This thesis studies a single item periodic review inventory problem with stochastic demand, random price and quotation cost. It differs from the traditional inventory model in that at the beginning of each period, a decision is made whether to pay the quotation cost to get the price information. If it is decided to request a price quote then the next decision is on how many units to order; otherwise, there will be no order. An (r, S1, S2) policy with r < S2, S1 <= S2 is proposed for the problem with two prices. It prescribes that when the inventory is less than or equal to r, the price quotation is requested; if the higher price is quoted, then order up to S1, otherwise to S2. There are two cases, r < S1 or S1 <= r. In the first case, every time the price is quoted, an order is placed. It is a single reorder point two order-up-to levels policy that can be considered as an extension of the (s, S) policy. In the second case, S1 <= r, it is possible to “request a quote but not buy” if the quoted price is not favorable when the inventory is between S1 and r. Two total cost functions are derived for the cases r < S1 <= S2 and S1 <= r < S2 respectively. Then optimization algorithms are devised based on the properties of the cost functions and tested in numerical study. The algorithms successfully find the optimal policies in all of the 135 test cases. Compared to the exhaustive search, the running time of the optimization algorithm is reduced significantly. The numerical study shows that the optimal (r, S1, S2) policy can save up to 50% by ordering up to different levels for different prices, compared to the optimal (s, S) policy. It also reveals that in some cases it is optimal to search price speculatively, that is with S1 < r, to request a quote but only place an order when the lower price is realized, when the inventory level is between S1 and r.

This thesis studies a single item periodic review inventory problem with stochastic demand, random price and quotation cost. It differs from the traditional inventory model in that at the beginning of each period, a decision is made whether to pay the quotation cost to get the price information. If it is decided to request a price quote then the next decision is on how many units to order; otherwise, there will be no order. An (r, S1, S2) policy with r < S2, S1 <= S2 is proposed for the problem with two prices. It prescribes that when the inventory is less than or equal to r, the price quotation is requested; if the higher price is quoted, then order up to S1, otherwise to S2. There are two cases, r < S1 or S1 <= r. In the first case, every time the price is quoted, an order is placed. It is a single reorder point two order-up-to levels policy that can be considered as an extension of the (s, S) policy. In the second case, S1 <= r, it is possible to “request a quote but not buy” if the quoted price is not favorable when the inventory is between S1 and r. Two total cost functions are derived for the cases r < S1 <= S2 and S1 <= r < S2 respectively. Then optimization algorithms are devised based on the properties of the cost functions and tested in numerical study. The algorithms successfully find the optimal policies in all of the 135 test cases. Compared to the exhaustive search, the running time of the optimization algorithm is reduced significantly. The numerical study shows that the optimal (r, S1, S2) policy can save up to 50% by ordering up to different levels for different prices, compared to the optimal (s, S) policy. It also reveals that in some cases it is optimal to search price speculatively, that is with S1 < r, to request a quote but only place an order when the lower price is realized, when the inventory level is between S1 and r.