Problem Statement: Continuous Review Inventory System

A retailer keeps an inventory for its bestselling SKU. The weekly demand rate for the SKU is horizontal and random. The mean value of demand rate is 200 units/week, and its standard deviation is 25 units/week. The order's shipment lead-time is 2 weeks. We assume there are 50 weeks in a year. The ordering cost is $500/order. The inventory holding cost is $15 per unit per year.

Suppose that the manager of the retailer uses the Continuous Review (Q) system to manage the inventory. The retailer aims at the cycle service level of 95%. Please answer the following questions.

Scenario 1.

a. Suppose that the manager chooses the order quantity with the purpose to minimize annual total costs associated with the cycle inventory. To achieve that goal, the manager should set the order quantity Q= ____ units.

(Please round your answer to whole number. Rounding up is preferred.)

b. Continue with Scenario 1 and use the Q value derived from the preceding question. On average, the total annual ordering cost is: $____.

(Please round your answer to keep one decimal place after the dot.)

Scenario 2.

c. Answer this question independent of Scenario 1. Suppose that the retailer has traditionally been using the order quantity of Q=572/order. The annual total costs for holding cycle inventories and safety stock is $____.

(Please round your answer to keep one decimal place after the dot.)