A Multi-stage Stochastic Programming Approach for Network Capacity Expansion with Multiple Sources of Capacity

TL;DR

This paper develops a multi-stage stochastic programming model for network capacity expansion considering multiple capacity sources and types, offering novel solution algorithms with superior performance.

Contribution

It introduces a comprehensive model integrating various capacity sources and types, along with two innovative solution methods for efficient problem solving.

Findings

Proposed algorithms outperform commercial software in numerical tests.

The model effectively captures multiple capacity sources and uncertainties.

Algorithms demonstrate convergence and computational efficiency.

Abstract

In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and contract capacity. We use a scenario tree to model the uncertainty, and build a multi-stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software.