Models for robust tactical planning in multi-stage production systems with uncertain demands.

*(English)*Zbl 1177.90120Summary: We consider the problem of designing robust tactical production plans, in a multi-stage production system, when the periodic demands of the finished products are uncertain. First, we discuss the concept of robustness in tactical production planning and how we intend to approach it. We then present and discuss three models to generate robust tactical plans when the finished-product demands are stochastic with known distributions. In particular, we discuss plans produced, respectively, by a two-stage stochastic planning model, by a robust stochastic optimization planning model, and by an equivalent deterministic planning model which integrates the variability of the finished-product demands. The third model uses finished-product average demands as minimal requirements to satisfy, and seeks to offset the effect of demand variability through the use of planned capacity cushion levels at each stage of the production system. An experimental study is carried out to compare the performances of the plans produced by the three models to determine how each one achieves robustness. The main result is that the proposed robust deterministic model produces plans that achieve better trade-offs between minimum average cost and minimum cost variability. Moreover, the required computational time and space are by far less important in the proposed robust deterministic model compared to the two others.

PDF
BibTeX
XML
Cite

\textit{E.-H. Aghezzaf} et al., Comput. Oper. Res. 37, No. 5, 880--889 (2010; Zbl 1177.90120)

Full Text:
DOI

##### References:

[1] | Ahmed, S.; King, A.J.; Parija, G., A multi-stage stochastic integer programming approach for capacity expansion under uncertainty, Journal of global optimization, 26, 1, 3-24, (2003) · Zbl 1116.90382 |

[2] | Ahmed, S.; Sahinidis, N.V., Robust process planning under uncertainty, Industrial and engineering chemistry research, 37, 5, 1883-1892, (1998) |

[3] | Ari, E.A.; Axsater, S., Disaggregation under uncertainty in hierarchical production planning, European journal of operational research, 35, 182-186, (1988) · Zbl 0639.90052 |

[4] | Bai, D.; Carpenter, T.; Mulvey, J.M., Making a case for robust optimisation models, Management science, 43, 7, 895-907, (1997) · Zbl 0890.90163 |

[5] | Bitran GR, Tirupati D. Hierarchical production planning. In: Graves SC, Rinnooy Kan AHG, Zipkin PH, editors, Handbooks on operations research and management science, vol. 4. Amsterdam: North-Holland; 1993. p. 523-68. |

[6] | Clay, R.L.; Grossmann, I.E., A disaggregation algorithm for the optimization of stochastic planning models, Computer chemical engineering, 21, 7, 751-774, (1997) |

[7] | Dauzere-Peres S, Lasserre JB. An integrated approach in production planning and scheduling. In: Lecture notes in economics and mathematical systems, 1994. · Zbl 0816.90070 |

[8] | Dempster MAH. A stochastic approach to hierarchical planning and scheduling. In: Dempster MAH, Lenstra JK, Rinnooy Kan AHG, editors, Deterministic and stochastic scheduling. Dordrecht: Reidel; 1982. p. 271-96. |

[9] | Dempster, M.A.H.; Fisher, M.L.; Jansen, L.; Lageweg, B.J.; Lenstra, J.K.; Rinnooy Kan, A.H.G., Analysis of heuristics for stochastic programming: results for hierarchical scheduling problems, Mathematics of operations research, 8, 525-537, (1983) · Zbl 0532.90078 |

[10] | Erschler, J.; Fontan, G.; Merce, C., Consistency of the disaggregation process in hierarchical planning, Operations research, 34, 464-469, (1986) · Zbl 0604.90068 |

[11] | Frenk, J.B.G.; Rinnooy Kan, A.H.G.; Stougie, L., A hierarchical scheduling problem with a well-solvable second stage, Annals of operations research, 1, 43-58, (1984) · Zbl 0671.90034 |

[12] | Galbraith, J., Designing complex organizations, (1973), Addison-Wesley Reading, MA |

[13] | Gfrerer, H.; Zapfel, G., Hierarchical model for production planning in the case of uncertain demand, European journal of operational research, 86, 142-161, (1995) · Zbl 0902.90076 |

[14] | Guan, Y.; Ahmed, S.; Nemhauser, G.L.; Miller, A.J., A branch and cut algorithm for the stochastic uncapacitated lot-sizing problem, Mathematical programming, 105, 1, 55-84, (2006) · Zbl 1085.90040 |

[15] | Hax, A.C.; Meal, H.C., Hierarchical integration of production planning and scheduling, (), 53-69 · Zbl 0356.90027 |

[16] | Kaut, M.; Wallace, S.W., Evaluation of scenario generation methods, Pacific journal of optimization, 3, 257-271, (2007) · Zbl 1171.90490 |

[17] | Kira, D.; Kusy, M.; Rakita, I., A stochastic linear programming approach to hierarchical production planning, Journal of the operational research society, 48, 207-211, (1997) · Zbl 0888.90081 |

[18] | Kouvelis, P.; Yu, G., Robust discrete optimization and its applications, (1997), Kluwer Academic Publishers Boston · Zbl 0873.90071 |

[19] | Laguna, M., Applying robust optimisation to capacity expansion of one location in telecommunications with demand uncertainty, Management science, 44, 11, 101-110, (1988) |

[20] | Lasserre, J.B.; Merce, C., Robust hierarchical production planning under uncertainty, Annals of operations research, 26, 73-87, (1990) · Zbl 0709.90051 |

[21] | Leung, S.C.H.; Wu, Y.; Lai, K.K., A robust optimization model for stochastic aggregate production planning, Production planning and control, 15, 5, 502-514, (2004) |

[22] | Malcolm, S.A.; Zenios, S.A., Robust optimization of power systems capacity expansion under uncertainty, Journal of the operational research society, 45, 1040-1049, (1994) · Zbl 0815.90108 |

[23] | Markowitz, H.M., Mean – variance analyses in portfolio choice and capital markets, (1987), Blackwell Oxford · Zbl 0757.90003 |

[24] | Mula, J.; Poler, R.; Garcia-Sabater, J.P.; Lario, F.C., Models for production planning under uncertainty, International journal of production economics, 103, 1, 271-285, (2006) |

[25] | Mulvey, J.M.; Vanderbei, R.J.; Zenios, S.A., Robust optimization of large-scale systems, Operations research, 43, 2, 264-281, (1995) · Zbl 0832.90084 |

[26] | Roux, W.; Dauzere-Peres, S.; Lasserre, J.B., Planning and scheduling in a multi-site environment, Production planning and control, 10, 19-28, (1999) |

[27] | Sethi, S.P.; Yan, H.; Zang, Q., Optimal and hierarchical controls in dynamic stochastic manufacturing systems: a survey, Manufacturing and service operations management, 4, 133-170, (2002) |

[28] | Thompson, S.D.; Davis, W.J., An integrated approach for modeling uncertainty in aggregate production planning, IEEE transactions on systems, man and cybernetics, 20, 1000-1012, (1990) |

[29] | Thompson, S.D.; Watanabe, D.T.; Davis, W.J., A comparative study of aggregate production planning strategies under conditions of uncertainty and cyclic product demands, International journal of production research, 31, 1957-1979, (1993) |

[30] | Yano, C.A.; Lee, H.L., Lot sizing with random yields: a review, Operations research, 43, 311-334, (1995) · Zbl 0832.90031 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.