Problem: The Grocery Store Organization (GSO) is going to sell a new product in their stores. They expect the warehouse in Montreal to have an annual demand of about 8000 cases of this product to process. We assume that the demand will be normally distributed throughout the 52 weeks of the year. Based on similar products in the warehouse, they estimate the inventory holding cost to be $5 per case per year. GSO's supplier sells each case of this product for $35 and guarantees a 2 week delivery delay. They charge an ordering cost of $120/order. If we estimate that the average weekly standard deviation of demand will be 9.5 and we want a service level of 90%, help GSO choose between using a fixed-order-quantity inventory model (Q-model) or a fixed-time-period inventory model (P-model).
a) If a Q-model is used to manage the inventory, determine the economic quantity to order and the reorder point.
b) If the warehouse chooses instead to order this product every Wednesday, what is the quantity that needs to be ordered if there are 187 cases in inventory when they place the order?
c) Compare the costs (annual inventory holding cost, annual ordering cost and total annual cost including purchase cost) for these two models. Which model should they choose and why? Note that the annual inventory holding cost is found by multiplying the inventory holding cost by the average annual inventory level.