Economic lot-sizing with remanufacturing: complexity and efficient formulations

Mathijn Jan Retel Helmrich, Raf Jans, Wilco van den Heuvel and Albert Wagelmans

No EI 2010-71, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: Within the framework of reverse logistics, the classic economic lot-sizing problem has been extended with a remanufacturing option. In this extended problem, known quantities of used products are returned from customers in each period. These returned products can be remanufactured, so that they are as good as new. Customer demand can then be fulfilled both from newly produced and remanufactured items. In each period, we can choose to set up a process to remanufacture returned products or produce new items. These processes can have separate or joint set-up costs. In this paper, we show that both variants are NP-hard. Furthermore, we propose and compare several alternative MIP formulations of both problems. Because ‘natural’ lot-sizing formulations provide weak lower bounds, we propose tighter formulations, namely shortest path formulations, a partial shortest path formulation and an adaptation of the (l, S, WW)-inequalities for the classic problem with Wagner-Whitin costs. We test their efficiency on a large number of test data sets and find that, for both problem variants, a (partial) shortest path type formulation performs better than the natural formulation, in terms of both the LP relaxation and MIP computation times. Moreover, this improvement can be substantial.

Keywords: lot-sizing; reformulations; remanufacturing; reverse logistics (search for similar items in EconPapers)
Date: 2010-12-22
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Citations: View citations in EconPapers (3)

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