**Fixed- Time-Period Model**

With a fixed-time-period model. inventory is counted at fixed intervals. such as every week or every month. Counting inventory and placing orders on a periodic basis are desirable for those situations when vendor make routine visits to customers and take "orders for their complete line of products, or when buyers want to combine orders to save on transportation costs. Other firms operate on a fixed time period to facilitate planning their victory

count; for example. Distributor X calls every two weeks and employees therefore know that all of Distributor X's products must be counted at that time. A convenient time interval can be chosen, or if only one item is involved it can be estimated by using the EOQ formula. Once the EOQ for the item is calculated, we can determine how many times a year we should place the order. from which we can then determine the period or interval between orders. For example. if the annual demand is 1,200 units and he EOQ is 100 units. then we know that we will place 12 orders throughout the year, and that there is a one-month interval between orders. With a fixed-time-period model. there is usually a ceiling or par inventory that is established for each item. As seen in Exhibit 16.5, the difference between the par value and the quantity on hand when the count is taken is the amount ordered, which will vary from period to period, depending on the actual usage (e.g .. Ql, Q2, and Q3, in Exhibit 16.5). Here, negative inventory, as seen in the third cycle in Exhibit 16.5, is treated as a backorder, which must be filled. Thus, in this model the time interval between orders remains fixed, but the quantity ordered varies, as compared to the fixed-order-quantity model where just the reverse is true: the order quantity remains fixed, but the time interval varies.

**Quantity-Discount Model**

The quantity-discount model takes into consideration the fact that the purchase cost of an item can vary with the order size. There are two types of quantity discounts: those given on an incremental basis and those given for all units. With the incremental approach. the quantity discount only applies to those units above a certain level. For example. the cost of a product is $65.00 per unit for quantities between I and 100 and 560.00 per unit for quantities over 100 units. We determine that we want to buy this product in quantities of 250 units at a time. ith the incremental approach, we would pay $65.00 for the first 100 units and $60.00 for the remaining 150 units. With tke all-units approach, which is presented here in detail, we would pay $60.00 apiece for all 250 units. Thus. the unit cost is determined by the size of the purchase order. To determine the optimal quantity to order with this model, we first calculate the EOQ or each unit cost. (Note: If using Has a holding cost instead of i. then H will vary along

with C.) If the resulting EOQs are all feasible, that is, the EOQs fall within their respective quantity ranges, then we select the EOQ that is a associated with the lowest unit cost. However, as is more often the case, some of the EOQs may not be feasible (i.e .. the quantity does not tall within the feasible unit-cost range). In these situations. we first calculate the total cost for each unit cost at the EOQ or EOQs where it is feasible. Where it is not feasible, we calculate the total cost at the minimum quantity where the respective unit cost is first applicable. These total costs are then compared and the quantity or EOQ associated \~ith the lowest total cost is the order quantity that is selected. Procedurally, the largest order quantity (lowest unit price) is solved first: if the resulting Q is valid r feasible, that is the answer. If not, the next largest order quantity (second lowest price) is derived. If that is feasible, the total cost of this Q is compared to the total cost of using the order quantity at the price break above, and the lowest total cost determines the optimal Q..