ANSWER FOR EXERCISE IN ROSS’s BOOK (CHAPTER 20, page 721-722, Question 11, 12 & 20)
11. The carrying costs are the average inventory times the cost of carrying an individual unit, so: Carrying costs = (2,500/2)($9) = $11,250 The order costs are the number of orders times the cost of an order, so: Order costs = (52)($1,700) = $88,400 The economic order quantity is: EOQ = [(2T × F)/CC]1/2 EOQ = [2(52)(2,500)($1,700)/$9]1/2 EOQ = 7,007.93 The firm’s policy is not optimal, since the carrying costs and the order costs are not equal. The company should increase the order size and decrease the number of orders. 12. The carrying costs are the average inventory times the cost of carrying an individual unit, so: Carrying costs = (300/2)($41) = $6,150 The order costs are the number of orders times the cost of an order, so: Restocking costs = 52($95) = $4,940 The economic order quantity is: EOQ = [(2T × F)/CC]1/2 EOQ = [2(52)(300)($95)/$41]1/2 EOQ = 268.87 The number of orders per year will be the total units sold per year divided by the EOQ, so: Number of orders per year = 52(300)/268.87 Number of orders per year = 58.02 The firm’s policy is not optimal, since the carrying costs and the order costs are not equal. The company should decrease the order size and increase the number of orders. 20. Since the company sells 700 suits per week, and there are 52 weeks per year, the total number of suits sold is: Total suits sold = 700 × 52 = 36,400 And, the EOQ is 500 suits, so the number of orders per year is: Orders per year = 36,400 / 500 = 72.80 To determine the day when the next order is placed, we need to determine when the last order was placed. Since the suits arrived on Monday and there is a 3 day delay from the time the order was placed until the suits arrive, the last order was placed Friday. Since there are five days between the orders, the next order will be placed on Wednesday Alternatively, we could consider that the store sells 100 suits per day (700 per week / 7 days). This implies that the store will be at the safety stock of 100 suits on Saturday when it opens. Since the suits must arrive before the store opens on Saturday, they should be ordered 3 days prior to account for the delivery time, which again means the suits should be ordered in Wednesday.