Self-Study Assignment

Transcription

1 Self-Study Assignment Refer to the textbook: 1. Inventory (Chapter 13) a) Solved problem #1 b) Solved problem #3 c) Solved problem #5 d) Solved problem #6 2. Aggregate planning (Chapter 14) a) Solved problem #1 3. Resource planning (Chapter 15) a) Solved problem #1 b) Solved problem #2 4. MPS (Supplement G) a) Solved problem (page 790)

2 Inventory Management Self-Study Assignment 1. George uses 1,500 per year of a certain subassembly that has an annual holding cost of $45 per unit. Each order placed costs George $150. He operates 300 days per year and has found that an order must be placed with his supplier 6 working days before he can expect to receive that order. For this subassembly, find e) Economic order quantity (EOQ) f) Annual holding cost g) Annual ordering cost h) Reorder point (R) 2. Stephanie is attempting to perform an inventory analysis on one of her most popular products. Annual demand for this product is 5,000 units; carrying cost is $50 per unit per year; order costs for her company typically run nearly $30 per order; and lead time average 10 days. (Assume 250 working days per year.) b) What is EOQ? c) What is the average inventory? d) What is the optimal number of orders per year? e) What is the optimal number of working days between orders? f) What is the total annual inventory cost (carrying cost + ordering cost)? g) What is the reorder point (R)? 3. Based on available information, lead time demand for CD-ROM drives averages 50 units (normally distributed), with a standard deviation of 5 drives. Management wants a 97% service level. c) What value of Z should be applied? d) How many drives should be carried as safety stock? e) What is the appropriate reorder point (R)?

3 4. An ophthalmologist s office operates 52 weeks per year, 6 days per week and uses a continuous review inventory system. It purchases disposable contact lenses for $11.70 per pair. The following information is available about these lenses. Demand = 90 pairs/week Order cost = $54/order Annual holding cost = 27% of cost Desired cycle-service level = 80% Lead time = 3 weeks (18 working days) Standard deviation of weekly demand = 15 pairs Current on-hand inventory is 320 pairs, with no open orders or backorders. a) What is EOQ? What should be the average tune between orders (in weeks)? b) What should R be? c) An inventory withdrawal of 10 pairs was just made. Is it time to reorder? d) The store currently uses a lot size of 500 units (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? e) What would be the annual cost saved by shifting from the 500-unit lot size to the EOQ? 5. Suppose that the ophthalmologist s office in Problem 4 uses a P system instead of a Q system. The average daily demand is 15 pairs (90/6), and the standard deviation of daily demand is pairs (15/ 6). a) What P (in working days) and T should be used to approximate the cost trade-off of the EOQ? b) How much more safety stock is needed than with a Q system? c) It s time for the periodic review. How much should be ordered? (current on-hand inventory is 320 pairs, and a withdrawal of 10 pairs was just made) 6. Weiss s paint store uses an (s, S) inventory system to control its stock levels. For a particularly popular white latex paint, historical data show that the distribution of 4 weeks demand is approximately normal, with mean 28 and standard deviation 8. Replenishment lead time for this paint is about 14 weeks. Each can of paint costs the store $6. Fixed costs of replenishment are $15 per order, and holding costs are based on a 30 percent annual rate of cost. a) Determine appropriate values of (s, S). Assume a 95% service level.

4 Solutions for Inventory Management: 1 (a) Economic Order Quantity: , 150 Q = = = 100 units H 45 where: D = period demand, S = setup or order cost, H = holding cost QH (b) Holding cost = = = $2, DS (c) Order cost = = = $2, Q 100 (d) Reorder point: 1500, Reorder point = demand during lead time = units day 6 days = 30 units (a) Economic Order Quantity: , 30 Q = = = H 50. or 78 units where: D = period demand, S = setup or order cost, H = holding cost 78 (b) Average inventory = = 39 units 2 Demand 5000, (c) Number of orders per year = = = 641. or 64 orders EOQ 78 (d) Assuming 250 business days per year, the optimal number of business days between orders is given by: 250 Optimal number of days = = 391. days 64 (e) (f) Total cost = order cost + holding cost DS QH 5, = + = + Q = 1, , 950 = $3, Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number. If an EOQ of is used, the order and carrying costs calculate to $1, for a total cost of $3, Reorder point: 5, 000 units Reorder point = demand during lead time = 10 days = 200 units 250 days This is not to say that we reorder when there are 200 units on hand (as there never are). The ROP indicates that orders are placed several cycles prior to their actual demand.

5 3 (a) Z = 188. (b) Safety Stock = Zσ = 188. ( 5) = 94. drives (c) ROP = = drives 4. (a) Economic order quantity d = 90 / week D = 4,680 S = $54 Price = $11.70 H=27%($11.70) = $3.159 EOQ = H = 2(4680)(54) = 160,000 = 400 pairs Time between orders, in weeks Q 400 = = years = 4.44 weeks D 4680 (b) Reorder point, R R= demand during protection interval + safety stock Demand during protection interval = d L = 90 * 3 = 270 pairs Safety stock = zσ L When the desired cycle-service level is 80%, z = σ L = σ t L =15 3 = 26 Safety stock = 0.84 * 26 = or about 22 pairs R = = 292 (c) Initial Inventory Position = OH + SR BO = = 310. Since inventory position remains above 292, it is not yet time to place an order. (d) Annual holding cost Q 500 H = (27%)($11.70) 2 2 Annual ordering cost D 4680 S = $54 Q 500 = $ = $ At the EOQ, these two costs are equal. When Q = 500, the annual holding cost is larger than the ordering cost, therefore Q is too large. Total costs are $ $ = $1,295.19

6 (e) Annual holding cost Q 400 H = (27%)($11.70) 2 2 Annual ordering cost D 4680 S = $54 Q 400 = $ = $ Total costs at EOQ: = $1,263.60, which is $31.59 less than when order quantity is 500 pairs. 5. Ophthalmologist s office with a P system (a) Referring to Review Problem 4, the EOQ is 400 pairs. When the demand rate is 15 per day, the average time between order is (400/15) = or about 27 days. The lead time is 3 weeks 6 days per week = 18 days. If the review period is set equal to the EOQ s average time between orders (27 days), then the protection interval (P + L) = ( ) = 45 days. For an 80% cycle-service level z = 0.84 σ P + L = σ t P + L σ P+L = = Safety stock = zσ = 0.84(41.08) = or 35 pairs P+L T = Average demand during the protection interval + Safety stock T = (15*45) + 35 = 710 (b) In problem 4, the Q system required a safety stock of 22 pairs to achieve an 80% cycle-service level. Therefore, the P system requires a safety stock which is larger by (35 22) = 13 pairs (c) From Review Problem 4, inventory position, IP = 310. The amount to reorder is T IP = = (a) Let s ignore the unfilled demand cost and assume the service level be 95%. Therefore, D=28 52/4=364, S=15, h=0.3 6= EOQ*= = 77 h s = 28 14/ = S = = 200