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Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions

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  • Mehmet Önal
  • H. Edwin Romeijn

Abstract

We study a multi‐item capacitated lot‐sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon. In this class of problems, the demand for each independent item in each time period is affected by pricing decisions. The corresponding demands are then satisfied through production in a single capacitated facility or from inventory, and the goal is to set prices and determine a production plan that maximizes total profit. In contrast with many traditional lot‐sizing problems with fixed demands, we cannot, without loss of generality, restrict ourselves to instances without initial inventories, which greatly complicates the analysis of the CLSTP. We develop two alternative Dantzig–Wolfe decomposition formulations of the problem, and propose to solve their relaxations using column generation and the overall problem using branch‐and‐price. The associated pricing problem is studied under both dynamic and static pricing strategies. Through a computational study, we analyze both the efficacy of our algorithms and the benefits of allowing item prices to vary over time. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • Mehmet Önal & H. Edwin Romeijn, 2010. "Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(2), pages 172-187, March.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:2:p:172-187
    DOI: 10.1002/nav.20394
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    1. William W. Trigeiro & L. Joseph Thomas & John O. McClain, 1989. "Capacitated Lot Sizing with Setup Times," Management Science, INFORMS, vol. 35(3), pages 353-366, March.
    2. Geunes, Joseph & Merzifonluoglu, Yasemin & Romeijn, H. Edwin, 2009. "Capacitated procurement planning with price-sensitive demand and general concave-revenue functions," European Journal of Operational Research, Elsevier, vol. 194(2), pages 390-405, April.
    3. Stephen M. Gilbert, 2000. "Coordination of Pricing and Multiple-Period Production Across Multiple Constant Priced Goods," Management Science, INFORMS, vol. 46(12), pages 1602-1616, December.
    4. Howard Kunreuther & Linus Schrage, 1973. "Joint Pricing and Inventory Decisions for Constant Priced Items," Management Science, INFORMS, vol. 19(7), pages 732-738, March.
    5. van den Heuvel, Wilco & Wagelmans, Albert P.M., 2006. "A polynomial time algorithm for a deterministic joint pricing and inventory model," European Journal of Operational Research, Elsevier, vol. 170(2), pages 463-480, April.
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