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### DSC HW 2

Course: DSC 335, Spring 2012
School: Oregon
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Word Count: 591

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Lowery HW Sarah #2 5. a) What is Dot Coms optimal order quantity? EOQ = = = 400 books b) What is the optimal number of orders per year? (32,000)/400 = 800 orders c) What is the optimal interval (in working days) between orders? 300/80 = 3.75 days d) What is demand during the lead time? =dL = (5days)(32,000/300) = 533 books e) What is the reorder point? =dL + SS = 533 + 0 = 533 books 7. a) What is the EOQ? What...

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Lowery HW Sarah #2 5. a) What is Dot Coms optimal order quantity? EOQ = = = 400 books b) What is the optimal number of orders per year? (32,000)/400 = 800 orders c) What is the optimal interval (in working days) between orders? 300/80 = 3.75 days d) What is demand during the lead time? =dL = (5days)(32,000/300) = 533 books e) What is the reorder point? =dL + SS = 533 + 0 = 533 books 7. a) What is the EOQ? What would be the average time between orders (in weeks)? d = 90/week D = 4,680 S = \$54 Price = \$11.70 H = 27% (11.70) = \$3.159 EOQ = = = = 400 bags Time between orders, in weeks: = = 0.08547 years = 4.44 weeks b) What should R be? Reorder point, R = demand during protection interval + safety stock R = dL = 90*3 = 270 bags SS = 0.84 * 26 = 21.82 or about 22 bags R= 270 + 22 = 292 c) An inventory withdrawal of 10 bags was just made. Is it time to reorder? Initial inventory position = OH + SR BO = 320 + 0 0 320 10 = 310. Inventory position remains above 292, so it is not time to place an order yet. d) The store currently uses a lot size of 500 bags (i.e., Q = 500). What is the annual holding cost of this policy? Annual ordering cost? Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large? Annual holding cost: Annual ordering cost: At the economic ordering quantity, the two costs are the same. When Q is 500 though, the annual holding cost is much larger than the ordering cost. This means that Q is far too large. Total costs are now \$1,295.19. e) What would be the annual cost saved by shifting from the 500-bag lot size to the EOQ? Annual holding cost: Annual ordering cost: quantity of Total costs are now \$1, 263.60, which is \$31.59 less than the previous order 500 bags. 1. (EOQ model) You (the buyer) manage the inventory of an item. Your forecast for the next years demand is 1,000 units for the whole You year. pay the supplier \$20 for each unit. It costs \$5 ordering cost to place an order, and the annual inventory holding cost for a unit is 20% of its purchase cost. a) Under the current policy, your order size is Q=100. What are the total (sum of) ordering (setup) costs and inventory holding costs over the next year? D = 1,000 /yr. c = \$20 /unit s = \$5 ordering cost to place order i = 20% H = (.20)(20) = 4 Q = 100 units Annual setup/ordering costs = Annual holding costs = b) If you use EOQ model to manage inventory. What is the EOQ? What is the corresponding total cost (including ordering and inventory holding costs) for the whole year? EOQ = Corresponding total costs (ordering and inventory holding costs) for the year: Annual ordering costs + Annual holding costs: += 2. (Continuous review system, with safety stock) A factory produces a part to supply its customers. The factory faces a random demand from its customers. The weekly demand has a normal distribution, with the expectation (mean) of 300 units and the standard deviation of 90 units. The production lead time is 4 weeks (thats it takes 4 weeks to finish a production run). The production manager uses the continuous review system to plan production. a) What is the safety stock necessary to achieve the service level of 98%? What is the corresponding reorder point? dbar = 300 units S.D. = 90 units L = 4 weeks *Uses continuous review system SS = Z ROP = (dbar)(L) + SS = (300)(4) +370 = 1,570 units b) Suppose the production manager must reduce the safety stock in the above question by 50%, by lowering the service level (while all other model parameters are unchanged). What will be the new service level (i.e., the probability of no stockout) that attains the reduced safety stock? SS = Z (90)(2) = (370/2) = 180Z = 185 Z=1.027 New service level needs to be 84% in order to reduce the safety stock by 50%.
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