The mixing set with divisible capacities

Abstract

Given rational numbers C 0,...,C m and b 0,...,b m , the mixing set with arbitrary capacities is the mixed-integer set defined by conditions s∈+∈C t z t ≥b t , 0≤t≤m, s≥∈0, z t integer, 0≤t≤m. Such a set has applications in lot-sizing problems. We study the special case of divisible capacities, i.e. C t /C t∈-∈1 is a positive integer for 1≤t≤m. Under this assumption, we give an extended formulation for the convex hull of the above set that uses a quadratic number of variables and constraints. © 2008 Springer-Verlag Berlin Heidelberg.