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MGNT 3430: Operations Management Fall 2014 Homework 10 Answers Q8 (p. 337). At Dot Com, a large retailer of popular books, demand is constant at 32, 000 books per year. The cost of placing an order to replenish stock is $10, and the annual cost of holding is $4 per book. Stock is received 5 working days after an order has been placed. No backordering is allowed. Assume 300 working da
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  MGNT 3430: Operations Management Fall 2014Homework 10 Answers Q8 (p. 337).  At Dot Com, a large retailer of popular books, demand is constant at 32 , 000 booksper year. The cost of placing an order to replenish stock is $10, and the annual cost of holding is$4 per book. Stock is received 5 working days after an order has been placed. No backordering isallowed. Assume 300 working days a year.a. What is Dot Com’s economic order quantity?b. What is the optimal number of orders per year?c. What is the optimal interval (in working days) between orders?d. What is the demand during the lead time?e. What is the reorder point?f. What is the inventory position immediately after an order has been placed? Answer.  Dot Coma. EOQ  =   2 DS H   =   2(32 , 000)($10)$4= 400 booksb. Optimal number of orders per year is DQ  = 32 , 000400 = 80 ordersc. Optimal time between orders is QD  = 40032 , 000 = 0 . 0125 yearsor 0 . 0125 years × 300 days/year = 3 . 75 daysd. Demand during the lead time¯ d  = 32 , 000 booksyear  × 1 year300 days = 32 , 000 books300 days L  = 5 days¯ dL  =  32 , 000300  (5) = 533 bookse. Demand and lead time are constraint - no need for safety stock. Reorder point is¯ dL  = 533 booksf. Inventory position (IP)IP = OH + SR − BO= 533 + 400 − 0= 933 books  Q9 (p. 337-338).  Leaky Pipe, a local retailer of plumbing supplies, faces demand for one of itsSKUs at a constant rate of 30 , 000 units per year. It costs Leaky Pipe $10 to process an order toreplenish stock and $1 per unit per year to carry the item in stock. Stock is received 4 workingdays after an order is placed. No backordering is allowed. Assume 300 working days a year.a. What is Leaky Pipe’s economic order quantity?b. What is the optimal number of orders per year?c. What is the optimal interval (in working days) between orders?d. What is the demand during the lead time?e. What is the reorder point?f. What is the inventory position immediately after an order has been placed? Answer.  Leaky Pipe, Inc.a. EOQ  =   2 DS H   =   2(30 , 000)($10)$1= 775 unitsb. Optimal number of orders per year is DQ  = 30 , 000775 = 39 ordersc. Optimal time between orders is QD  = 77530 , 000 = 0 . 02583 yearsor 0 . 02583 years × 300 days/year = 7 . 75 daysd. Demand during lead time is¯ dL  =  30 , 000300  (4 days) = 400 unitse. Demand and lead time are constraint - no need for safety stock. Reorder point is¯ dL  = 400 = 400 unitsf. Inventory position (IP)IP = OH + SR − BO= 400 + 775 − 0= 1 , 175 units  Q10 (p. 338).  Sam’s Cat Hotel operates 52 weeks per year, 6 days per week, and uses a continuousreview inventory system. It purchases kitty litter for $11 . 70 per bag. The following information isavailable about these bags. ã  Demand: 90 bags/week ã  Order cost: $54/order ã  Annual holding cost: 27 percent of cost ã  Desired cycle-service level: 80 percent (so  z   = 0 . 84) ã  Lead time: 3 weeks ã  Standard deviation of   weekly   demand: 15 bags ã  Current on-hand inventory is 320 bags, with no open orders or backorders.a. What is the EOQ? What should be the average time between orders (in weeks)?b. What should  R  be?c. An inventory withdrawal of 10 bags was just made. Is it time to reorder? Answer.  Sam’s Cat Hotela. Economic order quantity¯ d  = (90 bags/week)(52 weeks/year) = 4 , 680 bags/year S   = $54Value of each bag = $11 . 70 H   = (27%)($11 . 70) = $3 . 16 EOQ  =   2 DS H   =   2(4 , 680)(54)3 . 16 = 400 bags TBO EOQ  =  EOQD  = 4004 , 680 = 0 . 08547 yearsb. Reorder point, R R  = Average demand during lead time + Safety stock R  = ¯ dL + zσ d √  L = 90 × 3 + 0 . 84 × 15 ×√  3 = 270 + 22 = 292 bagsc. Initial inventory position =  OH  + SR − BO  = 320+0 − 0 = 320. When 10 bags are withdrawn,inventory position gets equal to 320 − 10 = 310 bags. Because inventory position remainsabove 292, it is not yet time to place an order.  Q26 (p. 340).  Osprey Sports stocks everything a musky fisherman could want in the Great NorthWoods. A particular musky lure has been very popular with local fishermen as well as those who buylures on the Internet from Osprey Sports. The cost to place orders with the supplier is $30/order;the demand averages 4 lures per day, with a standard deviation of 1 lure; and the inventory holdingcost is $1 . 00/lure/year. The lead time from the supplier is 10 days, with a standard deviation of 3days. It is important to maintain a 97 percent cycle-service level to properly balance service withinventory holding costs (i.e.,  z   = 1 . 88). Osprey Sports is open 350 days a year to allow the ownersthe opportunity to fish for musses during the prime season. The owners want to use a continuousreview inventory system for this item.a. What order quantity should be used?b. What reorder point should be used?c. What is the total annual cost for this inventory system? Answer.  Osprey Sportsa. The economic order quantity D  = 4 × 350 = 1 , 400 lures per year EOQ  =   2 DS H   =   2(1 , 400)($30)$1 =   84 , 000 = 289 . 83  290 luresb. Safety stock σ dLT   =   ¯ Lσ 2 d  + ¯ d 2 σ 2 LT   =   (10)(1) 2 + (4) 2 (3) 2 = 12 . 41 luresSafety stock = 1 . 88(12 . 41) = 23 . 33 or 23 luresReorder point¯ d ¯ L + Safety stock = (4)(10) + 23 = 63 luresc. The total annual cost for this continuous review system is C   =  Q 2  H   +  DQ  S   + ( H  )(Safety stock)=  2902  +  1 , 400290  $30 + ($1)(23)= $312 . 83
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