Decomposition techniques for hybrid MILP/CP models applied to scheduling and routing problems

Abstract

This chapter provides a review of decomposition algorithms for models that are formulated as hybrid mixed-integer linear/constraint programming problems, such as logic Benders Decomposition and Constraint Programming-Based Column Generation. We first focus the decomposition techniques on single stage scheduling problems with parallel machines where the hybrid model provides a natural representation as the decisions decompose into assignment and sequencing decisions. We describe a general decomposition algorithm for the hybrid MILP/CP model in terms of a Benders decomposition scheme, as well as in terms of a branch and cut framework. We then consider Vehicle Routing and Crew Rostering applications to illustrate how a Hybrid Branch-and-Price method can be applied, and we discuss the different models that have been proposed in the literature.