Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale

Perishable products constitute a sizeable component of inventories. A common question in a reselling situation involving a perishable (or a non-perishable) product is: what should be the size of the replenishment? When a product is highly perishable, the demand may need to be backlogged to contain costs due to deterioration. In this sense, perishability and backlogging are complementary conditions. In this paper we consider the problem of determining the lot size for a perishable good under finite production, exponential decay and partial backordering and lost sale. The problem is complex because it involves exponential and logarithmic expressions. We offer some new insights to this important managerial problem in inventory control. We show that as a constrained non-linear problem, it does have the convexity characteristics that make the problem easy to solve. Practitioners can solve this problem without resorting to Taylor's series approximation. They can solve the original problem using common non-linear programming software such as the Solver in Excel and be confident that the solution returned is the global minimum.