The stock at the beginning of period t denoted by xt , orders at the beginning of period t by ut , and random demand in period t (observed only after the orders are placed) by dt . We assume ordering cost 5, selling price 10 and holding cost 2. The demands in successive periods are i.i.d. with values (0, 1, 2, 3, 4) whose respective probabilities are 0.1, 0.2, 0.3, 0.2, 0.2. The capacity of the inventory is 12.

(2.1) Formulate an infinite horizon problem with discount factor 0.8 to determine the best re-order policy.

(2.2) Solve the problem in (2.1) by value and policy iteration methods.