A Lagrangean Relaxation Approach for Very-Large-Scale Capacitated Lot-Sizing

Abstract

In this paper, we develop a Lagrangean relaxation-based heuristic procedure to generate near-optimal solutions to very-large-scale capacitated lot-sizing problems (CLSP) with setup times and limited overtime. Our computational results show that large problems involving several thousand products and several thousand 0/1 integer variables can be solved in a reasonable amount of computer time to within one percent of their optimal solution. The proposed procedure is general enough to be applied directly or with slight modification to real-life production problems.inventory/production, deterministic models, inventory/production, material requirements planning, programming, large scale systems

A hybrid heuristic for the multi-plant capacitated lot sizing problem with setup carry-over

“…There are many approaches for the CLSP with a single item, with multiple items and with only one or multiple production centers. Usually these problems are tackled heuristically [24,12,5], though exact solution methods exist to solve them [4], [19] and [2].…”

“…There are many approaches for the CLSP with a single item, with multiple items and with only one or multiple production centers. Usually these problems are tackled heuristically [24,12,5], though exact solution methods exist to solve them [4], [19] and [2].The multi-plant capacitated lot sizing problem (MPCLSP) with multiple items and periods is composed of multiple production centers that produce all the same items as well as enabling transfers amongst the plants. Sambasivan and Schimidt [17] solved this problem with a heuristic based on transfers of production lots between the periods and the plants, while even better results were obtained by Sambasivan and Yahya [18] using a Lagrangian relaxation.…”

A genetic algorithm for multi-level, multi-machine lot sizing and scheduling

“…All three rnodels could be classified as small bücket models since only a few (one or two) items are produced per period. In contrast to this, the well-known capacitated lot sizing problem (CLSP) [3,7,10,14,23,26,27] represents a large bücket model since many items can be produced per period. Remember, the CLSP does not include sequence decisions and is thus a much "easier" problem.…”

Proportional lot sizing and scheduling: Some extensions

“…In contrast to this, the well-known capacitated lot sizing problem (CLSP) future demand must be stored in the inventory and thus cause item-specific holding costs. Most authors assume [3,10,18,26,28,29] represents a large bucket model since many items can be produced per period. Recall that that the holding costs for an item must be greater than or equal to the sum of the holding costs for all immediate the CLSP does not include sequence decisions and is thus a much ''easier'' problem.…”