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

Abstract

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. Since the multiple bundle membership of a scenario induces overlap between the bundles, we empirically investigate whether and how the amount of overlap controlled by a fuzzy exponent would affect the performance of the PHA. Experimental results for a less-than-truckload transportation network optimization problem show that the number of iterations required by the PHA to achieve convergence reduces dramatically with large fuzzy exponents, whereas the computation time increases significantly. Experimental studies were conducted to find out a good fuzzy exponent to strike a trade-off between the solution quality and the computational time.

Scheduled service network design with quality targets and stochastic travel times

“…Most of the studies on stochastic SSND focus on demand uncertainty. Thus, e.g., Lium, Crainic, and Wallace (2007) , Lium, Crainic, and Wallace (2009) , Bai, Wallace, Li, andChong (2014) , Jiang, Bai, Aickelin, andLanda-Silva (2017) , and Wang, Crainic, and Wallace (2020) discuss two-stage formulations and address the question of what may be lost by not integrating information about the stochastic nature of demand directly into the tactical planning methodology, highlighting consolidation as a powerful mean to hedge against fluctuation.…”

“…No such result exists in the integer case and, thus, only PH-based meta-heuristics are proposed for integer formulations. The method has been proven to be computationally efficient, however, for a wide range of problem settings, such as, operation planning ( Gonçalves, Finardi, & da Silva, 2012 ), lot-sizing ( Haugen, Løkketangen, & Woodruff, 2001 ), portfolio management ( Mulvey & Vladimirou, 1991 ), unit commitment and server location ( Gade et al, 2016;Guo, Hackebeil, Ryan, Watson, & Woodruff, 2015 ), scheduling ( Carpentier, Gendreau, & Bastin, 2013 ), resource allocation ( Watson & Woodruff, 2011 ), capacity planning and stochastic bin packing ( Crainic, Gobbato, Perboli, & Rei, 2016 ), network design ( Fan & Liu, 2010;Hvattum & Løkketangen, 2009;Mulvey & Vladimirou, 1991 ), and SND with demand uncertainty ( Crainic et al, 2011;Crainic, Hewitt, & Rei, 2014a;Jiang et al, 2017 ).…”