???? 2104502 Production and Operations Management ?????? ???? ?????????? ???? 5370377821 Homework – EOQ 1. A large automobile repair shop installs about 1,250 mufflers per year, 18 percent of which are for imported cars. All the imported-car mufflers are purchased from a single local supplier at a cost of $18. 50 each. The shop uses a holding cost based on a 25 percent annual interest rate. The set up cost for placing an order is estimated to be $28. ????????????? mufflers ???????????? 1250 ?? ?? /?? ? imported-car mufflers(D) ???????????? 18% ??? mufflers?????? = 0. 18*1250 = 225 ?? ?? /?? ???? imported-car mufflers(c) ??????? 18. 50$/?? ?? annual interest rate (I) = 25%?????????????? ?/?? holding cost(h) = I*c = 0. 25*18. 50 = 4. 625$/?? ?? /?? set up cost (K)= 28$/???? ? a. Determine the optimal number of imported-car mufflers the shop should purchase each time an order is placed, and the time between placement of orders. optimal number of imported-car mufflers (Q) = 2???? ? = 2? 28? 225 4. 625 = 52. 195 ? 53 ?? ?? /??? b. If replenishment lead time is six weeks, what is the reorder point based on the level of on-hand inventory? lead time = 6 weeks ??????????????????????? 52. 195 = 4. 31 ???? /?? ? ?? ? ? 1 Cycle (T) = 1 4. 31 225 = 0. 23 ?? = 12. 06 ??????? 6? 52. 195 ?????? 6 ??????? ???? ????? ??? = 12 . 06 = 25. 967 ? 26?? ?? ?????? ?? ???????????????????????????????????? 26?? ?? ? ? c. The current reorder policy is to buy imported-car mufflers only once a year. What are the additional holding and setup costs incurred by this policy? Reorder = 1 ?? holding cost(h) = = 520. 31$/?? 2 set up cost (K)= 28$/?? ?????? holding and setup costs = 548. 31$/?? ? 2. A local machine shop buys hex nuts and molly screws from the same supplier.
The hex nuts cost 15 cent each and the moll screws cost 38 cents each. A setup cost of $100 is assumed for all orders. This includes the costs of tracking and receiving the orders. Holding costs are based on a 25 percent annual interest rate. The shop uses an average of 20,000 hex nuts and 14,000 molly screws annually. ????????????? hex nuts(Dh) = 20,000 ?? ?? /?? molly screws(Dm) = 14000 ?? ?? /?? ???? hex nuts(Ch) = 15 cent/?? ?? =0. 15 $/?? ?? ???? molly screws (Cm) = 38 cent/?? ?? =0. 38 $/?? ?? annual interest rate (I) = 25%?????????????? ?/?? holding cost??? hex nuts (hh) = I*c = 0. 5*0. 15 = 0. 0375 $/?? ?? /?? holding cost??? molly screws (hm) = I*c = 0. 25*0. 38 = 0. 095 $/?? ?? /?? set up cost (K)= 100 $/???? ? a. Determine the optimal size of the orders of hex nuts and molly screws, and the optimal time between placement of orders of these two items. optimal number of hex nuts (Qh) = 2???? ? 1? 225 ? 4. 625 = 2? 100 ? 20000 0. 0375 = 10327. 95 ? 10328 ?? ?? /??? optimal number of molly screws (Qm) = 10328 5429 2???? ? = 2? 100 ? 14000 0. 095 = 5428. 96 ? 5429 ?? ?? /??? optimal time of hex nuts (Th) = 20000 = 0. 5164 ?? /???? = 26. 8528 ??????? /???? ? optimal time of molly screws (Tm) = 14000 = 0. 3878 ?? /???? = 20. 1648 ??????? /???? ? ? b. If both items are ordered and received simultaneously, the setup cost of $100 applies to the combined order. Compare the average annual cost of holding and setup if these items are ordered separately; if they are both ordered when the hex nuts would normally be ordered; and if they are both ordered when the molly nuts would normally be ordered. If ordered separately; hex nuts holding cost(h) = 0. 0375 ? 10328 set up cost (K)= 10328 = 193. 65$/?? total cost hex nuts = 387. 3$/?? olly screws holding cost(h) = 0. 095? 5429 2 100 ? 20000 = 193. 65 $/?? set up cost (K)= 5429 = 257. 87$/?? total cost molly screws = 515. 75$/?? ?????? total = 515. 74 $/?? ? If both ordered when the hex nuts would normally be ordered; ????????? 0. 5164 ?? /???? ? ? number of hex nuts (Qh) = 10328 ?? ?? /??? number of molly screws (Qm) = 14000*0. 5164 =7229. 6 ? 7230 ?? ?? /??? set up cost (K)= hex nuts 100 ? 20000 10328 2 100 ? 14000 = 257. 87 $/?? = 193. 65$/?? = 193. 65 $/?? holding cost(h) = molly screws 0. 0375 ? 10328 2 0. 095? 7230 holding cost(h) = = 343. 425 $/?? Total holding cost(h) = 193. 65 + 343. 425 = 537. 075$/?? Total cost = 193. 65 + 537. 075 = 730. 725 $/?? If both ordered when the molly nuts would normally be ordered; ????????? 0. 3878?? /???? ? ? number of hex nuts (Qh) = 20000*0. 3878=7756 ?? ?? /??? number of molly screws (Qm) = 5429 ?? ?? /??? set up cost (K)= hex nuts 100 ? 14000 5429 = 257. 87$/?? = 145. 425 $/?? holding cost(h) = molly screws 0. 0375 ? 7756 2 0. 095? 5429 holding cost(h) = = 257. 878 $/?? 2 Total holding cost(h) = 145. 425 + 257. 878 = 403. 303 $/?? Total cost = 257. 878+403. 303 = 661. 181 $/??
