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Title of Journal: Math Program

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Abbravation: Mathematical Programming

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Springer-Verlag

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10.1007/bf02587038

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1436-4646

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Single item lotsizing with nondecreasing capacit

Authors: Yves Pochet Laurence A Wolsey
Publish Date: 2008/07/15
Volume: 121, Issue: 1, Pages: 123-143
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Abstract

We consider the single item lotsizing problem with capacities that are nondecreasing over time When the cost function is i nonspeculative or Wagner–Whitin for instance constant unit production costs and nonnegative unit holding costs and ii the production setup costs are nonincreasing over time it is known that the minimum cost lotsizing problem is polynomially solvable using dynamic programming When the capacities are nondecreasing we derive a compact mixed integer programming reformulation whose linear programming relaxation solves the lotsizing problem to optimality when the objective function satisfies i and ii The formulation is based on mixing set relaxations and reduces to the known convex hull of solutions when the capacities are constant over time We illustrate the use and potential effectiveness of this improved LP formulation on a few test instances including instances with and without Wagner–Whitin costs and with both nondecreasing and arbitrary capacities over time

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