<p>We consider a two-stage stochastic program relevant to the planning of freight transportation carriers that must design a transportation network while facing uncertainty in shipment sizes. More precisely, we consider a planning problem relevant to carriers that have the operational flexibility to delay the scheduling of vehicle and shipment transportation moves until after shipment sizes have been observed. While such flexibility has the potential to reduce costs, the resulting mathematical program falls within the class of two-stage stochastic programs with integer recourse. Optimization problems within this class are challenging to solve as they are not amenable to solution by Benders decomposition, the induced second-stage scenario subproblems being (mixed) integer programs. Thus, linear programming duality theory alone is not sufficient to guarantee the convergence of a Benders scheme. To solve this problem, we adapt a recently proposed Benders-based algorithmic strategy that accommodates integer variables in both stages. We also present enhancement techniques for strengthening both the master problem and the subproblems it solves. With an extensive computational study, we demonstrate the superior performance of this algorithm to classical benchmarks and establish the impact of the enhancement techniques.</p>

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Stochastic scheduled service network design problem with flexible schedules: Mathematical formulations and benders decomposition-based solution approach

  • Simon Belieres,
  • Mike Hewitt

摘要

We consider a two-stage stochastic program relevant to the planning of freight transportation carriers that must design a transportation network while facing uncertainty in shipment sizes. More precisely, we consider a planning problem relevant to carriers that have the operational flexibility to delay the scheduling of vehicle and shipment transportation moves until after shipment sizes have been observed. While such flexibility has the potential to reduce costs, the resulting mathematical program falls within the class of two-stage stochastic programs with integer recourse. Optimization problems within this class are challenging to solve as they are not amenable to solution by Benders decomposition, the induced second-stage scenario subproblems being (mixed) integer programs. Thus, linear programming duality theory alone is not sufficient to guarantee the convergence of a Benders scheme. To solve this problem, we adapt a recently proposed Benders-based algorithmic strategy that accommodates integer variables in both stages. We also present enhancement techniques for strengthening both the master problem and the subproblems it solves. With an extensive computational study, we demonstrate the superior performance of this algorithm to classical benchmarks and establish the impact of the enhancement techniques.