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A review of tactical planning models

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Abstract

The aim of this paper is to give an overview on models and methods used to solve tactical planning problems. The modeling and the elaboration of the well-know tactical planning problems (master planning & scheduling, material requirement planning and multi-site planning) are discussed. These problems are modeled from two “lot sizing” models called the Capacitated Lot Sizing Problem (CLSP) and Multi Level Capacitated Lot Sizing Problem (MLCLSP). From both models, a lot of extensions has been proposed in the literature. The purpose of this paper is twofold: first, classifications of the CLSP and MLCLSP as well as their extensions are given. For each model, the major scientific contributions are mentioned. These classifications made from seventy papers give an overview of “lot sizing” models dedicated to the MPS, MRP and Multi-site and show the diversity of models. Second, from a classification, an analysis of methods used for each model is given. The instance size, best gap and reference for gap computation are given for each contribution. This work can be used to elaborate an optimization tool for tactical planning problematic such as Advanced Planning System.

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References

  1. Absi, N. & Kedad-Sidhoum, S. (2006). The multi-item capacitated lot-sizing problem with setup-times and shortage costs. Technical report

  2. Afentakis, P. & Gavish, B. (1986). Optimal lot-sizing algorithms for complex product structures. Operations Research, 34: 237–249

    MathSciNet  MATH  Google Scholar 

  3. Aliev, R.A., Fazlollahi, B., Guirimov, B.G. & Aliev, R.R. (2007). Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management. Information Sciences, 177 (20): 4241–4255

    Article  MATH  Google Scholar 

  4. Barany, I., Van Roy, T.J. & Wolsey, L.A. (1984). Strong formulations for multi-items capacitated lotsizing. Management Science, 30: 1255–1261

    MathSciNet  MATH  Google Scholar 

  5. Barbarosoglu, G. & Özdamar, L. (2000). Analysis of solution space-dependent performance of simulated annealing the case of the multilevel capacitated lot sizing problem. Computers and Operational Research, 27 (9): 895–903

    Article  MATH  Google Scholar 

  6. Belvaux, G. & Wolsey, L.A. (2000). Lot-sizing problems: modeling issues and a specialized branch-and-cut system BC-prod. Management Science, 46 (5): 724–738

    Article  Google Scholar 

  7. Berretta, R. & Rodrigues, L.F. (2004). A memetic algorithm for a multi stage capacitated lot-sizing problem. International Journal Production Economics, 87: 67–81

    Article  Google Scholar 

  8. Billington, P.J., McClain, J.O. & Thomas, L.J. (1986). Heuristics for multilevel lot-sizing with a bottleneck. Management Science, 32 (8): 989–1006

    MATH  Google Scholar 

  9. Billington, P.J., McClain, J.O. & Thomas, L.J. (1983). Mathematical programming approaches to capacity-constrained MRP systems: review, formulation and problem reduction. Management Science, 29: 1126–1141

    MATH  Google Scholar 

  10. Bitran, G.R. & Yanasse, H.H. (1982). Computational complexity of the capacitated lot size problem. Management Science. 46 (5): 724–738

    MathSciNet  Google Scholar 

  11. Blackburn, J. & Millen, R. (1985). An evaluation of heuristic performance in multi stage lot sizing systems. International Journal of Production Research, 23 (5): 857–866

    Article  MATH  Google Scholar 

  12. Blackburn, J. & Millen, R. (1982). Improved heuristics for multi stage requirements planning systems. Management Science, 28 (1): 44–56

    MATH  Google Scholar 

  13. Byrne, M.D. & Bakir, M.A. (1999). Production planning using a hybrid simulation-analytical approach. International Journal of Production Economics, 59: 305–311

    Article  Google Scholar 

  14. Chan, F.T.S, Chung, S.H. & Chan, S.W. (2005). A hybrid genetic algorithm for production and distribution. Omega, 33 (4): 345–355

    Article  Google Scholar 

  15. Chen, H. & Chu, C. (2003). A lagrangian relaxation approach for supply chain planning with order-setup costs and capacity constraints. Journal of Systems Science and Systems Engineering, 12 (1): 98–110

    Article  Google Scholar 

  16. Chen, W.H. & Thizy, J.M. (1990). Analysis of relaxation for the multi-item capacities lot-sizing problem. Annal of Operations Research, 26: 29–72

    Article  MathSciNet  MATH  Google Scholar 

  17. Clark, A.R. (2002). Approximate combinatorial optimization models for large-scale production lot sizing and scheduling with sequence-dependent setup times. In: IV ALIO/EURO Workshop on Applied Combinatorial Optimization, Pucón, Chile

  18. Clark, A.R. & Armentano, V.A. (1995). The application of valid inequalities to the multistage lot-sizing problem. Computers and Operations Research, 22: 669–680

    Article  MATH  Google Scholar 

  19. Dauzere-Peres, S. & Lasserre, J.B. (2002). On the importance of sequencing decisions in production planning and scheduling. International Transactions in Operational Research, 9 (6): 779–793

    Article  MathSciNet  MATH  Google Scholar 

  20. Degraeve, Z. & Jans, R. (2003). A new Dantzig-Wolfe reformulation and branch-and-price algorithm for the capacitated lot sizing model with set-up times. In:ERIM Report Series in Management ERS-2003-010-LIS, Erasmus University, Rotterdam

    Google Scholar 

  21. Dellaert, N. & Jeunet, J. (2002). Randomized multi-level lot-sizing heuristics for general product structures. European Journal of Operational Research, 148 (1): 211–228

    Article  Google Scholar 

  22. Dellaert, N. & Jeunet, J. (2000). Solving large unconstrained multilevel lot-sizing problems using a hybrid genetic algorithm. International Journal of Production Research, 38 (5): 1083–1099

    Article  MATH  Google Scholar 

  23. Diaby, M., Bahl, M.H., Karwan, H.C. & Zionts, S. (1992). A lagrangean relaxation approach for very-large-scale capacitated lot-sizing. Management Science, 38 (9): 1329–1340

    MATH  Google Scholar 

  24. Diaby, M., Bahl, M.H., Karwan, H.C. & Zionts, S. (1992). Capacitated lot-sizing and scheduling by lagrangean relaxation. European Journal of Operational Research, 59: 444–458

    Article  MATH  Google Scholar 

  25. Dixon, P.S. & Silver, E.A. (1981). A heuristic solution procedure for the multi-item, single level, limited capacity, lotsizing problem. Journal of Operations Management, 2: 23–39

    Article  Google Scholar 

  26. Dogramaci, A., Panayiotopoulos, J.C. & Adam, N.R. (1981). The dynamic lot-sizing problem for multiple items under limited capacity. AIIE Transactions, 13 (4): 294–303

    Google Scholar 

  27. Drexl, A. & Kimms, A. (1997). Lot sizing and scheduling — survey and extensions. European Journal of Operational Research, 99: 221–235

    Article  MATH  Google Scholar 

  28. Du Merle, O., Goffin, J.L., Trouiller, C., & Vial, J.P. (1997). A lagrangian relaxation of the capacitated multi-item lot sizing problem solved with an interior point cutting plane algorithm. Research paper, McGill University, Montréal, Canada

    Google Scholar 

  29. Eppen, G.D. & Martin, R.K. (1987). Solving multi-item lot-sizing problems using variable redefinition. Operations Research, 35: 832–848

    MATH  Google Scholar 

  30. Fleischmann, B. & Meyr, H. (2003). Planning hierarchy, modeling and advanced planning systems. In: de Kok, A.G., Graves, S.C. (eds.), Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science, 11: pp. 457–502

  31. Franca, P.M., Armentano, V.A., Berretta, R.E. & Clark, A. R. (1997). A heuristic for lot-sizing in multi-stage systems. Computers nd Operations Research, 24 (9): 861–874

    Article  MATH  Google Scholar 

  32. Garavelli, A.C., Geoffrey, O. & Garavelli, N.V. (1996).Global manufacturing systems: a model supported by genetic algorithms to optimize production planning. Computers & Industrial Engineering, 31 (1–2): 193–196

    Article  Google Scholar 

  33. Gelders, L.F., Maes, J. & Van Wassenhove, L.N. (1986). A branch and bound algorithm for the multi-item single level capacitated dynamic lotsizing problem, multi-stage production planning and inventory control. Lectures Notes in Economics and Mathematical Systems, 92–108

  34. Génin, P. (2003). Planification tactique robuste avec usage d’un A.P.S. Proposition d’un mode de gestion par plan de référence. PhD thesis, Ecole supérieure des mines de Paris

  35. Gilbert, K.C. & Madan, M.S. (1991). A heuristic for a class of production planning and scheduling problems. IIE Transactions, 23: 282–289

    Article  Google Scholar 

  36. Gnoni, M.G., Iavagnilio, R., Mossa, G., Mummolo, G. & Di Leva, A. (2003). Production planning of a multi-site manufacturing system by hybrid modelling: a case study from the automotive industry. International Journal of Production Economics, 85: 251–262

    Article  Google Scholar 

  37. Gopalakrishnan, M., Ding, K., Bourjolly, J.M. & Mohan, S. (2001). A tabu-search heuristic for the capacitated lot-sizing problem with set-up carryover. Management Science, 47 (6): 851–863

    Article  Google Scholar 

  38. Guinet, A. (2001). Multi-site planning: a transshipment problem. International Journal of Production Economics. 74 (1–3): 21–32

    Article  Google Scholar 

  39. Gupta, A. & Maranas, C.D. (2003). Managing demand uncertainty in supply chain planning. Computer and Chemical Engineering, 27: 219–1227

    Google Scholar 

  40. Gupta, D. & Magnusson, T. (2005). The capacitated lot-sizing and scheduling problem with sequence-dependent setup costs and setup times. Computers & Operations Research, 32: 727–747

    Article  MathSciNet  MATH  Google Scholar 

  41. Haase, K. & Kohlmorgen, U. (1995). Parallel genetic algorithm for the capacitated lotsizing problem. Operations Research Proceedings, 370–375

  42. Hagdorn, L., van Numen, J. & Ramondt, A. (1994). Forecasting-bridging the gap between sales and manufacturing. International Journal of Productions Economics, 37: 101–114

    Article  Google Scholar 

  43. Hassini, E. (2006). Order lot sizing with multiple capacitated suppliers offering lead time-dependent capacity reservation and unit price discounts. Production Planning Control, in press

  44. Haugen, K.K., Olstad, A. & Pettersen, B.I. (2006). The profit maximizing capacitated lot-size (PCLSP) problem. European Journal of Operational Research, in press

  45. Heinrich, C. & Schneeweiss, C. (1986). Multi-stage lot-sizing for general production systems. In: Axsater, S., Schneeweiss, C., Silver, E. (sds.), Lecture Notes in Economics and Mathematical Systems. Springer Verlag, Heidelberg, Germany

    Google Scholar 

  46. Hindi, K.S. (1996). Solving the CLSP by a tabu search heuristic. Journal of Operational Research Society, 47 (1): 151–161

    Article  MATH  Google Scholar 

  47. Hindi, K.S. (1995). Computationally efficient solution of multi-item capacitated lot sizing problems. Computers and Industrial Engineering, 28 (4): 709–719

    Article  Google Scholar 

  48. Hindi, K.S., Fleszar, K. & Charalambous, C. (2003). An effective heuristic for the CLSP with set-up times. Journal of Operational Research Society, 54: 490–498

    Article  MATH  Google Scholar 

  49. Huisman, D., Jans, R., Peeters, M. & Wagelmans, A.P.M. (2003). Combining column generation and lagrangian relaxation. Technical Report

  50. Jeunet, J. & Jonard, N. (2005). Single-point stochastic search algorithms for the multi-level lot-sizing problem. Computers and Operations Research, 32 (4): 985–1006

    Article  MathSciNet  MATH  Google Scholar 

  51. Kanayalkar, A.P. & Adil, G.K. (2005). An integrated aggregate and detailed planning in a multi-site production environment using linear programming. International Journal of Production Research, 43 (20): 4431–4454

    Article  Google Scholar 

  52. Karimi, B., Fatemi Ghomi, S.M.T. & Wilson, J.M. (2005). A tabu-search heuristic for the clsp with backlogging and set-up carry-over. Journal of Operational Research Society, 47 (6): 851–863

    Google Scholar 

  53. Karimi, B., Fatemi Ghomi, S.M.T. & Wilson, J.M. (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega, 31 (5): 365–378

    Article  Google Scholar 

  54. Katok, E., Lewis, H.S. & Harrison, T.P. (1998). Lot sizing in general assembly systems with setup costs, setup times, and multiple constrained resources. Management Science, 44 (6): 859–877

    MATH  Google Scholar 

  55. Kim, H.J. & Hosni, Y.A. (1998). Manufacturing lot-sizing under MRP II environment: an improved analytical model and a heuristic procedure. Computers and Industrial Engineering, 35 (3): 423–426

    Article  Google Scholar 

  56. Kirca, Ö. & Kökten, M. (1994). A new heuristic approach for the multi-item dynamic lot sizing problem. European Journal of Operational Research, 75: 332–341

    Article  MATH  Google Scholar 

  57. Kuik, R. & Salomon, M. (1990). Multi-level lot-sizing problem: evaluation of a simulated annealing heuristic. European Journal of Operational Research, 45 (1): 25–37

    Article  MathSciNet  MATH  Google Scholar 

  58. Kuik, R., Salomon, M., Van Wassenhove, L.N. & Maes, J. (1993). Linear programming, simulated annealing and tabu search heuristics for lotsizing in bottleneck assembly system. IIE Transactions, 25 (1): 62–72

    Article  Google Scholar 

  59. Lambrecht, M. & Vanderveken, H. (1979). Heuristic procedures for the single operation multi item loading problem. AIIE Transactions, 11: 319–326

    Google Scholar 

  60. Leung, J.M., Magnanti, T.L. & Vachani, R. (1989). Facets and algorithms for the capacitated lot sizing. Mathematical Programming, 45: 331–359

    Article  MathSciNet  MATH  Google Scholar 

  61. Lin, J.T. & Chen, Y.Y. (2007). A multi-site supply network planning problem considering variable time buckets— a TFL-LCD industry case. International Journal Manufacturing Technology, 33: 1031–1044

    Article  MathSciNet  Google Scholar 

  62. Liu, M.L. & Sahinidis, N.V. (1996). Optimization in process planning under uncertainty. Industrial Engineering Chemical Research, 35 5(11): 4154–4165

    Article  Google Scholar 

  63. Maes, J., McClain, J.O. & Van Wassenhove, L.N. (1991). Multilevel capacitated lotsizing complexity and LP-based heuristics. European Journal of Operations Research, 53: 131–148

    Article  MATH  Google Scholar 

  64. Maes, J., & Van Wassenhove, L.N. (1986). A simple heuristic for the multi-item single level capacitated lot sizing problem. Letters of the Operational Research Society, 4: 265–274

    Article  MATH  Google Scholar 

  65. Manne, A.S. (1958). Programming of economic lot sizes. Management Science, 4: 115–135

    Google Scholar 

  66. Marty, C. (1997). Le juste à temps produire autrement. 2ème édition, Edition Hermes, 124

  67. McDonald, C.M. & Karimi, I.A. (1997). Planning and scheduling of parallel semicontinuous processes. 1. production planning. Industrial Engineering Chemical Research, 36: 2691–2700

    Article  Google Scholar 

  68. Miller, A.J., Nemhauser, G.L. & Savelsbergh, M.W.P. (2000). Solving multi-item capacitated lot-sizing problems with setup-times by branch-and-cut. Technical Report

  69. Olhager, J., Rudberg, M. & Wikner, J. (2001). Long-term capacity management: linking the perspectives from manufacturing strategy and sales and operations planning. International Journal of Production Economics, 69 (2): 215–225

    Article  Google Scholar 

  70. Orlicky, J. (1975). Material Requirements Planning. McGraw-Hill, London

    Google Scholar 

  71. Özdamar, L. & Barbarosoglu, G. (2000). An integrated Lagrangean relaxationsimulated annealing approach to the multi-level multi-item capacitated lot sizing problem. International Journal of Production Economics, 68: 319–331

    Article  Google Scholar 

  72. Özdamar, L. & Bozyel, M.A. (2000). The capacitated lot sizing problem with overtime decisions and setup times. IIE Transactions, 32: 1043–1057

    Google Scholar 

  73. Özdamar, L., Birbil, S.I. & Portmann, M.C. (2002). Technical note: new result for the capacitated lot sizing problem with overtime decisions and setup times. Production Planning & Control, 13 (1): 2–10

    Article  Google Scholar 

  74. Pochet, Y. & Wolsey, L.(1991). Solving multi-item lot-sizing problems using strong cutting planes. Management Science, 37: 53–67

    MATH  Google Scholar 

  75. Pibernik, R. & Sucky, R. (2007). An approach to inter-domain master planning in supply chains. International Journal Production Economics, 108: 200–212

    Article  Google Scholar 

  76. Pirkul, H. & Jayaraman, V. (1998). A multi commodity, multi plant, capacitated facility location problem: formulation and efficient heuristic solution. Computers Operation Research, 25 (10): 869–878

    Article  MathSciNet  MATH  Google Scholar 

  77. Rizk, N. & Martel, A. (2001). Supply chain flow planning methods: a review of the lot-sizing literature. Working paper, DT-2001-AM-1, Université Laval (Canada)

  78. Roll, Y. & Karni, R. (1991). Multi item, multi level lot sizing with an aggregate capacity constraint. European Journal of Operational Research, 51: 73–87

    Article  Google Scholar 

  79. Rota, K. (1998). Coordination temporelle de centres gérant de façon autonome des ressources. Application aux chaínes logistiques intégrées en aéronautique. PhD Thesis, ENSAE

  80. Salomon, M., Kuik, R. & Van Wassenhove, L.N. (1993). Statistical search methods for lot-sizing problems. Annals Operations Research, 41: 453–468

    Article  MATH  Google Scholar 

  81. Sambasivan, M. & Yahya, S. (2005). A Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers. Computers & Operations Research, 32 (3): 537–555

    Article  MATH  Google Scholar 

  82. Stadler, H. (1996). Mixed integer programming model formulations for dynamic multi-item multi-level capacitated lotsizing. European Journal of Operational Research, 94: 561–581

    Article  Google Scholar 

  83. Tang, O. (2004). Simulated annealing in lot sizing problem. International Journal of Production Economics, 88 (2): 173–181

    Article  Google Scholar 

  84. Tempelmeier, H. & Derstro, M. (1996). A Lagrangean based heuristic for dynamic multi-item multi-level constrained lot sizing with setup times. Management Science, 42: 738–758

    MATH  Google Scholar 

  85. Tempelmeier, H. & Helber, S. (1994). A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures. European Journal of Operations. Research, 75: 296–311

    Article  MATH  Google Scholar 

  86. Thierry, C., Chapeaublanc, N., Lepage, P. & Bel, G. (1994). Multi-site planning: a centralized or a distributed approach?. In: Conference INRIA, Sophia Antipolis, France

  87. Thizy, J.M. & Van Wassenhove, L.N. (1985). Relaxation for the multi-item capacitated lotsizing problem: a heuristic implementation. IIE Transactions, 17: 308–313

    Article  Google Scholar 

  88. Timpe, C.H. & Kallrath, J. (2000). Optimal planning in large multi-site production networks. European Journal of Operational Research, 126: 422–435

    Article  MathSciNet  MATH  Google Scholar 

  89. Torabi, S.A. & Hassini, E. (2007). An interactive possibilistic programming approach for multipleobjective supply chain master planning. Fuzzy Sets and System, in press

  90. Trigeiro, W.W., Thomas, L.J. & McClain, J.O. (1989). Capacitated lot sizing with setup times. Management Science, 35: 353–366

    Google Scholar 

  91. Vob, S. & Woodruff, D.L. (2003). Introduction to Computational Optimization Models for Production Planning in a Supply Chain. Springer-Verlag Berlin, Heidelberg

    Google Scholar 

  92. Vollmann, T.E., Berry, D.W. & Whybark, D.C. (1997). Manufacturing Planning and Control Systems, 4th ed. New York et al.

  93. Voros, J. (2002). On the relaxation of multi-level dynamic lot-sizing models. International Journal of Production Economics, 77 (1): 53–61

    Article  Google Scholar 

  94. Wagner, H.M. & Whitin, T.M. (1958). Dynamic version of the economic lot sizemodel. Management Science, 5: 89–96

    Article  MathSciNet  Google Scholar 

  95. Wight, O. (1984). Manufacturing Resource Planning: MRP II: Unlocking America’s Productivity Potential Revised Edition. Oliver Wight editor

  96. Xie, J. & Dong, J. (2002). Heuristic genetic algorithms for GCLSP. Computers and Mathematics with Applications, 44: 263–276

    Article  MathSciNet  MATH  Google Scholar 

  97. Xie, J., Lee, T.S. & Zhao, X. (2004). Impact of forecasting error on the performance of capacitated multi-item production systems. Computers & Industrial Engineering, in press

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  1. Blaise Pascal University-Clermont Ferrand, LIMOS UMR 6158 campus des Cezeaux, 63173, Aubiere cedex, France

    Michael Comelli, Michel Gourgand & David Lemoine

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  1. Michael Comelli
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  2. Michel Gourgand
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Correspondence to David Lemoine.

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The original version was presented on ICSSSM’06.

Michael Comelli is a research master graduate in production management. Currently, he is a doctoral candidate in Computer Science at the University Blaise Pascal, in LIMOS Laboratory. His research interests concern Supply chain management, tactical planning optimization (Financial and physical flow optimization, value sharing), approximated methods (heuristicis, metaheuristics…).

Michel Gourgand is a Professor of Computer Science in the ISIMA at the University of Blaise Pascal (Clermont-Ferrand). His research and teaching interests include manufacturing system modelling, scheduling problems and supply chain management.

David Lemoine is a Master of Computer Science graduate from the University Blaise Pascal in France. Currently, he is a doctoral candidate in Computer Science at the University Blaise Pascal, in LIMOS Laboratory. His research interests concern tactical planning optimization (lot-sizing models…): mathematical programming (mathematical models, lagrangean relaxations…), approximated methods (heuristics, metaheuristics …).

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Comelli, M., Gourgand, M. & Lemoine, D. A review of tactical planning models. J. Syst. Sci. Syst. Eng. 17, 204–229 (2008). https://doi.org/10.1007/s11518-008-5076-8

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