A Lagrangian relaxation approach for stochastic network capacity expansion with budget constraints

Majid Taghavi () and Kai Huang ()
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Majid Taghavi: Dalhousie University
Kai Huang: McMaster University

Annals of Operations Research, 2020, vol. 284, issue 2, No 7, 605-621

Abstract: Abstract In this paper, we consider capacity expansion for network models subject to uncertainty and budget constraints. We use a scenario tree approach to handle the uncertainty and construct a multi-stage stochastic mixed-integer programming model for the network capacity expansion problem. We assume that permanent capacity and spot market capacity are available, which can be used permanently or temporarily by the decision maker respectively. By relaxing the budget constraints, we propose a heuristic Lagrangian relaxation method to solve the problem. Two algorithms are developed to find tight upper bounds for the Lagrangian relaxation procedure. The experimental results show superior performance of the proposed Lagrangian relaxation method compared with CPLEX.

Keywords: Capacity expansion; Scenario tree; Multi-stage stochastic integer programming; Lagrangian relaxation; Network flow; Spot market; Permanent capacity (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10479-018-2862-7

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