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An MILP for scheduling problems in an FMS with one vehicle

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  • Caumond, A.
  • Lacomme, P.
  • Moukrim, A.
  • Tchernev, N.

Abstract

This paper concerns the mathematical formulation and optimal solutions for the Flexible Manufacturing Systems Scheduling Problem (FMSSP) with one vehicle. This linear formulation differs from the previously published ones as it takes into account the maximum number of jobs allowed in the system, limited input/output buffer capacities, empty vehicle trips and no-move-ahead trips simultaneously. Our objective is to propose optimal solutions for small and medium-sized instances and to examine a number of commonly used assumptions and heuristics. Computational experiments are carried out on instances adapted from Bilge and Ulusoy [Bilge, Ü., Ulusoy, G., 1995. A time window approach to simultaneous scheduling of machines and material handling system in an FMS. Operations Research 43, 1058-1070] and the following heuristics are evaluated: FIFO (First In First Out) rules for input/output buffer management; and FIFO, SPT (Shortest Processing Time), STT (Shortest Travel Time) and MOQS (Maximum Outgoing Queue Size) rules concerning the vehicle. The consequences of classical assumptions are also studied: ignoring empty trips, ignoring no-move-ahead constraints, and ignoring vehicle-disjunction constraints. The numerical experiments provide a set of optimal solutions and allow to evaluate the performances of heuristic search schemes.

Suggested Citation

  • Caumond, A. & Lacomme, P. & Moukrim, A. & Tchernev, N., 2009. "An MILP for scheduling problems in an FMS with one vehicle," European Journal of Operational Research, Elsevier, vol. 199(3), pages 706-722, December.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:3:p:706-722
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    References listed on IDEAS

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    1. Ümit Bilge & Gündüz Ulusoy, 1995. "A Time Window Approach to Simultaneous Scheduling of Machines and Material Handling System in an FMS," Operations Research, INFORMS, vol. 43(6), pages 1058-1070, December.
    2. Liu, Jiyin & MacCarthy, B. L., 1997. "A global MILP model for FMS scheduling," European Journal of Operational Research, Elsevier, vol. 100(3), pages 441-453, August.
    3. Tharma Ganesharajah & Nicholas Hall & Chelliah Sriskandarajah, 1998. "Design and operational issues in AGV-served manufacturing systems," Annals of Operations Research, Springer, vol. 76(0), pages 109-154, January.
    4. Co, Christine G. & Tanchoco, J. M. A., 1991. "A review of research on AGVS vehicle management," Engineering Costs and Production Economics, Elsevier, vol. 21(1), pages 35-42, February.
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    Cited by:

    1. Lacomme, Philippe & Larabi, Mohand & Tchernev, Nikolay, 2013. "Job-shop based framework for simultaneous scheduling of machines and automated guided vehicles," International Journal of Production Economics, Elsevier, vol. 143(1), pages 24-34.
    2. Marie-Laure Espinouse & Grzegorz Pawlak & Malgorzata Sterna, 2017. "Complexity of Scheduling Problem in Single-Machine Flexible Manufacturing System with Cyclic Transportation and Unlimited Buffers," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 1042-1054, June.
    3. Hosseini, Amir & Otto, Alena & Pesch, Erwin, 2024. "Scheduling in manufacturing with transportation: Classification and solution techniques," European Journal of Operational Research, Elsevier, vol. 315(3), pages 821-843.
    4. Savic, Aleksandar & Kratica, Jozef & Milanovic, Marija & Dugosija, Djordje, 2010. "A mixed integer linear programming formulation of the maximum betweenness problem," European Journal of Operational Research, Elsevier, vol. 206(3), pages 522-527, November.
    5. Olatunde T. Baruwa & Miquel A. Piera, 2016. "A coloured Petri net-based hybrid heuristic search approach to simultaneous scheduling of machines and automated guided vehicles," International Journal of Production Research, Taylor & Francis Journals, vol. 54(16), pages 4773-4792, August.
    6. Philippe Lacomme & Aziz Moukrim & Alain Quilliot & Marina Vinot, 2019. "Integration of routing into a resource-constrained project scheduling problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 421-464, December.
    7. Sun, Yige & Chung, Sai-Ho & Wen, Xin & Ma, Hoi-Lam, 2021. "Novel robotic job-shop scheduling models with deadlock and robot movement considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 149(C).
    8. Topal, Erkan & Ramazan, Salih, 2010. "A new MIP model for mine equipment scheduling by minimizing maintenance cost," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1065-1071, December.
    9. Arash Amirteimoori & Reza Kia, 2023. "Concurrent scheduling of jobs and AGVs in a flexible job shop system: a parallel hybrid PSO-GA meta-heuristic," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 727-753, September.

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