Polyhedra for lot-sizing with Wagner-Whitin costs
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
The Continuous Mixing Polyhedron
Mathematics of Operations Research
Lot-sizing with production and delivery time windows
Mathematical Programming: Series A and B
SIAM Journal on Discrete Mathematics
Network Formulations of Mixed-Integer Programs
Mathematics of Operations Research
Lot-sizing with fixed charges on stocks: the convex hull
Discrete Optimization
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Here we study the discrete lot-sizing problem with an initial stock variable and an associated variable upper bound constraint. This problem is of interest in its own right, and is also a natural relaxation of the constant capacity lot-sizing problem with upper bounds and fixed charges on the stock variables. We show that the convex hull of solutions of the discrete lot-sizing problem is obtained as the intersection of two simpler sets, one a pure integer set and the other a mixing set with a variable upper bound constraint. For these two sets we derive both inequality descriptions and polynomial-size extended formulations of their respective convex hulls. Finally we carry out some limited computational tests on single-item constant capacity lot-sizing problems with upper bounds and fixed charges on the stock variables in which we use the extended formulations derived above to strengthen the initial mixed-integer programming formulations.