Fuzzy C-means-based scenario bundling for stochastic service network design

TL;DR

This paper introduces a fuzzy c-means clustering approach for scenario bundling in stochastic service network design, improving the decomposition of large-scale SMIPs by allowing scenarios to belong to multiple bundles with partial memberships.

Contribution

It proposes a novel fuzzy c-means-based scenario bundling method that enables scenarios to have partial memberships across multiple bundles, enhancing decomposition efficiency.

Findings

Fuzzy c-means allows scenarios to belong to multiple bundles.

Partial memberships improve scenario grouping flexibility.

Enhanced computational performance in stochastic network design.

Abstract

Stochastic service network designs with uncertain demand represented by a set of scenarios can be modelled as a large-scale two-stage stochastic mixed-integer program (SMIP). The progressive hedging algorithm (PHA) is a decomposition method for solving the resulting SMIP. The computational performance of the PHA can be greatly enhanced by decomposing according to scenario bundles instead of individual scenarios. At the heart of bundle-based decomposition is the method for grouping the scenarios into bundles. In this paper, we present a fuzzy c-means-based scenario bundling method to address this problem. Rather than full membership of a bundle, which is typically the case in existing scenario bundling strategies such as k-means, a scenario has partial membership in each of the bundles and can be assigned to more than one bundle in our method.