Abstract
In this paper we study the stochastic batch sizing problems. We provide a unifying treatment of the problem, in which we formulate a multistage recourse problem as well as a probabilistically constrained problem. The solution approach that we adopt for these problems may be classified as a branch and price (B&P) method. Through our computational experiments turns out that the proposed B&P methodology is quite effective for the recourse constrained model. We also demonstrate how tradeoffs between cost and reliability can be investigated for the stochastic batch-sizing problem.
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References
Aggarwal A. and Park J.K. Improved Algorithms for Economic Lot Size Problems. Operations Research 1993; 41:549–571.
Ahmed S., King A.J. and Parija G. A Multi-Stage Integr Programming Approach for Capacity Expansion under Uncertainty. E-SPSS print series 2001.
Baker K.R. An experimental study of the effectiveness of rolling schedule in production planning. Decisions Science 1977; 8:19–27.
Barnhart C., Johnson E.L., Nemhauser G.L., Savelsberg M.W.P. and Vance P.H. Branch-and-Price: Column Generation for Solving Huge Integer Programs. Operations Research 1998; 46:316–329.
Birge J.R. and Louveaux F. “Introduction to Stochastic Programming”, Springer, 1997.
Common Optimization INterface for Operations Research, http//www.coin-or.org
Haugen K.K., Løkketangen A. and Woodruff D.L. Progressive hedging as a meta-heuristic applied to stochastic lot-sizing. European Journal of Operational Research 2001; 132:116–122.
Hsu V.N. Dynamic Economic Lot Size Model with Perishable Inventory. Management Science 2000; 46:1159–1169.
Kuik R., Solomon M. and van Wassenhove L.N. Batching decisions: Structure and models. European Journal of Operational Research 1994; 75:243–263.
Krarup J. and Bilde O. “Plant location, set covering and economic lot size: An o(mn) algorithm for structured problems.” In Optimierung bei Graphentheoretishen und gauzzahligen Problemen, Collatz et al, eds. Birkhauser-Verlag, 1977.
Johnson E.L., Nemhauser G.L. and Savelsbergh M.W.P. Progress in Linear Programming Based Branch-and-Bound Algorithms: An Exposition. INFORMS Journal on Computing 1997; 75:243–263
Leung J.M.Y., Magnanti T.L. and Vachani R. Facets and Algorithms Capacitated Lot Sizing. Mathematical Programming 1989; 45:331–359.
Løkketangen A. and Woodruff D.L. Progressive Hedging and Tabu Search Applied to Mixed Integer (0,1) Multi-stage Stochastic Programming. Journal of Heuristics 1996; 2:111–128.
Lulli G. and Sen S. A Branch-and-Price Algorithm for Multistage Stochastic Integer Programming with Application to Stochastic Batch-Sizing Problems, submitted for publication.
Manne A.S. Programming of Lot Sizes. Management Science 1958; 4:115–135.
Martin R.K. “LargeScale Linear and Integer Optimization”. Kluwer Academic Publishers, 1999.
Miller A.J. A polynomial-Time Dynamic Algorithm for the Multi-Stage Stochastic Uncapacitated Lot-Sizing Problem. INFORMS Annual Conference; November 2001; Miami.
Miller A.J. and Ahmed S. Uncapacitated Stochastic Lot-Sizing Problem: Algorithms and Polyhedral Structure. INFORMS Annual Conference; November 2001; Miami.
Sen S. A Branch and Price Algorithm for Multi-stage Stochastic Integer Problems. INFORMS Annual Conference; November 2000; San Antonio.
Stadtler H. Improved Rolling Schedules for the Dynamic Single-Level Lot-Sizing Problem. Management Science 2000; 46:318–326.
Wagner H.M. and Whitin T.M. Dynamic Version of the Lot Size Model. Management Science 1958; 5:89–96.
Zangwill W.I. A deterministic multi-period production scheduling model with backlogging. Management Science 1966; 13:105–119.
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Lulli, G., Sen, S. (2003). Stochastic Batch-Sizing Problems: Models and Algorithms. In: Woodruff, D.L. (eds) Network Interdiction and Stochastic Integer Programming. Operations Research/Computer Science Interfaces Series, vol 22. Springer, Boston, MA. https://doi.org/10.1007/0-306-48109-X_5
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DOI: https://doi.org/10.1007/0-306-48109-X_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4020-7302-1
Online ISBN: 978-0-306-48109-3
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