# Problems

[Page 761 ( continued )]
1.

Hayes Electronics stocks and sells a particular brand of personal computer. It costs the firm \$450 each time it places an order with the manufacturer for the personal computers. The cost of carrying one PC in inventory for a year is \$170. The store manager estimates that total annual demand for the computers will be 1,200 units, with a constant demand rate throughout the year. Orders are received within minutes after placement from a local warehouse maintained by the manufacturer. The store policy is never to have stockouts of the PCs. The store is open for business every day of the year except Christmas Day. Determine the following.

[Page 762]
1. The optimal order quantity per order

2. The minimum total annual inventory costs

3. The optimal number of orders per year

4. The optimal time between orders (in working days)

2.

Hayes Electronics in Problem 1 assumed with certainty that the ordering cost is \$450 per order and the inventory carrying cost is \$170 per unit per year. However, the inventory model parameters are frequently only estimates that are subject to some degree of uncertainty. Consider four cases of variation in the model parameters: (a) Both ordering cost and carrying cost are 10% less than originally estimated, (b) both ordering cost and carrying cost are 10% higher than originally estimated, (c) ordering cost is 10% higher and carrying cost is 10% lower than originally estimated, and (d) ordering cost is 10% lower and carrying cost is 10% higher than originally estimated. Determine the optimal order quantity and total inventory cost for each of the four cases. Prepare a table with values from all four cases and compare the sensitivity of the model solution to changes in parameter values.

3.

A firm is faced with the attractive situation in which it can obtain immediate delivery of an item it stocks for retail sale. The firm has therefore not bothered to order the item in any systematic way. Recently, however, profits have been squeezed due to increasing competitive pressures, and the firm has retained a management consultant to study its inventory management. The consultant has determined that the various costs associated with making an order for the item stocked are approximately \$30 per order. She has also determined that the costs of carrying the item in inventory amount to approximately \$20 per unit per year (primarily direct storage costs and forgone profit on investment in inventory). Demand for the item is reasonably constant over time, and the forecast is for 19,200 units per year. When an order is placed for the item, the entire order is immediately delivered to the firm by the supplier. The firm operates 6 days a week plus a few Sundays, or approximately 320 days per year. Determine the following.

1. The optimal order quantity per order

2. The total annual inventory costs

3. The optimal number of orders to place per year

4. The number of operating days between orders, based on the optimal number of orders.

4.

The Western Jeans Company purchases denim from Cumberland Textile Mills. The Western Jeans Company uses 35,000 yards of denim per year to make jeans . The cost of ordering denim from the textile company is \$500 per order. It costs Western \$0.35 per yard annually to hold a yard of denim in inventory. Determine the optimal number of yards of denim the Western Jeans Company should order, the minimum total annual inventory cost, the optimal number of orders per year, and the optimal time between orders.

5.

The Metropolitan Book Company purchases paper from the Atlantic Paper Company. Metropolitan produces magazines and paperbacks that require 1,215,000 pounds of paper per year. The cost per order for the company is \$1,200; the cost of holding 1 pound of paper in inventory is \$0.08 per year. Determine the following.

1. The economic order quantity

2. The minimum total annual cost

3. The optimal number of orders per year

4. The optimal time between orders

6.

The Simple Simon Bakery produces fruit pies for freezing and subsequent sale. The bakery, which operates 5 days per week, 52 weeks per year, can produce pies at the rate of 64 pies per day. The bakery sets up the pie production operation and produces until a predetermined number ( Q ) of pies has been produced. When not producing pies, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of fruit pies is \$500. The cost of holding frozen pies in storage is \$5 per pie per year. The annual demand for frozen fruit pies, which is constant over time, is 5,000 pies. Determine the following.

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1. The optimal production run quantity ( Q )

2. The total annual inventory costs

3. The optimal number of production runs per year

4. The optimal cycle time (time between run starts)

5. The run length, in working days

7.

The Pedal Pusher Bicycle Shop operates 7 days per week, closing only on Christmas Day. The shop pays \$300 for a particular bicycle purchased from the manufacturer. The annual holding cost per bicycle is estimated to be 25% of the dollar value of inventory. The shop sells an average of 25 bikes per week. Frequently, the dealer does not have a bike in stock when a customer purchases it, and the bike is back ordered. The dealer estimates his shortage cost per unit back ordered, on an annual basis, to be \$250 due to lost future sales (and profits). The ordering cost for each order is \$100. Determine the optimal order quantity and shortage level and the total minimum cost.

8.

The Petroco Company uses a highly toxic chemical in one of its manufacturing processes. It must have the product delivered by special cargo trucks designed for safe shipment of chemicals. As such, ordering (and delivery) costs are relatively high, at \$2,600 per order. The chemical product is packaged in 1-gallon plastic containers. The cost of holding the chemical in storage is \$50 per gallon per year. The annual demand for the chemical, which is constant over time, is 2,000 gallons per year. The lead time from time of order placement until receipt is 10 days. The company operates 310 working days per year. Compute the optimal order quantity, the total minimum inventory cost, and the reorder point.

9.

The Big Buy Supermarket stocks Munchies Cereal. Demand for Munchies is 4,000 boxes per year (365 days). It costs the store \$60 per order of Munchies, and it costs \$0.80 per box per year to keep the cereal in stock. Once an order for Munchies is placed, it takes 4 days to receive the order from a food distributor. Determine the following.

1. The optimal order size

2. The minimum total annual inventory cost

3. The reorder point

10.

The Wood Valley Dairy makes cheese to supply to stores in its area. The dairy can make 250 pounds of cheese per day, and the demand at area stores is 180 pounds per day. Each time the dairy makes cheese, it costs \$125 to set up the production process. The annual cost of carrying a pound of cheese in a refrigerated storage area is \$12. Determine the optimal order size and the minimum total annual inventory cost.

11.

The Rainwater Brewery produces Rainwater Light Beer, which it stores in barrels in its warehouse and supplies to its distributors on demand. The demand for Rainwater is 1,500 barrels of beer per day. The brewery can produce 2,000 barrels of Rainwater per day. It costs \$6,500 to set up a production run for Rainwater. Once it is brewed, the beer is stored in a refrigerated warehouse at an annual cost of \$50 per barrel. Determine the economic order quantity and the minimum total annual inventory cost.

12.

The purchasing manager for the Atlantic Steel Company must determine a policy for ordering coal to operate 12 converters. Each converter requires exactly 5 tons of coal per day to operate , and the firm operates 360 days per year. The purchasing manager has determined that the ordering cost is \$80 per order and the cost of holding coal is 20% of the average dollar value of inventory held. The purchasing manager has negotiated a contract to obtain the coal for \$12 per ton for the coming year.

1. [Page 764]
2. Determine the optimal quantity of coal to receive in each order.

3. Determine the total inventory- related costs associated with the optimal ordering policy (do not include the cost of the coal).

4. If 5 days of lead time are required to receive an order of coal, how much coal should be on hand when an order is placed?

13.

The Pacific Lumber Company and Mill processes 10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, the logging company's supplier begins delivery to the lumber mill, at a rate of 60 logs per day. The lumber mill has determined that the ordering cost is \$1,600 per order and the cost of carrying logs in inventory before they are processed is \$15 per log on an annual basis. Determine the following.

1. The optimal order size

2. The total inventory cost associated with the optimal order quantity

3. The number of operating days between orders

4. The number of operating days required to receive an order

14.

The Roadking Tire Store sells a brand of tires called the Roadrunner. The annual demand from the store's customers for Roadrunner tires is 3,700. The cost to order tires from the tire manufacturer is \$420 per order. The annual carrying cost is \$1.75 per tire. The store allows shortages, and the annual shortage cost per tire is \$4. Determine the optimal order size, maximum shortage level, and minimum total annual inventory cost.

15.

The Laurel Creek Lawn Shop sells Fastgro Fertilizer. The annual demand for the fertilizer is 270,000 pounds. The cost to order the fertilizer from the Fastgro Company is \$105 per order. The annual carrying cost is \$0.25 per pound. The store operates with shortages, and the annual shortage cost is \$0.70 per pound. Compute the optimal order size, minimum total annual inventory cost, and maximum shortage level.

16.

Videoworld is a discount store that sells color televisions . The annual demand for color television sets is 400. The cost per order from the manufacturer is \$650. The carrying cost is \$45 per set each year. The store has an inventory policy that allows shortages. The shortage cost per set is estimated at \$60. Determine the following.

1. The optimal order size

2. The maximum shortage level

3. The minimum total annual inventory cost

17.

The University Bookstore at Tech stocks the required textbook for Management Science 2405. The demand for this text is 1,200 copies per year. The cost of placing an order is \$350, and the annual carrying cost is \$2.75 per book. If a student requests the book and it is not in stock, the student will likely go to the privately owned Tech Bookstore. It is likely that the student will not buy books at the University Bookstore in the future; thus the shortage cost to the University Bookstore is estimated to be \$45 per book. Determine the optimal order size, the maximum shortage level, and the total inventory cost.

18.

The A-to-Z Office Supply Company is open from 8:00 A.M. to 6:00 P.M. , and it receives 200 calls per day for delivery orders. It costs A-to-Z \$20 to send out its trucks to make deliveries. The company estimates that each minute a customer spends waiting for an order costs A-to-Z \$0.20 in lost sales.

1. How frequently should A-to-Z send out its delivery trucks each day? Indicate the total daily cost of deliveries.

2. If a truck could carry only six orders, how often would deliveries be made, and what would be the cost?

19.

The Union Street Microbrewery makes 1220 Union beer, which it bottles and sells in its adjoining restaurant and by the case. It costs \$1,700 to set up, brew, and bottle a batch of the beer. The annual cost to store the beer in inventory is \$1.25 per bottle . The annual demand for the beer is 18,000 bottles, and the brewery has the capacity to produce 30,000 bottles annually.

[Page 765]
1. Determine the optimal order quantity, the total annual inventory cost, the number of production runs per year, and the maximum inventory level.

2. If the microbrewery has only enough storage space to hold a maximum of 2,500 bottles of beer in inventory, how will that affect total inventory costs?

20.

Eurotronics is a European manufacturer of electronic components . During the course of a year, it requires container cargo space on ships leaving Hamburg bound for the United States, Mexico, South America, and Canada. Annually, the company needs 160,000 cubic feet of cargo space. The cost of reserving cargo space is \$7,000, and the cost of holding cargo space is \$0.80/ft 3 . Determine how much storage space Eurotronics should optimally order, the total cost, and how many times per year it should place orders to reserve space.

21.

The Summer Outdoor Furniture Company produces wooden lawn chairs. The annual demand from its store customers is 17,400 chairs per year. The transport and handling costs are \$2,600 each time a shipment of chairs is delivered to stores from its warehouse. The annual carrying cost is \$3.75 per chair .

1. Determine the optimal order quantity and minimum total annual cost.

2. The company is thinking about relocating its warehouse closer to its customers, which would reduce transport and handling costs to \$1,900 per order but increase carrying costs to \$4.50 per chair per year. Should the company relocate based on inventory costs?

22.

The Spruce Creek Vegetable Farm produces organically grown greenhouse tomatoes that are sold to area grocery stores. The annual demand for Spruce Creek's tomatoes is 270,000 pounds. The farm is able to produce 305,000 pounds annually. The cost to transport the tomatoes from the farm to the stores is \$620 per load. The annual carrying cost is \$0.12 per pound.

1. Compute the optimal order size, the maximum inventory level, and the total minimum cost.

2. If Spruce Creek can increase production capacity to 360,000 tomatoes per year, will it reduce total inventory cost?

23.

The Uptown Kiln is an importer of ceramics from overseas. It has arranged to purchase a particular type of ceramic pottery from a Korean artisan. The artisan makes the pottery in 120-unit batches and will ship only that exact number of units. The transportation and handling cost of a shipment is \$7,600 (not including the unit cost). The Uptown Kiln estimates its annual demand to be 900 units. What storage and handling cost per unit does it need to achieve in order to minimize its inventory cost?

24.

The I-75 Carpet Discount Store has an annual demand of 10,000 yards of Super Shag carpet. The annual carrying cost for a yard of this carpet is \$0.75, and the ordering cost is \$150. The carpet manufacturer normally charges the store \$8 per yard for the carpet; however, the manufacturer has offered a discount price of \$6.50 per yard if the store will order 5,000 yards. How much should the store order, and what will be the total annual inventory cost for that order quantity?

25.

The Fifth Quarter Bar buys Old World draft beer by the barrel from a local distributor. The bar has an annual demand of 900 barrels, which it purchases at a price of \$205 per barrel. The annual carrying cost is 12% of the price, and the cost per order is \$160. The distributor has offered the bar a reduced price of \$190 per barrel if it will order a minimum of 300 barrels. Should the bar take the discount?

[Page 766]
26.

The bookstore at State University purchases from a vendor sweatshirts emblazoned with the school name and logo. The vendor sells the sweatshirts to the store for \$38 apiece. The cost to the bookstore for placing an order is \$120, and the carrying cost is 25% of the average annual inventory value. The bookstore manager estimates that 1,700 sweatshirts will be sold during the year. The vendor has offered the bookstore the following volume discount schedule:

Order Size

Discount %

1299

300499

2

500799

4

800+

5

The bookstore manager wants to determine the bookstore's optimal order quantity, given the foregoing quantity discount information.

27.

Determine the optimal order quantity of sweatshirts and total annual cost in Problem 26 if the carrying cost is a constant \$8 per sweatshirt per year.

28.

The office manager for the Gotham Life Insurance Company orders letterhead stationery from an office products firm in boxes of 500 sheets. The company uses 6,500 boxes per year. Annual carrying costs are \$3 per box, and ordering costs are \$28. The following discount price schedule is provided by the office supply company:

Order Quantity (boxes)

Price per Box

200999

\$16

1,0002,999

14

3,0005,999

13

6,000+

12

Determine the optimal order quantity and the total annual inventory cost.

29.

Determine the optimal order quantity and total annual inventory cost for boxes of stationery in Problem 28 if the carrying cost is 20% of the price of a box of stationery.

30.

The 23,000-seat City Coliseum houses the local professional ice hockey, basketball , indoor soccer, and arena football teams , as well as various trade shows, wrestling and boxing matches, tractor pulls, and circuses. Coliseum vending annually sells large quantities of soft drinks and beer in plastic cups, with the name of the coliseum and the various team logos on them. The local container cup manufacturer that supplies the cups in boxes of 100 has offered coliseum management the following discount price schedule for cups:

Order Quantity (boxes)

Price per Box

2,0006,999

\$47

7,00011,999

43

12,00019,999

41

20,000+

38

[Page 767]

The annual demand for cups is 2.3 million, the annual carrying cost per box of cups is \$1.90, and the ordering cost is \$320. Determine the optimal order quantity and total annual inventory cost.

31.

Community Hospital orders latex sanitary gloves from a hospital supply firm. The hospital expects to use 40,000 pairs of gloves per year. The cost to order and to have the gloves delivered is \$180. The annual carrying cost is \$0.18 per pair of gloves. The hospital supply firm offers the following quantity discount pricing schedule:

Quantity

Price

09,999

\$0.34

10,00019,999

0.32

20,00029,999

0.30

30,00039,999

0.28

40,00049,000

0.26

50,000+

0.24

Determine the order size for the hospital.

32.

Tracy McCoy is the office administrator for the department of management science at Tech. The faculty uses a lot of printer paper, and although Tracy is constantly reordering , paper frequently runs out. She orders the paper from the university central stores. Several faculty members have determined that the lead time to receive an order is normally distributed, with a mean of 2 days and a standard deviation of 0.5 day. The faculty has also determined that daily demand for the paper is normally distributed, with a mean of 2 packages and a standard deviation of 0.8 package. What reorder point should Tracy use in order not to run out 99% of the time?

33.

Determine the optimal order quantity and total annual inventory cost for cups in Problem 30 if the carrying cost is 5% of the price of a box of cups.

34.

The amount of denim used daily by the Western Jeans Company in its manufacturing process to make jeans is normally distributed, with an average of 3,000 yards of denim and a standard deviation of 600 yards. The lead time required to receive an order of denim from the textile mill is a constant 6 days. Determine the safety stock and reorder point if the Western Jeans Company wants to limit the probability of a stockout and work stoppage to 5%.

35.

In Problem 34, what level of service would a safety stock of 2,000 yards provide?

36.

The Atlantic Paper Company produces paper from wood pulp ordered from a lumber products firm. The paper company's daily demand for wood pulp is a constant 8,000 pounds. Lead time is normally distributed, with an average of 7 days and a standard deviation of 1.6 days. Determine the reorder point if the paper company wants to limit the probability of a stockout and work stoppage to 2%.

37.

The Uptown Bar and Grill serves Rainwater draft beer to its customers. The daily demand for beer is normally distributed, with an average of 18 gallons and a standard deviation of 4 gallons. The lead time required to receive an order of beer from the local distributor is normally distributed, with a mean of 3 days and a standard deviation of 0.8 day. Determine the safety stock and reorder point if the restaurant wants to maintain a 90% service level. What would be the increase in the safety stock if a 95% service level were desired?

38.

In Problem 37, the manager of the Uptown Bar and Grill has negotiated with the beer distributor for the lead time to receive orders to be a constant 3 days. What effect does this have on the reorder point developed in Problem 37 for a 90% service level?

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39.

The daily demand for Sunlight paint at the Rainbow Paint Store in East Ridge is normally distributed, with a mean of 26 gallons and a standard deviation of 10 gallons. The lead time for receiving an order of paint from the Sunlight distributor is 9 days. Because this is the only paint store in East Ridge, the manager is interested in maintaining only a 75% service level. What reorder point should be used to meet this service level? The manager subsequently has learned that a new paint store will open soon in East Ridge, which has prompted her to increase the service level to 95%. What reorder point will maintain this service level?

40.

PM Computers assembles personal computers from generic components. It purchases its color monitors from a manufacturer in Taiwan; thus, there is a long and uncertain lead time for receiving orders. Lead time is normally distributed, with a mean of 25 days and a standard deviation of 10 days. Daily demand is also normally distributed, with a mean of 2.5 monitors and a standard deviation of 1.2 monitors . Determine the safety stock and reorder point corresponding to a 90% service level.

41.

PM Computers in Problem 40 is considering purchasing monitors from an American manufacturer that would guarantee a lead time of 8 days, instead of the Taiwanese company. Determine the new reorder point, given this lead time, and identify the factors that would enter into the decision to change manufacturers.

42.

The Corner Drug Store fills prescriptions for a popular children's antibiotic, amoxicillin. The daily demand for amoxicillin is normally distributed, with a mean of 200 ounces and a standard deviation of 80 ounces. The vendor for the pharmaceutical firm that supplies the drug calls the drugstore pharmacist every 30 days to check the inventory of amoxicillin. During a call, the druggist indicated that the store had 60 ounces of the antibiotic in stock. The lead time to receive an order is 4 days. Determine the order size that will enable the drugstore to maintain a 95% service level.

43.

The Fast Service Food Mart stocks frozen pizzas in a refrigerated display case. The average daily demand for the pizzas is normally distributed, with a mean of 8 pizzas and a standard deviation of 2.5 pizzas. A vendor for a packaged food distributor checks the market's inventory of frozen foods every 10 days, and during a particular visit, there were no pizzas in stock. The lead time to receive an order is 3 days. Determine the order size for this order period that will result in a 99% service level. During the vendor's following visit, there were 5 frozen pizzas in stock. What is the order size for the next order period?

44.

The Impanema Restaurant stocks a red Brazilian table wine it purchases from a wine merchant in a nearby city. The daily demand for the wine at the restaurant is normally distributed, with a mean of 18 bottles and a standard deviation of 4 bottles. The wine merchant sends a representative to check the restaurant's wine cellar every 30 days, and during a recent visit, there were 25 bottles in stock. The lead time to receive an order is 2 days. The restaurant manager has requested an order size that will enable him to limit the probability of a stockout to 2%. Determine the order size.

45.

The concession stand at the Blacksburg High School stadium sells slices of pizza during soccer games . Concession stand sales are a primary source of revenue for high school athletic programs, so the athletic director wants to sell as much food as possible. However, any pizza not sold is given away to the players, coaches, and referees, or it is thrown away. The athletic director wants to determine a reorder point that will meet, not exceed, the demand for pizza. Pizza sales are normally distributed, with a mean of 6 pizzas per hour and a standard deviation of 2.5 pizzas. The pizzas are ordered from Pizza Town restaurant, and the mean delivery time is 30 minutes, with a standard deviation of 8 minutes.

[Page 769]
1. Currently, the concession stand places an order when it has 1 pizza left. What level of service does this result in?

2. What should the reorder point be to have a 98% service level?

Introduction to Management Science (10th Edition)
ISBN: 0136064361
EAN: 2147483647
Year: 2006
Pages: 358

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