A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a mul...

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Veröffentlicht in:Journal of global optimization Jg. 26; H. 1; S. 3 - 24
Hauptverfasser: Ahmed, Shabbir, King, Alan J., Parija, Gyana
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Dordrecht Springer Nature B.V 01.05.2003
Schlagworte:
Algorithms
Approximation
Costs
Decision making
Dynamic programming
Economies of scale
Heuristic
Integer programming
Production capacity
Stochastic control theory
Stochastic models
ISSN:0925-5001, 1573-2916
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Zusammenfassung:This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1023/A:1023062915106