Deadlock Avoidance in Flexible Manufacturing Systems Using Finite Automata

Transcription

1 424 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 16, NO. 4, AUGUST 2000 TABLE IV NUMERICAL RESULTS FOR EXAMPLE 3 REFERENCES [1] H. Chen, C. Chu, and J. M. Proth, A more efficient Lagrangian relaxation approach to job shop scheduling problems, in Proc. IEEE Int. Conf. on Robotics and Automation, 1995, pp [2] C. Czerwinski and P. B. Luh, Scheduling products with bills of materials using an improved Lagrangian relaxation technique, IEEE Trans. Robot. Automat., vol. 10, pp , [3] I. Duenyas, A simple release policy for networks of queues with controllable inputs, Oper. Res., vol. 42, no. 6, pp , [4] Y. T. Herer and M. Masin, Mathematical programming formulation of CONWIP-based production lines and relationship to MRP, Int. J. Prod. Res., vol. 35, no. 4, pp , [5] J. Wang, P. B. Luh, X. Zhao, and J. Wang, An optimization-based algorithm for job shop scheduling, Sadhana, vol. 22, no. 2, pp , [6] P. B. Luh, L. Gou, Y. Zhang, T. Nagahora, M. Tsuji, K. Yoneda, T. Hasegawa, Y. Kyoya, and T. Kano, Job shop scheduling with group-dependent setups, finite buffers, and long time horizon, Ann. Oper. Res., vol. 76, pp , [7] M. L. Spearman, D. L. Woodruff, and W. J. Hopp, CONWIP: A pull alternate to Kanban, Int. J. Prod. Res., vol. 28, no. 5, pp , [8] L. M. Wein, Scheduling network of queues: Heavy traffic analysis of a multi-station network with controllable input, Oper. Res., vol. 40, no. 4, pp. S312 S334, Fig. 4. WIP distribution for Example 3. for the first 20 days because parts that have very early due dates are released to fully utilize the machines, regardless of the WIP level. The parts with very late due dates are not released in view of the existence of earliness penalties. The solution quality, as measured in terms of duality gap, however, is good for this case. In Case 2, CONWIP constraints with W =40 were added, and the WIP over the scheduling horizon is overlaid in Fig. 4. Compared to Case 1, the WIP levels are much lower. At the same time, the feasible cost increases only slightly because the CONWIP constraints were included in optimization, and the resulting schedule maintains good on-time delivery performance. The maximum WIP decreased drastically for the first 20 days and the delay on part completion is very small. V. CONCLUSIONS A new separable formulation for CONWIP-based job shop scheduling is presented. A Lagrangian relaxation-based algorithm is developed to solve the problem. Testing results demonstrate that it can generate schedules with controllable WIP levels. At the same time, good on-time delivery performance is obtained. The formulation can also be easily extended to cover other situations. For example, different part types may vary in size and value, and it may be more reasonable to have different weights for different part types in calculating WIP levels. This constant weighted WIP concept can be easily formulated by having weights for parts in (2.3). Another example is that a job shop may want to limit WIP levels down to individual part types or families of part types as opposed to having one WIP level for the entire factory. This can be similarly modeled by having the CONWIP constraints for selected part types or families of part types. ACKNOWLEDGMENT The authors would like to thank Y. Zhang and X. Zhao at the University of Connecticut for their assistance and invaluable suggestions. Deadlock Avoidance in Flexible Manufacturing Systems Using Finite Automata Ali Yalcin and Thomas O. Boucher Abstract A distinguishing feature of a flexible manufacturing system (FMS) is the ability to perform multiple tasks in one machine or workstation (alternative machining) and the ability to process parts according to more than one sequence of operations (alternative sequencing). In this paper, we address the issue of deadlock avoidance in systems having these characteristics. A deadlock-free and maximally permissive control policy that incorporates this flexibility is developed based on finite automata models of part process plans and the FMS. The resulting supervisory controller is used for dynamic evaluation of deadlock avoidance based on the remaining processing requirements of the parts. Index Terms Deadlock avoidance, finite automata, flexible manufacturing systems, supervisory control. I. INTRODUCTION A typical flexible manufacturing system (FMS) is composed of single machines or workstations that can perform various operations and a material handling system that interconnects these machines. Raw parts enter the system at discrete points in time. These parts are Manuscript received January 6, 1999; revised October 14, This paper was approved for publication by Associate Editor Y. Narahari and Editor P. Luh upon evaluation of the reviewers comments. A. Yalcin was with with the Department of Industrial Engineering, Rutgers University, Piscataway, NJ USA. He is now with the Department of Industrial and Management Systems Engineering, University of South Florida, Tampa, FL USA. T. O. Boucher is with with the Department of Industrial Engineering, Rutgers University, Piscataway, NJ USA. Publisher Item Identifier S X(00) X/00$ IEEE

2 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 16, NO. 4, AUGUST processed to completion by routing them through various machines or workstations according to individual process plans and the sequence of machines utilized differs among the parts. This is in distinction from a pipeline process in which workpieces follow the same predetermined route. After a part is completely processed, it is unloaded from the system. The flexibility in FMS s is the ability to perform multiple tasks in one machine or workstation (alternative machining), and also the ability to process a part according to more than one sequence of operations (alternative sequencing) [1]. Concurrent flow of multiple parts competing for a limited amount of resources in these systems may lead to deadlock [2] [6]. An important consideration in system design and control software design is the detection of deadlock and corrective action. Researchers have traditionally used Petri nets or graph theoretic approaches as the formalism and adopted various approaches such as deadlock prevention or deadlock avoidance policies to overcome the problem of deadlock in manufacturing [2], [4], [5], [7] [12]. Researchers in [3] present a review of current research in this area and define deadlock avoidance policies suitable for real-time implementation. They develop a discrete event dynamic model whose states provide the information on the current interactions between jobs and resources. As events relevant to the deadlock analysis take place, using the knowledge of the system s state, the occurrence of certain events that lead to deadlocks are inhibited. An important topic that has not been sufficiently addressed in the deadlock avoidance literature is the flexibility associated with FMS s. Even though many researchers have made reference to this topic in their work, they have not provided examples that take this flexibility into consideration when generating deadlock avoidance control patterns. In [13], Ezpeleta and Colom use colored Petri nets to model an FMS that processes parts while considering alternate part process plans. The model requires that the process plan to be followed is selected a priori; i.e., before the part is released into the cell. Ideally, a controller should be allowed to consider alternative routing of parts dynamically during the manufacture of the part. From a control point of view, incorporating this flexibility into the controller design should improve the performance of the manufacturing system [1]. In this paper, we address the problem of deadlock avoidance in flexible manufacturing cells with direct address material handling systems. We incorporate alternate machining and alternate sequencing within the control pattern. We present control policies that guarantee deadlock-free control of a flexible manufacturing cell while being maximally permissive. It is assumed that each job has a unique identification, each part occupies only one resource at a time and each resource can process one part at a time. We model the FMS using the framework introduced by Ramadge and Wonham [14] for modeling and control of discrete event systems (DES) based on formal languages generated by finite automata. Few researchers have so far used this framework as their formalism to model flexible manufacturing cells. In [15], Brandin discusses the implementation of such an approach to supervisory control of a manufacturing cell on programmable logic controllers. However, the behavioral specifications are such that only one part is processed at a time, eliminating the need to address the problem of deadlock avoidance. Fanti et al. in [16] address deadlock avoidance in assembly systems. They describe a control methodology based on two di-graphs that model the specific order in which the resources appear in all the working procedures and the interactions between jobs and resources based on the current state. The same research group developed control policies for a multicell FMS [17]. We model the functionality of the cell as a finite automaton, which describes the states of the resources and the possible part movements in the cell (cell model). The process plans for different part types are Fig. 1. FMC [18]. individually modeled as finite automata and are used to define the rules that govern the system. These finite automata for the process plans capture all the flexibility related to the processing of a particular part type. Depending on the parts that are scheduled for processing and the parts that are already in the cell, a finite automaton model is synthesized to describe combined remaining process requirements for those parts (requirements model). The cell model and the requirements model are coupled to generate a control pattern that guarantees the complete processing of the parts scheduled and the parts already in the cell. A new control pattern is generated only when a new part is scheduled for production. One advantage of the control policies proposed in this paper is that it allows the manufacturing cell and the process plans to be modeled separately. Consequently, the models are much smaller and easier to understand and new part types can be introduced to the system without making any changes on the existing models. Also, any physical changes in the cell can be made by modifying the cell model only, thus facilitating easier maintenance of the system. Another advantage of the proposed control policies is that the processing requirements are analyzed dynamically as the parts in the cell and the parts scheduled for production change. This dynamic evaluation leads to a much smaller model than a prevention policy, which requires that all the process plans of all the parts produced by the system be represented in one model, requiring extensive computation. In Section II, a small FMS is used to convey new ideas and methods. A finite automaton model for the manufacturing cell and finite automata models for process plans are generated, the synthesis method for the requirements model is demonstrated, and the coupled system and deadlock-free control pattern is presented for the manufacturing system. In Section III, a realistic example problem is presented as well as a discussion of the strengths and weaknesses of this approach. Finally, in Section IV, some conclusions are drawn. II. MODELING THE MANUFACTURING CELL AND PROCESSING REQUIREMENTS A. Manufacturing Cell Model The flexible manufacturing cell (FMC) in question will be modeled as a finite automaton which will represent the uncontrolled process. For illustrative purposes, we will consider the cell configuration used by Ezpeleta et al. [18], shown in Fig. 1. The cell has two machines, M1 and M2, and a robot which loads and unloads the machines as well as the cell itself through buffers I1 and O1. The transition graph for this cell is depicted in Fig. 2. The states of the FMC are represented by three letter words, which are the status of components M1, M2, and R1. For example, ibi is the state where M2 is busy and M1 and R1 are idle. The arrows are labeled by event names, which describe part movements from one component of the cell to another, changing the state of the system. For example, when the cell is in state iib, where there is a part on the robot, the part can be either loaded on M1 or M2, or unloaded from the cell. These events are described by R1M1, R1M2, and R1O1, respectively. Notice that in

3 426 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 16, NO. 4, AUGUST 2000 Fig. 2. Transition graph for cell in Fig. 2. Fig. 3. Transition graphs for part types A and B. state bbi, even though the robot is idle, it cannot load a new part to the cell. Since there are only two machines in the cell, and no in-process buffer, the robot has no location in which to place a new part. Therefore, in our plant model design, the maximum number of parts in a cell is restricted to the number of available processors (machines). Formally, the uncontrolled system is modeled by a finite automaton G =(6;Q;;q o ;Q m ) where 6 is the finite alphabet of event labels, which describe the movement of parts among the resources of the system. 6 is the union of two disjoint sets 6 u and 6 c, the set of uncontrollable and controllable events. For our example, 6 =fi1r1, R1M1, M1R1, R1M2, M2R1, R1O1g and 6 c =6, since these events describe the movement of the robot, which can be controlled by a supervisor that enables or disables the initiation of the event by the robot. Q is the set of states q, Q = fiii, iib, bii, ibi, bib, ibb, bbig. It is important that each q describes the state of the entire cell. : 62 Q! Q is the transition function. q o and Q m are the initial and the marked (final) states of the system. For our example, q o = Q m = iii. This final state is reached when there are no parts remaining in the FMC. B. Modeling the Process Plans The process plans are modeled as finite automata. The model of each process plan explicitly depicts the possible routes a part may take for complete processing. This facilitates modeling parts with alternate sequencing, parts that may visit a machine more than once, and alternate machining possibilities within the cell. Fig. 3 depicts the process plans for two part types: A and B. Part A is a part that has alternate sequencing. It has to visit M1 and then M2 for completion but can do this in any order. Part B is a part that needs to visit M1 and M2. Therefore, there is no flexibility associated with part B. The finite automaton model for each process plan will be used in synthesizing the requirements model for the cell. Fig. 4 depicts the models of part type A and B. For each part type model, there is a state associated with each resource the part may visit. There are also two additional nodes denoted by subscripts i and f which are the initial and final states of the automaton. The subscript i indicates that the part is in the input buffer; the subscript f indicates that the part has gone to the Fig. 4. Finite automata for part types A and B. output buffer. Let A and B be the state sets for part A and B, respectively. The arcs that connect these states are the possible part movements in the cell that transfer the parts in process from one resource to another. Formally, for each part type manufactured in the cell, we have a finite automaton model; e.g., part type A, A =(6; A; A;ai; af ), and part type B, B =(6; B; B ;b i ;b f ). The language generated by the finite automaton model of a part type, for example part A, is described as L(A) =f!j!6 3 ;(!; a 0 )Ag, where! is a string and 6 3 is the set of all strings over the alphabet 6. Among the strings in this language, those that take the initial state to a final state, namely (!; a 0 )=a f, are the sequences of events which complete the processing of the part. C. Requirement Model Synthesis The supervisor will restrict events in the cell so that the remaining processing requirements of the parts in the system can be completed. These processing requirements are determined from the individual process plans of the parts. The supervisor is dynamic and changes as parts are scheduled to be loaded into the cell. When the scheduler informs the supervisor that a part is available to enter the cell S, the requirement model is synthesized by shuffling (denoted by symbol k ) [14] the finite automata models for the parts already in the cell and the part queued in the input buffer for processing. Shuffling is done to obtain all the possible sequences for finishing the remaining processing requirements of the parts currently in the cell and the part queued in the input buffer. In order to keep track of which part is moved, we will modify event names to include the part identifier also. We have used part names identical with the part types for illustrative purposes. These names should be assigned so that it can uniquely identify a part in the cell. For example, M1R1, A corresponds to part A being moved from M1 to R1. Consider a point in time when part A is still being processed in machine 1 and part B is released to the cell (placed in the input buffer) for processing. The current states of finite automata models for parts A and B are a 2 and b i, respectively. We generate S=AkB as shown in Fig. 5. Formally, the supervisor

4 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 16, NO. 4, AUGUST TABLE I SUPERVISORY CONTROL PATTERN, 9 Fig. 5. Transition graph of the shuffle of parts A and B from initial state a b. Fig. 7. A robotized cell [3]. TABLE II DISTRIBUTION OF TIMES TO COMPUTE A NEW SUPERVISOR Fig. 6. Transition Graph of the Coupled Model. S consists of a finite automaton S and an output function 9. S =(S; 9), where S=(6; X; ;x o ; X m ) and :62!(0: disable,1: enable) such that (; x) =0 or 1 if 6 c and 1 if 6 u. Note that in Fig. 5, the initial state of S is x o = a 2b i. This is the combined current states of the individual parts in the cell and parts scheduled to enter the cell. The control pattern of the supervisor only takes into consideration the remaining processes when deciding on a sequence of events. The final state of S; X m = a f b f, is the combined final states of the parts. D. The Coupled System The coupled supervised discrete event process is defined as S=G =(6;Q2 X; 2 ; x o 2 q c ; X m 2 Q m ) where q c is the current state of the plant model. The transition graph for S=G is shown in Fig. 6. From the transition graph, we can determine L m (S=G) = [(M1R1; A R1M2; A M2R1; AR1O1; A I1R1; B R1M1; B M1R1; B R1M2; B M2R1; B; R1O1; B); (M1R1; A R1M2; A I1R1; B R1M1; B M2R1; A R1O1; A M1R1; B R1M2; B M2R1; B R1O1; B)]: The language L m (S=G), the marked sequences of events of the closed loop system, takes the coupled system from an initial state to the combined final state where all parts in the system are processed and unloaded. Therefore, all the strings in L m (S=G) are deadlock-free execution sequences. Note that the number of available execution sequences depends on the degree of flexibility in the cell. A supervisory control pattern that restricts the cell to executing sequences only in L m(s=g) guarantees deadlock-free control and full processing of all the parts in the cell. The control pattern 9 for the

5 428 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 16, NO. 4, AUGUST 2000 TABLE III EXAMPLE STATE SPACE AND CPU TIME (400-MHz PENTIUM II PROCESSOR, 128-MB RAM) supervisor synthesized above is shown in Table I.We can make some observations concerning Table I. At the time, the new part is queued for production, it can enter the cell since the robot is idle (a 2 bi; bii). However, the loading event I1R1 is disabled by the control pattern in state a 2 bi. If this event is allowed to happen, the cell would be deadlocked as can be seen in Fig. 6. The deadlock situation arises because part B is on the robot and it can only go to M1. However, M1 is occupied by part A and part A needs the robot to move it from M1 to M2. When the supervisor is in state a 6 bi, I1R1 is enabled along with M2R1. At this point, either of these events can take place depending on which event happens first in the cell. This is the reason why there are two separate sequences for Lm(S=G). Also, in state a 6 b 2, M1R1 is disabled to prevent another deadlock situation. From a control point of view, it is important to show that Lm(S=G) exists. Existence of a deadlock-free control pattern guarantees that, from a pool of legal parts, at least one processing schedule can be carried out without running into deadlock. We define a legal part as a part that can be completely processed in the manufacturing cell and unloaded if it is the only part in the cell. Therefore, for a pool of parts to be processed, processing only one part at a time will guarantee at least one deadlock-free sequence of events where all parts will eventually be processed and unloaded. It is clear from Fig. 6 that, when more than one deadlock sequence exists, there is an opportunity to choose from among the alternative sequences. Since the finite automaton is represented by a directed graph with unique initial and final nodes, it seems natural to apply network flow techniques to the optimal selection of the sequence. For a discussion of this point with respect to the framework of Ramadge and Wonham (RW), see [19]. III. IMPLEMENTATION A. Illustrated Example An FMC example introduced in [3] is reproduced in Fig. 7. There are six machines and two robots, which are used to transfer parts among machines. In [3], deadlock avoidance policies were evaluated for the cell and for jobs consisting of parts having single process plans. In this paper we define parts that incorporate alternative process plans as follows: W 1=[M1; (r1; r2); M2; r2; M3; M4; r2]; [M1; (r1; r2); M2; r2; M4; M3; r2] W 2 = [(M2; M5); r2; M6; r1] W 3 = [M3; M4; r2; (M1; M3); r2]: Operations within brackets indicate that the required operations can be performed by either of the process plans indicated. Operations within parenthesis indicate that the operation can be performed by either resource. In the example cell, it is assumed that an automatic transfer mechanism exists between M3 and M4 and that the first machine in each process plan is loaded from the outside [3]. Therefore, the shuffling of a new part into the requirements model di-graph is done when the part is loaded on a machine for the first operation of its process plan. The cell of Fig. 7 was simulated using service times generated from a gamma distribution (see [3, p. 359, Table I]). As in [3], jobs were allowed to arrive in the order 1, 2, 3, 1, 2, A total of 600 jobs were processed. After a transient period of 20 jobs, the performance of the algorithm that generates the new supervisory control pattern when a new part comes into the system was evaluated in steady state. In general, the state space of a model developed in the RW framework is known to increase exponentially as problem size increases. In the context of a manufacturing cell, the size of the problem is bounded by the size of the cell, the number of alternative process plans of the parts, and the remaining operations on the parts at the time a new supervisor is computed. The state space of the coupled system was based on up to six parts in various stages of processing on the six machines in the cell. We have found that, instead of shuffling all the part process plan operations that remain on each part, it is more efficient to use the already existing coupled system model. In effect, the existing coupled system model of the parts in the cell is shuffled with the new part entering the cell. Thus, the illegal transitions of the previously coupled parts have already been eliminated, yielding a smaller state space in the shuffling process. Shuffling is followed by coupling, which consists of a depth-first search of the di-graph [20] in order to eliminate paths that do not connect the initial state and final state. For a complete documentation of the source code, see [21]. The algorithm was run on a 400-MHz Pentium II with 128-MB RAM. Table II shows the distribution of CPU times of the algorithm for calculating a new supervisor. In general, over 99% of the executions were under 12 s. Given the fact that processing times for machining mechanical parts is typically in the order of tens of minutes, a supervisory controller response time in seconds would not seriously restrict the performance of the cell. However, the computational time grows as problem state space increases. Table III illustrates this point by showing examples of computation times from a range of state spaces encountered in the simulations. B. Strengths and Weaknesses of the Model The proposed model has the advantage of being able to be implemented on a controller such that evaluation of alternative possible routings of parts can be performed dynamically during production. The advantage of this approach becomes evident in the event of machine breakdowns, during which the controller will be able to reroute parts through other (available) machines. In addition, this approach yields a maximally permissive controller. The combination of these two factors should improve the overall cell performance. The models developed under this approach do suffer from computational complexity; i.e., the state space will grow exponentially with problem size. This limits the application of this methodology to relatively small manufacturing systems when compared to policies based on rules that can be evaluated in polynomial time [3], [11]. In addition, we have limited our application to cells with direct address material handling systems where buffers are not included. Modeling buffers requires that buffer visitations are specified in

6 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 16, NO. 4, AUGUST the process plans. Since availability of buffers will increase the system capacity, this will add to the computational complexity. In our example each machine has capacity of one part. Some manufacturing system designs employ machines that have capacities of more than one part; see for example [11]. IV. CONCLUSION In this paper, we have addressed the issue of real-time deadlock avoidance in flexible manufacturing cells. We have incorporated the flexibility associated with the alternative part process plans into the supervisory controller such that decisions regarding the routing of parts can be made dynamically. Other advantages of the described control policy for deadlock avoidance are that it accommodates alternative machining and alternative sequencing, is maximally permissive, and results in finite automata models are very easy to maintain. The proposed controller is appropriate for small manufacturing systems, such as the one illustrated in this paper. REFERENCES [1] M. D. Byrne and P. Chutima, Real time operational control of an FMS with full routing flexibility, Int. J. Prod. Econ., vol. 51, pp , [2] Z. A. Banaszak and B. H. Krogh, Deadlock avoidance in flexible manufacturing systems with concurrently competing process flows, IEEE Trans. Robot. Automat., vol. 6, pp , [3] M. P. Fanti, B. Maione, S. Mascolo, and B. Turchiano, Event-based feedback control for deadlock avoidance in flexible production systems, IEEE Trans. Robot. Automat., vol. 13, pp , [4] N. Viswanadham, Y. Narahari, and T. L. Johnson, Deadlock prevention and deadlock avoidance in flexible manufacturing systems using Petri net models, IEEE Trans. Robot. Automat., vol. 6, pp , [5] R. A. Wysk, N. S. Yang, and S. Joshi, Detection of deadlocks in flexible manufacturing cells, IEEE Trans. Robot. Automat., vol. 7, pp , [6] F. Chu and X. 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Martinez, Petri net based deadlock prevention policy for flexible manufacturing systems, IEEE Trans. Robot. Automat., vol. 11, pp , [19] R. Kumar and V. K. Garg, Optimal supervisory control of discrete event dynamical systems, SIAM J. Control Optim., vol. 33, pp , [20] R. E. Tarjan, Depth first search and linear graph algorithm, SIAM J. Comput., vol. 1, pp , [21] T. O. Boucher, D. Tai, and A. Yalcin, Algorithms for Implementing Deadlock Avoidance using Finite Automata, Ind. Eng. Dept., Rutgers Univ., Piscataway, NJ, Working Paper # , Optimal Rate Allocation in Unreliable, Assembly/Disassembly Production Networks with Blocking Vassilis S. Kouikoglou Abstract We consider finite-buffered production networks, in which each machine is capable of performing a single assembly and/or disassembly operation and it is subject of operation-dependent failures. We address the problem of allocating processing and repair rates to each machine so as to maximize the throughput of the system. This problem is shown to be equivalent to a convex minimization problem. The optimal allocation is found using a steepest-descent algorithm that employs discrete-event simulation for performance evaluation and gradient estimation. Index Terms Assembly systems, discrete event simulation, optimization methods, production systems, resource management. I. INTRODUCTION There is a large class of manufacturing systems that can be modeled as assembly/disassembly (AD) or fork/join networks of unreliable machines with intermediate buffers of finite capacity. Manufacturing flow lines and assembly lines are special cases of AD systems. Although assembly seems to be more important in manufacturing, the inclusion of disassembly is necessary for modeling several realistic situations (see, e.g., [1] [4] and references therein). Recycling, waste handling, cloth cutting, and sheet metal cutting are examples of disassembly operations. Assembly and disassembly operations can be used to model transfer mechanisms in which parts need to be attached to pallets to undergo a set of operations and, upon completion of these operations, the parts are unloaded and the pallets are released. Also, in kanban-controlled manufacturing systems, the attachment (detachment) of a production card to (from) a part corresponds to an assembly (disassembly) operation. Problems associated with the design of AD production systems have received considerable attention during the last decade. Typical design Manuscript received December 11, 1998; revised October 25, Paper approved by Associate Editor D. Wu and Editor P. Luh upon evaluation of the reviewers comments. This paper was presented in part at the IEEE 1999 International Conference on Robotics and Automation, Detroit, MI, May The author is with the Department of Production Engineering and Management, Technical University of Crete, University Campus, GR Chania, Greece. 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