Solving planning and scheduling problems with combined integer and constraint programming

Abstract.

There have been several reports on successful application of hybrid MIP/CP algorithms for solving otherwise difficult or intractable problems. However, the practical examples presented in many papers suffer from the fact that they are far away from being realistic, in terms of both their size and their complexity. This paper presents a realistic planning problem of the chemical industry, which has been successfully treated with a hybrid approach.

Realistic mid-term production planning in chemical industry very often contains decisions on lot-sizing, assignment and sequencing, which have to be made simultaneously. A widely-used approach for implementing decision-support systems for these problems is to decompose them into a lot-sizing and a sequencing subproblem, and to solve the two subproblems with different technologies.

While this approach is adequate in many cases, there are, however, some examples where the quality of the resulting schedule depends crucially on the simultaneity of the three different planning decisions. For a planning problem of this type we developed a very efficient hybrid MIP/CP solution strategy. The MIP acts as the master process, but either one of the solvers gets just a partial description of the problem. In this paper we present the planning problem, the solution technology and our practical experience with the implementation.