Lot sizing problem with batch ordering under periodic buyback contract and lost sales

We study the deterministic single-item lot sizing problem with batch ordering under the buyback contract (LSP-BB) in a system with one retailer and one supplier. We consider a fixed cost per batch replenished in addition to the classical lot sizing costs, making the procurement cost structure stepwise. We also consider lost sales option with a lost sales cost incurred for each unit of demand not satisfied. The buyback contract considered here consists in returning unused units at the end of every w periods, with a buyback revenue for each unit returned back. We study this problem under both FTL (full truck load) cost structure and only full batch replenishment assumption. We propose efficient and exact polynomial time algorithms for different extensions of this problem which is known to be NP-hard in the general case. To the best of our knowledge, it is the first time that the buyback contract is introduced in a multi-period lot sizing problem (LSP) in the literature. Moreover, batch ordering and lost sales issues have never been tackled in the same LSP model before our study. Hence, this paper provides efficient algorithms to solve the LSP with batch ordering and lost sales under the buyback contract not yet addressed in the literature.