Cutting planes from extended LP formulations

Given a mixed-integer set defined by linear inequalities and integrality requirements on some of the variables, we consider extended formulations of its continuous (LP) relaxation and study the effect of adding cutting planes in the extended space. In terms of optimization, extended LP formulations do not lead to better bounds as their projection onto the … Read more

Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

With stochastic integer programming as the motivating application, we investigate techniques to use integrality constraints to obtain improved cuts within a Benders decomposition algorithm. We compare the effect of using cuts in two ways: (i) cut-and-project, where integrality constraints are used to derive cuts in the extended variable space, and Benders cuts are then used … Read more

Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service System Staffing and Scheduling with Arrival Rate Uncertainty

We study server scheduling in multiclass service systems under stochastic uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels, and then determine schedules for the servers that cover these targets. We propose a new stochastic integer programming model that integrates these two decisions, which can yield lower … Read more