NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract

•Single-item lot sizing problem is studied under a capacity reservation contract.•Batch deliveries are allowed and the overall replenishment cost is stepwise.•Four NP-hard cases are identified and an efficient FPTAS is proposed.•Pseudo-polynomial time dynamic programming algorithm is given for the g...

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Vydáno v:European journal of operational research Ročník 257; číslo 2; s. 483 - 493
Hlavní autoři: Akbalik, Ayse, Hadj-Alouane, Atidel B., Sauer, Nathalie, Ghribi, Houcem
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.03.2017
Elsevier Sequoia S.A
Elsevier
Témata:
Algorithms
Capacity reservation contract
Complexity
Computer Science
Dynamic programming
Inventory
Lot sizing
Operations Research
Polynomial time algorithm
Polynomials
Studies
Lot sizing
Polynomial time algorithm
Capacity reservation contract
Inventory
Complexity
ISSN:0377-2217, 1872-6860
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Shrnutí:•Single-item lot sizing problem is studied under a capacity reservation contract.•Batch deliveries are allowed and the overall replenishment cost is stepwise.•Four NP-hard cases are identified and an efficient FPTAS is proposed.•Pseudo-polynomial time dynamic programming algorithm is given for the general case.•Polynomial time algorithms are proposed under restricted parameters. In this paper, we study the single-item lot sizing problem under a capacity reservation contract. A manufacturer is replenished by an external supplier with batch deliveries and a certain capacity is reserved at the supplier level with an advantageous cost. In addition to the classical ordering and inventory holding costs, for each batch ordered under the reserved capacity a fixed cost per batch is incurred; and for batches exceeding this capacity a higher fixed cost per batch is paid, typically through the purchase from the spot market. We identify various NP-hard cases, propose a pseudo-polynomial time dynamic programming algorithm under arbitrary parameters, show that the problem admits an FPTAS and give polynomial time algorithms for special cases. We finally state a list of open problems for further research.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2016.07.028