Levi, Retsef; Janakiraman, Ganesh; Nagarajan, Mahesh A 2-approximation algorithm for stochastic inventory control models with lost sales. (English) Zbl 1231.90045 Math. Oper. Res. 33, No. 2, 351-374 (2008). Summary: In this paper, we describe the first computationally efficient policies for stochastic inventory models with lost sales and replenishment lead times that admit worst-case performance guarantees. In particular, we introduce dual-balancing policies for lost-sales models that are conceptually similar to dual-balancing policies recently introduced for a broad class of inventory models in which demand is backlogged rather than lost. That is, in each period, we balance two opposing costs: the expected marginal holding costs against the expected marginal lost-sales cost. Specifically, we show that the dual-balancing policies for the lost-sales models provide a worst-case performance guarantee of two under relatively general demand structures. In particular, the guarantee holds for independent (not necessarily identically distributed) demands and for models with correlated demands such as the \(AR(1)\) model and the multiplicative autoregressive demand model. The policies and the worst-case guarantee extend to models with capacity constraints on the size of the order and stochastic lead times. Our analysis has several novel elements beyond the balancing ideas for backorder models. Cited in 14 Documents MSC: 90B05 Inventory, storage, reservoirs 90C59 Approximation methods and heuristics in mathematical programming Keywords:inventory; approximation; dual balancing; algorithms; lost sales PDFBibTeX XMLCite \textit{R. Levi} et al., Math. Oper. Res. 33, No. 2, 351--374 (2008; Zbl 1231.90045) Full Text: DOI