Procurement strategies for lost-sales inventory systems with all-units discounts.

*(English)*Zbl 1403.90060Summary: Despite the prevalence of all-units discounts in procurement contracts, these discounts pose a technical challenge to analyze procurement strategies due to neither concave nor convex ordering costs. In this paper, we consider the optimal procurement strategies with all-units discounts under the lost-sales setting. By assuming log-concave demands, we find that the optimal procurement strategies have a generalized \(Q\)-jump (\(s, S\)) structure by introducing a new notion of \(Q\)-jump single-crossing. In particular, a sufficient condition is provided for degenerating the optimal procurement strategies from a generalized \(Q\)-jump (\(s, S\)) structure into a \(Q\)-jump (\(s, S\)) structure, which is definitely optimal for the single-period problem. Extensive numerical results suggest that the \(Q\)-jump (\(s, S\)) policy as a heuristic performs considerably well when its optimality sufficient condition is violated. Our results can be extended to systems with multi-break all-units discounts, and systems with all-units discounts on batch ordering.

##### MSC:

90B05 | Inventory, storage, reservoirs |

##### Keywords:

inventory; procurement strategy; all-units discounts; quasi-convexity; \(Q\)-jump single-crossing
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\textit{H. Wang} et al., Eur. J. Oper. Res. 272, No. 2, 539--548 (2019; Zbl 1403.90060)

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