Emirates Journal for Engineering Research, 13 (2), 11-19 (2008) (Review Paper)
QUANTITATIVE MODELS FOR PLANNING AND SCHEDULING OF FLEXIBLE MANUFACTURING SYSTEM A.H.R. Zaied Technology Management Program, Arabian Gulf University, Bahrain Email:
[email protected] (Received November 2007 and accepted March 2008)
والعديد من البحوث,1983 وستيك1981 منذ نشر أول بحث عن مشاكل تخطيط نظم التصنيع المرنة بواسطة كل من سولبرج تم عمل دراسة مسحية للنماذج والطرق المقترحة في المراجع والتي تعالج, في ھذا البحث.تركز على حل ھذا النوع من المشاكل والھدف األساسي.(2007 وحتى1997 مشاكل تخطيط وجدولة نظم التصنيع المرنة خالل السنوات العشر الماضية )خالل من كما تعد ھذه.من ھذه الدراسة ھو معرفة كيفية معالجة مشاكل تخطيط وجدولة نظم التصنيع المرنة فعليا في النماذج المقترحة وقد تم تقسيم البحوث تحت الدراسة إلى سبع فئات طبقا.الدراسة أساس لتقييم وتحديد اتجاھات البحوث المستقبلية في ھذا المجال فنجد أن بعض البحوث قدمت أطر عمل لتفسير النماذج.لطبيعة مشاكل نظم التصنيع المرنة التي تعالجھا النماذج المقترحة والقليل منھا قد ركز على اقتراح نماذج كمية,والطرق المختلفة المستخدمة في شرح مشاكل تخطيط وجدولة نظم التصنيع المرنة يمكن استخدامھا في حل تلك المشاكل Since the publication of the first articles on the planning problems in flexible manufacturing systems (FMSs) proposed by Stecke and Solberg 1981 and Stecke 1983, much research has been devoted to the solution of these types of problems. This paper provides a survey of different approaches and models proposed in the literature to tackle the FMS planning and scheduling problems during the last ten years (between 1997 and 2007). The main goal of the survey is to see how the issues of FMS planning and scheduling are actually formalized in the proposed models. At the same time, it provides the basis for the evaluation of the areas for future research directions. Articles are classified into seven categories according to type of FMS problems. Some published articles provide frameworks to clarify different approaches and models to describe planning and scheduling problems in FMSs. Few focuses on proposing quantitative models can solve planning and scheduling problems. Keywords: FMS, planning and scheduling, quantitative models
1. INTRODUCTION Automation was introduced to production at the beginning of the 20th century and it helped to increase productivity and quality, while reducing costs. In the 1970s and 1980s, flexibility became essential in manufacturing systems to respond to varying demand for a larger variety of products, smaller production lots and model changes[60]. Flexibility is enabled in FMS by flexible and alternative production routes. Such alternative routes are made possible by different (or redundant) equipment types capable of performing the same operation or by different manufacturing processes that can be used to achieve the same final result[12]. The performance of a Flexible Manufacturing System (FMS) is highly dependent on the selection of the right scheduling policy for the control system. Such policy enables one to exploit as much as possible the system flexibility[18]. Scheduling policy, expressed by a selected dispatching rule, determines which job out of jobs waiting to be processed should be selected first. The dispatching
rules used can change dynamically and reflect the status of the shop floor[51]. Stecke and Raman[56] defined three stages of hierarchical decision making in an FMS: design, planning and scheduling and control decisions. Whereas Shouman et al[52,53] classified the basic decision problems in FMS in two main groups: design and operational problems. Chan and Swarnkar[17] classified the decisions related to FMS operations in two types: pre-release decisions and post-release decisions. This article will focus only on planning and scheduling problems in FMS and discuss the quantitative modes used to solve these problems.
2. MANUFACTURING SYSTEMS Black [8] defined Manufacturing System (MS) as “the collection of operations and processes used to produce a desired product”. Whereas, Harrell et al [24] defined Manufacturing Systems (MSs) as “the processing systems in which raw materials are transformed into finished products through a series of operations performed at workstations”. A manufacturing system
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organizes equipment, people, and information to fabricate and assemble finished goods that are shipped to a customer. This system may be as large as a factory or as small as a manufacturing cell. Kathryn[28] presented many models of manufacturing systems as follows: - Produce-to-order systems - Produce-to-Stock Systems - Flow Lines - Dynamic Job Shops - Flexible Manufacturing Systems - Transfer Lines - Flexible assembly systems - Multiple-Cell (Group Technology) Systems
3. FLEXIBLE MANUFACTURING SYSTEMS There are many definitions for Flexible manufacturing systems (FMSs). Jha[27] defined FMS as “a group of programmable production machines integrated with automated material handling equipment which are under the direction of a central controller to produce a variety of parts at non-uniform production rates, batch sizes and quantities”. Whereas Kim and Yano[31] defined FMS as “an automated manufacturing system consisting of numerically controlled machines capable of performing multiple functions, linked together by a material handling system, all controlled by a computer system”. Also, Askin and Standridge [4] defined FMS as “an integrated manufacturing system that consists of numerically controlled machines equipped with tool magazines and connected by a material handling system, where all system components are under computer control”. Jang et al[25] defined it as “a computer-controlled configuration of semi-dependent workstations and material-handling systems designed to efficiently manufacture multiple types of products ranging from low to medium volume”. Matta et al[37] said that the Flexible Manufacturing Systems (FMSs) have emerged as a highly competitive manufacturing strategy in the late twentieth century and has been a subject of intense research and exploration. It utilizes computer controlled automation systems to integrate the machine centers (MCs) with the material handling system (MHS). It is widely used in shop floors to produce a large set of product families in small/medium volumes. In FMSs, the high flexibility of machines allows manufacturing different products in different mix ratios, thus providing firms the ability to react quickly and efficiently to changes in products, volumes and mix ratios. Chan and Chan[14] defined Flexible Manufacturing System (FMS) as “an integrated computer controlled system that consists of, but not restricted to, computer numerical controlled (CNC) machine tools, and automated material and tool handling devices”. And Solimanpur et al[54] defined Flexible manufacturing system (FMS) as “a production system in which a set of machines and a flexible material-handling system like robot,
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automated guided vehicle (AGV), etc. are linked and controlled by a central computer.
4. PLANNING AND SCHEDULING OF FLEXIBLE MANUFACTURING SYSTEMS The increasing automation and complexity of manufacturing systems has highlighted the need for the development of improved planning and scheduling techniques for flexible manufacturing systems (FMS). Generally, when a Flexible Manufacturing System (FMS) is being planned, the objective is to design a system which will be efficient in the production of the entire range of parts. This cannot be achieved until the design, production planning, scheduling, and controlling stages work well. Depending on the required measure of planning and scheduling performance, many different models to solve planning and scheduling problems can be generated[62]. In a general sense, planning is more general decisionmaking than scheduling; however, distinctions between the two are usually fuzzy[7,40]. 4.1 Planning Pool et al[42] defined planning as a sequence of actions that will transfer the initial world into one in which the goal description is true. Whereas, Nishioka[40] defined planning as an activity for clarifying actions or operations to achieve a given goal and reserve enough resource capacity to hit minimum targets. 4.2 Scheduling In an FMS, the objective of scheduling is to optimize the use of resources so that the overall production goals are met. Scheduling deals with the exact allocation of resources to activities over time, i.e., finding a resource that will process the activity and finding the time of processing[10]. Sauer[47] stated that the main task of scheduling is the creation of schedules, which are temporal assignments of activities to resources where a number of goals and constraints have to regard. Srinoi et al[55] defined scheduling as the process of organizing, choosing and timing resource usage to carry out all the activities necessary to produce the desired outputs of activities and resources. Whereas, Nishioka[40] defined scheduling as an activity for allocating actions and operations to particular resources at particular times, taking into account various actual constraints and optimization of several evaluation parameters.
5. QUANTITATIVE MODELS FOR PLANNING AND SCHEDULING OF FMS There are many forms and models used in planning and scheduling of flexible manufacturing systems. In this section, various quantitative models of the FMS planning and scheduling which have appeared in the literature are reviewed. The goal of these revisions is to see how the issues of FMS planning and scheduling
Emirates Journal for Engineering Research, Vol. 13, No.2, 2008
Quantitative Models for Planning and Scheduling of Flexible Manufacturing System
are actually formalized in the proposed models. At the same time, it provides the basis for the evaluation of the areas for future research directions. The revision of the models shows that, the models solve the following problems: - Selection problems - Loading problems - Work in process problems - Part scheduling and allocation problems - Dispatching problems - Layout problems and - Costing & investment problems 5.1 Selection Problems (machine/tool/part) Machine selection is considered for particular sets of job requirements in applications of CIM models in FMS. Part selection involves selecting the part to be loaded at the input end of FMS on a pallet for subsequent launching into the system. Tool selection is used for selecting the request tool to be transferred to the required machine. Abou Gamila et al[2] analyzed the production-planning problem in flexible manufacturing systems. They developed a mathematical model to select machines and assign the operations of the selected part types and the required tools to machines to minimize the total processing time (T). Karsak [29] presented a fuzzy multi-criteria decision making (MCDM) framework based on the concepts of ideal and negative-ideal solutions for the selection of an FMS from a set of mutually exclusive alternatives. The proposed framework provides the means for incorporating the economic figure of merit as well as the strategic performance variables. Zhao and Wu[63] presented a genetic algorithm approach to flexible routing scheduling problems. They implemented the concepts of a flexible-routing scheduling problem, which involves routing selection, machine selection, and processing sequence selection. Karsak and Kuzgunkaya [30] presented a fuzzy multiple objective programming approaches to facilitate decision making in the selection of a flexible manufacturing system. In this study, the FMS alternatives had been evaluated incorporating their strategic and economic benefits using a fuzzy multiple objective programming technique. An integrated model that performs operation sequence and tool selection simultaneously in FMS under dynamic tool allocation was proposed by Lee et al [33] to minimize tool waiting time when the tool is absent. Buyurgan et al[11] proposed a heuristic approach for tool selection in flexible manufacturing systems (FMS). The proposed approach utilized the ratio of tool life over tool size (L=S) for tool selection and allocation. A simulation model based on a hypothetical FMS was developed to highlight the effect of tool life and size on the performance of a typical FMS. The hypothetical FMS was composed of: four machining centers, one input and one output buffer, a tool crib, and AGVs for parts and tools with deterministic transportation times.
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There were four part types and eight tool types. In the simulation model, a central buffering strategy had been adopted where machining centers have no input or output buffers. Parts enter the system from a central input buffer and exit from a central output buffer. Ecker and Gupta[21] studied the problem of scheduling a given set of precedence constraint tasks on a flexible machine equipped with a tool magazine where each task requires exactly one of the tools during its execution. They proposed a model followed the idea of an ideal sub graph of a scheduling problem, which is a dynamic programming approach. The concept used in their model was that of a SIT-graph which was constructed from subsets of independent tasks (SIT), each representing a sub problem of the given instance, and relations between them. The proposed model described two heuristic algorithms: Algorithm 1 (SITgraph algorithm) and Algorithm 2 (SIT-graph based heuristics). Chan and Swarnkar[17] presented a fuzzy goal programming approach for the machine tool selection and operation allocation problem of FMS. It determined the optimal machine tool combination and the assignment of the operation for the given part types to the available machines while maintaining the machining cost, material handling cost and set-up cost within certain limits. 5.2 Loading Problems Loading in FMSs is affected by the characteristics of the FMS under analysis, by the type of plant where the FMS is introduced, and by the production planning hierarchy where the loading module operates. The FMS loading decision is concerned with the allocation of operations and required tools to machines or workstations subject to resource and technological constraints of the system. Loading is one of the most critical decisions in FMS planning. Mohamed and Bernardo[38] analyzed the interface between tool planning and the FMS loading and routing decisions. It was shown that tool policy had a pronounced effect on the flexibility and the planned makespan of an FMS. Roh and Kim[44] proposed a due-date based loading and scheduling model for a flexible manufacturing system with an automatic tool transporter. The model focused on the problems of part loading, tool loading, and part sequencing with the objective of minimizing the total tardiness. Three heuristics had been developed. These heuristics were list scheduling, sequential, and iterative approaches. Also in 1997, Tiwari et al[58] proposed a heuristic approach and a Petri-net model with an objective of minimizing system unbalance and maximizing throughput for solving the machine-loading problem of an FMS. Atlihan et al [5] developed a generic modeling framework that addresses tactical planning problems of flexible manufacturing systems in a coherent manner. They proposed a generic 0-1 mixed integer programming formulation, which integrates batching, loading, and routing problems with their
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critical aspects related to a system's performance. Abou-Ali and Shouman [3] proposed a simulation model consists of eight machines (M/C1, M/C2, M/C3, M/C4, M/C5, M/C6, M/C7, and M/C8), storage buffer areas (BF1–BF8), receiving area, and three robots and pallets (ROB, ROB1 and ROB2). Three robots and pallets were used as available resources. Eight distinct part types entered to be processed within the proposed model (P1–P8) and left the FMS at load/unload stations and transferred between machine centers by available trucks. Based on a number of specific assumptions, 12 different dispatching strategies were considered. Kumar et al[32] studied the simple genetic algorithm and proposed a new methodology, constraint-based genetic algorithm (CBGA) to handle a complex variety of variables and constraints in a typical FMS-loading problem. To achieve this aim, two objective functions were introduced to minimize system unbalance leading to maximizing system utilization and to maximize throughput, leading to maximization of system efficiency. A heuristic model based on multi-stage programming approach was proposed by Nagarjuna et al[39] to solve machine loading problem in random FMS. The objective considered was to minimize the system unbalance while satisfying the technological constraints such as availability of machining time and tool slots. The objective function considered by them was maximization of total system-assigned workload. Li et al[36] proposed a mega-trend-diffusion technique to estimate the domain range of a small data set and produce artificial samples for training the modified back propagation neural network (BPNN). A simple FMS simulation model was constructed, it consisted of a load/unload station, three automatic guided vehicles (AGVs), four CNC machines, and four pairs of input/output buffers (IB/OB) for each CNC machine. 5.3 Work in Process Problems Work in process is materials/parts that have been released to manufacturing ,engineering, design, or other services under the contract and includes undelivered manufactured parts, assemblies, and products, either complete or incomplete. These items, no longer part of the raw materials inventory and not yet part of the finished goods inventory, may constitute a large inventory by themselves and create extra expense for the firm. A computer simulation model was proposed by Chan[13] in order to evaluate some control rules on the performance of flexible manufacturing system. Three control rules: dynamic alternative routings, planned alternative routings, and no alternative routings, were proposed to control the selection of alternative routing for each part. The effects of changing production ratios of different part types with the machine breakdowns on the performance of various control rules were discussed. Rossi and Dini[45] introduced a genetic algorithm model, that capable of generating optimized
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production plans in flexible manufacturing systems. The developed system was able to generate alternative plans following part-flow changes and unforeseen situations (dynamic scheduling). The key-point was the real-time response obtained by an optimized evolutionary strategy capable of minimizing the number of genetic operations needed to reach the optimal schedule in complex manufacturing systems. A one machine one part type infinite horizon discounted cost problem was considered and necessary and sufficient conditions on the failure rate function were derived for a hedging type policy to be optimal. Shoman et al[53] introduced a computer simulation model to evaluate the effects of various control rules on the performance of cellular manufacturing systems operating under different conditions. Whereas Chan et al[15] developed a framework for the evaluation of combinations of scheduling rules using fuzzy multicriteria decision-making techniques, which were called MAW, Max-Min, and Max-Max. A simulation model was used to illustrate the proposed techniques. They compared the results with a simple approach for multi-criteria decision-making method, which was called SAW. In 2003, Abou Gamila and Motavalli[1] analyzed the production planning problem in flexible manufacturing systems and proposed FMS planning model that aims to minimize the summation of maximum completion time, material handling time and total processing time. Also, Chen and Ho[19] proposed an approach to solve multi-objective production planning problems (MOPPPs) of FMS using an efficient multi-objective genetic algorithm EMOGA. The proposed approach had four objectives: minimization of total flow time, minimization of machine workload unbalance, minimization of greatest machine workload and minimization of total tool cost. Lee and Korbaa[34] proposed a model having two jobs and two machines for the analysis of a cyclic schedule for the determination of the optimal cycle time and the minimization of the Work in Process, especially FMS cyclic scheduling problem using unfolding timed Petri nets (UTPN). In the unfolding net UTPN, it had one function for computing the makespan time, as f(UTPN). The function f(UTPN) was the necessary time to go from the initial marking M0 to the object marking. The best schedule of the UTPN was obtained by minimizing the function f(UTPN). 5.4 Part Scheduling and Allocation Problems The part scheduling and allocation problem concerns the sequencing of parts from a resource queue to either a machine, material handler, or the system as a whole. In the example FMS, there are five queues or "incidences" where this problem could occur: the queues at the I/O station (system entry) and each of the machines. A microcomputer-based simulation model of a job-shop type flexible manufacturing system was presented by Tunali[59]. One of the main objectives of that study was to discuss how a
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Quantitative Models for Planning and Scheduling of Flexible Manufacturing System
combined process/discrete-event model could be used to schedule orders. The other was to present the results of a comparative simulation study on flexible and prefixed routing of parts in an FMS which was subjected to unexpected machine breakdowns. In 2001, Saygin et al [48] developed a real-time decisionmaking model to select routings for the parts in offline FMS scheduling. Hypothetical FMS consisted of seven machining centers, a loading and an unloading area, and six different part types were used. Three control rules, namely, first-in first-out/first available (FIFO/FA), equal probability loading (EPL), and dissimilarity maximization method/first-in first-out (DMM/ FIFO) were used. Fathi and Barnette [22] addressed the problem of scheduling a set of parts with given processing times and tool requirements on identical parallel machines. Three heuristic procedures were proposed for solving the problem; the local improvement approach, the list processing approach and the constructive approach. Their computational study showed that the local improvement approach and the constructive approach tend to perform better, especially in situations where the tool-requirement matrix had an apparent structure. Das and Canel[20] studied the problem of scheduling batches of parts in a flexible manufacturing system (FMS) and developed a model could be used to minimize the total production time (makespan) i.e. minimize production time, minimization of inter-batch setup times becomes an important task. A continuous real-time routing model was presented by Ozmutlu and Harmonosky[41] to minimize mean flow time of parts in a FMS with routing flexibility by making a selection among alternate routes based on the concept of the significant benefit in terms of waiting time of parts. The flexible manufacturing system considered in their study was one where each operation of a part can be processed by alternate machines. Each operation was assumed to have a primary machine and an alternate machine, which processes the same part with a certain penalty. Sharafali et al [50] considered an FMS environment for a made-to-order situation with jobs (part-families) arriving at random times and proposed a polling model (a multiple channel queuing system in which the queues were served in a cyclic or some other predetermined order, by a single server) with the objective of minimizing the total average cost. Three situations were compared: no mixing was allowed among part-families, a particular part-family with an independent production schedule and a particular partfamily with no independent production schedule. Sterna[57] concerned a small flexible manufacturing system consisting of three CNC machines: a lathe machine, milling machine and measurement center and a single robot. He formulated a model optimizing production plans within a single shift in order to minimize the late work, i.e. the amount of work executed after a given due date. The quality of a schedule obtained was estimated with regard to the
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late work criterion, which allows minimizing the parts of particular jobs which are not finished on time. 5.5 Dispatching Problems Dispatching strategies are crucial in scheduling of flexible manufacturing systems (FMSs), in which each operation of a job may be performed by any of the several machines. In 1997, Sharadapriyadarshini and Rajendran [49] presented a new heuristic model for scheduling a buffer constrained flow shop and flow line-based manufacturing cell with different bufferspace requirements. A real-time scheduling model for job dispatching rules in flexible manufacturing systems was developed by Jeong and Kim [26]. The job dispatching rules vary dynamically based on information from discrete event simulation that was used for evaluating candidate-dispatching rules. Also, the scheduling strategies were formed by combining the factors that might influence the mechanism performance. A beam search-based model for scheduling flexible manufacturing system was introduced by Sabuncuoglu and Karabuk[46]. The model considered finite buffer capacity, routing and automated guided vehicle schedules for a given scheduling period. Whereas dispatching strategies of rail-guided vehicles (RGV) in the load/unload area of a flexible manufacturing system with a bi-directional track had been presented by Lee and Maneesavet[35]. The model was focused on the load/unload area of the system, but the effective combination of RGV dispatching and scheduling rules to prioritize jobs in the buffer storage between the load/unload area and machine center was also explored. Five RGV dispatching rules were developed and evaluated. Banaszak et al[6] studied the development of an integrated FMS control model that includes essential features, such as routing of simultaneously processed work orders and batch dispatching, as well as dynamic vehicle path determination and conflict-free routing. They proposed a logistics-oriented modeling methodology for FMS distributed control design that provides the capability for rapid development and evaluation of the control policy. This methodology integrated workpiece flow structure design, buffer capacity assignment, and allocation of the dispatching rules that control the workflows. The interactive process between routing flexibility index, different interruption ratios, as well as sixteen dispatching polices were studied by Shouman et al[52]. The dispatching mechanisms that will perform the best with the considered measuring performance criteria for route flexibility index and model configuration had been pointed out. Chan et al[16] presented a simulation model of a flexible manufacturing system (FMS) which subjected to minimization three performance criteria simultaneously such as mean flow time (MFT), mean tardiness (MT), and mean earliness (MR). The FMS included five general-purpose machine workstations and one loading/unloading station. The
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system had a work in process (central buffer) area to hold all jobs to be processed. The pre-emptive method-one of the algorithms for solving the goal programming problem- was used by representing the multiple goals as a single objective function. The preemptive method started by prioritizing the goals in order of importance as judged by the decision-maker. The model was then optimized using one goal at a time. Also, Chan and Chan[14] studied the effects of different combinations of routing and dispatching strategies on the performances of an FMS under different scenarios. They suggested three routing strategies: No Alternate Routings (NAR), Alternate Routings Dynamic (ARD), and Alternate Routings Planned (ARP). Under this policy, alternative routings was specified using Linear Programming (LP) model. The objective of the LP model was to maximize the production rate, improving machine utilization and cycle time of the FMS. The optimal distribution of the total production quantity among the available routings could be determined before the actual production. 5.6 Layout Problems One of the problems encountered in the design and implementation of FMS is the layout of machines within the manufacturing cells. Layout of FMS involves distributing different resources in a given FMS and achieving maximum efficiency of the services offered. The layout has an important impact on the production time and cost, especially in the case of large FMS. Ficko et al[23] presented a model of layout designing of the flexible manufacturing system (FMS) in one or multiple rows with genetic algorithms (GAs). In the model, the automated guided vehicles (AGVs) for transport between components of the FMS were used. To solve the problem it was necessary to know the matrix of the transport quantities between the individual devices N in a time period using a proposed fitness function. Solimanpur et al[54] formulated the problem of single row machine layout in flexible manufacturing systems as a non-linear 0-1 programming model in which the distance between the machines was sequence dependent. They developed an ant algorithm to solve the layout of machines along a single row. Yang et al[61] studied the layout design problem in FMS. A two-step heuristic was proposed to solve material flow problem. It first solved a traditional block layout with directed flow path to minimize material handling costs by using a combined space-filling curve (SFC) and simulated annealing (SA) algorithm. The second step of the proposed methodology used the resulting flow sequence and relative positioning information from the first step as input to solve the detailed FMS layout, which included the spatial coordinates and orientation of each FMS cell.
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5.7 Costing and investment problems An accurate determination of cost components for the operation of FMS can play an important role in that FMS’s success. Managing costs across FMS means managing the costs incurred before the product is manufactured (upstream costs, i.e., research and development, and product design, and so on), while the product is manufactured (manufacturing costs), and after the product is manufactured (downstream costs, i.e., marketing, distribution, customer service, and so on). In 1999, Bruce and Albert[9] presented a strategic investment model for phased implementation of flexible manufacturing systems. Their model described a set of strategic, tactical, and operational models that could be used to analyze the phased implementation of flexible manufacturing system. The strategic model represented capital investment decisions, the tactical model represented aggregate production decision, and the operational model represented the functional form of the production costs. Also, Rezaie and Ostadi[43] introduced an integrated dynamic programming model in order to analyze the optimal and phased implementation of flexible technology in a manufacturing system. The objectives of the model were minimizing the cost network flow and represented capital investment decisions, aggregate production decisions, and the functional of the production costs.
6. DISCUSSION 6.1 General Discussion In the first part of the article, the definitions of the terms related to planning and scheduling problems have been mentioned, while in the second part, 43 different forms and models of planning and scheduling problem in FMS proposed in the literature are presented and discussed as shown in Figure 1. 6.2 Model Classifications According to Solving Approaches Planning and scheduling models can be classified into different approaches as follows: - Simulation-based scheduling with dispatching rules[26]. - Heuristics-oriented[61]. - Combinatorial optimization[55]. - Multi-criteria decision making[51]. 6.3 Model Classifications According to FMS Problems The analysis of the literature shows that: - Some articles deal with the same problem as shown in Table 1, even if the same situation existing. This is due to the large number of different key factors affecting FMS problem.
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Quantitative Models for Planning and Scheduling of Flexible Manufacturing System
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Table 1. FMS Problems Classification
Number of Models
6 5 4 3
FMS Problems
Models
Selection (machine / tool / part) (8 models)
Abou Gamila et al (2000), Karsak (2000), Zhao and Wu (2001), Karsak and Kuzgunkaya (2002), Lee et al (2003), Buyurgan et al (2004), Ecker and Gupta (2005) & Chan and Swarnkar (2006). Mohamed and Bernardo (1997), Roh and Kim (1997), Tiwari et al (1997), Atlihan et al (1999), Abou-Ali and Shouman (2004), Kumar et al (2006), Nagarjuna et al (2006) & Li et al (2007). Chan (1999), Rossi and Dini (2000), Shoman et al (2001), Chan et al (2002), Abou Gamila and Motavalli (2003), Chen and Ho (2005) & Lee and Korbaa, (2006). Tunali (1997), Saygin et al (2001), Fathi and Barnette (2002), Das and Canel (2005), Ozmutlu and Harmonosky (2005), Sharafali et al (2005) & Sterna (2007). Sharadapriyadarshini and Rajendran (1997), Jeong and Kim (1998), Sabuncuoglu and Karabuk (1998), Lee and Maneesavet (1999), Banaszak et al (2000), Shouman et al (2000), Chan et al (2003) & Chan and Chan (2004). Ficko et al (2004),Solimanpur et al (2005) & Yang et al (2005). Bruce and Albert (1999) & Rezaie and Ostadi (2007)
Loading (8 models)
2 1 0 1997
1999
2001
2003
2005
2007
Publication Year
Figure 1. Number of models discussed
-
-
Few articles present detailed real or realistic test cases which can be adopted as test beds for subsequent research work. Other articles give a general description of the models, the formulation process and how the model under analysis is integrated with other models.
6.4 Model Classifications According to Objectives and Constraints Having looked at the FMS problems, it is useful to analyze the articles in greater detail. For this purpose, this section provides a detailed analysis of the objective functions and the constraints adopted by various authors in their formulations. Objective functions: The objective functions are classified in to two main categories: - In the first category, the objective functions are directly connected with the goals of time minimization: minimizing the makespan (minimizing the time required to complete all jobs), minimizing maximum tardiness (minimizing the largest difference between completion times and due dates) and minimizing the total processing time as shown in Table 2. - In the second category the objective functions are directly connected with the goals of cost minimization (workload balancing among the machining centers, and maximization of the number of alternative routings for the various parts). Constraints: The constraints introduced in various formulations are grouped as assignment constraints, capacity constraints, and management constraints. - Assignment constraints: constraints which deal with the way the work can be assigned to the machines. - Capacity constraints: such as tool magazine capacity etc. - Management constraints: constraints which deal with preferences and workload balancing.
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Work in process (7 models) Part scheduling and allocation (7 models) Dispatching rules (8 models) Layout (3 models) Investment (2 models)
Table 2. Objectives of planning and scheduling models of FMSs Objective
Models
Category I: Minimizing Time (36 Model)
Mohamed and Bernardo (1997), Sharadapriyadarshini and Rajendran (1996 and 1997), Tiwari et al (1997), Tunali (1997),Roh and Kim (1997), Jeong and Kim (1998), Sabuncuoglu and Karabuk (1998), Atlihan et al (1999), Chan (1999), Lee and Maneesavet (1999), Abou Gamila et al (2000), Banaszak et al (2000), Rossi and Dini (2000), Karsak (2000), Shouman et al (2000), Zhao and Wu (2001), Shoman et al (2001), Saygin et al (2001), Chan et al (2002), Fathi and Barnette (2002), Abou Gamila and Motavalli (2003), Chan et al (2003), Lee et al (2003), Abou-Ali and Shouman (2004), Buyurgan et al (2004), Chan and Chan (2004), Ficko et al (2004), Kianfar (2005), Ecker and Gupta (2005), Das and Canel (2005), Ozmutlu and Harmonosky (2005), Solimanpur et al (2005), Kumar et al (2006), Lee and Korbaa (2006), Nagarjuna et al (2006), Li et al (2007) & Sterna (2007). Bruce and Albert (1999), Karsak and Kuzgunkaya (2002), Yang et al (2005), Chen and Ho (2005), Sharafali et al (2005), Chan and Swarnkar (2006) & Rezaie and Ostadi (2007).
Category II: Minimizing Cost (7 Model)
7. CONCLUSIONS Planning and scheduling is an important issue in production planning, particularly for FMSs, for the whole manufacturing plant, and for the productionplanning hierarchy. Planning problems include: the determination of which parts should be simultaneously machined, the optimal partition of machine tools into groups, allocations of pallets and fixtures to part types, and the assignment of operations and associated cutting tools among the limited-capacity tool magazines of the machine tools. Whereas, scheduling problems include determining the optimal input
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sequence of parts and an optimal sequence at each machine tool given the current part mix.
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