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106 Int. J. Services Operations and Informatics, Vol. 6, Nos. 1/2, 2011
Copyright © 2011 Inderscience Enterprises Ltd.
Production-distribution network analysis using an intelligent simulator
Abderrahmane Bensmaine* and Lyes Benyoucef INRIA-Nancy Grand-Est, COSTEAM-Project, ISGMP Bat. A, Metz, 57000, France Email: [email protected] Email: [email protected] *Corresponding author
Zaki Sari Automatic Laboratory of Tlemcen, AbouBekr Belkaid University, Algeria Email: [email protected]
Abstract: Existing simulation tools are able to map large size supply chains and can accommodate complex random phenomena. Nevertheless, they have significant weakness in the power of decision-making. Indeed, most of the problems of decision-making are typically determined by simplified rules. For this reason, involving optimisation tools in decision-making will allow the simulation to explore the real performance of a supply chain. Motivated by the limitations of existing supply chains simulation and optimisation tools, the aim of this study is to combine them in a single tool. More specifically, we aim to develop an ‘intelligent’ simulation tool with an embedded optimisation tool to solve various decision-making problems encountered during the simulation of a complex supply chain. Including an optimisation tool in a simulation tool allows accurate assessment of supply chains performances and overcome the lack of powers of decision-making in traditional simulation tools.
Keywords: supply chain; intelligent simulation; optimisation; decision-making.
Reference to this paper should be made as follows: Bensmaine, A., Benyoucef, L. and Sari, Z. (2011) ‘Production-distribution network analysis using an intelligent simulator’, Int. J. Services Operations and Informatics, Vol. 6, Nos. 1/2,
pp.106–123.
Biographical notes: Abderrahmane Bensamine is pursuing his PhD in Department of Industrial Engineering at University of Metz, France. He received his Engineering and Master of Science in Industrial Engineering from University of Tlemcen, Algeria, in 2007 and 2009, respectively. His main research interests include modelling and performance evaluation; and the simulation and optimisation of complex supply chains.
Lyes Benyoucef received his PhD in Operations Research at the National Polytechnic Institute of Grenoble, France, in 2000 and his HDR (Research Director Thesis) degree from the University of Metz, France, in 2008. He is a senior researcher (CR1-HDR) at INRIA. His main research interests include modelling and performance evaluation; and the simulation and optimisation of
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complex manufacturing systems and E-sourcing technologies. He is editorial board member of International Journal of Services Operations and Informatics, International Journal of Business Performance and Supply Chain Modeling and Journal of Operations and Logistics. He has also served on programme committees of many international conferences.
Zaki Sari received his Engineer Degree (1987) from the National Institute of Electricity and Electronics and Masters Degree (1990) from the National Polytechnic School Algiers in Electrical Engineering. He obtained his Doctorate Degree (2003) from Tlemcen University in Manufacturing Engineering. He is currently Professor in the Laboratoire d’Automatique at Tlemcen University, Algeria. His current research interests deal with modelling and simulation of automated systems used in manufacturing.
1 Context and motivation
1.1 Context
Supply Chain Management (SCM) is nowadays one of the active research topics in global logistics. It is noticed that competition in the future will not be between individual organisations but between competing supply chains. Thus, business opportunities are captured by groups of enterprises in the same network (supply chain). The main reason for these changes is the global competition that forces enterprises to focus on their core competences (i.e. to do what you do the best and let others do the rest) (Simchi et al., 2003; Christopher, 2004). Moreover, as technological complexity has increased, logistics and supply chains have become more complex and dynamic.
The design and management of modern supply chains require human knowledge and experience in order to determine (a) the number, location, capacity, and type of manufacturing plants, warehouses, and distribution centres to use, (b) the set of potential suppliers to select, (c) the transportation modes to use, and (d) the quantities of raw materials and finished products to purchase, produce, store and transport (among suppliers, plants, warehouses, distribution centres, and customers using different transportation modes). These are non-trivial decisions, especially at the international level. In fact, market demands, customer service, transport considerations, and pricing constraints all must be understood in order to effectively design and manage the supply chain. They represent most of the factors, which change constantly and sometimes unexpectedly. It is important to mention that supply chain design is a multi-criteria decision problem which includes both qualitative and quantitative criteria. Consequently, in order to design a robust supply chain, it is necessary to make a trade-off between tangible and intangible criteria some of which may be conflicting, such as cost and delivery.
Simulation has been identified as one of the best means to analyse and deal with stochastic natures existing in supply chain (Schunk and Plott, 2001). Its capability of capturing uncertainty, complex system dynamics and large-scale systems makes it attractive for supply chain study. It can help in the optimisation process by evaluating the impact of alternative policies. Therefore, many simulation models have been built to facilitate the use of simulation in designing, evaluating, and optimising supply chains (IBM Supply Chain Analyser, Autofat, Supply Chain Guru, Simflex, etc.).
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Supply chain simulation involves the simulation of the flow of material and information through multiple stages of manufacturing, transportation and distribution. It includes the simulation of the replenishments of incoming inventory and operations at each manufacturing stage, and shipments for the products from one stage to the next. However, running a supply chain simulation requires making numerous decisions, such as raw material supply, production planning/scheduling, inventory control, distribution planning, etc. Numerous random events adversely influence the performances of supply chains: random transportation times, demand fluctuations, supply disruptions, etc.
At the same time, thanks to several decades of theoretical and tool developments, state-of-the-art optimisation engines such as ILOG-CPLEX and DASH-XPRESS have proven to be able to solve real large size decision-making problems of millions of variables and millions of constraints. These optimisation engines are now used to power advanced Supply Chain Management tools (I2, Manugistics, SAP…) for solving complex supply chain planning/scheduling problems. Impressive cost reduction and customer satisfaction achievement are frequently reported and success stories are frequently reported by optimisation engine providers or by SCM tool providers.
The strength of SCM tools resides in their ability to efficiently coordinate activities through the whole supply chain: from demand planning, to procurement, to manufacturing, to inventory control and to distribution. These activities that were optimised locally in the past are now optimised globally through the use of SCM tools. Each of the two technologies has its advantages and disadvantages in supply chain design and management (Ingalls and Kasales, 1999).
1.2 Motivations
Existing simulation tools are capable of evaluating large supply chains while taking into account complex random phenomena. They permit the evaluation of operating performance prior to the execution of a plan (Chang and Makatsoris, 2010).
Dedicated simulation tools for supply chains have recently been proposed and allow the quick and easy-to-use modelling of a complex supply chain by following some standard modelling frameworks such as the SCOR model.
The key weakness of existing simulation tools is the lack of decision-making power. In all existing simulation tools, decision problems are typically solved by pre-specified operating rules such as reorder point rules for inventory control, Kanban-control and FIFO (first-in-first-out) rule for production scheduling. This is against the trend of extensive use of sophisticated advanced optimisation tools for integrated supply optimisation. Although the use of operating rules reflects the current practice of some existing supply chains, it does not allow the simulation to fully exhibit the true potential of an existing supply chain. Furthermore, the limitation of existing optimisation tools is their inability to incorporate random events. All optimisation tools are based on deterministic models and the quality of the results strongly depends on the quality of the estimated data such as demand forecasts and the variability of the random quantities (Fu, 2002).
The most problematic is the use of operating rules for evaluation of design alternatives of a new supply chain or for the reengineering of an existing supply chain. The choice of operating rules for a new supply chain is nearly impossible as the human expertise is not available. This problem will become more and more critical in the future as supply chains/networks will have most often a very short lifetime and be frequently reconfigured as business opportunities change.
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The rest of the paper is organised as follows: Section 2 presents some of the existing supply chain simulators. Section 3 discusses in detail the proposed approach. Section 4 illustrates the developed ‘intelligent’ simulation tool. Section 5 presents a case study and shows some of the obtained experimental results and analysis using the ‘intelligent’ simulation tool. Section 6 concludes the paper with some remarks and perspectives.
2 Supply chain simulation: state of the art
The literature is very rich with works that cover the supply chains simulation issue. Most of these works can be grouped according to the used approach in order to build the simulation model. More specifically, they can be divided into three main streams respectively process-oriented simulation, object-oriented simulation and agent-oriented simulation.
2.1 Process-oriented approaches
For this approach, the simulation model is described by a sequence of processes initiated by the occurrence of events in the system (supply chain for example).
Petrovic et al. (1998) proposed a model that expresses uncertainty using Fuzzy logic for the cases where data is not enough to describe the uncertainty, and probability distributions cannot be used. In the model, parameters were specified based on managers’ expertise using imprecise human language.
Ingalls (1998) presented the CSCAT (Compaq Supply Chain Analysis Tool). CSCAT is a discrete event Arena package developed by Compaq. It is easy to use and to configure; however, it is designed specifically for Compaq logistic network.
Schunk and Plott (2001) illustrated a commercial tool for supply chain simulation (Supply Solver). Supply Solver is based on previous software developed by Micro Analysis using Visual Basic. Its initial development is dedicated to industrial automobile manufacturing. Yet, it begins to be adapted for other industries. Decision-making problems are solved using Micro Saint OptQuest.
Jain et al. (2001) explored a high-level process-oriented simulation model. They highlighted the importance of choosing the adequate level of abstraction level when modelling. The model will be then detailed according to the objective of the simulation.
Vieira (2004) and Vieira and Júnior (2005) proposed three levels hierarchical model based on SCOR and implemented it using Arena. Many parameters are explicitly defined before simulating and supply chain performances considered are the average inventory level, service level, and cycle time between supplier and manufacturer. The developed model is not yet in its final state and need to be completed.
Presson and Araldi (2007) created an Arena package based on the SCOR model. The package aims to simplify supply chains modelling by a simple graphical way. Decisions are fixed before simulating, and it does not present any optimisation tool.
Cope et al. (2007) presented a new approach that generates simulation model based on data expressed in XML. This simulator is developed with simplicity in mind. Actually, it generates Arena simulation model automatically based on the information and the structure of supply chain encoded in XML.
Longo and Mirabelli (2008) developed a supply chain management tool based on modelling and simulation. The major aim is to develop a rapid and configurable tool with an intuitive graphic interface.
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2.2 Object-oriented approaches
Object-oriented approach has found many applications in complex systems description through its ability to decompose problems. Object-oriented approach facilitates the passage from models to programs (software).
Rosetti and Chan (2003) developed a new supply chain simulation framework using fundamental elements required to model a generic supply chain. A conceptual object-oriented study has been led using UML (Unified Modelling Language). Different classes were defined (Inventory, Distribution centre, Product …) along with their respective attributes, methods and relationships with other classes.
Biswas and Narahari (1998) proposed an object-oriented model for their tool DESSCOM (Decision Support for Supply Chains through Object Modelling). They mainly used two types of objects: structural objects (costumer, order, manufacturer, supplier, …) and policy objects (storage, production, orders management, demand planning, and supply planning ...).
Liu et al. (2004) presented another supply chain simulation tool named ‘EASY-SC’ using Java programming language. It integrates some optimisation methods to determine the values of some critical properties such as in inventory units.
Ding et al. (2004) proposed a tool-Box called ‘ONE’ (Optimisation methodology for Networked Enterprises). ‘ONE’ is a European project intend to propose a methodology for supply chain optimisation and simulation as well as the development of a tool supporting this methodology. The tool box is composed of three modules, respectively the simulation module, supply chain module which contains all the data of the logistic network, and the optimisation module.
Chatfield et al. (2006) criticised the SCOR model and its inability to serve as a simulation model unless it is augmented with additional details. The authors present a new tool named SISCO (Simulator for Integrated Supply Chain Operations) as a remediation to supply chain modelling and storage. It focuses on the way of storing a representation of the supply chain itself (and not the model) using an XML-based information storage. Optimisation is not yet included in SISCO.
Ding et al. (2007) presented a new tool called IBM SNOW (Supply-chain Network Optimisation Workbench). IBM SNOW is a software developed using the Java programming language. It helps in making strategic business decisions about the design and operation of supply chain. More specifically, using simulation and optimisation in a sequential manner, it addresses the design of supply chains using analytical methods for solving transportation and locations problems.
Cimino et al. (2010) presented an overview on some used discrete event simulation softwares in supply chain. The tools are criticised for their lack of speed when it comes to simulate a model with huge number of entities inside. They developed SCOPS (Supply Chain Order Performance Simulator), a flexible simulator used for inventory management problem, using a general purpose programming languages (Borland C++ Builder).
2.3 Agent-based approaches
Agent-based approaches try to capture the collaborative and implicit aspects in supply chains behaviour.
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Swaminathan et al. (1998) proposed an agent-based architecture to build supply chains network model. The architecture uses a generic agent that can be specialised to be used in different process.
‘MISSION’ (Modelling and Simulation Environments for Design, Planning and Operation of Globally Distributed Enterprises) is a reference architecture developed by the US National Institute of Standards and Technology (NIST) in collaboration with representatives from a number of outside organisations. Developers tried to keep a neutral interface that can be used in a distributed simulation with a third-party simulation tools used by other partners (McLean and Riddik, 2000; McLean and Leong, 2001; Umeda et al., 2001).
Van der Zee and van der Vorst (2005) developed another agent-based framework for supply chain optimisation. Agents represent the supply chain infrastructural elements. This architecture aims to improve the visibility of control elements scattered on the model.
Lemieux et al. (2009) presented a multi-agent simulator for the lumber industry, combined with an Advanced Planning and Scheduling system. This combination aims to evaluate the impact of different planning tactics on supply chains.
3 Proposed approach
Motivated by the limitations of existing supply chain simulation and optimisation tools, the approach proposed in this study is a hybrid approach that combines both simulation and optimisation. It takes advantage of the capability of a simulation tool for realistic evaluation of supply chains and the decision power of optimisation tools (Figure 1).
Figure 1 The developed intelligent simulation tool architecture
112 A. Bensmaine, L. Benyoucef and Z. Sari
The key features of the proposed approach can be characterised as follows:
1 A detailed enough simulation model is built and run (supply chain simulator). The simulation model takes into account important random phenomena such as random demand and transportation times.
2 The simulation can trigger calls for decision-making to sort possible alternatives.
3 Whenever a decision-making call is triggered, the optimisation tool automatically formulate the optimisation problem in a format understandable by both exact methods and dedicated heuristics. The decision-making problems include, for example, production-planning problems triggered according to a planning horizon and very short-term decision problems such as vehicle routing and production reschedule triggered whenever the problem arises.
4 After the formulation of the decision-making problem, according to its complexity, either exact method or a dedicated heuristic is called to solve it (optimisation).
5 After the resolution of the decision-making problem, the simulation continues according to the solution proposed by optimisation tool.
3.1 Three key phases
Our study involves three key phases respectively:
Phase 1: Decisions problems identification: There are various decision-making problems during the analysis (design/control) of any supply chain. These problems cover all three levels of decision-making, namely strategic, tactical and operational decisions. They include facilities location problems, supplier selection problem, supply planning, production planning, distribution planning, etc. The first phase begins by the identification of the set of decision-making problems encountered at the tactical and operational level for which solutions are needed.
Phase 2: Development of solution methods for the optimisation tool: Once identified, decisions problems are formulated and solved. The choice of formulation is important for the solving method development. To formulate the problem, we will use either mathematical programming (linear programming, integer programming, …) or metaheuristics coding (genetic algorithms, taboo search, …). For the resolution, methods/approaches will be developed and their effectiveness tested.
Phase 3: Implementation, integration and validation: The third phase consists of implementing, integrating and validating the intelligent simulation-optimisation tool.
For the validation of the developed ‘intelligent’ simulator, several realistic scenarios of different levels of complexity need to be generated and analysed. For the moment, we have two case studies proposed by our industrial partners in Growth-ONE project and dealing respectively with production-distribution network design and supplier selection problems.
1 The first case study, presented in this paper, is proposed for automotive industry (production and distribution network analysis of a car model from Italy to Germany). The problem consists in identifying the best strategies for production plannings in the assembly plants, inventory control in the distribution centres, transportation plannings from assembly plants to retailers through distribution centres using different connections and modes.
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2 The second case study, considered as one of our perspectives, is proposed for a textile industry. The problem deals with the identification of the best strategy integrating suppliers’ selection, inventory control policy in warehouse and transportation connections and modes identification.
3.2 Optimisation tool
During a supply chain simulation, numerous decisions require to be taken, particularly decisions regarding operation rules (sequencing problem in a mixed model assembly line, routing problem in a job-shop, …); even though the use of pre-defined operating rules reflects the current practice of some existing supply chains, using an optimiser allows the simulation to fully exhibit the true potential of an existing supply chain. Therefore, our simulator includes an optimisation tool to solve some of the encountered decision-making problems.
The proposed optimisation tool contains a set of decision problems with their respective resolution method classified in a unique catalogue. Once a decision problem is defined, the simulator will look for it in the catalogue, generate the model, run the resolution method, and then resume the simulation using optimisation result.
Depending on the complexity of the decision problem, mathematical programming or metaheuristics coding are used to represent it. Effective resolution methods are developed and implemented using metaheuristics (genetic algorithms for example).
4 Developed simulator
4.1 Modelling approach
Nowadays, supply chains are getting more and more complex. Moreover, in the today’s global market, customers’ demand is constantly changing and competition requires companies to provide products of best quality, delivered in a short time and with competitive prices. The developed simulation tool should be as general as possible to be able to simulate several supply chain configurations. The development of such a tool leads to real hard work when classical techniques are used; therefore, we decide to use the object-oriented modelling. Object-oriented modelling is characterised by the natural representation offered by the concept of objects to represent physical or conceptual real-world entities. Object-oriented approach has the advantages of ensuring reusability and extensibility of code for further development and improvements.
We identify four basic classes corresponding to the four categories of sites in supply chains (Figure 2), i.e. suppliers, factories, distribution centres and customers, named respectively Supplier, Manufacturer, Distributor and Customer. All of them derive from an abstract class named GenericFacility. Derivation is one of the most powerful characteristics of object-oriented paradigm. If at any point of the simulation we do not know – and do not care about – the type of a given facility, we can just consider it as ‘GenericFacility’, avoiding us from spending time on determining the real type.
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Figure 2 Class diagram of the basic classes constituting a supply chain
Moreover, we benefit from the derivations to determine an abstract class that we name ‘Link’. In the context of supply chains, we define two kinds of links that exist between facilities: transport links representing medium for physical flow (material flow) via the logistic network, and information links which represents the medium used for information exchange. We call them respectively TransportLink and InfoLink in the class diagram.
4.2 Implementation
The simulator is implemented using Java programming language with the free IDE NetBeans. Java is one of the most commonly used programming languages; its object-oriented nature makes it very suitable for our developed model.
Three layers constitute the developed simulator: engine layer, data layer and interface layer. The engine layer is the responsible part for model creation, simulation runs and reports generation. Data layer is a set of classes allowing an internal representation of supply chains. It is controlled by the engine layer. Interface layer serves as an interactive part that allows the user to introduce the structure of the supply chain and the necessary data associated to it.
The implemented Graphic User Interface (GUI) contains three essential parts, a main menu, a toolbar for an easy access to the commonly used functionalities, and a modelling area where a graphical representation of the simulated supply chain is drawn (Figure 3).
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Figure 3 Our graphic user interface (GUI) (see online version for colours)
Depending on which button is clicked, a particular window appears, allowing him/her to introduce data corresponding to the modelled supply chain. Globally talking, the user can do the following actions using the tool:
• Adding a new manufacturer: the user adds manufacturers using the ‘Manufacturer’ dialogue. He can choose within a pre-defined list the class of the process (job-shop, assembly line, …) the user can add a new facility using buttons on the toolbar. Depending on which button was clicked, a particular window appears, allowing him/her to introduce characteristics and data concerning the facility to be added. For example, the user can add a Manufacturer using the ‘Manufacturer’ dialogue. He can choose within a pre-defined list the class of the process (job-shop, assembly line, …) (see Figure 4).
• Creating a transportation link: users can add to the model a new transportation link between a ‘source’ and a ‘destination’. Previously introduced data and facilities are automatically accessible from all dialogues when needed. For example, users can directly access to facilities introduced until that time to specify the source and the destination of the link (see Figure 5).
• Creating a sourcing policy: a sourcing policy answers the question ‘who feed whom?’. It creates an information links that transmit demand from ‘client’ to ‘supplier’.
• Sometimes when there is an ambiguity concerning transportation, i.e. when a facility has several output transportation link, the user has to specify to the simulator which path should be taken by a particular product having a particular destination.
• Inserting a switch: transportation and information policies depend sometimes on conditions that change dynamically during the simulation run. Putting a switch on the model allows the products flowing through the supply chain to take the right path.
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Figure 4 Adding a new manufacturer dialogue (see online version for colours)
Figure 5 Adding a new transportation link dialogue (see online version for colours)
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Gradually as the user creates the simulation model, a schema representing the supply chain is drawn on the dedicated area (Figure 6).
Figure 6 Graphical representation of a simulated supply chain (see online version for colours)
5 Experimental results and analysis
To see the impacts of embedding an optimisation tool within a simulator on the supply chains performances, we compare the performances given by the simulation of the supply chain presented in Figure 7 in respectively two cases (with and without optimisation). We show how decision-making simplifications will affect the performances resulting from simulation.
The first simulation (classical simulation) is executed without any mean of decision-making, and where all the operational rules are fixed before launching the simulation. While in the second simulation (intelligent simulation) the optimisation tool is activated. For our case study, this tool will be responsible for sequencing cars in the assembly plants that is widely encountered in the automobile industry.
The production and distribution network of Figure 7 is composed of two plants (factories 1 and 2), five distribution centres (CDC, RDC1, RDC2, RDC3 and RDC4) and five customer areas. The two factories and CDC are located in country A. The other sites respectively RDC1, RDC2, RDC3, RDC4 and the five client areas are located in country B.
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Figure 7 Configuration of the studied supply chain (see online version for colours)
Vehicles are conveyed from factories to customers via different sites using different transport modes. All the vehicles produced by the two plants, are accumulated in CDC. To reduce the cost of transportation, standard vehicles are transported by ships to RDC1, where they are stored in advance. Instead, to reduce travel time, personalised vehicles are conveyed directly by train to the corresponding RDC. The vehicles are then distributed by truck to customers.
Customers generate weekly independent orders. Demand’s size follows a certain probability distribution (e.g. normal distribution). For each customer order a due date is associated according to a certain probability distribution. If an order is fulfilled before its due date, then it will be considered as ‘satisfied’, otherwise it will be considered as ‘not satisfied’. According to a ratio given by each customer, each order is divided into two parts: one for standard vehicles and another part for personalised vehicles. The two orders are treated differently. Orders for personalised cars are directly assigned to the less charged factory, while orders for standards cars are served by the corresponding RDCs if there exist enough vehicles at RDC1, otherwise, they are placed on a waiting queue until the next delivery.
In our case, a factory consists mainly of a mixed model assembly line. The assembly line itself is composed of eight different workstations. Each station is responsible to perform a specified task. Furthermore, the main operational rule which influences the network performances is the sequencing rule in the factories. From a productivity point of view, it is more advantageous to sequence vehicles that share some attributes, one after the other. For example, it is more profitable to have a number of consecutive vehicles with the same colour as the cleaning of paint guns introduce set-up time and extra costs. Also, if a number of vehicles have the same destination then it is more profitable if they are on the same assembly sequence.
There is another class of attributes that have an opposite effect on sequencing. Consider an optional component (open roof for example), a portion of vehicles will require the operation of installing this option. Often, such an operation takes more time to be achieved than other operations that are common to all jobs (cars in our case), that is why the section of the assembly line reserved for this operation must be longer than the
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sections reserved for other operations. Since the number of operators assigned to such an operation is proportional to the average load, the jobs that require this operation must be spaced fairly on the sequence.
If two consecutive jobs require the operation of installing the option, then operators may be unable to complete the task on the second job, because operators will complete their work on the first job when he is about to leave the station, then proceed to the second job, which is relatively close to the exit of the station. So it may be impossible to complete the work before the job leaves the station (operators can work on a job only if it is in their station).
Two alternative approaches are used in automotive industry to complete the tasks that operators could not finish (Drexl et al., 2006). In USA, dedicated staff is used to perform tasks not completed by the primary operators. In Japan, the operator pushes a button to stop the conveyor when it fails to complete its task on time. In this study, we adopt the Japanese approach.
For the classical simulation, the FIFO strategy as a prefixed sequencing rule is used, whereas for our intelligent simulation tool, a method implemented using genetic algorithms (GA) based on due dates and set-up times is considered. At anytime during the simulation, when a production order for vehicles (standard or personalised cars) is assigned to one of the two factories, the simulator halts the simulation, call the optimisation tool and wait for the optimised sequence to be returned, and then resume the simulation.
The resolution by genetic algorithms usually starts with the coding phase. It concerns the definition of the structure of the chromosome, which is then used for population evolution. As part of this work, we propose a code so that every gene in the chromosome represents a job (vehicle), and the complete chromosome represents a sequence.
If there are, for example, six different models types (type 1, type 2, …, type 6), and the sequence to optimise has a size of eight jobs, then coding is done on a chromosome with eight genes, each gene will contain a job (a number between 1 and 6 representing the job’s type) (see Figure 8). In our case, we use 1 for standard and 2 for personalised vehicles respectively.
Figure 8 A simple example of chromosome
Pseudocode of the used genetic algorithm Generate population
n = number_of_iterations
repeat n times {
For each individual in the population {
Evaluate(individual)
}
Select_individuals_from (population)
p_Crossover (selected_individuals)
Select_individuals_from (population)
p_Mutation (selected_individuals)
}
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Fitness proportionate selection, also known as roulette-wheel selection, is used in our implementation. For each individual, the probability of being selected is proportional to its adaptation to the problem.
Once selected, individuals are reproduced using Crossover (see Figure 9) or Mutation (see Figure 10). Mutation and Crossover are not always applied on selected individuals, indeed, a given Mutation and Crossover probability p is used (that is why we called them p_Crossover and p_Mutation in the pseudocode, where p = 0.7). To keep the sequence coherent, a control operation is executed after each operation of Crossover/Mutation.
Figure 9 Illustration of GA Crossover operator (see online version for colours)
Figure 10 Illustration of GA Mutation operator (see online version for colours)
The following two objective functions are used in order to evaluate the fitness function:
1 Minimising set-up time: minimise (Σcjk) over all individuals, where cjk is the set-up time between jobs j and k.
2 Minimising downtimes resulting from jobs requiring ‘option’ operation that are not fairly spaced: let ψ(l) be the downtime required if a station have to operate on two jobs that are spaced by l positions. The more l is important, the more ψ(l) is reduced. ψ(l) =0 when l > lmin. The objective is to minimise (Σψ(l)) over all individuals.
Both mentioned above objective functions are expressed in time, and the overall fitness function can then be calculated as:
min(αΣcjk + β Σψ(l)) over all individuals.
where α and β are the respective weights (in our case, we took α = 0.9 and β = 0.8). We simulate this network on a one-year horizon. A warm-up period, lasting one
month, is used to reduce the impact of initial conditions on the simulation results. The used key performance indicator is the customer satisfaction level, defined as the
percentage of total number of customers orders fulfilled within the associated due dates. We do not consider performance indicator values during the first month in the statistical analysis. For both simulation scenarios, five replications are performed.
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Based on the sequence size, Rabbani et al. (2006) classify sequencing problems into two classes, respectively problems with small size and problems with large size. In our case the sizes vary between 5 and 12 for the small problem size, and between 20 and 30 for large size problems. To cover the whole classes, we consider sequences of different sizes, ranging from 5 to 30 vehicles. The simulation was launched on a Pentium IV 3GHz. Obtained results are summarised in Table 1. Table 1 Obtained results
Simulation Type Satisfaction Level Classical Simulation (FIFO) 49.5%
Sequence Size 5 55.61%
10 60.22%
15 64.11%
20 66.05% 25 66.77%
Inte
llige
nt S
imul
atio
n
30 67.00%
From Table 1, we state that the two different types of simulation do not give the same results. Indeed, we see a difference going from 7% up to 18%. This is due to the integration of the optimisation tool in the intelligent simulation tool. The optimisation tool reduces the downtime of the assembly line, which translates into greater productivity. Moreover, the optimisation tool gives preferential treatment to vehicles with closer due dates. These two characteristics together created this marked improvement in the supply chain performances.
We can also notice that the supply chain performs better with long sequences, this is due to the way in which due dates were assigned to orders. It is clear that the optimisation of long sequences minimises set-up time by grouping more identical jobs one after another in the sequence, but it also increases the risk of delaying jobs by sequencing them at the end of the sequence. However, if due dates have got a small variation interval, the risk of delaying a job in a long sequence is less likely to happen.
6 Conclusions and perspectives
Motivated by the limitations of existing supply chains simulation and optimisation tools, in this paper we present an ‘intelligent’ simulation tool with an embedded intelligent optimisation engine for solving various decision-making problems encountered in the simulation of a supply chain.
Embedding an intelligent optimisation engine in a simulation tool allows precise evaluation of the performances of a supply chain and allows overcoming the lack of decision powers of traditional simulation tools. On the other hand, the combination of simulation and optimisation allows taking into account phenomena such as random events, business organisational issues and complex system dynamics that cannot be easily captured in an optimisation model. To illustrate the applicability of the tool, a simple example of a production-distribution network analysis is presented.
122 A. Bensmaine, L. Benyoucef and Z. Sari
As perspectives, we plan to identify the maximum number of operational decisions rules that can be encountered during supply chains simulation, and develop their respective solution methods. For more interactivity, we will build a neutral input/output interface that allows the tool to communicate with other tools when needed (possibly during a ‘Simulation-based Optimisation’). Moreover, we plan to improve the simulator by using some computer science techniques like multithreading, XML-based files to describe supply chains, and graphical model building/editing.
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