LS-LIB: a library of reformulations, cut separation algorithms and primal heuristics in a high-level modeling language for solving MIP production planning problems

Much progress has been made in recent years in solving certain classes of production planning problems using mixed integer programming. One of the major challenges is how to make this expertise available and easy to use to the non-specialist and to the practitioners. Here we describe a modeling approach and tool LS-LIB, and report on computational results. LS-LIB is a library of primitives to declare procedures/subroutines/global constraints in a high-level modeling language that we believe offers an interesting partial answer to this challenge. LS-LIB provides routines for problem reformulation, cut generation, and heuristics to find good feasible solutions quickly. The user must provide an initial formulation of his problem in the modeling language MOSEL. Then using his knowledge of the problem he must first classify each product or sku according to a simple three field scheme: [production type, capacity type, variant] proposed recently. Then it is a simple matter to use the global constraints of LS-LIB by adding a few lines to his initial MOSEL formulation to get a tightened formulation and/or call the appropriate cut separation routines. The heuristic procedures are called in a similar fashion. We illustrate the use of LS-LIB on an intractable two-level problem, and a hard multi-level problem.