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Capacitated lot sizing and scheduling with parallel machines and shared buffers: A case study in a packaging company

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Abstract

The aim of this work is to propose a solution approach for a capacitated lot sizing and scheduling real problem with parallel machines and shared buffers, arising in a packaging company producing yoghurt. The problem has been formulated as a hybrid Continuous Set-up and Capacitated Lot Sizing Problem (CSLP–CLSP). A new effective two stage optimisation heuristic based on the decomposition of the problem into a lot sizing problem and a scheduling problem has been developed. An assignment of mixture to buffers is made in the first stage, and therefore the corresponding orders are scheduled on the production lines by performing a local search. Computational tests have been performed on the real data provided by the company. The heuristic exhibits near-optimal solutions, all obtained in a very short computational time.

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References

  • Ahmadi, R.H., S. Dasu, and C.S. Tang. (1992). “The Dynamic Line Allocation Problem.” Management Science, 38, 1341–1353.

    Google Scholar 

  • Bahl, H.C., J.N.D. Gupta, and L.P. Ritzman. (1987). “Determining Lot Sizes and Resource Requirements: A Review.” Operations Research, 35, 329–345.

    Google Scholar 

  • Bankston, J.B. and R.M. Harnett. (2000). “An Heuristic Algorithm for A Multi-Product, Single Machine Capacitated Production Scheduling Problem.” Computers and Operations Research, 27, 77–92.

    Article  Google Scholar 

  • Barany, I., T.J. van Roy, and L.A. Wolsey. (1984). “Strong Formulations for Multi-Item Capacitated Lot Sizing.” Management Science, 30(10), 1255–1261.

    Google Scholar 

  • Cattrysse, D., J. Maes, and L.N. van Wassenhove. (1990). “Set Partitioning and Column Generation Heuristics for Capacitated Dynamic Lot Sizing.” European Journal of Operational Research, 46, 38–47.

    Article  Google Scholar 

  • Cattrysse, D., R. Kuik, M. Salomon, and L.N. van Wassenhove. (1993). “A Dual Ascent and Column Generation Heuristic for the Discrete Lot Sizing and Scheduling Problem with Set-up Times.” Management Science, 39, 477–486.

    Google Scholar 

  • Chen, W.-H. and J.-M. Thizy. (1990). “Analysis of Relaxations for the Multi-item Capacitated Lot Sizing Problem.” Annals of Operations Research, 26, 29–72.

    Article  Google Scholar 

  • Cheng, T.C.E. and C.C.S. Sin. (1990). “A State-of-the-art Review of Parallel-machine Scheduling Research.” European Journal of Operational Research, 47, 271–292.

    Google Scholar 

  • De Matta, R. and M. Guignard. (1994). “Studying the Effects of Production Loss Due to Set-up in Dynamic Production Scheduling.” European Journal of Operational Research, 72, 62–73.

    Article  Google Scholar 

  • De Matta, R. and M. Guignard. (1995). “The Performance of Rolling Production Schedules in a Process Industry.” IIE Transactions, 27, 564–573.

    Google Scholar 

  • Diaby, M. (2000). “Integrated Batch Size and Set-up Reduction Decisions in Multi-product, Dynamic Manufacturing Environments.” International Journal of Production Economics, 67(3), 219–233.

    Article  Google Scholar 

  • Drexl, A. and A. Kimms. (1997). “Lot Sizing and Scheduling—Survey and Extensions.” European Journal of Operational Research, 99(2), 221–235.

    Article  Google Scholar 

  • Drexl, A. and C. Jordan. (1998). “Discrete Lot Sizing and Scheduling by Batch Sequencing.” Management Science, 44(5), 698–713.

    Google Scholar 

  • Elmaghraby, S.E. (1978). “The Economic Lot Scheduling Problem (ELSP): Review and Extensions.” Management Science, 24, 587–598.

    Google Scholar 

  • Eppen, G.D. and R. Kipp Martin. (1987). “Solving Multi-item Capacitated Lot Sizing Problems Using Variable Redefinition.” Operations Research 35(6), 832–848.

    Google Scholar 

  • Fleishmann, B., and H. Meyr. (1997). “The General Lot Sizing and Scheduling Problem.” OR Spektrum 19(1), 11–21.

    Google Scholar 

  • Gelders, L.F., J. Maes, and L.N. van Wassenhove. (1986). “A Branch and Bound Algorithm for the Multi-item Single Level Capacitated Dynamic Lot Sizing Problem.” In S. Axsater, C. Scheeweiss, and E. Silver (Eds), Multi-stage Production Planning and Inventory Control, Lecture Notes in Economic and Mathematical Systems, vol. 226, pp. 92–108, (Berlin: Springer-Verlag).

  • Haase, K. (1996). “Capacitated Lot Sizing with Sequence Dependent Setup Costs.” OR Spektrum, 18, 51–59.

    Article  Google Scholar 

  • Hindi, K.S. (1996). “Solving the CLSP by a Tabu Search Heuristic.” Journal of the Operational Research Society, 47, 151–161.

    Article  Google Scholar 

  • Kang, S., K. Malik, and L.J. Thomas. (1999). “Lot Sizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs.” Management Science, 45, 273–289.

    Google Scholar 

  • Kirca, Ömer. and M. Kökten. (1994). “A New Heuristic Approach for the Multi-item Dynamic Lot Sizing Problem.” European Journal of Operational Research, 75, 332–341.

    Article  Google Scholar 

  • Leachman, R.C., A. Gascon, and Z.K. Xiong. (1993). “Multi-item Single-machine Scheduling with Material Supply Constraints.” Journal of Operational Research Society, 44(11), 1145–1153.

    Article  Google Scholar 

  • Maes, J., J.O. McClain, L.N. van Wassenhove. (1991). “Multilevel Capacitated Lot Sizing Complexity and LP Based Heuristics.” European Journal of Operational Research, 53, 131–148.

    Article  Google Scholar 

  • Magnanti, T.L. and R. Vachani. (1990). “A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs.” Operations Research, 38(3), 456–473.

    Google Scholar 

  • Meyr, H. (2000). “Simultaneous Lot Sizing and Scheduling by Combining Local Search with Dual Reoptimization.” European Journal of Operational Research, 120(2), 311–326.

    Article  Google Scholar 

  • Meyr, H. (2002). “Simultaneous Lot Sizing and Scheduling on Parallel Machines.” European Journal of Operational Research, 139(2), 277–292.

    Article  Google Scholar 

  • Rogers, J. (1958). “A Computational Approach to the Economic Lot Scheduling Problem.” Management Science, 4, 264–291.

    Google Scholar 

  • Smith-Daniels, V.L. and D.E. Smith-Daniels. (1986). “A Mixed-integer Programming Model for Lot Sizing and Sequencing Packaging Lines in the Process Industries.” IIE Transactions, 18, 278–285.

    Google Scholar 

  • Sox, C.R. and Y. Gao. (1999). “The Capacitated Lot Sizing Problem with Setup Carry-over.” IIE Transactions, 31(2), 173–181.

    Article  Google Scholar 

  • Sung, C.S., Y.H. Kim, and S.H. Yoon. (2000). “A Problem Reduction and Decomposition Approach for Scheduling for A Flowshop of Batch Processing Machines.” European Journal of Operational Research, 121(1), 179–192.

    Article  Google Scholar 

  • van Eijl, C.A. and C.P.M. van Hoesel. (1997). “On the Discrete Lot Sizing and Scheduling Problem with Wagner-Whitin Costs.” Operations Research Letters, 20, 7–13.

    Article  Google Scholar 

  • Wagner, H.M. and T.M. Whitin. (1958). “Dynamic Version of the Economic Lot Size Model.” Management Science, 5, 89–96.

    Article  Google Scholar 

  • Woodruff, D.L. and M.L. Spearman. (1992). “Sequencing and Batching for Two Classes of Jobs with Deadlines and Setup Times.” Production and Operations Management, 1(1), 87–102.

    Article  Google Scholar 

  • The milk and dairy products market in 2002, research notes by Ismea and the Osservatorio Latte di Cremona.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di L’Aquila, Via Vetoio – Coppito, 67100, L’Aquila, Italy

    Fabrizio Marinelli

  2. Dipartimento di Progettazione e Gestione Industriale, Università degli Studi di Napoli “Federico II”, Piazzale Tecchio 80, 80125, Napoli, Italy

    Maria Elena Nenni

  3. Dipartimento di Informatica e Sistemistica, Università degli Studi di Napoli “Federico II”, Via Claudio 21, 80125, Napoli, Italy

    Antonio Sforza

Authors
  1. Fabrizio Marinelli
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  2. Maria Elena Nenni
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  3. Antonio Sforza
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Correspondence to Fabrizio Marinelli.

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Marinelli, F., Nenni, M.E. & Sforza, A. Capacitated lot sizing and scheduling with parallel machines and shared buffers: A case study in a packaging company. Ann Oper Res 150, 177–192 (2007). https://doi.org/10.1007/s10479-006-0157-x

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