A Lagrangean relaxation approach for very-large-scale capacitated lot-sizing
Article Abstract:
The capacitated lot-sizing problem (CLSP) refers to the issue of production planning for a number of items over several time periods in which the demand for the items may fluctuate from one period to another. A heuristic method based on Lagrangean relaxation and subgradient optimization was developed in an attempt to arrive at near-optimal solutions to very-large-scale CLSPs. The relative generality of the method allows it to be applied, with little or no modifications, to actual situations occuring in the manufacturing setting. It can solve CLSPs involving as much as 5000 items and 30 time periods.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1992
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An O(T2) algorithm for the NI-G-NI-ND capacitated lot size problem
Article Abstract:
A group of capacitated, dynamic lot size problems are examined in which the set-up expenses do not increase over time. Unit holding expenses show an arbitrary pattern. Production costs do not increase and capacities do not decrease. The characteristics of the best solution for this problem are studied, and the concept of candidate sub-plan is developed. It is shown that only the candidate sub-plans have to be studied in looking for the best solution. A dynamic programming algorithm is then developed which includes the concept of a candidate sub-plan and which has run-time complexity of O(T2).
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1988
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Strong Formulations for Multi-Item Capacitated Lot Sizing
Article Abstract:
A class of valid inequalities are used to reformulate multi-item capacitated lot-sizing problems. The process creates problems that are facets of the single-item uncapacitate problem. The inequalities can be generated as part of a cutting plane algorithm. Tables contain numerical results.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1984
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