Polynomial Time Algorithms for Some Multi-Level Lot-Sizing Problems with Production Capacities

32 Pages Posted: 20 Jul 2002

See all articles by Stan van Hoesel

Stan van Hoesel

Maastricht School of Business and Economics

H. Edwin Romeijn

University of Florida - Department of Industrial and Systems Engineering

Dolores Romero Morales

Maastricht University - Department of Quantitative Economics

Albert P. M. Wagelmans

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT); Erasmus University Rotterdam (EUR) - Department of Econometrics

Date Written: June 17, 2002

Abstract

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.

Keywords: Lot-sizing, Integration of Production Planning and Transportation, Dynamic Programming, Polynomial Time Algorithms

JEL Classification: C61, M, M11, R4

Suggested Citation

van Hoesel, Stan and Romeijn, H. Edwin and Romero Morales, Dolores and Wagelmans, Albert P. M., Polynomial Time Algorithms for Some Multi-Level Lot-Sizing Problems with Production Capacities (June 17, 2002). Tinbergen Institute Working Paper No. 02-066/4; and ERIM Report Series Reference No. ERS-2002-59-LIS. Available at SSRN: https://ssrn.com/abstract=318220 or http://dx.doi.org/10.2139/ssrn.318220

Stan Van Hoesel

Maastricht School of Business and Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands

H. Edwin Romeijn

University of Florida - Department of Industrial and Systems Engineering ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States

Dolores Romero Morales

Maastricht University - Department of Quantitative Economics ( email )

P.O. Box 616
Maastricht, 6200 MD
Netherlands
++ 31 43 388 38 15 (Phone)
++ 31 43 388 48 74 (Fax)

HOME PAGE: http://www.personeel.unimaas.nl/D.Romero

Albert P. M. Wagelmans (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus Center for Optimization in Public Transport (ECOPT) ( email )

3000 DR Rotterdam
Netherlands
+31 10 408 2576 (Phone)
+31 10 408 9162 (Fax)

Erasmus University Rotterdam (EUR) - Department of Econometrics

P.O. Box 1738
3000 DR Rotterdam
Netherlands

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