Bounds for probabilistic integer programming problems
Discrete Applied Mathematics - Workshop on discrete optimization DO'99, contributions to discrete optimization
Multimodal Express Package Delivery: a Service Network Design Application
Transportation Science
The Probabilistic Set-Covering Problem
Operations Research
MIP reformulations of the probabilistic set covering problem
Mathematical Programming: Series A and B
A hub location inventory model for bicycle sharing system design: Formulation and solution
Computers and Industrial Engineering
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Astochastic, mixed-integer program (MIP) involving joint chance constraints is developed that generates least-cost vehicle redistribution plans for shared-vehicle systems such that a proportion of all near-term demand scenarios are met. The model aims to correct short-term demand asymmetry in shared-vehicle systems, where flow from one station to another is seldom equal to the flow in the opposing direction. The model accounts for demand stochasticity and generates partial redistribution plans in circumstances when demand outstrips supply. This stochastic MIP has a nonconvex feasible region. A novel divide-and-conquer algorithm for generating p-efficient points, used to transform the problem into a set of disjunctive, convex MIPs and handle dual-bounded chance constraints, is proposed. Assuming independence of random demand across stations, a faster cone-generation method is also presented. In a real-world application for a system in Singapore, the potential of redistribution as a fleet management strategy and the value of accounting for inherent stochasticities are demonstrated.