Research Article Development and Application of Milk-Run Distribution …downloads.hindawi.com/journals/mpe/2014/536459.pdf · 2019. 7. 31. · Research Article Development and Application

Research ArticleDevelopment and Application ofMilk-Run Distribution Systems in the Express IndustryBased on Saving Algorithm

Zhenlai You and Yang Jiao

School of Economics and Management Yanshan University Qinhuangdao Hebei 066004 China

Correspondence should be addressed to Zhenlai You yzlaiysueducn

Received 9 December 2013 Revised 13 February 2014 Accepted 14 February 2014 Published 20 March 2014

Academic Editor Huaiqin Wu

Copyright copy 2014 Z You and Y Jiao 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

This paper introduces the milk-run schema into the express distribution logistics through the feasibility analysis of applicationof cyclic goods-taking schema in the express industry In order to reach fully loaded as far as possible in distribution the articleimproves the traditional model adoptingmulti-objective decision and conforming constraint conditions toMilk-run schema evenapproximating the practical truth solves model through the C-W saving algorithm It can effectively shorten the distance and Lowercosts by means of reasonable route planning Finally the paper has verified the model and its effectiveness of arithmetic applicationby means of cases analysis

1 Introduction

Cyclic goods taking also called Milk-run originates fromnorthern pasture of the United Kingdom and is a kind oftransportation and delivery way which is created for solvingthe problems of transportation and delivery of milk Truckstransport bottles filled with milk to every gate in accordancewith the routes predesigned by the law of intelligent vehiclepath planning and collect the empty bottles on the back wayto milk house [1] After this this goods-taking schema isapplied to production distribution and other activities inevery walk of life [2]

Milk-run model in the earliest was used in automobilemanufacturing enterprises in the domestic Scholars car-ried out related research of milk-run model in automotiveindustry in the theoretical and practical aspects [3 4] Wewrite this paper to research the milk-run model and improvealgorithm on vehicle scheduling problem (VwSP) and vehiclerouting problem (VRP) Afterwards third-party logisticscompanies provide on-time delivery service and add the timewindow constraints in the Milk-run model when they joinin the express industry [5] In applying research on milk-run model in domestic Xu writes an article introducing

the advantages processes and responsibilities of milk-runmodel and analyzing how to design the route and to deter-mine the parameters of transport vehicles [6]

Foreign Milk-run model application study is not onlyused in the automotive industry but also in conveniencegroups such as the famous company 7-Eleven In theoreticalresearch Chopra and Meindl divided the logistics systeminto four parts in 2006 respectively as direct shipping milk-run cross docking and tailored network and the milk-runmodel belongs to one of the four kinds of logistics systems[7] Du et al studied the parameter setting of real-time vehicledistribution system based on milk-run model [8]

As an advanced distribution schema milk-run is appliedto logistics activities of various industries [9]However not somany researches of milk-run has applied in express industryThis paper puts forward some late-model express distributionschema applying milk-run schema by means of researchingcurrent situation of express industry anddistribution schemaThe schema combines advantages of Milk-run schema andpractical truth of express distribution and saves logisticscost by means of optimizing distribution schema under thepremise of satisfying timely and effective express service Onthe design of milk-run module the module of this paper is

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 536459 6 pageshttpdxdoiorg1011552014536459

2 Mathematical Problems in Engineering

different from traditional distributionmodule It relies on thereality andmakes it more feasibleThismodule highlights thecharacteristics of milk-run and defines the size and weight ofback and forth Solving the smallest distance and the lowestcost minimum target not only ensure the effectiveness ofexpress delivery but also ensure lower cost of the expresscompanies

2 Feasibility Analysis of Milk-Run inExpress Delivery Industry

Faced with the situation that the competition of expressdelivery industry becomes increasingly fierce only keepingits feet in the market enterprises need to squeeze logisticscost However a majority of express delivery industries donot form a scale and they still adopt the old-fashioneddeliverymethods without planningThis leads to rare expresscompanies forming large scale and owning internationalcompetitiveness in express enterprises of China Meanwhiledue to being ignorant of how to improve logistic efficiencyand how to reduce logistics cost there is a large gap betweeninternal and external quality of service [10 11] So it isreducing logistics cost and improving quality of service atthe same time to get a leg up on this competition Thecombination betweenMilk-run schema and express industrycan promote benign development of express enterprises

21 Improving the Vehicle Load Factors and Reducing Trans-portation Cost The main purpose of Milk-run model is tomake full use of vehiclesrsquo space and tries to deliver the fullloaded goods to designated place [12] Considering cycle-taking cargo and express delivery industry effective unionthe vehicle can be make full use of space greatly improvethe vehiclersquos load factors and avoid the waste of emptyvehicles At the same time through effective path planningit can not only shorten the distribution distance reducethe reciprocating weeks to return the goods in transit andavoid the waste of time on the way but also save the costof transportation The time and cost as the main competitivefactors of express delivery industry play a vital role [13]

22 Promoting the Establishment and Perfection of Infor-mation Platform Nowadays information technology has apivotal position in all walks of lifeMilk-run requests logisticscenter and each distribution point to fully share informationand requires its information with high accuracy so logisticscenter can arrange distribution reasonably according to theinformation accurately planning the path In the process asthe role of information to link the things together becomesmore and more obvious the construction of the integrationof network information platform in the Courier industry cangive full play to the cycle trend of pickup advantage [14] Atthe same time in the process of implementation of infor-mation management circulation pickup pattern applicationalso will continue to promote the perfection of informationplatform

23 Improving the Efficiency and Quality of Service In theprocess of Milk-run the processing time of ship discharge

the cargowill be increased efficiencywill be reduced deliverytime will be delayed and even quality of service will beaffected if there is no regular standard [15]Therefore in orderto avoid unnecessary waste in process of delivery establishinga unified standard to express mail packing process of enter-prises not only makes loading and moving more convenientbut also arranges vehicle load space reasonably Standardizedoperation could decrease its fault rate as well as improvingstaff quality and quality of service even thewhole enterprises

3 Establishment of Milk-Run Delivery Schema

Themodelrsquos parameters are defined follows

119896 the number of vehicle 119896 = 1 2 119899

119881119896 the rated volume of vehicle 119896

119894 transportation node number 119894 = 1 2 3 119897

119894 = 0 distribution center

119882119894 the rated load of vehicle 119896

119889119894119895 the transport distance of node 119894 to node 119895

119881119894 the volume of the goods delivered to the node 119894

1198811015840

119894 the volume of the goods received by the node 119894

119882119894 the weight of the goods delivered to the node 119894

1198821015840

119894 the weight of the goods received by the node 119894

1198881 the vehicle transportation cost of per unit distance

1198882 represents vehicle fixed cost of each use

119881119896 the biggest cargo volume of vehicle 119896

119882119896 represents the biggest cargo weight of vehicle 119896

119910119896119895 =

1 if The task of 119894 isperformed by vehicle 1198950 otherwise

119909119894119895119896 =

1 if Vehicle 119896 from client 119894drive to customer 1198950 otherwise

(1)

Then we establish the modelopt

min 1199111 =119871

sum

119894=0

119871

sum

119895=0

119871

sum

119896=0

119889119894119895119909119894119895119896 (2)

min 1199111 =119871

sum

119894=0

119871

sum

119895=0

119871

sum

119896=0

1198891198941198951199091198941198951198961198881 + 1198991198882 (3)

st

Mathematical Problems in Engineering 3

Logistics LogisticsNode i

Node j

Node i

Node j

center o center o

Figure 1 The principle diagram of the saving algorithm

1 ⩽

119870

sum

119896=1

119910119896119894 ⩽ 2 119894 = 1 2 119897 (4)

119899

sum

119896=1

119871

sum

119895=0

119909119894119895119896 =

119899

sum

119896=1

119910119896119894 119894 = 1 2 119897 (5)

119899

sum

119896=1

119871

sum

119895=0

119909119894119895119896 =

119899

sum

119896=1

119910119896119895 119895 = 1 2 119897 (6)

119897

sum

119895=0

1199090119895119896 =

119897

sum

119895=0

1199091198950119896 ⩽ 1 (7)

119899

sum

119894=0

1198811015840

119894119910119896119894 =

119897

sum

119894=119899+1

119881119894119910119896119894 ⩽ 119881119896 (8)

119899

sum

119894=0

1198821015840

119894119910119896119894 =

119897

sum

119894=119899+1

119882119894119910119896119894 ⩽ 119882119896 (9)

Formulas (2) and (3) are the objective functionThe objectiveof the model is the smallest total distance and transportationcost Constraint formula (4) represents each node havingvehicle service and at most two vehicles serve the same nodeFormulas (5) and (6) represent the effectiveness of vehiclearrival It means that a vehicle reaches a node that can beserved Formula (7) indicates that as long as the task iscompleted the vehicle must return to the distribution centerFormulas (8) and (9) respectively represent the load andvolume constraints Each node can only be served by onevehicle in the traditional modelrsquos constraint However whenyou solve the model you may obtain a nonoptimal solutionTheoretically the total number of vehicles is required in theplan formula (10)

119899 = max[sum119871

119894=0119882119894

119882119896

] [sum119871

119894=01198821015840

119894

119882119896

]

[sum119871

119894=0119881119894

V119896] [sum119871

119894=01198811015840

119894

119881119896

]

(10)

As each node has only one vehicle for service due to thetraditional model solution so that all the cargo at each nodecan only be installed in one vehicle Even if the vehicle is notfully loaded if a node cannot be one-time carried the residualcargo the vehicle must return distribution centers In thismodel the service at each node is not limited to one vehiclethe vehicle can be achieved load in the process

4 Model Solution

Milk-run model is a typical NP-hard problem for such prob-lems using the exact algorithm to obtain the global optimalsolution is more difficult and the amount of calculation willincrease with the size of the problem increasing exponentially[16 17] Therefore the current path for such a large-scaleproblem is more inclined to use heuristic algorithms forsolving them not to bothering to solve the problem of theexact optimal solution but stressing to obtain satisfactorysolution by reducing the computational complexity [18ndash20]

Including a variety of heuristic algorithms this paper usesthe CW saving algorithm to solve the model The core idea isto calculate the saving distance because ofmerging two pathsaccording to the value of savings to merge the two paths untilthe vehicle is full-loaded and then using the second vehicleon the same way until all goods are delivered to designatedlocation

In Figure 1 when the logistics center distributes goods to 119894and 119895 respectively the shortest distance of the line 119894 is definedas119889119894 = 119889119894119900+119889119900119894 and the shortest distance of the line 119895 is definedas 119889119895 = 119889119895119900 + 119889119900119895 Connecting the line 119894 and 119895 using the samevehicle for shipment the transportation distance is definedas 119889119894119895119900 = 119889119900119894 + 119889119900119895 + 119889119894119895 In this case the transport distanceof saving is defined as Δ119889 = 2119889119900119894 + 2119889119900119895 minus (119889119900119894 + 119889119900119895 + 119889119894119895) =119889119900119894+119889119900119895minus119889119894119895 (the formula of savings in transport) Obviouslyit also saves the use of one vehicle at this time effectivelyreducing the use of vehicles fixed costs and transportationcosts

The step of improved saving algorithm is defined asfollows

Step 1 Calculate the savings value of the distance betweeneach node by using the formula of savings in transport Thenlist the saving distance matrix [Δ119889119894119895]

Step 2 Order the Δ119889119894119895 by ascending order

Step 3 Analyze array [Δ119889119894119895] exit the cycle if it is emptyset otherwise choose the maximum saving value of the twodistribution nodes 119894 and 119895 and judge whether the two nodesare satisfied by the following conditions

The nodes 119894 119895 are not in the line which has beenconstructed

The node 119894 or 119895 is in the line which has been constructedand it is directly connected with the logistics center

The nodes 119894 and 119895 are respectively in two different lineswhich have been constructed and directly connected with thelogistics center If nodes 119894 and 119895 fulfilled the above conditionsgo to Step 4


Step 4 Calculate the volume and weight of goods of twonodes which are distributed and selected If the volume orweight is not beyond the vehiclesrsquo constraint connect 119894 and119895 otherwise turn to Step 5

Step 5 Connect 119894 119895 nodes and determine whether thereis a splitting case if so the vehicle is loaded to the full-shipped back to the logistics center connect 119894 and 119895 node anddetermine whether there is splitting case if so the vehiclecan be loaded to full shipped back to the logistics center andcomplete the cycle of the vehicle k update the informationof the remaining cargo then the distribution of node willbe in the next cycle Otherwise the cargo of 119894 and 119895 can becompleted by one vehicle and turn to Step 6

Step 6 Select the remaining delivery node for the maximumsaving value and go to Step 3

The result of traditional models uses the savings algo-rithm to obtain the scheduling of the vehicles as shown inTable 3

5 Case Study

Courier CompanyW is a private express delivery company inChina in the process of the development the enterprise rec-ognizes the importance of management advances technol-ogy and begins to introduce advancedmanagement conceptsand automated technology With the increasing competitionin the courier industry companies who can stand out inforce in the cornier industry become increasingly aware ofthe need to improve internal courier safety efficiency andlow cost In this paper W express company introduces thatmilk-run model is the background and collects and analyzesthe statistical data of a certain region The introduction ofmilk-run model effectively reduces logistics costs improvesthe vehiclersquos load factor and reduces unnecessary waste

51 Wrsquos Introduction to the Basic Situation Wrsquos has tendistribution points in a region where the location of thedistribution is shown in Figure 2

For example extracting the data on March 1 2012 theinformation of the goods delivered to the distribution centerand received from the every distribution node is shown inTable 1

The maximum cargo volume of delivery vehicles is 10and the biggest loading capacity is 25 tons Vehicle unitdistance transport cost is 20 yuankm and the fixed costof one vehicle is 400 yuan (RMB) According to the weightand volume of distribution and without taking into accountsthe information of received goods before applying the Milk-run model the enterprise designs a distribution route Allthe goods will be delivered to the designated distributionnode and then the goods will be collected back to thedistribution center in original wayThe traditionalmodels areoften applied to the situation that the vehicle achieves its fullload but there also some other goods that cannot be loadedor the vehiclersquos empty load rate is relatively high For examplethe quantity of goods to be shipped to distribution center ofthe line 0-3-7-0 distribution is 28 tons while it is exceeding

160

140

120

100

80

60

40

20

0160140120100806040200

Figure 2 The layout of W company distribution node in a givenarea

Distribution center

5

10

94

7

3

8

2

6

1

Figure 3 The distribution path graph before the optimization

the maximum load of the vehicle the companyrsquos approachis to wait until the next day to dispose the remainder Itnot only leads to increased logistics costs but also reducesthe efficiency of the express company The company can notmeet customers need in time and has a disadvantage in timebenefit Wrsquos delivery rote before taking milk-run model isshown in Figure 3 It needs five vehicles to complete the taskfor a total driving distance of 7548 km

Adopt saving algorithm model and the distance matrixof the distribution node is shown in Table 2

The vehicle scheduling and optimized path are shown inTable 4 by using improved savings algorithm

The optimized path is shown in Figure 4 according to theoptimized route and vehicle scheduling information

The result is based on saving algorithm the cycle pickupuses a total of four vehicles transporting a total distanceof 6458 km distribution and transportation actual averageloading rate of 84 percent and actual average loading rateof 99 percent and for a total average effective loading was915 percent Compared to the original model of transportless use of a truck the actual loading rate has been improvedto avoid the condition of delaying caused by not meeting therequirements The benefit of milk-run model that contrastswith the previous models is shown in Table 5

We can clearly see the significant efficiency gains byoptimizing path route in taking milk-run model from thetable Fewer vehicles shortened transport distance improvedload factor all of that reduce the cost of logistics enterprisesand improve the efficiency to some extent Meanwhile it canavoid the delay of goods and ensure the goods to be instantly


Table 1 W companys deliver goods information in a given area

Distributionnode no

Coordinates ofsupplier

Weight of thedelivered goods (t)

Volume ofdelivered goods (m3)

Weight ofreceived goods (t)

Volume ofreceived goods (m3)

1 (35 80) 08 35 06 172 (44 67) 12 3 04 283 (76 78) 03 32 19 464 (33 80) 12 43 16 345 (78 3) 07 22 11 296 (53 85) 11 21 18 277 (70 136) 07 23 09 278 (7 3) 02 11 07 219 (145 137) 13 22 07 1210 (85 4) 09 31 02 21

Table 2 Distance matrix of the distribution node

0 1 2 3 4 5 6 7 8 9 100 01 166 02 01 158 03 342 41 338 04 178 02 17 43 05 716 882 725 75 892 06 21 187 201 24 206 857 07 747 66 737 583 671 1332 538 08 731 819 739 1019 813 71 94 1472 09 1235 1239 1229 908 1257 1498 1057 75 1924 010 743 91 752 745 921 071 871 1328 78 1459 0

Table 3 The path and scheduling information of vehicles before optimization

Vehicle Vehicle path Total transportationdistance

Weight ofdistribution (t)

Volume ofdistribution (m3)

Weight ofreceived (t)

Volume ofreceived (m3)

1 0-5-10-8-0 2206 18 64 2 712 0-7-9-0 2732 2 45 16 393 0-1-4-0 364 2 78 22 514 0-2-6-0 421 23 51 22 555 0-3-0 684 03 32 19 46

Table 4 Vehicle scheduling information and optimized path




Weight ofreceival (t)

Volume ofreceival (m3)

1 0-10-5-8-2-0 2316 18 64 24 992 0-7-9-3-0 2747 23 77 25 653 0-4-1-6-0 602 2 84 25 584 0-3-6-2-0 793 23 45 25 5

Table 5 The contradistinction between milk-run model and the previous model of Wrsquos

Transportation schema Vehicleusage

Total transportationdistance (km)

Vehicle loadedrate ()

Transportation taskcompletion

Transportation cost(Yuan)

Normal schema 5 8692 7480 unfinished 37384Milk-run schema 5 6407 7320 finished 32814Improved milk-run schema 4 6458 9150 finished 28916


1

2

6

9

4

85

10

7

3

Figure 4 Optimization of path graph

and accurately transported finally it will reduce the cost of itstime and enhance the Wrsquos competitive advantage over time

6 Conclusion

This paper introduces the application of milk-run schemato express delivery industry and establishes a multiobjectivepath optimization schema which has the shortest distanceand the lowest cost Through the case analysis resultswe can conclude that milk-run model applied to expressdelivery industry can improve load factors shorten shipmentdistance advance time efficiency fulfill transport demandand reduce logistics transportation cost However comparedwith complexity of having impact on logistics transportationfactors this schema is relatively simple and time window andenvironmental logistics concept will be added in schema inthe further research and the schema will tend to be moreaccurate and practical

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors would like to thank the Natural Science Foun-dation of Heibei Province (no G2013203385) for supportingthis work

References

[1] I Satoh ldquoA formal approach for Milk-run transport logisticsrdquoIEICE Transactions on Fundamentals of Electronics Communi-cations and Computer Sciences vol E91A no 11 pp 3261ndash32682008

[2] Y Zimeng H Yanguang and J Hui ldquoThe Optimizationsimulation of Milk-run model on aviation spare partsrdquo ScienceTechnology and Engineering vol 1 pp 37ndash41 2012

[3] L Liu and X W Tang ldquoA study on vendors lead time decisionmodelrdquo Systems Engineering vol 23 no 8 pp 42ndash45 2005

[4] S J Sadjadi M Jafari and T Amini ldquoA new mathematicalmodeling and a genetic algorithm search for Milk run problem(an auto industry supply chain case study)rdquo InternationalJournal of Advanced Manufacturing Technology vol 44 no 1-2pp 194ndash200 2009

[5] T Du F KWang and P Y Lu ldquoA real-time vehicle-dispatchingsystem for consolidating Milk runsrdquo Transportation Research Evol 43 no 5 pp 565ndash577 2007

[6] X Qiuhua ldquoThe practice and application of Milk-run model atShanghai GMrdquo Automobile and Parts vol 3 pp 21ndash24 2003

[7] S Chopra and P Meindl Supplier Chain Management-Strategies Planning and Operation Tsinghua University PressBeijing China 2006


[9] H Kilic M Durmusoglu and M Baskak ldquoClassification andmodeling for in-plant Milk-run distribution systemsrdquo Interna-tional Journal of Advanced Manufacturing Technology vol 62no 9ndash12 pp 1135ndash1146 2012

[10] G Faxia and L Shaoke ldquoDiscussion of the private courierindustry problems and countermeasuresrdquoHebei TransportationResearch vol 02 pp 65ndash68 2010

[11] Y Jingdong S Yinping and L Qian ldquoChinas express deliveryindustrys current situation problems and countermeasuresrdquoChina Science and Technology Information vol 18 pp 205ndash2072008

[12] N Arvidsson ldquoThe Milk run revisited a load factor paradoxwith economic and environmental implications for urbanfreight transportrdquo Transportation Research A vol 51 pp 56ndash622013

[13] M Holweg and J Miemczyk ldquoDelivering the ldquo3-day carrdquomdashthe strategic implications for automotive logistics operationsrdquoJournal of Purchasing and Supply Management vol 9 no 2 pp63ndash71 2003

[14] N Kumar ldquoSupply chain design at jaguar bring nirvana tohalewoodrdquo Supply Chain Forum vol 3 no 1 pp 74ndash80 2002

[15] X J He J G Kim and J C Hayya ldquoThe cost of lead-timevariability the case of the exponential distributionrdquo Interna-tional Journal of Production Economics vol 97 no 2 pp 130ndash142 2005

[16] L Jun L Xiebing andG Yaohuang ldquoGenetic algorithmof non-loaded vehicle scheduling problemrdquo Systems EngineeringTheoryMethodology Applications vol 03 pp 235ndash239 2000

[17] J Chen and TWu ldquoVehicle routing problemwith simultaneousdeliveries and pickupsrdquo Journal of the Operational ResearchSociety vol 57 no 5 pp 579ndash587 2006

[18] N A Wassan A H Wassan and G Nagy ldquoA reactivetabu search algorithm for the vehicle routing problem withsimultaneous pickups and deliveriesrdquo Journal of CombinatorialOptimization vol 15 no 4 pp 368ndash386 2008

[19] J Y Potvin and S Bengio ldquoThe vehicle routing problem withtime windows part II genetic searchrdquo INFORMS Journal onComputing vol 8 no 2 pp 165ndash172 1996

[20] B E Gillett and L R Miller ldquoA heuristic algorithm for thevehicle dispatch problemrdquo Opration Research vol 22 pp 240ndash349 1974

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different from traditional distributionmodule It relies on thereality andmakes it more feasibleThismodule highlights thecharacteristics of milk-run and defines the size and weight ofback and forth Solving the smallest distance and the lowestcost minimum target not only ensure the effectiveness ofexpress delivery but also ensure lower cost of the expresscompanies

2 Feasibility Analysis of Milk-Run inExpress Delivery Industry

Faced with the situation that the competition of expressdelivery industry becomes increasingly fierce only keepingits feet in the market enterprises need to squeeze logisticscost However a majority of express delivery industries donot form a scale and they still adopt the old-fashioneddeliverymethods without planningThis leads to rare expresscompanies forming large scale and owning internationalcompetitiveness in express enterprises of China Meanwhiledue to being ignorant of how to improve logistic efficiencyand how to reduce logistics cost there is a large gap betweeninternal and external quality of service [10 11] So it isreducing logistics cost and improving quality of service atthe same time to get a leg up on this competition Thecombination betweenMilk-run schema and express industrycan promote benign development of express enterprises

21 Improving the Vehicle Load Factors and Reducing Trans-portation Cost The main purpose of Milk-run model is tomake full use of vehiclesrsquo space and tries to deliver the fullloaded goods to designated place [12] Considering cycle-taking cargo and express delivery industry effective unionthe vehicle can be make full use of space greatly improvethe vehiclersquos load factors and avoid the waste of emptyvehicles At the same time through effective path planningit can not only shorten the distribution distance reducethe reciprocating weeks to return the goods in transit andavoid the waste of time on the way but also save the costof transportation The time and cost as the main competitivefactors of express delivery industry play a vital role [13]

22 Promoting the Establishment and Perfection of Infor-mation Platform Nowadays information technology has apivotal position in all walks of lifeMilk-run requests logisticscenter and each distribution point to fully share informationand requires its information with high accuracy so logisticscenter can arrange distribution reasonably according to theinformation accurately planning the path In the process asthe role of information to link the things together becomesmore and more obvious the construction of the integrationof network information platform in the Courier industry cangive full play to the cycle trend of pickup advantage [14] Atthe same time in the process of implementation of infor-mation management circulation pickup pattern applicationalso will continue to promote the perfection of informationplatform

23 Improving the Efficiency and Quality of Service In theprocess of Milk-run the processing time of ship discharge

the cargowill be increased efficiencywill be reduced deliverytime will be delayed and even quality of service will beaffected if there is no regular standard [15]Therefore in orderto avoid unnecessary waste in process of delivery establishinga unified standard to express mail packing process of enter-prises not only makes loading and moving more convenientbut also arranges vehicle load space reasonably Standardizedoperation could decrease its fault rate as well as improvingstaff quality and quality of service even thewhole enterprises

3 Establishment of Milk-Run Delivery Schema

Themodelrsquos parameters are defined follows

119896 the number of vehicle 119896 = 1 2 119899

119881119896 the rated volume of vehicle 119896

119894 transportation node number 119894 = 1 2 3 119897

119894 = 0 distribution center

119882119894 the rated load of vehicle 119896

119889119894119895 the transport distance of node 119894 to node 119895

119881119894 the volume of the goods delivered to the node 119894

1198811015840

119894 the volume of the goods received by the node 119894

119882119894 the weight of the goods delivered to the node 119894

1198821015840

119894 the weight of the goods received by the node 119894

1198881 the vehicle transportation cost of per unit distance

1198882 represents vehicle fixed cost of each use

119881119896 the biggest cargo volume of vehicle 119896

119882119896 represents the biggest cargo weight of vehicle 119896

119910119896119895 =

1 if The task of 119894 isperformed by vehicle 1198950 otherwise

119909119894119895119896 =

1 if Vehicle 119896 from client 119894drive to customer 1198950 otherwise

(1)

Then we establish the modelopt

min 1199111 =119871

sum

119894=0

119871

sum

119895=0

119871

sum

119896=0

119889119894119895119909119894119895119896 (2)

min 1199111 =119871

sum

119894=0

119871

sum

119895=0

119871

sum

119896=0

1198891198941198951199091198941198951198961198881 + 1198991198882 (3)

st



Node j

Node i

Node j

center o center o


1 ⩽

119870

sum

119896=1

119910119896119894 ⩽ 2 119894 = 1 2 119897 (4)

119899

sum

119896=1

119871

sum

119895=0

119909119894119895119896 =

119899

sum

119896=1

119910119896119894 119894 = 1 2 119897 (5)

119899

sum

119896=1

119871

sum

119895=0

119909119894119895119896 =

119899

sum

119896=1

119910119896119895 119895 = 1 2 119897 (6)

119897

sum

119895=0

1199090119895119896 =

119897

sum

119895=0

1199091198950119896 ⩽ 1 (7)

119899

sum

119894=0

1198811015840

119894119910119896119894 =

119897

sum

119894=119899+1

119881119894119910119896119894 ⩽ 119881119896 (8)

119899

sum

119894=0

1198821015840

119894119910119896119894 =

119897

sum

119894=119899+1

119882119894119910119896119894 ⩽ 119882119896 (9)


119899 = max[sum119871

119894=0119882119894

119882119896

] [sum119871

119894=01198821015840

119894

119882119896

]

[sum119871

119894=0119881119894

V119896] [sum119871

119894=01198811015840

119894

119881119896

]

(10)


4 Model Solution
















5 Case Study





160

140

120

100

80

60

40

20

0160140120100806040200


Distribution center

5

10

94

7

3

8

2

6

1










Distributionnode no






1 (35 80) 08 35 06 172 (44 67) 12 3 04 283 (76 78) 03 32 19 464 (33 80) 12 43 16 345 (78 3) 07 22 11 296 (53 85) 11 21 18 277 (70 136) 07 23 09 278 (7 3) 02 11 07 219 (145 137) 13 22 07 1210 (85 4) 09 31 02 21


0 1 2 3 4 5 6 7 8 9 100 01 166 02 01 158 03 342 41 338 04 178 02 17 43 05 716 882 725 75 892 06 21 187 201 24 206 857 07 747 66 737 583 671 1332 538 08 731 819 739 1019 813 71 94 1472 09 1235 1239 1229 908 1257 1498 1057 75 1924 010 743 91 752 745 921 071 871 1328 78 1459 0







1 0-5-10-8-0 2206 18 64 2 712 0-7-9-0 2732 2 45 16 393 0-1-4-0 364 2 78 22 514 0-2-6-0 421 23 51 22 555 0-3-0 684 03 32 19 46







1 0-10-5-8-2-0 2316 18 64 24 992 0-7-9-3-0 2747 23 77 25 653 0-4-1-6-0 602 2 84 25 584 0-3-6-2-0 793 23 45 25 5









1

2

6

9

4

85

10

7

3



6 Conclusion




Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Node j

Node i

Node j

center o center o


1 ⩽

119870

sum

119896=1

119910119896119894 ⩽ 2 119894 = 1 2 119897 (4)

119899

sum

119896=1

119871

sum

119895=0

119909119894119895119896 =

119899

sum

119896=1

119910119896119894 119894 = 1 2 119897 (5)

119899

sum

119896=1

119871

sum

119895=0

119909119894119895119896 =

119899

sum

119896=1

119910119896119895 119895 = 1 2 119897 (6)

119897

sum

119895=0

1199090119895119896 =

119897

sum

119895=0

1199091198950119896 ⩽ 1 (7)

119899

sum

119894=0

1198811015840

119894119910119896119894 =

119897

sum

119894=119899+1

119881119894119910119896119894 ⩽ 119881119896 (8)

119899

sum

119894=0

1198821015840

119894119910119896119894 =

119897

sum

119894=119899+1

119882119894119910119896119894 ⩽ 119882119896 (9)


119899 = max[sum119871

119894=0119882119894

119882119896

] [sum119871

119894=01198821015840

119894

119882119896

]

[sum119871

119894=0119881119894

V119896] [sum119871

119894=01198811015840

119894

119881119896

]

(10)


4 Model Solution
















5 Case Study





160

140

120

100

80

60

40

20

0160140120100806040200


Distribution center

5

10

94

7

3

8

2

6

1










Distributionnode no






1 (35 80) 08 35 06 172 (44 67) 12 3 04 283 (76 78) 03 32 19 464 (33 80) 12 43 16 345 (78 3) 07 22 11 296 (53 85) 11 21 18 277 (70 136) 07 23 09 278 (7 3) 02 11 07 219 (145 137) 13 22 07 1210 (85 4) 09 31 02 21


0 1 2 3 4 5 6 7 8 9 100 01 166 02 01 158 03 342 41 338 04 178 02 17 43 05 716 882 725 75 892 06 21 187 201 24 206 857 07 747 66 737 583 671 1332 538 08 731 819 739 1019 813 71 94 1472 09 1235 1239 1229 908 1257 1498 1057 75 1924 010 743 91 752 745 921 071 871 1328 78 1459 0







1 0-5-10-8-0 2206 18 64 2 712 0-7-9-0 2732 2 45 16 393 0-1-4-0 364 2 78 22 514 0-2-6-0 421 23 51 22 555 0-3-0 684 03 32 19 46







1 0-10-5-8-2-0 2316 18 64 24 992 0-7-9-3-0 2747 23 77 25 653 0-4-1-6-0 602 2 84 25 584 0-3-6-2-0 793 23 45 25 5









1

2

6

9

4

85

10

7

3



6 Conclusion




Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














5 Case Study





160

140

120

100

80

60

40

20

0160140120100806040200


Distribution center

5

10

94

7

3

8

2

6

1










Distributionnode no






1 (35 80) 08 35 06 172 (44 67) 12 3 04 283 (76 78) 03 32 19 464 (33 80) 12 43 16 345 (78 3) 07 22 11 296 (53 85) 11 21 18 277 (70 136) 07 23 09 278 (7 3) 02 11 07 219 (145 137) 13 22 07 1210 (85 4) 09 31 02 21


0 1 2 3 4 5 6 7 8 9 100 01 166 02 01 158 03 342 41 338 04 178 02 17 43 05 716 882 725 75 892 06 21 187 201 24 206 857 07 747 66 737 583 671 1332 538 08 731 819 739 1019 813 71 94 1472 09 1235 1239 1229 908 1257 1498 1057 75 1924 010 743 91 752 745 921 071 871 1328 78 1459 0







1 0-5-10-8-0 2206 18 64 2 712 0-7-9-0 2732 2 45 16 393 0-1-4-0 364 2 78 22 514 0-2-6-0 421 23 51 22 555 0-3-0 684 03 32 19 46







1 0-10-5-8-2-0 2316 18 64 24 992 0-7-9-3-0 2747 23 77 25 653 0-4-1-6-0 602 2 84 25 584 0-3-6-2-0 793 23 45 25 5









1

2

6

9

4

85

10

7

3



6 Conclusion




Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Distributionnode no






1 (35 80) 08 35 06 172 (44 67) 12 3 04 283 (76 78) 03 32 19 464 (33 80) 12 43 16 345 (78 3) 07 22 11 296 (53 85) 11 21 18 277 (70 136) 07 23 09 278 (7 3) 02 11 07 219 (145 137) 13 22 07 1210 (85 4) 09 31 02 21


0 1 2 3 4 5 6 7 8 9 100 01 166 02 01 158 03 342 41 338 04 178 02 17 43 05 716 882 725 75 892 06 21 187 201 24 206 857 07 747 66 737 583 671 1332 538 08 731 819 739 1019 813 71 94 1472 09 1235 1239 1229 908 1257 1498 1057 75 1924 010 743 91 752 745 921 071 871 1328 78 1459 0







1 0-5-10-8-0 2206 18 64 2 712 0-7-9-0 2732 2 45 16 393 0-1-4-0 364 2 78 22 514 0-2-6-0 421 23 51 22 555 0-3-0 684 03 32 19 46







1 0-10-5-8-2-0 2316 18 64 24 992 0-7-9-3-0 2747 23 77 25 653 0-4-1-6-0 602 2 84 25 584 0-3-6-2-0 793 23 45 25 5









1

2

6

9

4

85

10

7

3



6 Conclusion




Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1

2

6

9

4

85

10

7

3



6 Conclusion




Acknowledgment


References




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Development and Application of Milk-Run Distribution …downloads.hindawi.com/journals/mpe/2014/536459.pdf · 2019. 7. 31. · Research Article Development and Application