Chapter 12 Inventory Management Answers Part 5

156) Clement Bait and Tackle has been buying a chemical water conditioner for its bait (to help keep its baitfish alive) in an optimal fashion using EOQ analysis. The supplier has now offered Clement a discount of $0.50 off all units if the firm will make its purchases monthly or $1.00 off if the firm will make its purchases quarterly. Current data for the problem are: D = 720 units per year; S = $6.00, I = 20% per year; P = $25. a. What is the EOQ at the current behavior? b. What is the annual total cost, including product cost, of continuing their current behavior? c. What are the annual total costs, if they accept either of the proposed discounts? d. At the cheapest of the total costs, are carrying costs equal to ordering costs? Explain. Answer: (a) Q* = (b) TC = 720 ∙ 25 + 2 720 6 = 41.57 or 42 units at a time. .2 25 720 41.57 ∙6+ ∙ .2 ∙ 25 = 18000 + 103.92 = 103.92 + $18,207.85 11 .57 2 (c) Placing orders on a monthly basis implies twelve orders per year where Q = 720 / 12 = 60. Placing orders on a quarterly basis implies four orders per year where Q = 720/4 = 180. (d) They are not; accepting the discount requires an order quantity that is not EOQ. Purchasing 42 units at a time led to setup costs and holding costs of $104 each. With the more favorable discount, setup costs are $24 while holding costs are $432.. Quantity Unit Price, P Q* (Square root formula) Order Quantity Holding cost Setup cost Product cost Total cost, Tc Range 1 1-59 $25 Range 2 60-179 $24.5 Range 3 179+ $24 41.57 41.57 41.99 60 42.43 180 103.92 103.93 18,000.00 72 147 17,640 24 432 17,280 $18,207.85 $17,859 $17,736 Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-6 42 157) The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost. What is the optimal order quantity, given the following price breaks for purchasing the item? What price should the firm pay per unit? What is the total annual cost at the optimal behavior? Quantity 1-9 10 - 999 1,000 - 4,999 5,000 or more Price $2.95 per unit $2.50 per unit $2.30 per unit $1.85 per unit Answer: Range 1 and Range 2 are irrelevant, because the EOQ is larger than the upper end of each range. The firm should pay $1.85 per unit by ordering 5000 units at a time. This is above the 2014 EOQ of the next higher price break. Since the firm is not ordering an EOQ amount, ordering costs and carrying costs will not be equal, but total costs are still minimized. Q* (Square root formula) Order Quantity Holding cost Setup cost Unit costs Total cost, Tc Range 3 1805.788 1805.788 Range 4 2013.468 5000 $415.33 $415.33 $23,000.00 $925.00 $150.00 $18,500.00 $23,830.66 $19,575.00 Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-6 43 158) A local artisan uses supplies purchased from an overseas supplier. The owner believes the assumptions of the EOQ model are met reasonably well. Minimization of inventory costs is her objective. Relevant data, from the files of the craft firm, are annual demand (D) =150 units, ordering cost (S) = $42 per order, and holding cost (H) = $4 per unit per year a. How many should she order at one time? b. How many times per year will she replenish her inventory of this material? c. What will be the total annual inventory costs associated with this material? d. If she discovered that the carrying cost had been overstated, and was in reality only $1 per unit per year, what is the corrected value of EOQ? Answer: a. Q* = b. N = 2 150 42 4 = 56.12. She should order 56 units at a time. 150 = 2.67 She should place about 2.67 orders per year. 56.12 c. The inventory costs are $112 for holding and $112 for ordering, or $224 total. d. At the lower value for H, the EOQ will be doubled to 112.25. Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 44 159) The annual demand for an item is 40,000 units. The cost to process an order is $40 and the annual inventory holding cost is $3 per item per year. What is the optimal order quantity, given the following price breaks for purchasing the item? Quantity 1-1,499 1,500 - 4,999 5,000 or more Price $2.50 per unit $2.30 per unit $2.25 per unit a. What is the optimal behavior? b. Does the firm take advantage of the lowest price available? Explain. Answer: a. Purchase 1500 units at a time, paying $2.30 each. b. It is not advantageous to pay $2.25 if that requires ordering 5000 units. The annual cost is $97,820.00 at the $2.25 price versus $95,316.67 annual cost at the $2.30 price. Q* (Square root formula) Order Quantity Range 1 1032.796 1032.796 Range 2 1032.796 1500 Range 3 1032.796 5000 Holding cost Setup cost $1,549.19 $1,549.19 $2,250.00 $1,066.67 $7,500.00 $320.00 Unit costs $100,000.00 $92,000.00 $90,000.00 Total cost, Tc $103,098.39 $95,316.67 $97,820.00 Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-6 45 160) Groundz Coffee Shop uses 4 pounds of a specialty tea weekly; each pound costs $16. Carrying costs are $1 per pound per week because space is very scarce. It costs the firm $8 to prepare an order. Assume the basic EOQ model with no shortages applies. Assume 52 weeks per year, closed on Mondays. a. How many pounds should Groundz order at a time? b. What is total annual cost (excluding item cost) of managing this item on a cost-minimizing basis? c. In pursuing lowest annual total cost, how many orders should Groundz place annually? d. How many days will there be between orders (assume 310 operating days) if Groundz practices EOQ behavior? Answer: a. Q* = b. TC = c. N = 2 4 52 8 = 8. Groundz should order 8 pounds per order. 1 52 4 52 8 4 52 8 ∙8+ 8 ∙ 1 ∙ 52 = 208 + 208 + 416. The firm will spend $416 annually. 2 = 26 .Groundz should order 26 times per year. d. Days between orders will be 310/26 or approximately every 12 working days. Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 46 161) Pointe au Chien Containers, Inc., manufactures in batches; the manufactured items are placed in stock. Specifically, the firm is questioning how best to manage a specific wooden crate for shipping live seafood, which is sold primarily by the mail/phone order marketing division of the firm. The firm has estimated that carrying cost is $4 per unit per year. Other data for the crate are: annual demand 60,000 units; setup cost $300. The firm currently plans to satisfy all customer demand from stock on hand. Demand is known and constant. a. What is the cost minimizing size of the manufacturing batch? b. What is the total cost of this solution? Answer: The cost-minimizing batch size is Q* = 300 + 2 60000 300 4 = 3000 crates. This will cost 3000 ∙ 4 = 6000 + 6000 = $12,000 per year in inventory management costs. 2 Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 162) Holding costs are $35 per unit per year, the ordering cost is $120 per order, and sales are relatively constant at 300 per month. What is the optimal order quantity? What are the annual inventory management costs? Answer: Order size is Q* = annual inventory costs are 2 300 12 120 35 = 157.12 or 157; 157 12 300 12 ∙ 120 + ∙ 35 + 2749.55 + 2749.55 = $5,499.10. 157 12 2 Diff: 2 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 163) An organization has had a policy of ordering 70 units at a time. Their annual demand is 340 units, and the item has an annual carrying cost of $2. The assumptions of the EOQ are thought to apply. For what value of ordering cost would this order size be optimal? Answer: Start with the economic order quantity model, and solve for S. 47 60000 ∙ 3000 70 = 702 2 2(340) S becomes S = = $14.41 2 2 340 Diff: 3 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 164) Joe's Camera shop has a favorite model that has annual sales of 145. The cost to place an order to replenish inventory is $25 per order, and annual inventory costs are $20. Assume the store is open 350 days per year. a. What is the optimal order size? b. What is the optimal number of orders per year? c. What is the optimal number of days between orders? d. What is the annual inventory cost? Answer: a. The optimal order size is Q* = 2 145 25 20 = 19.04, or approximately 19 units. b. The optimal number of orders per year is N = 145 / 19.04 = 7.62 or 8 orders. c. The optimal number of days between orders is 350/7.62 = 45.9 days. d. The annual inventory cost is 145 19.04 ∙ 25 + ∙ 20 = 190.39 + 190.39 = $380.78 19.04 2 Diff: 3 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 48 165) The inventory management costs for a certain product are S =$8 to order, and H=$1 to hold for a year. Annual demand is 2400 units. Consider the following ordering plans: (a) order all 2400 at one time, (b) order 600 once each quarter, and (c) order 200 once each month. Calculate the annual costs associated with each plan. Plot these values. Is there another plan, cheaper than any of these? Calculate this, and plot it (plot at least five points) on the grid below. Label your graph carefully. Answer: TC2400 = 8 ∙ 1 + 1 ∙ Q* = 2 2400 8 1 2400 600 200 = 1208; TC600 = 8 ∙ 4 + 1 ∙ = 332; TC200 = 8 ∙ 12 + 1 ∙ = 196 2 2 2 = 196 is the cheapest solution. The graph cannot easily show the difference between Q = 196 and Q = 200, but the increase in cost for Q = 600 and Q = 2400 are dramatic. Diff: 3 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3 49 166) Consider a product with a daily demand of 400 units, a setup cost per production run of $100, a monthly holding cost per unit of $2.00, and an annual production rate of 292,000 units. The firm operates and experiences demand 365 days per year. Suppose that management mistakenly used the basic EOQ model to calculate the batch size instead of using the POQ model. How much money per year has that mistake cost the company? Answer: d = 400 units D = 400(365) = 146,000 units S = $100 H = $2.00(12) = $24 p = 292,000 / 365 = 800 units The firm actually ordered EOQ = {[2(146,000)100] / 24} 1/2 = 1103 units. The firm should have ordered POQ = {[2(146,000)100] / [24(1-400/800)]}1/2 = 1560 units. The annual cost of the wrong policy is (146,000/1103)($100) + (1103/2)($24)(1 -400/800) = $13,237 + $6,618 = $19,855. The annual cost of the correct policy is (146,000/1560)($100) + (1560/2)($24)(1 -400/800) = $9,359 + $9,360 = $18,719. Thus, the mistake cost $19,855 - $18,719 = $1,136 per year. Diff: 3 Topic: Inventory models for independent demand AACSB: Analytic Skills Objective: LO12-3, LO12-5 167) Consider a local club selling Christmas trees. If trees cost $15 and sell for $60 with no salvage value, what is the ideal service level? If salvage value is increased to $5, what is the change in service level? Answer: Service level = Cs/(Cs+Co) = 45/(45+15)= .75 or 75% New service level = Cs/(Cs+Co)=45/(45+10) = .82, or an increase of .07 or 7% Diff: 2 Topic: Single-period model AACSB: Analytic Skills Objective: LO12-7 168) Consider a local club selling Christmas trees. If demand is normal with a mean of 200 and a standard deviation of 50, how many trees should the club stock if service level must be greater than 95%? Answer: Z value for 95% service level is 1.65, thus ideal inventory is 200+50(1.65)=282.5=283 trees Diff: 2 Topic: Single-period model AACSB: Analytic Skills Objective: LO12-7 50 169) Demand for gallons of milk is normal with a weekly mean of 50 and standard deviation of 15. How many additional gallons of milk must be stocked to increase the service level from 50% to 80%? Answer: Z for 50% is 0, Z for 80% is .84. Thus the increase in milk stock would be 15(.84) -15(0)= 12.6 = 13 gallons extra Diff: 2 Topic: Single-period model AACSB: Analytic Skills Objective: LO12-7 170) Milk is stocked at the grocery store each week. At the end of the week unsold milk is reduced in price by 70% and always sells for this lower price instantly. If demand for milk is normal with a mean of 200 gallons and standard deviation of 25 gallons, find the price a fresh gallon of milk sells for. Assume a service level of 95% and that the store purchases milk for $2 per gallon. Answer: Service level = Cs/(Cs +Co). If the selling price per gallon is X the salvage price is .3X. Thus Cs=X-2 and Co=2-.3X. Solving .95 =X-2/(X-2+2-.3X) gives X = $5.97, so the milk sells for $5.97 per gallon. Diff: 2 Topic: Single-period model AACSB: Analytic Skills Objective: LO12-7 171) A newspaper boy is trying to perfect his business in order to maximize the money he can save for a new car. Paper sales are normally distributed, with a mean of 100 and standard deviation of 10. He sells papers for $.5 and pays $.30 for them. Unsold papers are trashed with no salvage value. How many papers should he order each day and what % of the time will he experience a stockout? Are there any drawbacks to the order size proposed and how could the boy address such issues? Answer: Service level = Cs/(Cs +Co) = .2/(.2+.3) = .4 Z value for this service level is -.25 (read the value for .6 on the one-sided table and reverse its sign (since .6-.5=.1 and we want .5-.1=.4) Thus he should stock 100+(-.25)(10) = 97.5 = 98 papers If service level is 40% he will experience stockout 1-Service level % of the time = 100%-40% = 60% of the time will be a stockout The main drawback is the high % of the time that there will be a stockout. Customers could become unhappy and demand could plummet. Thus the boy must be careful to balance his optimum order size with one that will keep customers satisfied. Increasing the salvage value would go a long way to increasing the ideal service level. Diff: 2 Topic: Single-period model AACSB: Analytic Skills Objective: LO12-7 51