The mixing set with a knapsack constraint arises in deterministic equivalent of probabilistic programming problems with finite discrete distributions. We first consider the case that the probabilistic program has equal probabilities for each scenario. We study the resulting mixing set with a cardinality constraint and propose facet-defining inequalities that subsume known explicit inequalities for this … Read more
This paper presents a robust branch-cut-and-price algorithm for the Heterogeneous Fleet Vehicle Routing Problem (HFVRP), vehicles may have various capacities and fixed costs. The columns in the formulation are associated to $q$-routes, a relaxation of capacitated elementary routes that makes the pricing problem solvable in pseudo-polynomial time. Powerful new families of cuts are also proposed, … Read more
This paper presents a robust branch-cut-and-price algorithm for the Capacitated Minimum Spanning Tree Problem (CMST). The variables are associated to $q$-arbs, a structure that arises from a relaxation of the capacitated prize-collecting arborescence probem in order to make it solvable in pseudo-polynomial time. Traditional inequalities over the arc formulation, like Capacity Cuts, are also used. … Read more