Joint product durability and lot sizing models

This paper concerns the simultaneous selection of product durability and order quantity for items that deteriorate over time. Choices of product durability are modelled as the values of a single design parameter that affects the distribution of the time-to-onset of deterioration (TOD). Once deterioration has begun, individual items are assumed to have exponential remaining lifetimes. We analyze two scenarios. In the first case items are guaranteed to be good if used prior to an expiry date. Therefore, TOD is a constant and the store manager may choose an appropriate value (at cost). In the second case, TOD is a random variable. Then, the design parameter can affect TOD distribution in either mean-preserving or variance-preserving or mixed manner. We report insightful numerical examples for each case and derive highly plausible conditions, which when true, imply that the corresponding expected cost per unit time is strictly quasi-convex.