Abstract
In this paper we present a branch and bound algorithm for the multi item capacitated lotsizing problem. The bounding procedure is based on a Lagrangean relaxation of the problem. The multipliers are updated using subgradient optimization.
Although this algorithm can solve the problem to optimality, it is mainly used as a heuristic. Extensive computational results are reported for a large number of problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Barani, I., Van Roy, T.J., and Wolsey, L.A., “Strong Formulations for Multi-item Capacitated Lot Sizing”, Management Science, vol.30, n°10, October 1984, pp.1255–1261.
Bitran, G., and Yannasse, H., “Computational Complexity of the Capacitated Lot Size Problem”, Management Science, vol.28, no10, October 1982, pp.1174–1186.
Dixon, P.S., and Silver, E.A., “A Heuristic Solution Procedure for the Multi-item, Single Level, Limited Capacity, Lot Sizing Problem”, Journal of Operations Management, vol.2, no1, October 1981, pp.23–39.
Dogramaci, A., Panayiotopoulos, J.E., and Adam, N.R., “The Dynamic Lot Sizing Problem for Multiple Items under Limited Capacity”, AIIE Transactions vol.13, no4, December 1981, pp.294–303.
Dzielinsky, B.P., and Gomory, R.E., “Optimal Programming of Lot Sizes, Inventory and Labor Allocations”, Management Science, vol.11, no9, July 1965, pp.874–890.
Fisher, M.L., “The Lagrangean Relaxation Method for Solving integer Programming Problems”, Management Science, vol.27, no1, Jan.1981, pp.1–18.
Florian, M., Lenstra, J.K., and Rinnooy Kan A.H.G., “Deterministic Production Planning: Algorithms and Complexity”, Management Science, vol.26, no7, July 1980, pp.122–20.
Kami, R., and Roll, Y., “A Heuristic Algorithm for the Multi-item Lot Sizing Problem with Capacity Constraints”, HE Transactions, vol.14, no4, December 1982, pp.249–356.
Lambrecht, M.R., and Vanderveken, H., “Heuristic Procedure for the Single Operation Multi-item Loading Problem”, AIIE Transactions, vol.11, no4, December 1979, pp.319–326.
Lasdon, L.S., and Terjung, R.C., “An Efficient Algorithm for Multi-item Scheduling”, Operations Research, vol.19, no2, July-August 1971, pp.946–969.
Maes, J., and Van Wassenhove, L.N., “Multi-item Single Level Capacitated Dynamic Lot Sizing Heuristics: A Computational Comparison, part I”, WP 84–27 K.U.Leuven, Department of Industrial Management.
Maes, J., and Van Wassenhove, L.N., “Multi-item Single Level Capacitated Dynamic Lot Sizing Heuristics: A Computational Comparison, part II”, WP 85–08 K.U.Leuven, Department of Industrial Management.
Manne, A.S., “Programming of Economic Lot Sizes”, Management Science, vol.4, no2, January 1958, pp.115–135.
Thizy, J.M., and Van Wassenhove, L.N., “A Subgradient Algorithm for the Multi-item Capacitated Lot Sizing Problem”, Research Report EES, 83–14, Princeton University, December 1983, to appear in IIE-Transactions.
Wagner, H.M., and Whitin, T.M., “Dynamic Version of the Economic Lot Size Model”, Management Science, October 1958, pp.89–96.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gelders, L.F., Maes, J., van Wassenhove, L.N. (1986). A Branch and Bound Algorithm for the Multi Item Single Level Capacitated Dynamic Lotsizing Problem. In: Axsäter, S., Schneeweiss, C., Silver, E. (eds) Multi-Stage Production Planning and Inventory Control. Lecture Notes in Economics and Mathematical Systems, vol 266. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51693-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-51693-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16436-4
Online ISBN: 978-3-642-51693-1
eBook Packages: Springer Book Archive