Optimality Gap of Constant-Order Policies Decays Exponentially in the Lead Time for Lost Sales Models

Optimality Gap of Constant-Order Policies Decays Exponentially in the Lead Time for Lost Sales Models

Inventory models with lost sales and large lead times have traditionally been considered intractable, due to the curse of dimensionality which arises from having to track the set of orders placed but not yet received (i.e. pipeline vector). Recently, Goldberg et al. (2012) laid the foundations for a new approach to solving these models, by proving that as the lead time grows large (with the oth...

Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead Times

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Asymptotic Optimality of Order-Up-To Replenishment Policies for Serial Inventory Systems with Lost Sales

We study the optimal policy for a serial inventory system under periodic review when excess demand at the retailer (i.e., the most downstream stage) is lost. We focus on “high service level environments” (i.e., systems where the cost of a lost sale is high compared to inventory holding costs). These environments are typical of products whose margins are high relative to their holding costs. Whe...

Electronic Companion — “ Asymptotic Optimality of Order - Up - To Policies in Lost Sales Inventory Systems ” by Woonghee

Asymptotic Optimality of Order-Up-To Policies in Lost Sales Inventory Systems

We study a single-product single-location inventory system under periodic review, where excess demand is lost and the replenishment lead time is positive. The performance measure of interest is the long run average holding cost and lost sales penalty. For a large class of demand distributions, we show that when the lost sales penalty becomes large compared to the holding cost, the relative diff...