TABLE OF CONTENTS Consider a producer who manufactures a good to meet a set of outstanding orders over a finite number of time periods, T. Producing the good in any time period t requires a production setup at a cost S t and each unit costs an additional p t to manufacture. We let M( t) denote the set of all orders that request delivery in period t (we assume zero delivery lead time for ease of exposition; the model easily extends to a constant delivery lead time without loss of generality), and let m denote an index for orders. The manufacturer has a capacity to produce C t units in period t, t = 1, , T. We assume that that no shortages are permitted, i.e., no planned backlogging [a], and that items can be held in inventory at a cost of h t per unit remaining at the end of period t. Let d mt denote the quantity of the good requested by order m for period t delivery, for which the customer will pay r mt per unit, and suppose the producer is free to choose any quantity between zero and d mt in satisfying order m in period t (i.e., rationing is possible, and the customer will take as much of the good as the supplier can provide, up to
