An efficient approach for solving the lot-sizing problem with time-varying storage capacities

Note on “An efficient approach for solving the lot-sizing problem with time-varying storage capacities”

“…Figure 1: Illustration of the geometric technique of Wagelmans et al (1992) 4 Mistakes in Gutiérrez et al (2008) Gutiérrez et al (2008) apply the technique of Wagelmans et al (1992) to solve the problem with inventory bounds. To that end, they use the recursive variable G(t), the optimal cost to satisfy the demands in periods t, .…”

“…Given the (deterministic) demands for a finite planning horizon of length T , find a production plan at minimal cost such that all demand is satisfied, while the inventory level in each period should be no larger than the storage capacity. Toczylowski (1995) Gutiérrez et al (2008) improved the running time to O(T log T ) time. In this note, we show that the algorithm of Gutiérrez et al (2008) does not lead to an optimal solution in general.…”

“…Toczylowski (1995) Gutiérrez et al (2008) improved the running time to O(T log T ) time. In this note, we show that the algorithm of Gutiérrez et al (2008) does not lead to an optimal solution in general.…”

“…In Section 3 we briefly describe the geometric technique of Wagelmans et al (1992), which is applied in Gutiérrez et al (2008). Furthermore, in Section 4 we show why the algorithm of Gutiérrez et al (2008) does not lead to an optimal solution in general. Finally, this note ends with some concluding remarks in Section 5.…”

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AbstractIn a recent paper Gutiérrez et al (2008) show that the lot-sizing problem with inventory bounds can be solved in O(T log T ) time. In this note we show that their algorithm does not lead to an optimal solution in general.

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