Polynomial time algorithms for some multi-level lot-sizing problems with production capacities

C.P.M. van Hoesel, H.E. Romeijn, M.D. Romero Morales, A. Wagelmans

Research output: Working paper / PreprintWorking paper

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We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic lot-sizing model, adding stationary production capacities at the manufacturer, as well as multiple intermediate storage levels (including the retailer level), and transportation between these levels. Allowing for general concave production costs and linear holding costs, we provide polynomial time algorithms for the cases where the transportation costs are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. The running times of the algorithms are remarkably insensitive to the number of levels in the supply chain.
Original languageEnglish
Place of PublicationMaastricht
PublisherMaastricht University School of Business and Economics
Number of pages32
Publication statusPublished - 1 Jan 2002

Publication series

SeriesMETEOR Research Memorandum

JEL classifications

  • c61 - "Optimization Techniques; Programming Models; Dynamic Analysis"
  • m11 - Production Management
  • r40 - Transportation Systems: General


  • lot-sizing
  • integration of production planning and transportation
  • dynamic programming
  • polynomial time algorithms

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