Tight MIP Formulations for Bounded Up/Down Times and Interval-Dependent Start-Ups

M. Queyranne () and L.A. Wolsey ()
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M. Queyranne: Université catholique de Louvain, CORE, Belgium
L.A. Wolsey: Université catholique de Louvain, CORE, Belgium

No 2015036, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: Switching machines on and off is an important aspect of unit commitment problems and production planning problems, among others. Here we study tight mixed integer programming formulations for two aspects of such problems: bounded length on- and off-intervals, and interval-dependent start-ups. For the problem with both these aspects we develop a tight (convex hull) formulation involving additional variables. For the bounded interval problem we present a tight network dual formulation based on new integer variables that allows us to simultaneously treat lower and upper bounds on the interval lengths. This in turn leads to more general results, including simpler proofs of known tight formulations for problems with just lower bounds. For the interval-dependent start-up problem we develop a path formulation that allows us to describe the convex hull of solutions in the space of machine-on and interval-dependent start-up variables.

Keywords: production sequencing; unit commitment; bounded up/down times; interval-dependent startups; tight MIP formulations; convex hulls (search for similar items in EconPapers)
JEL-codes: C44 C61 (search for similar items in EconPapers)
Date: 2015-07-01
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Citations: View citations in EconPapers (2)

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