Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems

The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have non-zero objective function coeÆcients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CP based branch and bound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the least cost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It Email: [email protected] Author to whom correspondence should be addressed. Email: [email protected]