Production Planning and Mixed Integer
Programming
Laurence A. Wolsey
CORE, Université catholique de
A
wide variety of production planning and supply chain management problems can be
formulated as mixed integer programs. Even though the commercial mixed integer
programming (MIP) solvers have made remarkable progress in recent years, it
still makes a significant difference in terms of solution quality and running
time if one uses the “right” formulation for one’s problem.
First
we show that a simple mixed integer set, called the mixing set, plays a major
role in generating new and tight formulations for a several important
production planning problems, in both their un-capacitated and constant
capacity versions:
the lot-sizing problem with production time windows
the stochastic lot-sizing problem with a scenario tree
the multi-item problem with a joint set-up cost
as well
as
the
lot-sizing problem with varying capacities.
Secondly
we discuss an automatic reformulation, cutting plane and heuristics library
LS-LIB that allow rapid access to much that is known about tight formulations
for production planning problems. Computational results on a couple of
industrial cases are presented.