The single-item lot-sizing problem with immediate lost sales

e introduce a profit maximization version of the well-known Wagner-Whitin model for the deterministic uncapacitated single-item lot-sizing problem with lost sales. Demand cannot be backlogged, but it does not have to be satisfied, either. Costs and selling prices are assumed to be time-variant, differentiating our model from previous models with lost sales. Production quantities and levels of lost sales in different periods represent a two-fold decision problem. We first transform the total profit function into a special total cost function. We then prove several properties of an optimal solution. A forward recursive dynamic programming algorithm is developed to solve the problem optimally in O(T ) time, where T denotes the number of periods in the problem horizon. The proposed algorithm can solve problems of sizes up to 400 periods in less than a second on a 500 MHz Pentium III processor. (Lot-Sizing; Dynamic Programming; Conservation Period; Profit) ∗ Corresponding author. Tel.: ++1-765-743-9552; Fax:++1-765-494-1526. E-mail address: [email protected] W THE SINGLE-ITEM LOT-SIZING PROBLEM WITH IMMEDIATE LOST SALES