Q* is the EOQ Book equations R annual demand hholding cost per unit per year v ~ purchasing cost per unit K~ ordering cost per order . Q quantity ordered at a time It follows that: Purchasing cost per year= v x R Holding cost per year= h x Q/2 Ordering cost per year= K x R/Q Q* = 2xKxR h Lecture Notes equations let D be the avg. demand per unit time let C be the per-unit cost (to you) of inventory let h be the inventory holding rate (watch time units) let H be hC let S be the ordering cost (incl. shipping) We write total cost as follows Total Cost Ordering Costs (or setup cost) + Holding Costs TC = Number of Orders Placed a Year * S + Average Inventory * hC Annual Demand (D) * S + TC = Q (quantity ordered each time) *nc then take the derivative wrt Q and set it equal to zero to find the optimum order quantity (EOQ): EOQ= 2.D.S H Question 2. (11 points) Part A. A beer distributor sells 500 cases of regular 12-oz. Budweiser per week for 50 weeks each year - assume that there are 50 weeks in a year - from its warehouse in Central Austin. The distributor currently orders a one-week supply of 500 cases at the beginning of each week from a supplier at a purchase cost of $8 per case. They also pay a fixed cost of $100 for each delivery. The beer distributor estimates its annual per-case inventory holding cost (cost of capital, insurance, etc.) at 25 percent of purchase cost. (a) What is the distributor's annual ordering plus holding costs (in $)? (1) (b) What is the distributor's ordering plus holding costs (in $) per case of beer? Round up or down to two significant figures after the decimal point. (c) How long (in weeks) on average does a case of beer sit on the distributor's shelf before it is sold? Do not round up or down. (1) (1) (d) What order size would you recommend to the beer distributor? Choose the nearest integer. (1) (e) For the distributor, what is the minimum possible annual cost (in $) of ordering and holding? Choose the nearest integer. (1) (f) For the distributor, what is the minimum possible cost (in $) of ordering and holding per case of beer? Round up or down to two significant figures after the decimal point. (1) (g) Consider the reduction in the cost of ordering and holding per case of beer if the distributor switches to the EOQ policy. Is it More or Less than 35%? (1) Part B. A consultant recommends that the same beer distributor replace the Central Austin warehouse with two smaller and identical warehouses - one in north Austin and the other in South Austin. The motivation is to be closer to customers. The current demand of 500 cases per week would be split evenly between the two smaller warehouses and each new warehouse would operate independently. Each new warehouse would face the same costs as the current warehouse: purchase cost of $8 per case of beer, fixed cost of $100 for each delivery from the supplier, and annual per-case inventory holding cost (cost of capital, insurance, etc.) at 25 percent of purchase cost. Furthermore, assume that both new warehouses would use the EOQ policy. Suppose that the distributor follows the consultant's recommendation and ends up operating two warehouses. (h) What would be the EOQ (in cases) for the North Austin warehouse? Choose the nearest integer. (1) (i) What would be the (average) number of deliveries to the South Austin warehouse by the supplier every year? Choose the nearest integer. (1) (j) How much (in $) on average would the distributor have to pay per year for deliveries by the supplier? Choose the nearest hundred (= a multiple of 100). (k) For the distributor, what would be the annual ordering plus holding costs ($)? Choose the nearest integer. (1) (1)