Design of a Distribution Network Using Primal-Dual Decomposition

Amethodtosolvethedesignofadistributionnetworkforbottleddrinkscompanyisintroduced.Thedistributionnetworkproposed includes three stages: manufacturing centers, consolidation centers using cross-docking, and distribution centers. The problem is formulated using a mixed-integer programming model in the deterministic and single period contexts. Because the problem considersseveralelementsineachstage,adirectsolutionisverycomplicated.Formedium-to-largeinstancestheproblemfallsinto large scale. Based on that, a primal-dual decomposition known as cross decomposition is proposed in this paper. This approach allows exploring simultaneously the primal and dual subproblems of the original problem. A comparison of the direct solution withamixed-integerlinealprogrammingsolverversusthecrossdecompositionisshownforseveralrandomlygeneratedinstances. Resultsshowthegoodperformanceofthemethodproposed

Planning of integrated mobility-on-demand and urban transit networks

We envision a multimodal transportation system where Mobility-on-Demand (MoD) service is used to serve the first mile and last mile of transit trips. For this purpose, the current research formulates an optimization model for designing an integrated MoD and urban transit system. The proposed model is a mixed-integer non-linear programming model that captures the strategic behavior of passengers in a multimodal network through a passenger assignment model. It determines which transit routes to operate, the frequency of the operating routes, the fleet size of vehicles required in each transportation analysis zone to serve the demand, and the passenger flow on both road and transit networks. A Benders decomposition approach with several enhancements is proposed to solve the given optimization program. Computational experiments are presented for the Sioux Falls multimodal network. The results show a significant improvement in the congestion in the city center with the introduction and optimization of an integrated transportation system. The proposed design allocates more vehicles to the outskirt zones in the network (to serve the first mile and last mile of transit trips) and more frequency to the transit routes in the city center. The integrated system significantly improves the share of transit passengers and their level of service in comparison to the base optimized transit system. The sensitivity analysis of the bus and vehicle fleet shows that increasing the number of buses has more impact on improving the level of service of passengers compared to increasing the number of MoD vehicles. Finally, we provide managerial insights for deploying such multimodal service.Comment: 39 pages, 6 figure