Using composite variable modeling to achieve realism and tractability in production planning: An example from automotive stamping

Applying traditional mathematical programming techniques to problems in production planning can lead to tremendous challenges. These include non-linearities, very large numbers of constraints and weak linear programming relaxations. To ensure tractability, problems are often either simplified in scope or limited in instance size, resulting in solutions that may no longer address important real-world issues. As an alternative, this paper considers the use of models based on composite variables (variables that capture multiple decisions simultaneously) as a way to solve complex production planning problems. The scheduling of an automotive stamping facility is used as a demonstrative example, and it is shown how composite variable models and a novel corresponding algorithm can lead to high-quality, realistic solutions with acceptable run times. In the proposed approach, batch sizes, labor availability or sequencing of part types is not restricted and the number of changeovers is not fixed a priori. In addition, sequence-dependent changeover times and varying due dates are allowed. Computational results are presented using data from Ford Motor Company.[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix]