Optimal Ordering and Issuing for Perishable Inventory Management Problem with A Minimum Inventory Volume Constraint

We study a perishable inventory system that requires to maintain a fresh and large quantity of inventory at all times. For example, certain pharmaceuticals are kept for emergency preparedness and response operations. We aim to maximize the profit by optimizing the joint problem of the ordering and issuing policies while maintaining a minimum amount of perishable inventory. First, we consider a linear price model such that the primary and secondary market price functions are linearly decreasing in age. We present the optimal issuing policy if the ordering policy is given and fixed. We then consider optimizing the joint problem of the ordering and issuing policies. We first derive the revenue functions when the FIFO (first-in, first-out) or LIFO (last-in, first-out) issuing policies are used and the optimality condition is presented. Next, we consider a problem with stepwise (2-step) price functions. For the problem with given order quantity, the optimal issuing policy is sensitive to all parameters of the primary and secondary market price functions, and the revenue function is non-convex and non-differentiable. Thus a heuristic issuing policy is proposed. Some characteristics of the optimal policy are discussed and the properties of the FIFO, LIFO, and heuristic policies are presented. We then present results for the joint problem of the ordering and issuing policies and show that some of the analytical results from the problem with given order quantity still hold.