A Hybrid Programming Framework for Resource-Constrained Scheduling Problems

Resource-constrained scheduling problems appear frequently at different levels of decisions in manufacturing, logistics, computer networks, software engineering etc. They are usually characterized by many types of constraints, which often make them unstructured and difficult to solve (NP-complete). Traditional mathematical programming (MP) approaches are deficient because their representation of allocation constraints is artificial (using 0-1 variables). Unlike traditional approaches, declarative constraint logic programming (CLP) provides for a natural representation of heterogeneous constraints. In CLP we state the problem requirements by constraints; we do not need to specify how to meet these requirements. CLP approach is very effective for binary constraints (binding at most two variables). If there are more variables in the constraints and the problem requires further optimization, the efficiency decreases dramatically. This paper presents a hybrid programming framework for constrained scheduling problems where two environments (mathematical programming and constraint logic programming) were integrated. This integration, hybridization as well as a transformation of the problem helped reduce the combinatorial problem substantially. In order to compare the effectiveness of the proposed framework, also made implementation of illustrative example separately for the two environments MP and CLP.