A robust lot sizing problem with ill-known demands

The paper deals with a lot sizing problem with ill-known demands modeled by fuzzy intervals whose membership functions are possibility distributions for the values of the uncertain demands. Optimization criteria, in the setting of possibility theory, that lead to choose robust production plans under fuzzy demands are given. Some algorithms for determining optimal robust production plans with respect to the proposed criteria, and for evaluating production plans are provided. Some computational experiments are presented.

[1]  Didier Dubois,et al.  Possibility Theory - An Approach to Computerized Processing of Uncertainty , 1988 .

[2]  J. Mula,et al.  The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand , 2010 .

[3]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[4]  G. Dudek,et al.  Collaborative Planning in Supply Chains: A Negotiation-Based Approach , 2004 .

[5]  Caroline Thierry,et al.  Design of cooperative processes in a customer-supplier relationship: An approach based on simulation and decision theory , 2009, Eng. Appl. Artif. Intell..

[6]  Didier Dubois,et al.  Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge , 2003, Eur. J. Oper. Res..

[7]  Juite Wang,et al.  Fuzzy decision modeling for supply chain management , 2005, Fuzzy Sets Syst..

[8]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..

[9]  Colleen Crum,et al.  Supply Chain Collaboration: How to Implement CPFR and Other Best Collaborative Practices , 2005 .

[10]  Alf Kimms,et al.  Lot sizing and scheduling -- Survey and extensions , 1997 .

[11]  Radivoj Petrovic,et al.  Supply chain modelling using fuzzy sets , 1999 .

[12]  Masahiro Inuiguchi,et al.  Minimax regret solution to linear programming problems with an interval objective function , 1995 .

[13]  KasperskiAdam,et al.  Choosing robust solutions in discrete optimization problems with fuzzy costs , 2009 .

[14]  D. Dubois,et al.  When upper probabilities are possibility measures , 1992 .

[15]  C. Kao,et al.  A single-period inventory model with fuzzy demand , 2002 .

[16]  R. Meyer.  The Validity of a Family of Optimization Methods , 1970 .

[17]  E. Aiyoshi,et al.  Necessary conditions for min-max problems and algorithms by a relaxation procedure , 1980 .

[18]  Sunil Agrawal,et al.  Impact of information sharing and lead time on bullwhip effect and on-hand inventory , 2009, Eur. J. Oper. Res..

[19]  Tien-Fu Liang,et al.  Application of fuzzy sets to manufacturing/distribution planning decisions with multi-product and multi-time period in supply chains , 2009, Expert Syst. Appl..

[20]  D. Dubois,et al.  Possibility theory and data fusion in poorly informed environments , 1994 .

[21]  Yian-Kui Liu,et al.  Fuzzy Minimum-Risk Material Procurement Planning Problem , 2008, 2008 Fourth International Conference on Natural Computation.

[22]  Bernard Grabot,et al.  Integration of uncertain and imprecise orders in the MRP method , 2005, J. Intell. Manuf..

[23]  Dorit S. Hochbaum,et al.  Technical Note - Solving Linear Cost Dynamic Lot-Sizing Problems in O(n log n) Time , 2008, Oper. Res..

[24]  Raul Poler Escoto,et al.  Fuzzy optimization for supply chain planning under supply, demand and process uncertainties , 2009, Fuzzy Sets Syst..

[25]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[26]  Josefa Mula,et al.  Quantitative models for supply chain planning under uncertainty: a review , 2009 .

[27]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[28]  A. M. Geoffrion.  Generalized Benders decomposition , 1972 .

[29]  J. K. Lenstra,et al.  Deterministic Production Planning: Algorithms and Complexity , 1980 .

[30]  Didier Dubois,et al.  On latest starting times and floats in activity networks with ill-known durations , 2003, Eur. J. Oper. Res..

[31]  Bela Martos,et al.  Nonlinear programming theory and methods , 1977 .

[32]  R. Tavakkoli-Moghaddam,et al.  A fuzzy aggregate production planning model for make-to-stock environments , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

[33]  Bernard Grabot,et al.  Modelling of ill-known requirements and integration in production planning , 2011 .

[34]  Josefa Mula,et al.  Production , Manufacturing and Logistics A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment , 2010 .

[35]  Adam Kasperski,et al.  Choosing robust solutions in discrete optimization problems with fuzzy costs , 2009, Fuzzy Sets Syst..

[36]  Manuel Laguna,et al.  A heuristic to minimax absolute regret for linear programs with interval objective function coefficients , 1999, Eur. J. Oper. Res..

[37]  Manoranjan Maiti,et al.  A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints , 2008, Eur. J. Oper. Res..

[38]  Vineet Padmanabhan,et al.  Comments on "Information Distortion in a Supply Chain: The Bullwhip Effect" , 1997, Manag. Sci..

[39]  Raul Poler Escoto,et al.  Material Requirement Planning with fuzzy constraints and fuzzy coefficients , 2007, Fuzzy Sets Syst..

[40]  John M. Wilson,et al.  The capacitated lot sizing problem: a review of models and algorithms , 2003 .

[41]  Rafik A. Aliev,et al.  Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management , 2007, Inf. Sci..

[42]  Yian-Kui Liu,et al.  Modeling fuzzy multi-period production planning and sourcing problem with credibility service levels , 2009, J. Comput. Appl. Math..

[43]  A Gerodimos,et al.  Robust Discrete Optimization and its Applications , 1996, J. Oper. Res. Soc..

[44]  G. K. Beekman-Love,et al.  Introduction to materials management , 1978 .

[45]  J. R. Tony Arnold,et al.  Introduction to Materials Management , 1991 .

[46]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[47]  L. LeeHau,et al.  Information Distortion in a Supply Chain , 1997 .