6-20 Lila Battle has determined that the annual demand for number 6 screws is 100,000 screws. Lila, who works in her brother’s hardware store, is in charge of purchasing. She estimates that it costs $10 every time an order is placed. This cost includes her wages, the cost of the forms used in placing the order, and so on. Furthermore, she estimates that the cost of carrying one screw in inventory for a year is one-half of 1 cent. Assume that the demand is constant throughout the year.

1. How many number 6 screws should Lila order at a time if she wishes to minimize total inventory cost?

2. How many orders per year would be placed? What would the annual ordering cost be?

3. What would the average inventory be? What would the annual holding cost be?

6-21 It takes approximately eight working days for an order of number 6 screws to arrive once the order has been placed. (Refer to Problem 6-20.) The demand for number 6 screws is fairly constant, and on average, Lila has observed that her brother’s hardware store sells 500 of these screws each day. Because the demand is fairly constant, Lila believes that she can avoid stockouts completely if she orders the number 6 screws only at the correct time. What is the ROP?

6-22 Lila’s brother believes that she places too many orders for screws per year. He believes that an order should be placed only twice per year. If Lila follows her brother’s policy, how much more would this cost every year over the ordering policy that she developed in Problem 6-20? If only two orders were placed each year, what effect would this have on the ROP?

6-23 Barbara Bright is the purchasing agent for West Valve Company. West Valve sells industrial valves and fluid control devices. One of the most popular valves is the Western, which has an annual demand of 4,000 units. The cost of each valve is $90, and the inventory carrying cost is estimated to be 10% of the cost of each valve. Barbara has made a study of the costs involved in placing an order for any of the valves that West Valve stocks, and she has concluded that the average ordering cost is $25 per order. Furthermore, it takes about two weeks for an order to arrive from the supplier, and during this time, the demand per week for West valves is approximately 80.

1. What is the EOQ?

2. What is the ROP?

3. Is the ROP greater than the EOQ? If so, how is this situation handled?

4. What is the average inventory? What is the annual holding cost?

5. How many orders per year would be placed? What is the annual ordering cost?

6-24 Ken Ramsing has been in the lumber business for most of his life. Ken’s biggest competitor is Pacific Woods. Through many years of experience, Ken knows that the ordering cost for an order of plywood is $25 and that the carrying cost is 25% of the unit cost. Both Ken and Pacific Woods receive plywood in loads that cost $100 per load. Furthermore, Ken and Pacific Woods use the same supplier of plywood, and Ken was able to find out that Pacific Woods orders in quantities of 4,000 loads at a time. Ken also knows that 4,000 loads is the EOQ for Pacific Woods. What is the annual demand in loads of plywood for Pacific Woods?

6-25 Shoe Shine is a local retail shoe store located on the north side of Centerville. Annual demand for a popular sandal is 500 pairs, and John Dirk, the owner of Shoe Shine, has been in the habit of ordering 100 pairs at a time. John estimates that the ordering cost is $10 per order. The cost of the sandal is $5 per pair. For John’s ordering policy to be correct, what would the carrying cost as a percentage of the unit cost have to be? If the carrying cost was 10% of the cost, what would the optimal order quantity be?

6-26 In Problem 6-20, you helped Lila Battle determine the optimal order quantity for number 6 screws. She had estimated that the ordering cost was $10 per order. At this time, though, she believes that this estimate was too low. Although she does not know the exact ordering cost, she believes that it could be as high as $40 per order. How would the optimal order quantity change if the ordering cost were $20, $30, and $40?

6-27 Ross White’s machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a supplier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per bracket per year is $1.50 (or 10% of the unit cost), and the ordering cost per order is $18.75. There are 250 working days per year.

1. What is the EOQ?

2. Given the EOQ, what is the average inventory? What is the annual inventory holding cost?

3. In minimizing cost, how many orders would be placed each year? What would be the annual ordering cost?

4. Given the EOQ, what is the total annual inventory cost (including purchase cost)?

5. What is the time between orders?

6. What is the ROP?

6-28 Ross White (see Problem 6-27) wants to reconsider his decision of buying the brackets and is considering making the brackets in-house. He has determined that setup cost would be $25 in machinist time and lost production time and that 50 brackets could be produced in a day once the machine has been set up. Ross estimates that the cost (including labor time and materials) of producing one bracket would be $14.80. The holding cost would be 10% of this cost.

1. What is the daily demand rate?

2. What is the optimal production quantity?

3. How long will it take to produce the optimal quantity? How much inventory is sold during this time?

4. If Ross uses the optimal production quantity, what would be the maximum inventory level? What would be the average inventory level? What is the annual holding cost?

5. How many production runs would there be each year? What would be the annual setup cost?

6. Given the optimal production run size, what is the total annual inventory cost?

7. If the lead time is one-half day, what is the ROP?

6-29 Upon hearing that Ross White (see Problems 6-27 and 6-28) is considering producing the brackets in-house, the vendor has notified Ross that the purchase price would drop from $15 per bracket to $14.50 per bracket if Ross would purchase the brackets in lots of 1,000. Lead times, however, would increase to 3 days for this larger quantity.

1. What is the total annual inventory cost plus purchase cost if Ross buys the brackets in lots of 1,000 at $14.50 each?

2. If Ross does buy in lots of 1,000 brackets, what is the new ROP?

3. Given the options of purchasing the brackets at $15 each, producing them in-house at $14.80, and taking advantage of the discount, what is your recommendation to Ross White?

6-30 After analyzing the costs of various options for obtaining brackets, Ross White (see Problems 6-27 through 6-29) recognizes that although he knows that the lead time is 2 days and the demand per day averages 10 units, the demand during the lead time often varies. Ross has kept very careful records and has determined that lead time demand is normally distributed with a standard deviation of 1.5 units.

1. What Z value would be appropriate for a 98% service level?

2. What safety stock should Ross maintain if he wants a 98% service level?

3. What is the adjusted ROP for the brackets?

4. What is the annual holding cost for the safety stock if the annual holding cost per unit is $1.50?

6-31 Annual demand for the Dobbs model airplane kit is 80,000 units. Albert Dobbs, president of Dobbs’ Terrific Toys, controls one of the largest toy companies in Nevada. He estimates that the ordering cost is $40 per order. The carrying cost is $7 per unit per year. It is 25 days from the time that Albert places an order for the model airplane kits until they are received at his warehouse. During this time, the daily demand is estimated to be 450 units.

1. Compute the EOQ, ROP, and optimal number of orders per year.

2. Albert now believes that the carrying cost may be as high as $14 per unit per year. Furthermore, he estimates that the lead time may be 35 days instead of 25 days. Redo part (a), using these revised estimates.

6-32 Morgan Arthur has spent the past few weeks determining inventory costs for Armstrong, a toy manufacturer located near Cincinnati, Ohio. She knows that annual demand will be 30,000 units per year and that the carrying cost will be $1.50 per unit per year. The ordering cost, on the other hand, can vary from $45 per order to $50 per order. During the past 450 working days, Morgan has observed the following frequency distribution for the ordering cost:

Morgan’s boss would like Morgan to determine an EOQ value for each possible ordering cost and to determine an EOQ value for the expected ordering cost.

6-33 Douglas Boats is a supplier of boating equipment for the states of Oregon and Washington. It sells 5,000 White Marine WM-4 diesel engines every year. These engines are shipped to Douglas in a shipping container of 100 cubic feet, and Douglas Boats kepng the warehouse full of these WM-4 motors. The warehouse can hold 5,000 cubic feet of boating supplies. Douglas estimates that the ordering cost is $10 per order, and the carrying cost is estimated to be $10 per motor per year. Douglas Boats is considering the possibility of expanding the warehouse for the WM-4 motors. How much should Douglas Boats expand, and how much would it be worth for the company to make the expansion? Assume demand is constant throughout the year.

6-34 Northern Distributors is a wholesale organization that supplies retail stores with lawn care and household products. One building is used to store Neverfail lawn mowers. The building is 25 feet wide by 40 feet deep by 8 feet high. Anna Oldham, manager of the warehouse, estimates that about 60% of the warehouse can be used to store the Neverfail lawn mowers. The remaining 40% is used for walkways and a small office. Each Neverfail lawn mower comes in a box that is 5 feet by 4 feet by 2 feet high. The annual demand for these lawn mowers is 12,000, and the ordering cost for Northern Distributors is $30 per order. It is estimated that it costs Northern $2 per lawn mower per year for storage. Northern Distributors is thinking about increasing the size of the warehouse. The company can do this only by making the warehouse deeper. At the present time, the warehouse is 40 feet deep. How many feet of depth should be added onto the warehouse to minimize the annual inventory costs? How much should the company be willing to pay for this addition? Remember that only 60% of the total area can be used to store Neverfail lawn mowers. Assume all EOQ conditions are met.

6-35 Lisa Surowsky was asked to help in determining the best ordering policy for a new product. Currently, the demand for the new product has been projected to be about 1,000 units annually. To get a handle on the carrying and ordering costs, Lisa prepared a series of average inventory costs. Lisa thought that these costs would be appropriate for the new product. The results are summarized in the following table. These data were compiled for 10,000 inventory items that were carried or held during the year and were ordered 100 times during the past year. Help Lisa determine the EOQ.

6-36 Jan Gentry is the owner of a small company that produces electric scissors used to cut fabric. The annual demand is 8,000 scissors, and Jan produces the scissors in batches. On average, Jan can produce 150 scissors per day, and during the production process, demand for scissors has been about 40 scissors per day. The cost to set up the production process is $100, and it costs Jan 30 cents to carry one pair of scissors for one year. How many scissors should Jan produce in each batch?

6-37 Jim Overstreet, inventory control manager for Itex, receives wheel bearings from Wheel-Rite, a small producer of metal parts. Unfortunately, Wheel-Rite can produce only 500 wheel bearings per day. Itex receives 10,000 wheel bearings from Wheel-Rite each year. Since Itex operates 200 working days each year, its average daily demand for wheel bearings is 50. The ordering cost for Itex is $40 per order, and the carrying cost is 60 cents per wheel bearing per year. How many wheel bearings should Itex order from Wheel-Rite at one time? Wheel-Rite has agreed to ship the maximum number of wheel bearings that it produces each day to Itex when an order has been received.

6-38 North Manufacturing has a demand for 1,000 pumps each year. The cost of a pump is $50. It costs North Manufacturing $40 to place an order, and the carrying cost is 25% of the unit cost. If pumps are ordered in quantities of 200, North Manufacturing can get a 3% discount on the cost of the pumps. Should North Manufacturing order 200 pumps at a time and take the 3% discount?

6-39 Linda Lechner is in charge of maintaining hospital supplies at General Hospital. During the past year, the mean lead time demand for bandage BX-5 was 60. Furthermore, the standard deviation for BX-5 was 7. Linda would like to maintain a 90% service level. What safety stock level do you recommend for BX-5?

6-40 Linda Lechner has just been severely chastised for her inventory policy. (See Problem 6-39.) Sue Surrowski, her boss, believes that the service level should be either 95% or 98%. Compute the safety stock levels for a 95% and a 98% service level. Linda knows that the carrying cost of BX-5 is 50 cents per unit per year. Compute the carrying cost that is associated with a 90%, a 95%, and a 98% service level.

6-41 Ralph Janaro simply does not have time to analyze all of the items in his company’s inventory. As a young manager, he has more important things to do. The following is a table of six items in inventory along with the unit cost and the demand in units.

1. Find the total amount spent on each item during the year. What is the total investment for all of these?

2. Find the percentage of the total investment in inventory that is spent on each item.

   IDENTIFICATION CODE	UNIT COST ($)	DEMAND IN UNITS
   XX1	5.84	1,200
   B66	5.40	1,110
   3CPO	1.12	896
   33CP	74.54	1,104
   R2D2	2.00	1,110
   RMS	2.08	961

3. Based on the percentages in part (b), which item(s) would be classified in categories A, B, and C using ABC analysis?

4. Which item(s) should Ralph most carefully control using quantitative techniques?

6-42 Thaarugo, Inc., produces a GPS device that is becoming popular in parts of Scandinavia. When Thaarugo produces one of these, a printed circuit board (PCB) is used, and it is populated with several electronic components. Thaarugo determines that it needs about 16,000 of this type of PCB each year. Demand is relatively constant throughout the year, and the ordering cost is about $25 per order; the holding cost is 20% of the price of each PCB. Two companies are competing to become the dominant supplier of the PCBs, and both have now offered discounts, as shown in the following table. Which of the two suppliers should be selected if Thaarugo wishes to minimize total annual inventory cost? What would be the annual inventory cost?

6-43 Dillard Travey receives 5,000 tripods annually from Quality Suppliers to meet his annual demand. Dillard runs a large photographic outlet, and the tripods are used primarily with 35-mm cameras. The ordering cost is $15 per order, and the carrying cost is 50 cents per unit per year. Quality is starting a new option for its customers. When an order is placed, Quality will ship one-third of the order every week for three weeks instead of shipping the entire order at one time. Weekly demand over the lead time is 100 tripods.

1. What is the order quantity if Dillard has the entire order shipped at one time?

2. What is the order quantity if Dillard has the order shipped over three weeks using the new option from Quality Suppliers, Inc.? To simplify your calculations, assume that the average inventory is equal to one-half of the maximum inventory level for Quality’s new option.

3. Calculate the total cost for each option. What do you recommend?

6-44 Quality Suppliers, Inc., has decided to extend its shipping option. (Refer to Problem 6-43 for details.) Now, Quality Suppliers is offering to ship the amount ordered in five equal shipments, one each week. It will take five weeks for this entire order to be received. What are the order quantity and total cost for this new shipping option?

6-45 The Hardware Warehouse is evaluating the safety stock policy for all its items, as identified by the SKU code. For SKU M4389, the company always orders 80 units each time an order is placed. The daily demand is constant, at 5 units per day; the lead time is normally distributed, with a mean of three days and a standard deviation of two days. Holding cost is $3 per unit per year. A 95% service level is to be maintained.

1. What is the standard deviation of demand during the lead time?

2. How much safety stock should be carried, and what should be the reorder point?

3. What is the total annual holding cost?

6-46 For SKU A3510 at the Hardware Warehouse, the order quantity has been set at 150 units each time an order is placed. The daily demand is normally distributed, with a mean of 12 units and a standard deviation of 4. It always takes exactly five days for an order of this item to arrive. The holding cost has been determined to be $10 per unit per year. Due to the large sale volume of this item, management wants to maintain a 99% service level.

1. What is the standard deviation of demand during the lead time?

2. How much safety stock should be carried, and what should be the reorder point?

3. What is the total annual holding cost?

6-47 H & K Electronic Warehouse sells a 12-pack of AAA batteries, and this is a very popular item. Demand for this is normally distributed, with an average of 50 packs per day and a standard deviation of 16. The average delivery time is five days, with a standard deviation of two days. Delivery time has been found to be normally distributed. A 96% service level is desired.

1. What is the standard deviation of demand during the lead time?

2. How much safety stock should be carried, and what should be the reorder point?

6-48 Xemex has collected the following inventory data for the six items that it stocks:

Lynn Robinson, Xemex’s inventory manager, does not feel that all of the items can be controlled. What order quantities do you recommend for which inventory product(s)?

6-49 Georgia Products offers the following discount schedule for its 4- by 8-foot sheets of good-quality plywood:

Home Sweet Home Company orders plywood from Georgia Products. Home Sweet Home has an ordering cost of $45. The carrying cost is 20%, and the annual demand is 100 sheets. What do you recommend?

6-50 Sunbright Citrus Products produces orange juice, grapefruit juice, and other citrus-related items. Sunbright obtains fruit concentrate from a cooperative in Orlando consisting of approximately 50 citrus growers. The cooperative will sell a minimum of 100 cans of fruit concentrate to citrus processors such as Sunbright. The cost per can is $9.90.

Last year, the cooperative developed the Incentive Bonus Program to give an incentive to their large customers to buy in quantity. It works like this: if 200 cans of concentrate are purchased, 10 cans of free concentrate are included in the deal. In addition, the names of the companies purchasing the concentrate are added to a drawing for a new personal computer. The personal computer has a value of about $3,000, and currently about 1,000 companies are eligible for this drawing. At 300 cans of concentrate, the cooperative will give away 30 free cans and will also place the company name in the drawing for the personal computer. When the quantity goes up to 400 cans of concentrate, 40 cans of concentrate will be given away free with the order. In addition, the company is also placed in a drawing for the personal computer and a free trip for two. The value of the trip for two is approximately $5,000. About 800 companies are expected to qualify and to be in the running for this trip.

Sunbright estimates that its annual demand for fruit concentrate is 1,000 cans. In addition, the ordering cost is estimated to be $10, while the carrying cost is estimated to be 10%, or about $1 per unit. The firm is intrigued with the Incentive Bonus Program. If the company decides that it will keep the free cans, the trip, or the computer if they are won, what should it do?

6-51 John Lindsay sells CDs that contain 25 software packages that perform a variety of financial functions, including net present value, internal rate of return, and other financial programs typically used by business students majoring in finance. Depending on the quantity ordered, John offers the following price discounts. The annual demand is 2,000 units on average. His setup cost to produce the CDs is $250. He estimates the holding cost to be 10% of the price, or about $1 per unit per year.

1. What is the optimal number of CDs to produce at a time?

2. What is the impact of the following quantity–price schedule on the optimal order quantity?

   QUANTITY ORDERED
   FROM	TO	price
   1	500	$10.00
   501	1,000	9.99
   1,001	1,500	9.98
   1,501	2,000	9.97

6-52 Teresa Granger is the manager of Chicago Cheese, which produces cheese spreads and other cheese-related products. E-Z Spread Cheese is a product that has always been popular. The probability of sales, in cases, is as follows:

A case of E-Z Spread Cheese sells for $100 and has a cost of $75. Any cheese that is not sold by the end of the week is sold to a local food processor for $50. Teresa never sells cheese that is more than a week old. Use marginal analysis to determine how many cases of E-Z Spread Cheese to produce each week to maximize average profit.

6-53 Harry’s Hardware does a brisk business during the year. During Christmas, Harry’s Hardware sells Christmas trees for a substantial profit. Unfortunately, any trees not sold at the end of the season are totally worthless. Thus, the number of trees to stock for a given season is a very important decision. The following table reveals the demand for Christmas trees:

Harry sells trees for $80 each, but his cost is only $20.

1. Use marginal analysis to determine how many trees Harry should stock at his hardware store.

2. If the cost increases to $35 per tree and Harry continues to sell trees for $80 each, how many trees should Harry stock?

3. Harry is thinking about increasing the price to $100 per tree. Assume that the cost per tree is $20. With the new price, it is expected that the probability of selling 50, 75, 100, or 125 trees will be 0.25 each. Harry does not expect to sell more than 125 trees with this price increase. What do you recommend?

6-54 In addition to selling Christmas trees during the Christmas holidays, Harry’s Hardware sells all the ordinary hardware items (see Problem 6-53). One of the most popular items is Great Glue HH, a glue that is made just for Harry’s Hardware. The selling price is $4 per bottle, but unfortunately, the glue gets hard and unusable after one month. The cost of the glue is $1.20. During the past several months, the mean sales of glue have been 60 units, and the standard deviation is 7. How many bottles of glue should Harry’s Hardware stock? Assume that sales follow a normal distribution.

6-55 The marginal loss on Washington Reds, a brand of apples from the state of Washington, is $35 per case. The marginal profit is $15 per case. During the past year, the mean sales of Washington Reds in cases was 45,000 cases, and the standard deviation was 4,450. How many cases of Washington Reds should be brought to market? Assume that sales follow a normal distribution.

6-56 Linda Stanyon has been the production manager for Plano Produce for over eight years. Plano Produce is a small company located near Plano, Illinois. One produce item, tomatoes, is sold in cases, with daily sales averaging 400 cases. Daily sales are assumed to be normally distributed. In addition, 85% of the time the sales are between 350 and 450 cases. Each case costs $10 and sells for $15. All cases that are not sold must be discarded.

1. Using the information provided, estimate the standard deviation of sales.

2. Using the standard deviation in part (a), determine how many cases of tomatoes Linda should stock.

6-57 Paula Shoemaker produces a weekly stock market report for an exclusive readership. She normally sells 3,000 reports per week, and 70% of the time her sales range from 2,900 to 3,100. The report costs Paula $15 to produce, but Paula is able to sell reports for $350 each. Of course, any reports not sold by the end of the week have no value. How many reports should Paula produce each week?

6-58 Emarpy Appliance produces all kinds of major appliances. Richard Feehan, the president of Emarpy, is concerned about the production policy for the company’s best-selling refrigerator. The demand for this has been relatively constant at about 8,000 units each year. The production capacity for this product is 200 units per day. Each time production starts, it costs the company $120 to move materials into place, reset the assembly line, and clean the equipment. The holding cost of a refrigerator is $50 per year. The current production plan calls for 400 refrigerators to be produced in each production run. Assume there are 250 working days per year.

1. What is the daily demand of this product?

2. If the company were to continue to produce 400 units each time production starts, how many days would production continue?

3. Under the current policy, how many production runs per year would be required? What would the annual setup cost be?

4. If the current policy continues, how many refrigerators would be in inventory when production stops? What would the average inventory level be?

5. If the company produces 400 refrigerators at a time, what would the total annual setup cost and holding cost be?

6-59 Consider the Emarpy Appliance situation in Problem 6-58. If Richard Feehan wants to minimize the total annual inventory cost, how many refrigerators should be produced in each production run? How much would this save the company in inventory costs compared with the current policy of producing 400 in each production run?

6-60 This chapter presents a material structure tree for item A in Figure 6.12. Assume that it now takes 1 unit of item B to make every unit of item A. What impact does this have on the material structure tree and the number of items D and E that are needed?

6-61 Given the information in Problem 6-60, develop a gross material requirements plan for 50 units of item A.

6-62 Using the data from Figures 6.12–6.14, develop a net material requirements plan for 50 units of item A assuming that it takes only 1 unit of item B for each unit of item A.

6-63 The demand for product S is 100 units. Each unit of S requires 1 unit of T and 0.5 ounce of U. Each unit of T requires 1 unit of V, 2 units of W, and 1 unit of X. Finally, each unit of U requires 0.5 ounce of Y and 3 units of Z. All items are manufactured by the same firm. It takes two weeks to make S, one week to make T, two weeks to make U, two weeks to make V, three weeks to make W, one week to make X, two weeks to make Y, and one week to make Z.

1. Construct a material structure tree and a gross material requirements plan for the dependent inventory items.

2. Identify all levels, parents, and components.

3. Construct a net material requirements plan using the following on-hand inventory data:

   ITEM	S	T	U	V	W	X	Y	Z
   On-Hand Inventory	20	20	10	30	30	25	15	10

6-64 The Webster Manufacturing Company produces a popular type of serving cart. This product, the SL72, is made from the following parts: 1 unit of part A, 1 unit of part B, and 1 unit of subassembly C. Each subassembly C is made up of 2 units of part D, 4 units of part E, and 2 units of part F. Develop a material structure tree for this.

6-65 Blair H. Dodds III runs a medium- to large-sized home eBay business dealing in vintage photographs. The annual demand for his photos is approximately 50,000. The annual overhead cost (excluding the purchase price) to buy the photographs is $4,000 per year. Given that this cost represents the optimal annual ordering cost and the optimal ordering quantity is 400 photographs at a time, determine the ordering cost and the average inventory level.

6-66 The lead time for each of the parts in the SL72 (Problem 6-64) is one week, except for part B, which has a lead time of two weeks. Develop a net material requirements plan for an order of 800 SL72s. Assume that currently there are no parts in inventory.

6-67 Refer to Problem 6-66. Develop a net material requirements plan assuming that there are currently 150 units of part A, 40 units of part B, 50 units of subassembly C, and 100 units of part F in inventory.