processing-time-plus-wait 119889119894 = 119886119894 + 119896119909119901119894 + 119902119909282930313233343536 WPPW Weighted processing-time-plus-wait 119889119894 = 119886119894 + 1199082119909119896119909119901119894 + 1199081119909119902119909

35 Simulation Study In the beginning of the study theshop floor is scheduled according to available jobs on handWhen a new job arrives at the shop floor according to anexponential distribution the job list is updated and theproblem turns into dynamic JSSP To solve the dynamicproblem a discrete event simulation has been establishedfor a job shop configuration to validate the performance ofthe dispatching and due date rules If we choose the rightdistributions for the job arrivals and operation durationswe can get more effective solutions for the simulations Thesimulation input data which have several jobs machinesoperations and routes were given in Table 5 Briefly jobs havedifferent routes and they must be processed on each machineonly once When a new job arrives at the shop floor it istaken to the machine queue according to the selected routeby the algorithm Machines are allocated according to thedispatching rule for the jobs waiting in the machine queueAfter that processing times of each job are distributed witha normal distribution The due dates are determined usingselected due date assignment rule Finally 23 dispatching and37 due date assignment rules are utilized and simulation isrun till all jobs finish on the shop floor

The steps of the simulation are as follows

(i) Execute the algorithm to generate an individual solu-tion

(ii) When a new job comes to the shop floor determineweights operation times operation precedence anddurations and route for the job

(iii) Calculate the due date according to the selected duedate assignment rule for the job

(iv) The first operation of the job enters the queue of themachine to be assigned

(v) The machine selects the operation from the pendingoperations according to the selected dispatching rule

(vi) The completion time for the last operation of the jobis determined as the departure time of the job

(vii) The earliness tardiness (ET) and due dates (D) forthe job are calculated using the objective functionwhich is given in (8)

(viii) The solution is optimized by running steps of theproposed metaheuristics

4 Solution Techniques

41 Genetic Algorithm (GA) In 1975 Holland [115] proposedGA which has a good performance in solving difficultproblems by mimicking the biological evolution process GAworks based on the population of solutions which has a


Table 5 Dispatching rules

Rule No Name Explanation Equations

0-1-2 WATC Weighted Apparent Tardiness Cost 119868119894 = 119908119894119901119894 119890(119898119886119909(1199041198971198861198881198960)119870119901)

3-4-5 ATC Apparent Tardiness Cost 119868119894 = 1119901119894 119890(119898119886119909(1199041198971198861198881198960)119870119901)

6 WMS Weighted Minimum Slack 119868119894 = minus (119904119897119886119888119896) 1199081198947 MS Minimum Slack 119868119894 = minus (119904119897119886119888119896)8 WSPT Weighted shortest process time 119868119894 = 1199081198941199011198949 SPT Shortest process time 119868119894 = 1

11990111989410 WLPT Weighted longest process time 119868119894 = 11990111989411990811989411 LPT Longest process time 119868119894 = 11990111989412 WSOT Weighted shortest operation time 119868119894 = 11990811989411990111989411989513 SOT Shortest operation time 119868119894 = 1

11990111989411989514 WLOT Weighted longest operation time 119868119894 = 119901119894119895

11990811989415 LOT Longest operation time 119868119894 = 11990111989411989516 EDD Earliest due date 119868119894 = 1

11988911989417 WEDD Weighted Earliest due date 119868119894 = 11990811989411988911989418 ERD Earliest release date 119868119894 = 1

11988611989419 WERD Weighted earliest release date 119868119894 = 11990811989411988611989420 SIRO Service in random order 11990311988611989911988911990011989821 FIFO First in first out 119868119894 = 1

11988611989422 LIFO Last in first out 119868119894 = 119886119894

Table 6 Shop configurations

Shop Floors 1 2 3 4 5 6 7 8Number of jobs 25 50 75 100 125 150 175 200Number of operations 10 10 10 10 10 10 10 10Number of machines 5 10 15 20 25 30 35 40Number of routes 5 5 5 5 3 3 3 3Iteration size 150 150 100 100 75 75 50 50

common use in the field of scheduling and IPPS Thanks tothe popularity of GA and its easy-to-implement structureresearchers commonly implement GA to solve a variety ofproblems including scheduling related problems Geneticoperators are the most important part of the development ofGA modeling In this study selection crossover and muta-tion GA operators were employed To increase performance

with GA it is needed to consider some parameters suchas the number of initial populations crossover rate muta-tion rate the maximum number of generations length ofchromosomes encoding the chromosomes and decoding theindividuals and calculating and formulating fitness functionin an efficient way Algorithm 1 shows the pseudocode forGA


(1) DO Random Search(2) BEGIN to Initialize population(3) Evaluate population(4) Rank chromosomes(5) for i le iter size do(6) Ranking selection for parents(7) Crossover(8) Mutation(9) Replace population(10) Return 119904119906119898(11) end for

Algorithm 1 Genetic algorithm

The main steps of GA are as follow

(1) Initialization of population A random search wasperformed in 10 of the total number of iterationsbefore the genetic algorithm was applied Best 10chromosomes from random search generate an initialpopulation for GA Figure 1 shows a sample chromo-some

(2) GA operators Next step is to generate a new popula-tion from the mating pool through genetic operatorswhich are crossover and mutation

(a) Crossover Operator selects two chromosomesas parents and creates new child individualsIn the beginning the crossover operator deter-mines the crossover point size which is calcu-lated using formula119862119904119894119911119890 = 119891119897119900119900119903(01times119873)whereN is the chromosome length so 119862119904119894119911119890 is relatedto the length of the chromosome For exampleif N is equal to 27 which is the value of the firstshop floor 119862119904119894119911119890 is calculated as 2 Each geneon a chromosome has a different probabilityto be selected as a crossover point where duedate rule gene and dispatching rule gene have adominant probability of 05 and the rest of thegenes share the other 05 equally An example ofcrossover operation is given in Figure 2

(b) Mutation Operator selects a dynamic numberof points changing according to the length ofthe chosen chromosome and changes it to anappropriate value from the domain Each geneof the chromosome has a different probabilityto be selected as a mutation point where the duedate rule gene and dispatching rule gene have adominant probability of 05 and the rest of thegenes share the other 05 equally An exampleof mutation operation is given in Figure 3119872119904119894119911119890 is the number of mutation points which iscalculated using formula119872119904119894119911119890 = 119891119897119900119900119903(05times119873)

(c) Selection Process of selecting parents isrepeated until the stopping criteria are metwhich is the maximum iteration size Theaverage fitness value of the population decreases

in time as the chromosomes with the bestfitness values are selected for the new gen-eration(i) Ranking selection method A linear rank-

ing selection method is used in whichthe best chromosome in a populationgets more probability to be selected Thismethod is chosen because the best andworst fitness values get closer as the iter-ations go on in time In the last iterationthe fitness values are almost equalThis willcause the algorithm to use the same proba-bilities when selecting among the best andthe worst chromosomes Contrary to theuse of fitness values alone sorting individ-uals and assigning probabilities accordingto their positions will give better solutionsto this problem In the ranking selectionmethod chromosomes have the probabilityof being selected according to their rankingand these probabilities are fixed for alliterations In this study the preferred prob-ability for 10 chromosomes is [03 02 015012 010 007 003 002 0006 0004]respectively Table 7 shows the differencesin selection probabilities between roulettewheel and ranking selection methods forthe initial and last population

(3) Updating the population As the population sizeneeds to be limited to a fixed number which is 10 forthis study 10 best chromosomes will always survive atthe end of the iteration

42 Tabu Algorithm (TA) Glover [116] proposed the funda-mental framework of TA which is a metaheuristic algorithmdesigned to find a near-optimum solution for complexproblems It starts from an initial solution generated basedon local search After it finds a feasible solution TA tries toget better fitness values by selecting the best individual in eachiteration TA searches space for finding a good neighborhoodIt stores the previous bad solutions in a tabu list This processis repeated until the maximum iteration number is reachedThe tabu list is updated and compared to the current solutionat every single iteration The size of the tabu list is kept fixedto usememory effectively Algorithm2 shows the pseudocodefor TA and variable neighborhood search algorithm for TAand SA is illustrated in Figure 4

43 Simulated Annealing (SA) SA is used to solve large-scaleoptimization problems which was developed by Kirkpatricket al [117] based on the cooling and recrystallization pro-cess of hot materials SA is another neighborhood searchalgorithm and widely used to solve big combinatorial opti-mization problems It is used in many problems in numerousdisciplines in particular global extremum is searched withinthemany local extrema [118] SA evaluates the neighborhoodswith the fitness value but it might choose the worst move


Chromosomes

Gene Number

Shop floor 1Due date assignment Dispatching rule

N = 27 n = 25Routes of jobs

rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Figure 1 A sample chromosome

Shop floor 1 2size = C Crossover points [5 12]

Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points

Figure 2 A sample crossover operation

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Shop floor 1 Mutation points [5 12]

Parent

Child

2size = M

Figure 3 A sample mutation operation

in each iteration to escape from a local minimum Theprobability of selecting a solution is given by an exponentialcontrol function in which the parameter of the functionwill decrease during the execution which is given in (9) SAdiffers from TA as it diversifies the solutions by randomizingthem while TA diversifies them by forcing new solutionsAlgorithm 3 shows the pseudocode for SA

119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)

where 119875119886119888119888119890119901119905 is the acceptance rate 119879 is the temperature119896119861 is the Boltzmann constant 119864119894 is the fitness value of thecurrent solution and 119864119905 is the fitness value of the nextsolution 119875119886119888119888119890119901119905 depends on the value of the 119879 At the firstiteration the temperature is high when it moves to the nextiterations the temperature is decreased gradually

5 Experimental Results

A computer program in Python programing language wasdeveloped to solve DIPPSDDA using Jupyter IDE on acomputer which has Intel i5-6200U processor with 230GHzspeed and 8GB of memory The most used package list todevelop the program can be given as follows sequencesmatrices and probability calculations used in this study werecoded using theNumPy library [119]ThePandas library [120]provides important conveniences for data analysis and datascience and was used to analyze data in tablesTheMatplotliblibrary [121] was used to visualize the graphs in the study andanalyze the data A library named Salabim [122] was used forthe simulation which is an important part of this study

A discrete event simulation (DES) model was developedto represent a job shop scheduling system for this study At119905 = 0 there is no job and the machines are ready to operateDiscrete event simulation updates the system itself when a


Start choosing a shop floor

Generate a random initial solution XDue Date Rule Dispatching Rule and

Routes of Jobsi=0

Evaluate solution x Run Simulation

i=i+1

Are stoppingcriteria met Yes Stop

No

Generate a number of random pointsfrom solution X

Change value of points to another valueSave solution X as solution Y

No

Evaluate solution Y Run Simulation

Solution y isbetter thansolution X

Yes

Solution X = Solution Y

Figure 4 Variable neighborhood search (VNS) algorithm flow chart

job arrives The arrival time was assigned to the next jobbased on the cumulative time of the interarrivals so far Thearrival intervals of jobs and the number of jobs within theseintervals in each shop floors are provided with histogramgraphs in Figure 5 The first graph shows the arrival times forthe first 4 shop floors and the next 4 shop floors are shown in

the second graph as giving all shop floors at the same chartreduces the readability of the chart It is also assumed that thetime between arrivals is an integer number The arrival timeof the next job is calculated by adding the value generated bythe exponential distribution function to the arrival time ofthe previous job


Table 7 The differences between the selection probabilities of the roulette wheel and ranking selection methods

Chromosome Fitness Roulette wheel selection probability Ranking selection probabilityInitial Population Best 18942 01277 0300

Average 24153 01000 0100Worst 38076 00635 0004

Sum of fitness 241530Last Population Best 15921 01011 0300

Average 16118 01000 0100Worst 16312 00987 0004

Sum of fitness 161180

(1) BEGIN to Choose shop floor 119899119898 119900(2) Generate initial solution 119904119900119897119906119905119894119900119899119909(3) 119894 larr997888 1(4) while 119894119905119890119903119886119905119894119900119899 lt 119894119905119890119903 119904119894119911119890 do(5) if 119904119900119897119906119905119894119900119899119909 not in tabu list then(6) 119894 larr997888 119894 + 1(7) Generate 119904119900119897119906119905119894119900119899119910 using VNS(8) if 119904119900119897119906119905119894119900119899119910 lt 119904119900119897119906119905119894119900119899119909 then return 119904119900119897119906119905119894119900119899119910(9) end if(10) else(11) Update tabu list return 119904119900119897119906119905119894119900119899119909(12) end if(13) end while

Algorithm 2 Tabu algorithm

(1) BEGIN to Choose shop floor 119899119898 119900(2) Generate 119904119900119897119906119905119894119900119899119909(3) 119905119890119898119901119890119903119886119905119906119903119890 larr997888 100(4) 119904119900119897119906119905119894119900119899119904 larr997888 Oslash(5) while 119905119890119898119901119890119903119886119905119906119903119890 gt 0 do(6) Generate 119904119900119897119906119905119894119900119899119910 using VNS(7) 120575 larr997888 119904119900119897119906119905119894119900119899119910 minus 119904119900119897119906119905119894119900119899119909(8) if 120575 lt 0 then return 119904119900119897119906119905119894119900119899119910(9) else(10) Calculate 119875119886119888119888119890119901119905(11) if 119875119886119888119888119890119901119905 lt 119903119886119899119889119900119898 then return 119904119900119897119906119905119894119900119899119910(12) elsereturn 119904119900119897119906119905119894119900119899119909(13) end if(14) end if(15) 119905119890119898119901119890119903119886119905119906119903119890 larr997888 119905119890119898119901119890119903119886119905119906119903119890 minus 100119894119905119890119903119886119905119894119900119899119904119894119911119890(16) solutionsappend(119904119900119897119906119905119894119900119899119909)(17) end while

Algorithm 3 Simulated annealing

Another purpose of this study is to determine the benefitof the integration of due date assignment and the dispatchingrules with process planning by realizing 4 different levels ofintegration At the first level of integration SIRO dispatchingrule and RDM due date assignment rule were tested It canalso be said that no rules are applied to this level At thesecond level of integration dispatching rules are included inthe problem However due date assignment rule is still being

determined with RDM and only the benefit of determiningthe dispatching rule is attempted At the third level ofintegration the dispatching rule was left as SIRO and thedue date assignment rules were applied At the fourth levelof integration the improvement in the solution has beenobserved in the case where all the dispatching rules and duedate assignment rules are applied where process planningweighted scheduling and weighted due date assignmentfunctions are fully integrated According to these tests resultsshow that full integration level always gives the best resultSolutions of different integration levels for 8th shop floor arecompared in Table 8 Full integration level has been observedto have the best performance as shown in Table 8

Experimental results of VNS SA TA GA and HAalgorithms are compared with each other and comparedwith the results of the ordinary solution which is foundwithout applying any algorithms The number of iterations isdetermined based on the characteristics of the algorithms asGA is population-based and SA and TA are individual-basedIn each iteration of the GA 10 individuals are generatedHowever only one individual is produced in each iterationof the SA and TA algorithms Therefore the number ofiterations given to GA is not equal to the SA and TAalgorithms Iteration numbers of SA and TA algorithms aretaken as ten times of GA iteration number Best meanand worst results of VNS SA TA GA and HA algorithmsare recorded The performance graphs of the algorithms areplotted separately for each shop floor and given in Figure 6

As mentioned before the developed model is a run ondiscrete event-time simulation Simulation outputs have beenexamined instantaneously proving that the system workscorrectly according to the different due date and dispatchingrules different shop floor types and different types of jobsand machinery Simulation trace records all the movementsobtained over time until the last job is completed For betterreading of simulation results Gantt charts for the first twoshop floors are given in Figures 7 and 8 Figure 7 shows theGantt chart for the first shop floor in which the best solutionfrom TA algorithm is calculated with the chromosome of [96 4 1 3 0 4 3 2 4 2 2 0 3 3 0 2 1 4 1 2 2 1 1 3 01] with 16328 fitness value Figure 8 shows the Gantt chartfor the second shop floor in which the best solution fromGATA is calculated with the chromosome of [3 17 3 2 22 2 2 4 3 3 1 2 2 4 4 1 1 0 0 1 3 3 3 0 3 0 0 3 22 2 2 2 3 2 0 1 4 2 3 2 2 4 1 2 1 3 2 0 1 3] with


5-8 shop floors1-4 shop floors

00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500

timeSF Shop Floor SF Shop Floor

SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival

sFigure 5 Job arrival times

Table 8 Comparison of solutions at different integration levels for shop floor 8

Level Algorithm Best Average Worst CPU (s)1-SIRO-RDM VNS 167078 167078 167239 330

SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683

2-DSP-RDM VNS 152483 157295 166559 325SA 164810 166470 168302 335TA 152066 156820 165437 332GA 158377 158529 158608 698HA 159213 163313 166677 698

3-SIRO-DD VNS 164739 164742 165104 168SA 164108 165484 167416 171TA 163527 163665 164923 202GA 113505 153061 162352 350HA 164308 165490 166706 295

4-DSP-DD VNS 131205 133974 132221 329SA 12850 129005 130006 328TA 125575 126085 130491 329GA 126541 128032 129851 348HA 124618 125560 129851 337

31109 fitness value The Gantt charts of larger shop floorsare not graphically presented because they are complex andimpossible to follow In addition to the classical Gantt chartsindicators are added to the graphs which show the arrivals ofjobs In the Gantt chart each job is represented with a colorbar and all box pieces represent the single operation of a job

6 Discussion and Conclusions

We studied the integration of process planning schedulingand due date assignment manufacturing functions that arerelated to and affecting the performance of each other in adynamic shop floor where jobs arrive to the system stochas-tically In actual manufacturing model these functions are

also affected by various events such as urgent orders ordercancellations maintenance machine breakdowns and delaysin supplies However studies on the integration of processplanning scheduling and due date assignment are limitedand most of these studies are working in a static environ-ment our work focused on designing effective algorithmfor the dynamic integrated problem As only schedulingproblem is NP-Hard integration of scheduling with othermanufacturing function is also NP-Hard Thus it is essentialto use a heuristic solution for such a problem We havedeveloped 4 different puremetaheuristic algorithms and theircombination algorithms to solve DIPPSDDA Our objectivefor DIPPSDDA was to minimize the earliness tardiness anddue date times of each job in 8 different shop floors Even


Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

Figure 6 Best average and worst performances of proposed algorithms on different shop floors

with integrating these functions are not enough to modelreal-world problems thoroughly Based on the tested exper-iments it was shown that the proposed hybrid algorithm(GATA) and TA algorithms have generally a good frame

for the integration problem Besides GATA and TA showhigher reliability to solve DIPPSDDA Unfortunately it is notpossible to make a benchmark to test the performance of theproposed system as it is a new field in the literatureThemain


m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820

job0job1job2job3job4

job5

Shop floor 1

job6job7job8job9




Mac

hine

s

Figure 7 Schedule of the best solution generated from GATA in shop floor 1

0

job0job1job2job3job4job5job6job7job8job9





93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2

Figure 8 Schedule of the best solution generated from TA in the shop floor 2

contribution of this study is to develop a new model which iscalled DISPPSDA over the current IPPS and DIPPS models

The study also demonstrates the benefits of running duedate assignment and dispatching rules with process planselection together Shop floors have been run without anydue date assignment and dispatching rule then the rules are

integrated step by step As a result it is observed that the bestresults are obtained at full integration level

This study is one of the few studies on dynamic inte-grated process planning and scheduling The following threesuggestions can be the objectives of future work Firstlythe flexibility of operations and operation numbers or the


flexibility of processes and numbers can be integrated into thestructure of DIPPSDDA Secondly the work can be furthertailored to the dynamic events such as machine breakdownscancellation of jobs and the arrival of new urgent jobs Lastlyin the objective function of the problem earliness tardinessand due date times are punished In addition more objectivescan be specified to the problem such as makespan machinebalance rates and minimumwait times of each jobThus theproblem can be made multiobjective

Data Availability

The ldquotxtrdquo data used to support the findings of this study areincluded within the Supplementary Materials

Conflicts of Interest

The authors declare that they have no conflicts of interest

Supplementary Materials

The data produced for the study were generated specificallyfor this study because there is no other similar data in theliterature in which process planning scheduling and duedate assignment rules are employed The data belonging tothe shop floors produced by using NumPy library in thePython programming language were separated according tothe shop floors and saved as ldquotxtrdquo files Firstly the time of jobarrivals is generated according to the exponential distribu-tion and saved in the file ldquoarrivals shop floor numbertxtrdquoSecondly the machine sequences for each alternative processplan of the jobs are saved in the file ldquomachine numbersshop floor numbertxtrdquo and the processing times are savedin the file ldquooperation durations shop floor numbertxtrdquoFinally weights are given in the file ldquoweights shop floornumbertxtrdquo (Supplementary Materials)

References

[1] Y F Zhang A N Saravanan and J Y H Fuh ldquoIntegration ofprocess planning and scheduling by exploring the flexibility ofprocess planningrdquo International Journal of Production Researchvol 41 no 3 pp 611ndash628 2003

[2] X Li L Gao X Shao C Zhang and C Wang ldquoMathe-matical modeling and evolutionary algorithm-based approachfor integrated process planning and schedulingrdquo Computers ampOperations Research vol 37 no 4 pp 656ndash667 2010

[3] W Tan and B Khoshnevis ldquoIntegration of process planning andscheduling-a reviewrdquo Journal of Intelligent Manufacturing vol11 no 1 pp 51ndash63 2000

[4] M Gen L Lin and H Zhang ldquoEvolutionary techniques foroptimization problems in integrated manufacturing systemState-of-the-art-surveyrdquo Computers amp Industrial Engineeringvol 56 no 3 pp 779ndash808 2009

[5] X Li L Gao C Zhang and X Shao ldquoA review on integratedprocess planning and schedulingrdquo International Journal ofManufacturing Research vol 5 no 2 pp 161ndash180 2010

[6] R K Phanden A Jain and R Verma ldquoIntegration of processplanning and scheduling a state-of-the-art reviewrdquo Interna-tional Journal of Computer IntegratedManufacturing vol 24 no6 pp 517ndash534 2011

[7] H I Demir and H Taskin Integrated process planning schedul-ing and due-date assignment [phd thesis] Sakarya UniversitySakarya Turkey 2005

[8] H I Demir and C Erden ldquoSolving process planning andweighted scheduling with wnoppt weighted due-date assign-ment problem using some pure and hybrid meta-heuristicsrdquoSakarya Universitesi Fen Bilimleri Enstitusu Dergisi vol 21 no2 pp 210ndash222 2017

[9] C Erden H I Demir A Goksu and O Uygun ldquoSolvingprocess planning ATC scheduling and due-date assignmentproblems concurrently using genetic algorithm for weightedcustomersrdquo Academic Platform-Journal of Engineering and Sci-ence 2018

[10] H I Demir O Uygun I Cil M Ipek and M Sari ldquoProcessplanning and scheduling with slk due-date assignment whereearliness tardiness and due-dates are punishedrdquo Journal ofIndustrial and Intelligent Information vol 3 no 3 2014

[11] H I Demir T Cakar M Ipek B Erkayman and O CanpolatldquoProcess planning and scheduling with PPW due-date assign-ment using hybrid searchrdquo International Journal of Science andTechnology vol 2 no 1 pp 20ndash37 2016

[12] H I Demir A H Kokcam F Simsir and O Uygun ldquoSolvingprocess planning weighted earliest due date scheduling andweighted due date assignment using simulated annealing andevolutionary strategiesrdquoWorld Academy of Science Engineeringand Technology International Journal of Industrial andManufac-turing Engineering vol 11 no 9 pp 1512ndash1519 2017

[13] H Luss andM B Rosenwein ldquoA due date assignment algorithmfor multiproduct manufacturing facilitiesrdquo European Journal ofOperational Research vol 65 no 2 pp 187ndash198 1993

[14] P De J B Ghosh andC EWells ldquoScheduling about a commondue date with earliness and tardiness penaltiesrdquo Computers ampOperations Research vol 17 no 2 pp 231ndash241 1990

[15] S Li C T Ng and J Yuan ldquoGroup scheduling and duedate assignment on a single machinerdquo International Journal ofProduction Economics vol 130 no 2 pp 230ndash235 2011

[16] M Y Kovalyov ldquoBatch scheduling and common due dateassignment problem an NP-hard caserdquo Discrete Applied Math-ematics The Journal of Combinatorial Algorithms Informaticsand Computational Sciences vol 80 no 2-3 pp 251ndash254 1997

[17] V Gordon and W Kubiak ldquoSingle machine scheduling withrelease and due date assignment to minimize the weightednumber of late jobsrdquo Information Processing Letters vol 68 no3 pp 153ndash159 1998

[18] G I Adamopoulos and C P Pappis ldquoScheduling under acommon due-date on parallel unrelated machinesrdquo EuropeanJournal of Operational Research vol 105 no 3 pp 494ndash5011998

[19] T C E Cheng and M Y Kovalyov ldquoComplexity of parallelmachine scheduling with processing-plus-wait due dates tominimize maximum absolute latenessrdquo European Journal ofOperational Research vol 114 no 2 pp 403ndash410 1999

[20] V S Gordon and V A Strusevich ldquoEarliness penalties on asingle machine subject to precedence constraints SLK due dateassignmentrdquo Computers amp Operations Research vol 26 no 2pp 157ndash177 1999


[21] D Biskup and H Jahnke ldquoCommon due date assignment forscheduling on a single machine with jointly reducible process-ing timesrdquo International Journal of Production Economics vol69 no 3 pp 317ndash322 2001

[22] G Mosheiov and U Yovel ldquoMinimizing weighted earliness-tardiness and due-date cost with unit processing-time jobsrdquoEuropean Journal of Operational Research vol 172 no 2 pp528ndash544 2006

[23] J-B Wang ldquoSingle machine scheduling with common due dateand controllable processing timesrdquo Applied Mathematics andComputation vol 174 no 2 pp 1245ndash1254 2006

[24] Y Xia B Chen and J Yue ldquoJob sequencing and due dateassignment in a single machine shop with uncertain processingtimesrdquo European Journal of Operational Research vol 184 no 1pp 63ndash75 2008

[25] D Shabtay ldquoDue date assignments and scheduling a singlemachine with a general earlinesstardiness cost functionrdquoCom-puters ampOperations Research vol 35 no 5 pp 1539ndash1545 2008

[26] V S Gordon and V A Strusevich ldquoSingle machine schedulingand due date assignment with positionally dependent process-ing timesrdquo European Journal of Operational Research vol 198no 1 pp 57ndash62 2009

[27] H Allaoua and I Osmane ldquoVariable parameters lengths geneticalgorithm for minimizing earliness-tardiness penalties of singlemachine scheduling with a common due daterdquo Electronic Notesin Discrete Mathematics vol 36 no C pp 471ndash478 2010

[28] N H Tuong and A Soukhal ldquoDue dates assignment and JITscheduling with equal-size jobsrdquo European Journal of Opera-tional Research vol 205 no 2 pp 280ndash289 2010

[29] YQ Yin T C E ChengDH Xu andC CWu ldquoCommonduedate assignment and scheduling with a rate-modifying activityto minimize the due date earliness tardiness holding andbatch delivery costrdquo Computers amp Industrial Engineering vol63 no 1 pp 223ndash234 2012

[30] S Li C T Ng and J Yuan ldquoScheduling deteriorating jobswith CONSLK due date assignment on a single machinerdquoInternational Journal of Production Economics vol 131 no 2 pp747ndash751 2011

[31] X Qi G Yu and J F Bard ldquoSingle machine scheduling withassignable due datesrdquoDiscrete AppliedMathematicsThe Journalof Combinatorial Algorithms Informatics and ComputationalSciences vol 122 no 1-3 pp 211ndash233 2002

[32] C T D Ng T C Cheng M Kovalyov and S S Lam ldquoSinglemachine scheduling with a variable common due date andresource-dependent processing timesrdquoComputersampOperationsResearch vol 30 no 8 pp 1173ndash1185 2003

[33] T C Cheng Z-L Chen and N V Shakhlevich ldquoCommon duedate assignment and scheduling with ready timesrdquo Computersamp Operations Research vol 29 no 14 pp 1957ndash1967 2002

[34] A C Nearchou ldquoA differential evolution approach for the com-mon due date earlytardy job scheduling problemrdquo Computersamp Operations Research vol 35 no 4 pp 1329ndash1343 2008

[35] K-C Ying ldquoMinimizing earlinesstardiness penalties for com-mon due date single-machine scheduling problems by a recov-ering beam search algorithmrdquo Computers Industrial Engineer-ing vol 55 no 2 pp 494ndash502 2008

[36] S S Panwalkar M L Smith and A Seidmann ldquoCommon duedate assignment to minimize total penalty for the one machinescheduling problemrdquo Operations Research vol 30 no 2 pp391ndash399 1982

[37] T C Cheng ldquoAn alternative proof of optimality for the commondue-date assignment problemrdquo European Journal of OperationalResearch vol 37 no 2 pp 250ndash253 1988

[38] D Biskup and T C E Cheng ldquoSingle-machine schedulingwith controllable processing times and earliness tardiness andcompletion time penaltiesrdquo Engineering Optimization vol 31no 1-3 pp 329ndash336 1999

[39] S K Gupta and T Sen ldquoMinimizing a quadratic function of joblateness on a single machinerdquo Engineering Costs and ProductionEconomics vol 7 no 3 pp 187ndash194 1983

[40] J Bank and F Werner ldquoHeuristic algorithms for unrelated par-allelmachine schedulingwith a commondue date release datesand linear earliness and tardiness penaltiesrdquoMathematical andComputer Modelling vol 33 no 4-5 pp 363ndash383 2001

[41] T C Cheng ldquoOptimal due-date determination and sequenc-ing with random processing timesrdquo Applied MathematicalModelling Simulation and Computation for Engineering andEnvironmental Systems vol 9 no 8 pp 573ndash576 1987

[42] J B Sidney ldquoOptimal single-machine scheduling with earlinessand tardiness penaltiesrdquo Operations Research vol 25 no 1 pp62ndash69 1977

[43] A Seidmann S S Panwalkar and M L Smith ldquoOptimalassignment of due-dates for a single processor schedulingproblemrdquo International Journal of Production Research vol 19no 4 pp 393ndash399 1981

[44] T Ibaraki and Y Nakamura ldquoA dynamic programming methodfor singlemachine schedulingrdquoEuropean Journal of OperationalResearch vol 76 no 1 pp 72ndash82 1994

[45] V Lauff and F Werner ldquoScheduling with common due dateearliness and tardiness penalties for multimachine problems asurveyrdquoMathematical and Computer Modelling vol 40 no 5-6pp 637ndash655 2004

[46] V S Gordon J M Proth and C Chu ldquoA survey of the state-of-the-art of common due date assignment and schedulingresearchrdquoEuropean Journal of Operational Research vol 139 no1 pp 1ndash25 2002

[47] T C E Cheng andM C Gupta ldquoSurvey of scheduling researchinvolving due date determination decisionsrdquo European Journalof Operational Research vol 38 no 2 pp 156ndash166 1989

[48] K R Baker ldquoSequencing rules and due-date assignments in ajob shoprdquo Management Science vol 30 no 9 pp 1093ndash11041984

[49] W E Wilhelm and H-M Shin ldquoEffectiveness of alternateoperations in a flexible manufacturing systemrdquo InternationalJournal of Production Research vol 23 no 1 pp 65ndash79 1985

[50] G Chryssolouris S Chan and N P Suh ldquoAn integratedapproach to process planning and schedulingrdquo CIRP Annals -Manufacturing Technology vol 34 no 1 pp 413ndash417 1985

[51] R M Sundaram and S-s Fu ldquoProcess planning and schedulingΓ a method of integration for productivity improvementrdquoComputers amp Industrial Engineering vol 15 pp 296ndash301 1988

[52] BKhoshnevis andQMChen ldquoIntegration of process planningand scheduling functionsrdquo Journal of Intelligent Manufacturingvol 2 no 3 pp 165ndash175 1991

[53] M Birman and G Mosheiov ldquoA note on a due-date assign-ment on a two-machine flow-shoprdquo Computers amp OperationsResearch vol 31 no 3 pp 473ndash480 2004

[54] X Cai V Y S Lum and JM T Chan ldquoScheduling about a com-mon due date with job-dependent asymmetric earliness andtardiness penaltiesrdquo European Journal of Operational Researchvol 98 no 1 pp 154ndash168 1997


[55] LMin andWCheng ldquoGenetic algorithms for the optimal com-mon due date assignment and the optimal scheduling policyin parallel machine earlinesstardiness scheduling problemsrdquoRobotics and Computer-IntegratedManufacturing vol 22 no 4pp 279ndash287 2006

[56] G Mosheiov ldquoA common due-date assignment problem onparallel identical machinesrdquo Computers amp Operations Researchvol 28 no 8 pp 719ndash732 2001

[57] V Vinod and R Sridharan ldquoSimulation modeling and analysisof due-date assignment methods and scheduling decision rulesin a dynamic job shop production systemrdquo International Journalof Production Economics vol 129 no 1 pp 127ndash146 2011

[58] T Yang Z He and K K Cho ldquoAn effective heuristic methodfor generalized job shop scheduling with due datesrdquo Computersamp Industrial Engineering vol 26 no 4 pp 647ndash660 1994

[59] S R Lawrence ldquoNegotiating due-dates between customers andproducersrdquo International Journal of Production Economics vol37 no 1 pp 127ndash138 1994

[60] J N D Gupta K Kruger V Lauff F Werner and Y N SotskovldquoHeuristics for hybrid flow shops with controllable processingtimes and assignable due datesrdquo Computers amp OperationsResearch vol 29 no 10 pp 1417ndash1439 2002

[61] D Chen S Li and G Tang ldquoSingle machine schedulingwith common due date assignment in a group technologyenvironmentrdquo Mathematical and Computer Modelling vol 25no 3 pp 81ndash90 1997

[62] D Shabtay and G Steiner ldquoThe single-machine earliness-tardiness scheduling problem with due date assignment andresource-dependent processing timesrdquo Annals of OperationsResearch vol 159 pp 25ndash40 2008

[63] T N Wong C W Leung K L Mak and R Y K Fung ldquoAnagent-based negotiation approach to integrate process planningand schedulingrdquo International Journal of Production Researchvol 44 no 7 pp 1331ndash1351 2006

[64] M K Lim and Z Zhang ldquoA multi-agent based manufacturingcontrol strategy for responsivemanufacturingrdquo Journal ofMate-rials Processing Technology vol 139 no 1-3 pp 379ndash384 2003

[65] P Gu S Balasubramanian and D H Norrie ldquoBidding-basedprocess planning and scheduling in a multi-agent systemrdquoComputers amp Industrial Engineering vol 32 no 2 pp 477ndash4961997

[66] X Li C Zhang L Gao W Li and X Shao ldquoAn agent-basedapproach for integrated process planning and schedulingrdquoExpert Systems with Applications vol 37 no 2 pp 1256ndash12642010

[67] M Lim and D Zhang ldquoAn integrated agent-based approach forresponsive control of manufacturing resourcesrdquo Computers ampIndustrial Engineering vol 46 no 2 pp 221ndash232 2004

[68] T N Wong C W Leung K L Mak and R Y FungldquoIntegrated process planning and schedulingreschedulingmdashanagent-based approachrdquo International Journal of ProductionResearch vol 44 no 18-19 pp 3627ndash3655 2006

[69] P S Ow and T E Morton ldquoThe single machine earlytardyproblemrdquoManagement Science vol 35 no 2 pp 177ndash191 1989

[70] C Y Lee and J Y Choi ldquoA genetic algorithm for job sequenc-ing problems with distinct due dates and general early-tardypenalty weightsrdquo Computers amp Operations Research vol 22 no8 pp 857ndash869 1995

[71] C Moon and Y Seo ldquoEvolutionary algorithm for advancedprocess planning and scheduling in a multi-plantrdquo Computersamp Industrial Engineering vol 48 no 2 pp 311ndash325 2005

[72] M Zandieh and M A Adibi ldquoDynamic job shop schedulingusing variable neighbourhood searchrdquo International Journal ofProduction Research vol 48 no 8 pp 2449ndash2458 2010

[73] S-C Lin E D Goodman and W F Punch ldquoA geneticalgorithm approach to dynamic job shop scheduling problemsrdquoin Proceedings of the 7th International Conference on GeneticAlgorithms 1997

[74] T C E Cheng ldquoA heuristic for common due-date assignmentand job scheduling on parallel machinesrdquo Journal of the Opera-tional Research Society vol 40 no 12 pp 1129ndash1135 1989

[75] K R Baker and G D Scudder ldquoSequencing with earliness andtardiness penalties a reviewrdquoOperations Research vol 38 no 1pp 22ndash35 1990

[76] B Yuan C-Y Zhang X-Y Shao and Z-B Jiang ldquoAn effectivehybrid honey bee mating optimization algorithm for balancingmixed-model two-sided assembly linesrdquo Computers amp Opera-tions Research vol 53 pp 32ndash41 2015

[77] X LiW Li X Cai and FHe ldquoAhoney-beemating optimizationapproach of collaborative process planning and scheduling forsustainablemanufacturingrdquo in Proceedings of the 2013 IEEE 17thInternational Conference on Computer Supported CooperativeWork in Design (CSCWD) pp 465ndash470 IEEE Whistler BCCanada June 2013

[78] X X Li W D Li X T Cai and F Z He ldquoA hybrid optimizationapproach for sustainable process planning and schedulingrdquoIntegrated Computer-Aided Engineering vol 22 no 4 pp 311ndash326 2015

[79] L Liqing L Hai L Gongliang and Y Guanghong ldquoIntegratedproduction planning and scheduling systemdesignrdquo inProceed-ings of the 2017 8th IEEE International Conference on SoftwareEngineering and Service Science (ICSESS) pp 731ndash734 IEEEBeijing China November 2017

[80] K Lian C Zhang X Shao and L Gao ldquoOptimization ofprocess planning with various flexibilities using an imperialistcompetitive algorithmrdquo The International Journal of AdvancedManufacturing Technology vol 59 no 5-8 pp 815ndash828 2012

[81] S Zhang Y Xu Z Yu W Zhang and D Yu ldquoCombiningextended imperialist competitive algorithmwith a genetic algo-rithm to solve the distributed integration of process planningand scheduling problemrdquo Mathematical Problems in Engineer-ing vol 2017 Article ID 9628935 13 pages 2017

[82] X Li L Gao and X Wen ldquoApplication of an efficient modifiedparticle swarm optimization algorithm for process planningrdquoThe International Journal of Advanced Manufacturing Technol-ogy vol 67 no 5ndash8 pp 1355ndash1369 2013

[83] F Zhao Y Hong D Yu Y Yang and Q Zhang ldquoA hybridparticle swarm optimisation algorithm and fuzzy logic forprocess planning and production scheduling integration inholonic manufacturing systemsrdquo International Journal of Com-puter Integrated Manufacturing vol 23 no 1 pp 20ndash39 2010

[84] Y W Guo W D Li A R Mileham and G W Owen ldquoAppli-cations of particle swarm optimisation in integrated processplanning and schedulingrdquo Robotics and Computer-IntegratedManufacturing vol 25 no 2 pp 280ndash288 2009

[85] Y-J Tseng F-Y Yu and F-Y Huang ldquoA green assemblysequence planning model with a closed-loop assembly anddisassembly sequence planning using a particle swarm opti-mization methodrdquoThe International Journal of Advanced Man-ufacturing Technology vol 57 no 9-12 pp 1183ndash1197 2011

[86] H Zhu W Ye and G Bei ldquoA particle swarm optimization forintegrated process planning and schedulingrdquo in Proceedings of


the 2009 IEEE 10th International Conference on Computer-AidedIndustrial Design Conceptual Design pp 1070ndash1074 IEEE 2009

[87] Y W Guo W D Li A R Mileham and G W OwenldquoOptimisation of integrated process planning and schedulingusing a particle swarm optimisation approachrdquo InternationalJournal of Production Research vol 47 no 14 pp 3775ndash37962009

[88] L I Ba Y Li M Yang et al ldquoA mathematical model for mul-tiworkshop IPPS problem in batch productionrdquo MathematicalProblems in Engineering vol 2018 Article ID 7948693 16 pages2018

[89] W D Li and C A McMahon ldquoA simulated annealing-basedoptimization approach for integrated process planning andschedulingrdquo International Journal of Computer Integrated Man-ufacturing vol 20 no 1 pp 80ndash95 2007

[90] A A R Hosseinabadi H Siar S Shamshirband M Shojafarand M H N Md Nasir ldquoUsing the gravitational emulationlocal search algorithm to solve the multi-objective flexibledynamic job shop scheduling problem in Small and MediumEnterprisesrdquo Annals of Operations Research vol 229 no 1 pp451ndash474 2014

[91] A B Farahabadi and A Hosseinabadi ldquoPresent a new hybridalgorithm scheduling flexible manufacturing system consider-ation cost maintenancerdquo International Journal of Scientific ampEngineering Research vol 4 no 9 pp 1870ndash1875 2013

[92] H Xia X Li and L Gao ldquoA hybrid genetic algorithm withvariable neighborhood search for dynamic integrated processplanning and schedulingrdquo Computers amp Industrial Engineeringvol 102 pp 99ndash112 2016

[93] J N Hooker ldquoA hybrid method for planning and schedulingrdquoConstraints An International Journal vol 10 no 4 pp 385ndash4012005

[94] X Y Li X Y Shao L Gao andW R Qian ldquoAn effective hybridalgorithm for integrated process planning and schedulingrdquoInternational Journal of Production Economics vol 126 no 2pp 289ndash298 2010

[95] W Huang Y Hu and L Cai ldquoAn effective hybrid graph andgenetic algorithm approach to process planning optimizationfor prismatic partsrdquo The International Journal of AdvancedManufacturing Technology vol 62 no 9ndash12 pp 1219ndash1232 2012

[96] W Zhang M Gen and J Jo ldquoHybrid sampling strategy-basedmultiobjective evolutionary algorithm for process planning andscheduling problemrdquo Journal of Intelligent Manufacturing vol25 no 5 pp 881ndash897 2014

[97] C W Leung T N Wong K L Mak and R Y K FungldquoIntegrated process planning and scheduling by an agent-basedant colony optimizationrdquo Computers amp Industrial Engineeringvol 59 no 1 pp 166ndash180 2010

[98] R Ramasesh ldquoDynamic job shop scheduling A survey ofsimulation researchrdquo Omega vol 18 no 1 pp 43ndash57 1990

[99] P D Dominic S Kaliyamoorthy and M S Kumar ldquoEfficientdispatching rules for dynamic job shop schedulingrdquo The Inter-national Journal of Advanced Manufacturing Technology vol -1no 1 pp 1-1 2003

[100] M E Aydin and E Oztemel ldquoDynamic job-shop schedulingusing reinforcement learning agentsrdquoRobotics and AutonomousSystems vol 33 no 2 pp 169ndash178 2000

[101] S Li Z Wu and X Pang ldquoJob shop scheduling in real-timecasesrdquo The International Journal of Advanced ManufacturingTechnology vol 26 no 7-8 pp 870ndash875 2005

[102] D Y Sha and C-H Liu ldquoUsing datamining for due date assign-ment in a dynamic job shop environmentrdquo The InternationalJournal of Advanced Manufacturing Technology vol 25 no 11-12 pp 1164ndash1174 2005

[103] L Zhang L Gao and X Li ldquoA hybrid genetic algorithm andtabu search for a multi-objective dynamic job shop schedulingproblemrdquo International Journal of Production Research vol 51no 12 pp 3516ndash3531 2013

[104] C R Lin H Chen and Q Xiao ldquoDynamic integrated processplanning and schedulingrdquo Journal of the Chinese Institute ofEngineers vol 18 no 2 pp 21ndash32 2001

[105] T N Wong C W Leung K L Mak and R Y K FungldquoDynamic shopfloor scheduling in multi-agent manufacturingsystemsrdquo Expert Systems with Applications vol 31 no 3 pp486ndash494 2006

[106] M R Yu B Yang and Y Chen ldquoDynamic integration ofprocess planning and scheduling using a discrete particle swarmoptimization algorithmrdquo Advances in Production Engineering ampManagement vol 13 no 3 pp 279ndash296 2018

[107] H Meissner and J C Aurich ldquoImplications of cyber-physicalproduction systems on integrated process planning andschedulingrdquo Procedia Manufacturing vol 28 pp 167ndash173 2019

[108] H Lee and C Ha ldquoSustainable integrated process planningand scheduling optimization using a genetic algorithm with anintegrated chromosome representationrdquo Sustainability vol 11no 2 p 502 2019

[109] Y Yin Y YangDWang T C Cheng andC-CWu ldquoIntegratedproduction inventory and batch delivery scheduling with duedate assignment and two competing agentsrdquo Naval ResearchLogistics (NRL) vol 65 no 5 pp 393ndash409 2018

[110] B Mor ldquoMinmax scheduling problems with common due-date and completion time penaltyrdquo Journal of CombinatorialOptimization pp 1ndash22 2018

[111] A Teymourifar and G Ozturk ldquoNew dispatching rules anddue date assignment models for dynamic job shop schedulingproblemsrdquo International Journal ofManufacturing Research vol13 no 4 pp 302ndash329 2018

[112] M L Pinedo Scheduling Theory Algorithms and SystemsSpringer Cham Switherland 5th edition 2016

[113] L Chunlin Z J Xiu and L Layuan ldquoResource schedulingwith conflicting objectives in grid environments Model andevaluationrdquo Journal of Network and Computer Applications vol32 no 3 pp 760ndash769 2009

[114] H Van Luu and X Tang ldquoAn efficient algorithm for schedulingsensor data collection through multi-path routing structuresrdquoJournal of Network and Computer Applications vol 38 no 1 pp150ndash162 2014

[115] J H Holland Adaptation in Natural and Artificial Systems AnIntroductory Analysis with Applications to Biology Control andArtificial Intelligence University ofMichigan Press Oxford UK1975

[116] F Glover ldquoTabu search a tutorialrdquo Interfaces vol 20 no 4 pp74ndash94 1990

[117] S Kirkpatrick C D Gelatt and M P Vecchi ldquoOptimization bysimulated annealingrdquo Science vol 220 no 4598 pp 671ndash6801983

[118] S Kirkpatrick ldquoOptimization by simulated annealing quanti-tative studiesrdquo Journal of Statistical Physics vol 34 no 5-6 pp975ndash986 1984

[119] T EOliphantAguide toNumPy vol 1 Trelgol PublishingUSA2006


[120] W McKinney ldquoData structures for statistical computing inpythonrdquo in Proceedings of the 9th Python in Science Conferencevol 445 pp 51ndash56 Austin TX USA 2010

[121] J D Hunter ldquoMatplotlib a 2D graphics environmentrdquo Comput-ing in Science amp Engineering vol 9 pp 90ndash95 2007

[122] R van der Ham ldquosalabim discrete event simulation andanimation in Pythonrdquo Journal of Open Source Software vol 3no 27 p 767 2018

Hindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Decision SciencesAdvances in


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Submit your manuscripts atwwwhindawicom


(SA) tabu algorithm (TA) evolutionary strategies (ES) andhybrid algorithms to improve the global performance of theIPPSDDA problem In this study in addition to the otherstudies on IPPSDDA we considered a dynamic schedulingmodel in which each job enters the system at a randomtime and we introduced the integration of process planningdynamic scheduling and due date assignment (DIPPSDDA)problem The main contribution and the point at whichthis study is separated from other studies is to build adiscrete event simulation model for IPPSDDA problem thatcan adapt to unexpected and sudden internal or externalchanges (dynamic events) in a manufacturing system Westudied new job arrivals that may occur in real shop floorsas dynamic event for this study Furthermore it is also aimedat solving the DIPPSDDA problem with different efficientmetaheuristic algorithms which are simulated annealing(SA) tabu algorithm (TA) genetic algorithm (GA) and thecombination of GASA GATA to improve the performanceof the solutions The proposed model has been built withthe advantages of object-oriented programming (OOP) anddiscrete event simulation (DES) to enhance the flexibility ofthe model

This paper is organized as follows Section 1 is theintroduction part of the study A review of related worksis presented in Section 2 The background and definitionof DIPPSDDA are given in Section 3 Section 4 discussessolution techniques for the DIPPSDDA Section 5 gives thecomputational results and analysis of the study Conclusionsand future researches are also summarized in Section 6

2 Related Works

Minimizing costs by eliminating wastes is a core principleof a just-in-time (JIT) production philosophy Thus deter-mining due dates as close as possible to their due dates isinseparable from this philosophy If companies can completetheir productions on given due dates they can make morerealistic plans and have optimum capacity usage for shopfloors In this way resources are used efficiently and thecompany increases customer satisfaction In most modernJIT companies a job is expected to be completed in its timeThe completion of jobs after their due dates could lead toan increase in costs and a decrease in customer satisfactionand worst customer loss On the other hand the completionof jobs before their due date can cause inventory holdingcosts Integrated systems were proposed by considering theprocess planning and scheduling or scheduling with due dateassignment together to avoid ineffective production Someof the earlier studies reported that it is possible to findthe optimal due dates and optimal sequences of jobs usingdifferent heuristic algorithms [13ndash20] The objective of thesestudies is to minimize the cost related to due date assignmentand scheduling functions

Besides some of the recent studies on SWDDA canbe given such as [21ndash30] There are 3 types of due dateassignment models in the literature as follows

(i) Common due date assignment (CON) a predefinedcommon due date for each job

(ii) Due date assignment considering process times slackdue dates (SLK) total-work-content (TWK) process-ing plus due dates (PPW) etc

(iii) Assignment of due dates according to given values

Scheduling problems with an optimized due date hasbeen the subject of considerable works over the last severaldecades Determining the due date is amatter that needs to beemphasized in terms of customer satisfaction for companiesIf the due dates are not met the companies may face variousproblems Some of the studies on scheduling together withthe due date covered both single machine scheduling andmultimachine problems Scheduling studies considering duedates for single machine problems can often be seen in theliterature such as [17 23 26 31ndash35] Panwalkar and Smith[36] have studied the problem of determining the commondue date for the scheduling problem consisting of 119899 jobs andone machine in the shop floor At the end of the study theproblem was solved using a polynomial bound schedulingalgorithm Cheng [37] has set common due dates for each jobto minimize delay for a single machine scheduling problemBiskup andCheng [38] have attempted to solve the problemofsinglemachine scheduling and the assignment of due dates inwhich job is done with cramped process times In Gupta andSenrsquos [39] study decisions about scheduling batching andthe due date assignment were combined for a single machinescheduling problem with 119899 groups of jobs Bank and Werner[40] determined the duration of release and the duration ofthe transaction time for each job and assigned a common duedate Cheng [41] has aimed to find the optimal due dates fora scheduling problem He has emphasized that the heuristicmethod finds effective solutions for the problem

An early study on the single machine scheduling prob-lem with early and late due date penalties was conductedby Sidney [42] In another study the same problem wasaddressed again by Seidmann et al [43] and an algorithmwas developed to improve the solution performances Otherstudies in which ET are penalized for single machineschedules can be given such as [32ndash34 44]

On the other hand there are still many studies in theliterature in which there is more than one machine Allthese studies have attempted to determine common due datesfor each job With the intuitive use of heuristic algorithmsmany machine scheduling problems such as job floor typeproduction can be solved There is also a published literaturereview for multimachine scheduling problems conducted byLauff and Werner [45] in which researchers used for solvingthe multimachine scheduling problem a specific due date Inanother review study Gordon et al [46] drew a frameworkfor the common due date and scheduling problems In theirliterature study the models in which single machine andparallel machines are included and the other studies in theliterature on this subject were reviewed A study list onSWDDAclassified based on subjects or objectives of the studyis given in Table 1 Other examples of studies on schedulingwith due date assignment can be found in [46ndash48]

In a classic manufacturing model process planning andscheduling functions are carried out separately where onlyfixed process plans are transferred to the scheduling stage























same time









119904119897119886119888119896 = 119889119894 minus 119901119894 minus 119905 (1)



119879119895 = max (119888119895 minus 119889119895 0) (2)

119864119895 = max (119889119895 minus 119888119895 0) (3)

119875119863 = 119908119895 times (8 times ( 119863119895480)) (4)


119875119864 = 119908119895 times (5 + 4 times ( 119864119895480)) (5)

119875119879 = 119908119895 times (6 + 6 times ( 119879119895480)) (6)

119875119905119900119905119886119897 = 119875119863 + 119875119864 + 119875119879 (7)


119891119898119894119899 =119899sum119895=1

119875119905119900119905119886119897 (8)



















































Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018






























same time









119904119897119886119888119896 = 119889119894 minus 119901119894 minus 119905 (1)



119879119895 = max (119888119895 minus 119889119895 0) (2)

119864119895 = max (119889119895 minus 119888119895 0) (3)

119875119863 = 119908119895 times (8 times ( 119863119895480)) (4)


119875119864 = 119908119895 times (5 + 4 times ( 119864119895480)) (5)

119875119879 = 119908119895 times (6 + 6 times ( 119879119895480)) (6)

119875119905119900119905119886119897 = 119875119863 + 119875119864 + 119875119879 (7)


119891119898119894119899 =119899sum119895=1

119875119905119900119905119886119897 (8)



















































Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018





















same time









119904119897119886119888119896 = 119889119894 minus 119901119894 minus 119905 (1)



119879119895 = max (119888119895 minus 119889119895 0) (2)

119864119895 = max (119889119895 minus 119888119895 0) (3)

119875119863 = 119908119895 times (8 times ( 119863119895480)) (4)


119875119864 = 119908119895 times (5 + 4 times ( 119864119895480)) (5)

119875119879 = 119908119895 times (6 + 6 times ( 119879119895480)) (6)

119875119905119900119905119886119897 = 119875119863 + 119875119864 + 119875119879 (7)


119891119898119894119899 =119899sum119895=1

119875119905119900119905119886119897 (8)



















































Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018
















119904119897119886119888119896 = 119889119894 minus 119901119894 minus 119905 (1)



119879119895 = max (119888119895 minus 119889119895 0) (2)

119864119895 = max (119889119895 minus 119888119895 0) (3)

119875119863 = 119908119895 times (8 times ( 119863119895480)) (4)


119875119864 = 119908119895 times (5 + 4 times ( 119864119895480)) (5)

119875119879 = 119908119895 times (6 + 6 times ( 119879119895480)) (6)

119875119905119900119905119886119897 = 119875119863 + 119875119864 + 119875119879 (7)


119891119898119894119899 =119899sum119895=1

119875119905119900119905119886119897 (8)



















































Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018
























































Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018







































Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018























Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018









Chromosomes

Gene Number



rule

11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26



Parent 1 11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

10 10 1 4 1 3 4 0 3 3 2 1 1 3 3 4 0 3 20 2 2 2 0 0 4 4

10 10 1 4 1 3 1 3 1 1 0 4 1 3 3 4 0 3 20 2 2 2 0 0 4 4

11 8 0 1 2 2 4 0 3 3 2 1 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

Parent 2

Child 1

Child 2

Crossover points


11 8 0 1 2 2 1 3 1 1 0 4 1 3 0 0 3 2 1 3 1 2 1 0 3 0 4

11 8 0 1 2 1 1 3 1 1 0 4 3 3 0 0 3 2 1 3 1 2 1 0 3 0 4


Parent

Child

2size = M



119875119886119888119888119890119901119905 = 119890(minus((119864119905minus119864119894)119864119894)119896119861119879) (9)








Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018











Routes of Jobsi=0


i=i+1


No



No



Yes








Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018











Average 24153 01000 0100Worst 38076 00635 0004


Average 16118 01000 0100Worst 16312 00987 0004












00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018










00 500 1000 1500 2000 2500

time500 1000 1500 2000 2500 3000 3500


SF 1SF 2SF 3SF 4

SF 5

SF 6SF 7

SF 8

0

5

10

15

20

25

30

35

Num

ber o

f Arr

ival

s

0

10

20

30

40

50

Num

ber o

f Arr

ival




SA 166296 166528 166740 336TA 154097 158397 166253 333GA 157626 157843 157966 698HA 159639 159875 160079 683









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018









Shop Floor1

best avg worst

170

180

190

Perfo

rman

ce

200

210

Shop Floor2

Perfo

rman

ce

best avg worst310

320

330

340

350

360

370

Shop Floor4

GASATA

GASAGATA

best avg worst

600

620

640

660

680

Perfo

rman

ce

700

720

Shop Floor3

best avg worst420

440

460

480

Perfo

rman

ce

500

520

540

560

580

Shop Floor5

best avg worst

800

820

840

860

880

Perfo

rman

ce

900

920

Shop Floor6

best avg worst

900

1000

1100

1200

1300

Perfo

rman

ce

1400

1500

Shop Floor8

best avg worst1250

1300

1350

Perfo

rman

ce 1400

1450

Shop Floor7

best avg worst

Perfo

rman

ce

1150

1200

1250

1100

1050

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA

GASATA

GASAGATA





m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018









m5

m4

m3

m2

m1

82 164 246 328 410 492 574 656 738 820


job5

Shop floor 1

job6job7job8job9




Mac

hine

s


0






93 186 279 372 465 558 651 744 837 930

m1

m2

m3

m4

m5

m6

Mac

hine

s m7

m8

m9

m10

Shop floor 2








Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018










Data Availability






References







































































































































Journal of












Journal of







Volume 2018






Volume 2018


























































































































Journal of












Journal of







Volume 2018






Volume 2018























































































Journal of












Journal of







Volume 2018






Volume 2018






















































Journal of












Journal of







Volume 2018






Volume 2018



















Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

Solving Integrated Process Planning, Dynamic Scheduling