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12: CHAPTER INVENTORY MANAGEMENT TRUE/FALSE
1. According to the global company profile, Amazon.com's advantage in inventory management comes from its almost fanatical use of economic order quantity and safety stock calculations. False (Global company profile, easy) A major challenge in inventory management is to maintain a balance between inventory investment and customer service. True (Introduction, easy) Which item to order and with which supplier the order should be placed are the two fundamental issues in inventory management. False (Introduction, moderate) One function of inventory is to take advantage of quantity discounts. True (Functions of inventory, easy) Work-in-process inventory is devoted to maintenance, repair, and operations. False (Functions of inventory, easy) ABC analysis classifies inventoried items into three groups, usually based on annual units or quantities used. False (Inventory management, easy) In ABC analysis, "A" Items are the most tightly controlled. True (Inventory management, moderate) ABC analysis is based on the presumption that carefully controlling all items is necessary to produce important inventory savings. False (Inventory management, easy) Cycle counting is an inventory control technique exclusively used for cyclical items. False (Inventory management, moderate) One advantage of cycle counting is that it maintains accurate inventory records. True (Inventory management, moderate) In cycle counting, the frequency of item counting and stock verification usually varies from item to item depending upon the item's classification. True (Inventory management, moderate) Retail inventory that is unaccounted for between receipt and time of sale is known as shrinkage. True (Inventory management, moderate) The demand for automobiles would be considered an independent demand. True (Inventory models, moderate)
2.
3.
4. 5. 6.
7. 8.
9. 10. 11.
12. 13.
14. 15.
Insurance and taxes on inventory are part of the costs known as setup or ordering costs. False (Inventory models, easy) If setup costs are reduced by substantial reductions in setup time, the production order quantity is also reduced. True (Inventory models, and Inventory models for independent demand, easy) The EOQ model is best suited for items whose demand is dependent on other products. False (Inventory models for independent demand, moderate) In the simple EOQ model, if annual demand were to increase, the EOQ would increase proportionately. False (Inventory models for independent demand, moderate) At the economic order quantity, holding costs are equal to purchasing costs. False (Inventory models for independent demand, moderate) In the simple EOQ model, if the carrying cost were to double, the EOQ would also double. False (Inventory models for independent demand, moderate) In the production order quantity (POQ) model, inventory does not arrive in a single moment but flows in at a steady rate, resulting in a larger lot size than in an otherwise identical EOQ problem. True (Inventory models for independent demand, moderate) The reorder point is the inventory level at which action is taken to replenish the stocked item. True (Inventory models for independent demand, moderate) In the quantity discount model, it is possible to have a cost-minimizing solution where annual ordering costs do not equal annual carrying costs. True (Inventory models for independent demand, moderate) In the quantity discount model, the cost of acquiring goods (product cost) is not a factor in determining lot size. False (Inventory models for independent demand, easy) Service level is the complement of the probability of a stockout. True (Probabilistic models and safety stock, moderate) Units of safety stock are additions to the reorder point that allow for variability in the rate of demand, the length of lead time, or both. True (Probabilistic models and safety stock, easy) Safety stock in inventory systems depends only on the average demand during the lead time. False (Probabilistic models and safety stock, moderate) The fixed-period inventory model can have a stockout during the review period as well as during the reorder period, which is why fixed-period models require more safety stock than fixed-quantity models. True (Inventory models for independent demand, easy)
16. 17.
18. 19. 20.
21. 22.
23.
24. 25.
26. 27.
MULTIPLE CHOICE
28. Which of the following statements regarding Amazon.com is false? 1. a. The company was opened by Jeff Bezos in 1995. 2. b. The company was founded as, and still is, a "virtual retailer" with no inventory. 3. c. The company is now a world-class leader in warehouse management and automation. 4. d. The company uses both United Parcel Service and the U.S. Postal Service as shippers. 5. e. Amazon obtains its competitive advantage through inventory management. b (Global company profile, moderate) 29. Which of the following is a function of inventory? 1. a. to decouple or separate parts of the production process 2. b. to decouple the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers 3. c. to take advantage of quantity discounts 4. d. to hedge against inflation 5. e. All of the above are functions of inventory. e (Functions of inventory, moderate) 30. Which of the following would not generally be a motive for a firm to hold inventories? 1. a. to decouple or separate parts of the production process 2. b. to provide a stock of goods that will provide a selection for customers 3. c. to take advantage of quantity discounts 4. d. to minimize holding costs 5. e. All of the above are functions of inventory. d (Functions of inventory, moderate) 31. Which of the following is not one of the four main types of inventory? 1. a. raw material inventory 2. b. work-in-process inventory 3. c. maintenance/repair/operating supply inventory 4. d. safety stock inventory 5. e. All of these are main types of inventory. d (Functions of inventory, moderate) 32. Which of the following statements about ABC analysis is false? 1. a. ABC analysis is based on the presumption that controlling the few most important items produces the vast majority of inventory savings. 2. b. In ABC analysis, "A" Items are tightly controlled, have accurate records, and receive regular review by major decision makers. 3. c. In ABC analysis, "C" Items have minimal records, periodic review, and simple controls. 4. d. ABC analysis is based on the presumption that all items must be tightly controlled to produce important cost savings. 5. e. All of the above statements are true.
d (Inventory management, moderate) 33. All of the following statements about ABC analysis are true except 1. a. inventory may be categorized by measures other than dollar volume 2. b. it categorizes on-hand inventory into three groups based on annual dollar volume 3. c. it is an application of the Pareto principle 4. d. it states that all items require the same degree of control 5. e. it states that there are the critical few and the trivial many inventory items d (Inventory management, moderate) 34. ABC analysis is based upon the principle that 1. a. all items in inventory must be monitored very closely 2. b. there are usually a few critical items, and many items which are less critical 3. c. an item is critical if its usage is high 4. d. more time should be spent on class C items because there are more of them 5. e. an item is critical if its unit price is high b (Inventory management, moderate) 35. ABC analysis divides on-hand inventory into three classes, generally based upon 1. a. item quality 2. b. unit price 3. c. the number of units on hand 4. d. annual demand 5. e. annual dollar volume e (Inventory management, moderate) 36. Cycle counting 1. a. is a process by which inventory records are verified once a year 2. b. provides a measure of inventory accuracy 3. c. provides a measure of inventory turnover 4. d. assumes that all inventory records must be verified with the same frequency 5. e. assumes that the most frequently used items must be counted more frequently b (Inventory management, moderate) 37. Which of the following statements regarding control of service inventories is true? 1. a. Service inventory is a fictional concept, because services are intangible. 2. b. Service inventory needs no safety stock, because there's no such thing as a service stockout. 3. c. Effective control of all goods leaving the facility is one applicable technique. 4. d. Service inventory has carrying costs but not setup costs. 5. e. All of the above are true. c (Inventory management, moderate) 38. The two most basic inventory questions answered by the typical inventory model are
1. 2. 3. 4. 5.
a. timing and cost of orders b. quantity and cost of orders c. timing and quantity of orders d. order quantity and service level e. ordering cost and carrying cost
c (Inventory models for independent demand, moderate) 39. Among the advantages of cycle counting is that it 1. a. makes the annual physical inventory more acceptable to management 2. b. does not require the detailed records necessary when annual physical inventory is used 3. c. does not require highly trained people 4. d. allows more rapid identification of errors and consequent remedial action than is possible with annual physical inventory 5. e. does not need to be performed for less expensive items d (Inventory management, moderate) 40. Which of the following are elements of inventory holding costs? 1. a. housing costs 2. b. material handling costs 3. c. investment costs 4. d. pilferage, scrap, and obsolescence 5. e. All of the above are elements of inventory holding cost. e (Inventory models, moderate) 41. Which of the following is not an assumption of the economic order quantity model shown below?
*
2 D S
Q= H 1. 2. 3. 4. 5.
a. b. c. d. e. Demand is known, constant, and independent. Lead time is known and constant. Quantity discounts are not possible. Production and use can occur simultaneously. The only variable costs are setup cost and holding (or carrying) cost.
d (Inventory models for independent demand, moderate) 42. The primary purpose of the basic economic order quantity model shown below is
*
2 D S
Q=
H 1. 2. 3. 4. 5.
a. b. c. d. e. to calculate the reorder point, so that replenishments take place at the proper time to minimize the sum of carrying cost and holding cost to maximize the customer service level to minimize the sum of setup cost and holding cost to calculate the optimum safety stock
d (Inventory models for independent demand, moderate) 43. If the actual order quantity is the economic order quantity in a problem that meets the assumptions of the economic order quantity model shown below, the average amount of inventory on hand Q 2 D SH
*=
1. 2. 3. 4. 5.
44.
a. b. c. d. e.
is smaller the smaller is the holding cost per unit is zero is one-half of the economic order quantity is affected by the amount of product cost All of the above are true.
c (Inventory models for independent demand, difficult) A certain type of computer costs $1,000, and the annual holding cost is 25%. Annual demand is 10,000 units, and the order cost is $150 per order. What is the approximate economic order quantity? 1. a. 16 2. b. 70 3. c. 110 4. d. 183 5. e. 600 c (Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
45.
Most inventory models attempt to minimize 1. a. the likelihood of a stockout 2. b. the number of items ordered 3. c. total inventory based costs 4. d. the number of orders placed 5. e. the safety stock c (Inventory models for independent demand, easy)
46.
In the basic EOQ model, if the cost of placing an order doubles, and all other values remain constant, the EOQ will 1. a. increase by about 41% 2. b. increase by 100% 3. c. increase by 200%
4. d. increase, but more data is needed to say by how much 5. e. either increase or decrease
a (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 47. In the basic EOQ model, if D=6000 per year, S=$100, H=$5 per unit per month, the economic order quantity is approximately 1. a. 24 2. b. 100 3. c. 141 4. d. 490 5. e. 600 c (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 48.
1. 2. 3. 4. 5.
49.
Which of the following statements about the basic EOQ model is true? a. If the ordering cost were to double, the EOQ would rise. b. If annual demand were to double, the EOQ would increase. c. If the carrying cost were to increase, the EOQ would fall. d. If annual demand were to double, the number of orders per year would increase. e. All of the above statements are true.
e (Inventory models for independent demand, difficult) Which of the following statements about the basic EOQ model is false? 1. a. If the setup cost were to decrease, the EOQ would fall. 2. b. If annual demand were to increase, the EOQ would increase. 3. c. If the ordering cost were to increase, the EOQ would rise. 4. d. If annual demand were to double, the EOQ would also double. 5. e. All of the above statements are true. d (Inventory models for independent demand, moderate)
50.
A product whose EOQ is 40 experiences a decrease in ordering cost from $90 per order to $10. The revised EOQ is 1. a. three times as large 2. b. one-third as large 3. c. nine times as large 4. d. one-ninth as large 5. e. cannot be determined b (Inventory models for independent demand, difficult) {AACSB: Analytic Skills}
51.
A product whose EOQ is 400 experiences a 50% increase in demand. The new EOQ is 1. a. unchanged 2. b. increased by less than 50% 3. c. increased by 50% 4. d. increased by more than 50% 5. e. cannot be determined
b (Inventory models for independent demand, difficult) {AACSB: Analytic Skills} 52. For a certain item, the cost-minimizing order quantity obtained with the basic EOQ model was 200 units and the total annual inventory (carrying and setup) cost was $600. The inventory carrying cost per unit per year for this item is 1. a. $1.50 2. b. $2.00 3. c. $3.00 4. d. $150.00 5. e. not enough data to determine c (Inventory models for independent demand, difficult) {AACSB: Analytic Skills} 53. A product has demand of 4000 units per year. Ordering cost is $20 and holding cost is $4 per unit per year. The EOQ model is appropriate. The cost-minimizing solution for this product will cost _____ per year in total annual inventory costs. 1. a. $400 2. b. $800 3. c. $1200 4. d. zero; this is a class C item 5. e. cannot be determined because unit price is not known
b (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 54. A product has demand of 4000 units per year. Ordering cost is $20 and holding cost is $4 per unit per year. The cost-minimizing solution for this product is to order 1. a. all 4000 units at one time 2. b. 200 units per order 3. c. every 20 days 4. d. 10 times per year 5. e. none of the above b (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 55. Which of the following statements regarding the reorder point is true? 1. a. The reorder point is that quantity that triggers an action to restock an item. 2. b. There is a reorder point even if lead time and demand during lead time are constant. 3. c. The reorder point is larger than d x L if safety stock is present. 4. d. The fixed-period model has no reorder point. 5. e. All of the above are true. e (Inventory models for independent demand, and Probabilistic models and safety stock, moderate) 56. The EOQ model with quantity discounts attempts to determine
1. a. what is the lowest amount of inventory necessary to satisfy a certain service level 2. b. what is the lowest purchasing price 3. c. whether to use fixed-quantity or fixed-period order policy
4. d. how many units should be ordered 5. e. what is the shortest lead time
d (Inventory models for independent demand, moderate) 57. An inventory decision rule states "when the inventory level goes down to 14 gearboxes, 100 gearboxes will be ordered." Which of the following statements is true? 1. a. One hundred is the reorder point, and 14 is the order quantity. 2. b. Fourteen is the reorder point, and 100 is the order quantity. 3. c. The number 100 is a function of demand during lead time. 4. d. Fourteen is the safety stock, and 100 is the reorder point. 5. e. None of the above is true. b (Inventory models for independent demand, moderate) 58. Which of the following statements regarding the production order quantity model is true? 1. a. It applies only to items produced in the firm's own production departments. 2. b. It relaxes the assumption that all the order quantity is received at one time. 3. c. It relaxes the assumption that the demand rate is constant. 4. d. It minimizes the total production costs. 5. e. It minimizes inventory. b (Inventory models for independent demand, moderate) Which of these statements about the production order quantity model is false? 1. a. The production order quantity model is appropriate when the assumptions of the basic EOQ model are met, except that receipt is noninstantaneous. 2. b. Because receipt is noninstantaneous, some units are used immediately, not stored in inventory. 3. c. Average inventory is less than one-half of the production order quantity. 4. d. All else equal, the smaller the ratio of demand rate to production rate, the larger is the production order quantity. 5. e. None of the above is false. d (Inventory models for independent demand, difficult) 60. The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, setup cost is $50, holding cost is $12 per unit per year, the daily demand rate is 10 and the daily production rate is 100. The production order quantity for this problem is approximately 1. a. 139 2. b. 174 3. c. 184 4. d. 365 5. e. 548 c (Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
59.
61.
A production order quantity problem has daily demand rate = 10 and daily production rate = 50. The production order quantity for this problem is approximately 612 units. The average inventory for this problem is approximately 1. a. 61 2. b. 245 3. c. 300 4. d. 306 5. e. 490 b (Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
62.
Which category of inventory holding costs is much higher than average for rapid-change industries such as PCs and cell phones? 1. a. housing costs 2. b. material handling costs 3. c. labor cost 4. d. parts cost 5. e. pilferage, scrap, and obsolescence e (Inventory models, moderate)
63.
1. 2. 3. 4. 5.
64.
When quantity discounts are allowed, the cost-minimizing order quantity a. is always an EOQ quantity b. minimizes the sum of holding and ordering costs c. minimizes the unit purchase price d. may be a quantity below that at which one qualifies for that price e. minimizes the sum of holding, ordering, and product costs
e (Inventory models for independent demand, moderate) Which of the following statements about quantity discounts is false? 1. a. The cost-minimizing solution may or may not be where annual holding costs equal annual ordering costs. 2. b. In inventory management, item cost becomes relevant to inventory decisions only when a quantity discount is available. 3. c. If carrying costs are expressed as a percentage of value, EOQ is larger at each lower price in the discount schedule. 4. d. The larger annual demand, the less attractive a discount schedule will be. 5. e. The smaller the ordering cost, the less attractive a discount schedule will be. d (Inventory models for independent demand, moderate)
65.
If the standard deviation of demand is six per week, demand is 50 per week, and the desired service level is 95%, approximately what is the statistical safety stock? 1. a. 8 units 2. b. 10 units 3. c. 16 units 4. d. 64 units 5. e. cannot be determined without lead time data
e (Probabilistic models with constant lead time, moderate) 66. A specific product has demand during lead time of 100 units, with a standard deviation of 25 units. What safety stock (approximately) provides a 95% service level? 1. a. 41 2. b. 55 3. c. 133 4. d. 140 5. e. 165 a (Probabilistic models with constant lead time, moderate) {AACSB: Analytic Skills} 67. Demand for dishwasher water pumps is 8 per day. The standard deviation of demand is 3 per day, and the order lead time is four days. The service level is 95%. What should the reorder point be? 1. a. about 18 2. b. about 24 3. c. about 32 4. d. about 38 5. e. more than 40 e (Probabilistic models with constant lead time, moderate) {AACSB: Analytic Skills} The purpose of safety stock is to a. replace failed units with good ones b. eliminate the possibility of a stockout c. eliminate the likelihood of a stockout due to erroneous inventory tally d. control the likelihood of a stockout due to the variability of demand during lead time e. protect the firm from a sudden decrease in demand
68.
1. 2. 3. 4. 5.
d (Probabilistic models with constant lead time, moderate) 69. The proper quantity of safety stock is typically determined by 1. a. minimizing an expected stockout cost 2. b. carrying sufficient safety stock so as to eliminate all stockouts 3. c. meeting 95% of all demands 4. d. setting the level of safety stock so that a given stockout risk is not exceeded 5. e. minimizing total costs d (Probabilistic models with constant lead time, moderate) 70.
1. 2. 3. 4. 5.
If demand is not uniform and constant, then stockout risks can be controlled by a. increasing the EOQ b. placing an extra order c. raising the selling price to reduce demand d. adding safety stock e. reducing the reorder point d (Probabilistic models with constant lead time, moderate)
71.
If daily demand is normally distributed with a mean of 15 and standard deviation of 5, and lead time is constant at 4 days, 90 percent service level will require safety stock of approximately 1. a. 7 units 2. b. 10 units 3. c. 13 units 4. d. 16 units 5. e. 26 units c (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
72.
If daily demand is constant at 10 units per day, and lead time averages 12 days with a standard deviation of 3 days, 95 percent service requires a safety stock of approximately 1. a. 28 units 2. b. 30 units 3. c. 49 units 4. d. 59 units 5. e. 114 units c (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
73.
In a safety stock problem where both demand and lead time are variable, demand averages 150 units per day with a daily standard deviation of 16, and lead time averages 5 days with a standard deviation of 1 day. The standard deviation of demand during lead time is approximately 1. a. 15 units 2. b. 100 units 3. c. 154 units 4. d. 500 units 5. e. 13,125 units c (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} The fixed-period inventory model requires more safety stock than the fixed-quantity models because 1. a. a stockout can occur during the review period as well as during the lead time 2. b. this model is used for products that have large standard deviations of demand 3. c. this model is used for products that require very high service levels 4. d. replenishment is not instantaneous 5. e. setup costs and holding costs are large a (Probabilistic models and safety stock, moderate)
74.
75.
1. 2. 3. 4. 5.
A disadvantage of the fixed-period inventory system is that a. it involves higher ordering costs than the fixed quantity inventory system b. additional inventory records are required c. the average inventory level is decreased d. since there is no count of inventory during the review period, a stockout is possible e. orders usually are for larger quantities d (Fixed-period systems, moderate)
76.
An advantage of the fixed-period inventory system is that 1. a. the supplier will be more cooperative 2. b. there is no physical count of inventory items when an item is withdrawn 3. c. no inventory records are required 4. d. orders usually are for smaller order quantities 5. e. the average inventory level is reduced b (Fixed-period systems, moderate)
FILL-IN-THE BLANK
77. Amazon's original concept of operating without inventory has given way to a model in which Amazon is a world-class leader in _______________. warehouse management and automation (Global company profile, easy) Inventory that separates various parts of the production process performs a ___________ function. decoupling (Functions of inventory, easy) _____________ inventory is material that is usually purchased, but has yet to enter the manufacturing process. Raw material (Functions of inventory, easy) ______________ is a method for dividing on-hand inventory into three classifications based on annual dollar volume. ABC analysis (Inventory management, easy) _____________ is a continuing reconciliation of inventory with inventory records. Cycle counting (Inventory management, easy) _____________ is the time between placement and receipt of an order. Lead time (Inventory models for independent demand, easy) In an economic order quantity problem, the total annual cost curve is at its _____________ where holding costs equal setup costs. minimum (Inventory models for independent demand, easy) For a given level of demand, annual holding cost is larger as the order quantity is _____________. larger (Inventory models for independent demand, easy) A(n) __________ model gives satisfactory answers even with substantial variations in its parameters. robust (Inventory management, moderate) In the production order quantity model, the fraction of inventory that is used immediately and not stored is represented by the ratio of_____________. demand rate to production rate (Inventory models for independent demand, easy) _____________ is extra stock that is carried to serve as a buffer. Safety stock (Inventory management, easy)
78. 79.
80.
81. 82. 83. 84. 85. 86.
87.
88.
In a quantity discount problem, if the savings in product cost is smaller than the increase in the sum of setup cost and holding cost, the discount should be _____________. rejected or refused (Inventory models for independent demand, easy) ____________ is the complement of the probability of a stockout. Service level (Probabilistic models with constant lead time, moderate) If a safety stock problem includes parameters for average daily demand, standard deviation of demand, and lead time, then _____________ is variable and ___________ is constant. demand, lead time (Probabilistic models and safety stock, easy) When demand is constant and lead time is variable, safety stock computation requires three inputs: the value of z, _____________, and the standard deviation of lead time. daily demand (Probabilistic models and safety stock, moderate) A(n) ____________ system triggers inventory ordering on a uniform time frequency. fixed-period (Fixed-period systems, moderate)
89. 90.
91.
92.
SHORT ANSWERS
93. Explain what "decoupling" means in the context of inventory management. Decoupling means to separate various parts of the production process. Each of the parts can then function at its own best pace. (Functions of inventory, moderate) What are the main reasons that an organization has inventory? Reasons to carry inventory include decoupling or separating parts of the production process, decoupling the firm from fluctuations in demand and providing a stock of goods that will provide a selection for customers, taking advantage of quantity discounts, and providing a hedge against inflation. (Introduction, moderate) List the four types of inventory. The four types of inventory are raw material, work-in-process, maintenance/repair/operating supply (MRO), and finished goods. (Functions of inventory, easy) What is MRO an acronym for? What is the function of MRO inventories? MRO inventories are devoted to maintenance/repair/operating supplies. They exist because the need and timing for maintenance and repair of some equipment are unknown. (Functions of inventory, easy) Describe ABC inventory analysis in one sentence. What are some policies that may be based upon the results of an ABC analysis? ABC inventory analysis is a method for dividing on-hand inventory into three classifications based on annual dollar volume. Some policies include: purchasing resources expended on supplier development should be higher for individual A items than for C items; A items should have tighter physical inventory control, and forecasting A items may warrant more care. (Inventory management, moderate) What is cycle counting? Cycle counting is an audit to reconcile inventory with inventory records. (Inventory management, easy) Define shrinkage. List three or more examples of shrinkage. Shrinkage is retail inventory that is unaccounted for between receipt and sale. Examples will vary, but may include inventory
94.
95.
96.
97.
98. 99.
damaged prior to sale, stolen prior to sale, and inventory "lost" due to sloppy paperwork. (Inventory management, easy) 100. What are the techniques to control service inventories? Techniques to control service inventories include good personnel selection, training, and discipline; tight control of incoming shipments; and effective control of all goods leaving the facility. (Inventory management, moderate) 101. When is a good time for cycle-counting personnel to audit a particular item? In deciding when to verify inventory through cycle counting, the important considerations are (a) the verification takes place according to a formal schedule, and (b) inventory records of particularly important items are verified more often, those of less important items, less often. As the text suggests, the schedule can be weekly, monthly, or any other criteria, such as when an item goes to zero or when the item is to be ordered. (Inventory management, moderate) 102. Several inventory models assume "independent demand." Explain what that term means and why the assumption is important. Independent demand means that demand for one particular item does not affect, and is not affected by, demand for a different item. When item demands are dependent, such as when wheels are demanded for assembly onto lawnmowers, independent ordering with EOQ may not be appropriate. 103. List the typical components that constitute inventory holding or carrying costs. Typical components of inventory holding or carrying costs include housing costs, material handling costs, labor cost from extra handling, investment costs, pilferage, scrap, and obsolescence. (Inventory models, moderate) 104. Describe the costs associated with ordering and maintaining inventory. Costs that are associated with ordering and maintaining inventory include initial purchase cost of the item, holding cost (insurance, space, heat, light, security, warehouse personnel, etc.), obsolescence or deterioration cost (particularly important in perishable goods or in a product that is undergoing rapid technological evolution), and ordering or setup cost (cost of forms, clerical processing, etc., or cost of machine setup). (Inventory models, moderate) 105. List the typical cost components that constitute ordering costs in inventory systems. Typical components of ordering costs include cost of supplies, forms, order processing, clerical support, and so forth. (Inventory models, moderate) 106. Compare the assumptions of the production order quantity model to those of the basic EOQ model. All are the same, except the assumption that receipt of inventory is instantaneous, which holds for EOQ, but not POQ. (Inventory models for independent demand, moderate) 107. In some inventory models, the optimal behavior occurs where ordering costs and carrying costs are equal to one another. Provide an example of a model where this "rule" does not hold; explain how the model's results are optimal anyway. This rule will not hold in all instances of quantity discount models. In order to take advantage of a discount, it may be cheaper to order a quantity that is not an EOQ. The goal in quantity discount models is to minimize the sum of ordering, carrying, and purchase costs. (Inventory models for independent demand, moderate) 108. In the basic economic order quantity model and in the production order quantity model, optimal behavior occurs where annual setup costs equal annual holding costs. Is this a coincidence, or a
fundamental element of these models? Answer in a well-constructed paragraph. This equality is not a coincidence. It follows from the objective of both models, which is the minimization of total inventory costs for that product. In both of these models, total cost minimization occurs where the setup cost and holding cost elements intersect. The formulas for Q* and Q*P follow from that point of equality. (Inventory models for independent demand, moderate) 109. What are the assumptions of the EOQ model? The more important assumptions of the basic EOQ model are demand is known and constant over time, the lead time, that is, the time between the placement of the order and the receipt of the goods, is known and constant, the receipt of the inventory is instantaneous; i.e., the goods arrive in a single batch, at one instant in time, quantity discounts are not possible, the only variable costs are the cost of setting up or placing an order and the cost of holding or storing inventory over time, and if orders are placed at the right time, stockouts or shortages can be completely avoided. (Inventory models for independent demand, moderate) 110. Assume two inventory problems with identical demand, holding cost, and setup cost. In one, goods arrive instantly, but in the other goods arrive at a measurable rate. Which of these problems will have the larger optimal order quantity? Why? The problem with instantaneous delivery is an EOQ problem, and its optimal order quantity is Q*. The problem with noninstantaneous delivery is a POQ problem, with optimal order quantity Q*P. The POQ problem will yield a higher order quantity than the basic model, other things equal, because the maximum inventory level (and thus the effective carrying charge) is less. Maximum inventory is less because some items are used immediately and never enter inventory. (Inventory models for independent demand, moderate) 111. How sensitive is the EOQ to variations in demand or costs? The EOQ is relatively insensitive to small changes in demand or setup or carrying costs because the cost curve is relatively flat around the EOQ. For example, if demand increases by 10%, EOQ will increase by approximately 5%. (Inventory models for independent demand, moderate) 112. What is a reorder point? A reorder point is the inventory level (point) at which action is taken (an order placed) to replenish the stocked item. (Inventory models for independent demand, easy) 113. Define service level. The service level is the percentage of demand met by available stock; it is the complement of the probability of a stockout. (Probabilistic models and safety stock, moderate) 114. What happens to the cost of the inventory policy when the service level increases? The cost of the inventory policy increases dramatically with increases in service level. (Probabilistic models and safety stock, moderate) 115. How would a firm go about determining service level? Service level is a difficult parameter to determine. Basically, the firm uses its subjective judgment to balance the cost of additional inventory against the cost of lost goodwill due to stockouts or shortages. (Probabilistic models and safety stock, moderate) 116. What is a fixed-period system? It is a system in which inventory orders are made at regular time intervals. (Fixed-period systems, easy)
117. Describe the difference between a fixed-quantity and a fixed-period inventory system? In a fixedquantity inventory system, when the quantity on hand reaches the reorder point, an order is placed for the specified quantity. In a fixed-period inventory system, an order is placed at the end of the period. The quantity ordered is that needed to bring on-hand inventory up to a specified level. (Fixed-period systems, moderate)
PROBLEMS
118. Lead time for one of Montegut Manufacturing's fastest moving products is 4 days. Demand during this period averages 100 units per day. What would be an appropriate re-order point? Re-order point = demand during lead time = 100 units/day * 4 days = 400 units. (Inventory models for independent demand, easy) {AACSB: Analytic Skills} 119. Montegut Manufacturing produces a product for which the annual demand is 10,000 units. Production averages 100 per day, while demand is 40 per day. Holding costs are $2.00 per unit per year; set-up costs $200.00. If they wish to produce this product in economic batches, what size batch should be used? What is the maximum inventory level? How many order cycles are there per year? How much does management of this good in inventory cost the firm each year? This problem requires economic order quantity, noninstantaneous delivery.
*
2DS
2 * 10000 * 200
QP =
= =
1825 .7 or 1826 units.
H (1 d / p) 2.00(1 40 /100)
The maximum inventory level is Q units.
1d
= 1825.7 1 40 = 1095.45 or 1095
p 100 D 10000
There are approximately N== = 5.48 cycles per year.
Q 1826 Annual inventory management costs total 5.48 $200 + (1095.45/ 2) $2 = $2,190.89 or $2,191. (Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
120. Your company has compiled the following data on the small set of products that comprise the specialty repair parts division. Perform ABC analysis on the data. Which products do you suggest the firm keep the tightest control over? Explain. SKU R11 S22 Annual Demand 250 75 Unit Cost $250 $90
T33 U44 V55
20 150 100
$60 $150 $75
R11 and U44 represent over 80% of the firm's volume in this area. R11 is classified A, U44 is classified B, and all others are C. The tightest controls go to R11, then U44 because of their high percentage of sales volume. Dollar % Dollar Cumulative Volume Unit cost volume volume $-vol % Class
R11 250 $250 $62,500 62.22% 62.22% A U44 150 $150 $22,500 22.40% 84.62% B V55 100 $75 $7,500 7.47% 92.09% C S22 75 $90 $6,750 6.72% 98.81% C T33 20 $60 $1,200 1.19% 100.00% C Total $100,450 (Inventory management, moderate) {AACSB: Analytic Skills} 121. Perform an ABC analysis on the following set of products. Item A211 B390 C003 D100 E707 F660 G473 H921 Annual Demand 1200 100 4500 400 35 250 1000 100 Unit Cost $9 $90 $6 $150 $2000 $120 $90 $75
The table below details the contribution of each of the eight products. Item G473 is clearly an A item, and items A211, B390, and H921 are all C items. Other classifications are somewhat subjective, but one choice is to label E707 and D100 as A items, and F660 and C003 as B items. Item Annual Unit Volume Cumulative Cumulative Demand Cost volume percent
G473 1000 $90 $90,000 $90,000 29.6% E707 35 $2,000 $70,000 $160,000 52.6% D100 400 $150 $60,000 $220,000 72.3% F660 250 $120 $30,000 $250,000 82.2% C003 4500 $6 $27,000 $277,000 91.0% A211 1200 $9 $10,800 $287,800 B390 94.6% 100 $90 $9,000 $296,800 97.5%
H921 100 $75 $7,500 $304,300 100.0% $304,300 (Inventory management, moderate) {AACSB: Analytic Skills}
122. Thomas' Bike Shop stocks a high volume item that has a normally distributed demand during the reorder period. The average daily demand is 70 units, the lead time is 4 days, and the standard deviation of demand during the reorder period is 15.
1. 2. 3. 4.
a. How much safety stock provides a 95% service level to Thomas? b. What should the reorder point be? a. SS = 1.65 x 15 = 24.75 units or 25 units b. ROP = (70* 4) + 25 = 305 units. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
123. The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 600 units, S = $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost? Quantity Price 1 to 49 $5.00 per unit 50 to 249 $4.50 per unit 250 and up $4.10 per unit
The firm should order 250 units at a time, paying $4.10 per unit. Holding costs are much larger than ordering costs, but this is offset by the unit price reduction. The annual total cost is $2,661.75. The EOQ value for the $4.50 price has an annual cost of $2,880.
Minimum quantity Unit Price, P Q* (Square root formula) Order Quantity Holding cost Setup cost Unit costs Total cost, Tc Range 11 $5.00 Range 250 $4.50 Range 3 250 $4.10
126.49 Discarded
133.33 133.33 $90.00 $90.00 $2,700.00 $2,880.00
139.69 250
$153.75 $48.00 $2,460.00 $2,661.75
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
124. The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair which costs $300. The annual holding cost rate is 40%, annual demand is 900, and the order cost is $20 per order. The lead time is 4 days. Because demand is variable (standard deviation of daily demand is 2.4 chairs), PCE has decided to establish a customer service level of 90%. The store is open 300 days per year. 1. a. What is the optimal order quantity? 2. b. What is the safety stock? 3. c. What is the reorder point? (a) The optimal order quantity is Q = 2 900 20 = 17.32 or 17 chairs.
*
.4 300 1. (b) Safety Stock is SS = 1.29 2.4 4 = 6.19 or 6 chairs. 2. (c) ROP= lead time demand + safety stock = (3 chairs/day * 4) + 6.19 = 18 chairs.
(Inventory models for independent demand, and Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} Central University uses $123,000 of a particular toner cartridge for laser printers in the student computer labs each year. The purchasing director of the university estimates the ordering cost at $45 and thinks that the university can hold this type of inventory at an annual storage cost of 22% of the purchase price. How many months' supply should the purchasing director order at one time to minimize the total annual cost of purchasing and carrying? First, calculate the EOQ from the data provided. In this problem, the "units" are dollars, and the "price" of each is 1.
Q* =
2 123000 45 = 7093.53
.22
One month's usage is 123000/12 = $10,250. EOQ = 7094. Months usage = 7094/10250 = 0.69, or about three weeks usage. (This is supported by the order frequency of 17 per year). (Inventory models for independent demand, difficult) {AACSB: Analytic Skills} The soft goods department of a large department store sells 175 units per month of a certain large bath towel. The unit cost of a towel to the store is $2.50 and the cost of placing an order has been estimated to be $12.00. The store uses an inventory carrying charge of 27% per year. Determine the optimal order quantity, order frequency, and the annual cost of inventory management. If, through automation of the purchasing process, the ordering cost can be cut to $4.00, what will be the new economic order quantity, order frequency, and annual inventory management cost? Explain these results. Annual demand is 175 x 12 = 2100. At S=$12, the EOQ is 273 units, and there are about 8 orders per year. Annual costs of inventory management are $184.44. These results are detailed in the calculations below. 2 2100 12 ; N = 2100 = 7.69 Q
*=
= 273.25
.27 2.5 273.25
2100 273.25 TC = 12 + .27 2.5 = 92.22 + 92.22 = 184.44 273.25 2 At S=$4, EOQ falls to 158, and order frequency rises to 13. Annual inventory management costs fall to $106.48. The lower order cost encourages smaller, more frequent orders. 2 2100 4 = 157.76 ; N = 2100 = 13.31
Q=
*
.27 2.5 157.76
2100 157.76 TC = 12 + .27 2.5 = 53.24 + 53.24 = 106.48 157.76 2 (Inventory models for independent demand, difficult) {AACSB: Analytic Skills}
A firm that makes electronic circuits has been ordering a certain raw material 250 ounces at a time. The firm estimates that carrying cost is 30% per year, and that ordering cost is about $20 per order. The current price of the ingredient is $200 per ounce. The assumptions of the basic EOQ model are thought to apply. For what value of annual demand is their action optimal? This problem reverses the unknown of a standard EOQ problem.
2 D 20 250 .3 200
2
250 = ;solving for D results in D = = 93,750 .3 200 2 20 (Inventory models for independent demand, difficult) {AACSB:
Analytic Skills} A printing company estimates that it will require 1,000 reams of a certain type of paper in a given period. The cost of carrying one unit in inventory for that period is 50 cents. The company buys the paper from a wholesaler in the same town, sending its own truck to pick up the orders at a fixed cost of $20.00 per trip. Treating this cost as the order cost, what is the optimum number of reams to buy at one time? How many times should lots of this size be bought during this period? What is the minimum cost of maintaining inventory on this item for the period? Of this total cost, how much is carrying cost and how much is ordering cost? This is an EOQ problem, even though the time period is not a year. All that is required is that the demand value and the carrying cost share the same time reference. This will require approximately 3.5 orders per period. Setup costs and carrying costs are each $70.71, and the annual total is $141.42.
2 1000 20 1000
= 283 ; N == 3.54
EOQ = 0.50 282.84 282.84 1000
Carrying cost = .50 = 70.71 ; setup cost = 20 = 70.71
2 282.82 (Inventory models for independent demand, moderate) {AACSB:
Analytic Skills} The Rushton Trash Company stocks, among many other products, a certain container, each of which occupies four square feet of warehouse space. The warehouse space currently available for storing this product is limited to 600 square feet. Demand for the product is 15,000 units per year. Holding costs are $4 per container per year; Ordering costs are $5 per order. 1. a. What is the cost-minimizing order quantity decision for Rushton? 2. b. What is the total inventory-related cost of this decision? 3. c. What is the total inventory-related cost of managing the inventory of this product, when the limited amount of warehouse space is taken into account? 4. d. What would the firm be willing to pay for additional warehouse space?
The warehouse will hold only 150 containers. The annual cost at Q=150 is 100 x 5 + 75 x 4 = $800. The EOQ is about 194, more than there is room to store. Total cost at Q=194 is $774.60. This cost is $25.40 less than current cost, which reflects the limited storage space. Rushton would consider paying up to $25.40 for a year's rental of enough space to store 44 additional containers. (Inventory models for independent demand, difficult) {AACSB: Analytic
Skills} Given the following data: D=65,000 units per year, S = $120 per setup, P = $5 per unit, and I = 25% per year, calculate the EOQ and calculate annual costs following EOQ behavior. EOQ is 3533 units, for a total cost of $4,415.88
*
2 65000 120
Q= = 3532.7 .25 5 DQ 65000 3533 TC = S + H =120 + .25 5 = 2207.94 + 2207.94 = 4415.88 Q 2 3533 2 (Inventory models for independent demand, moderate) {AACSB: Analytic
Skills}
131. A toy manufacturer makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continuous, the motors are intermittent flow. Data on the manufacture of the motors appears below. Annual demand (D) = 50,000 units Daily subassembly production rate = 1,000 Setup cost (S) = $85 per batch Daily subassembly usage rate = 200 Carrying cost = $.20 per unit per year
1. 2. 3. 4. 5.
a. To minimize cost, how large should each batch of subassemblies be? b. Approximately how many days are required to produce a batch? c. How long is a complete cycle? d. What is the average inventory for this problem? e. What is the total inventory cost (rounded to nearest dollar) of the optimal behavior in this problem?
*
2DS
2 * 50000 * 85
(a) QP =
= =
7288 .7 or 7289 units.
H (1 d / p) .2*(1 200 /1000) 1. (b) It will take approximately 7289/ 1000 = 7.3 days to make these units. 2. (c) A complete cycle will last approximately 7289 / 200 = 36 days. 3. (d) The maximum inventory level is Q 1 d = 7288.7 1 200 = 5831 units.
p 1000
Average inventory is 5831 / 2 = 2,915 (not one-half of 7283). (e) Total inventory management costs are
50000 5831 TC = 85 + .2 = 583.09 + 583.09 = $1,166.19 7289 2 (Inventory models for independent demand, moderate) {AACSB: Analytic
Skills} 132. Louisiana Specialty Foods can produce their famous meat pies at a rate of 1650 cases of 48 pies each per day. The firm distributes the pies to regional stores and restaurants at a steady rate of 250 cases per day. The cost of setup, cleanup, idle time in transition from other products to pies, etc., is $320. Annual holding costs are $11.50 per case. Assume 250 days per year.
1. a. Determine the optimum production run.
2. b. Determine the number of production runs per year. 3. c. Determine maximum inventory. 4. d. Determine total inventory-related (setup and carrying) costs per year.
*
2DS
2 * 62500 * 320
(a) QP =
= =
2024 .7 or 2025 cases.
H (1 d / p) 11.5*(1 250 /1650) 1. (b) There will be 62,500 / 2024.7 = 30.87 runs per year. d 250 2. (c) The maximum inventory level is Q 1 = 2024.7 1 = 1717.9 units.
p 1650
(d) Total inventory management costs are
62500 1717.9 TC =320 +11.5 = 9878.04 + 9878.04 = $19,756.09 2024.7 2
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills} Holstein Computing manufactures an inexpensive audio card (Audio Max) for assembly into several models of its microcomputers. The annual demand for this part is 100,000 units. The annual inventory carrying cost is $5 per unit and the cost of preparing an order and making production setup for the order is $750. The company operates 250 days per year. The machine used to manufacture this part has a production rate of 2000 units per day.
1. 2. 3. 4.
a. Calculate the optimum lot size. b. How many lots are produced in a year? c. What is the average inventory for Audio Max? d. What is the annual cost of preparing the orders and making the setups for Audio Max?
This problem requires the production order quantity model. The optimum lot size is 6,124; this lot size will be repeated 16.33 times per year. The total inventory management cost will be $24,494.90, and average inventory will be 2,449.49 units.
*
2DS
2 *100000 * 750
(a) QP = = 6123 .7 or 6124 units.
= H (1 d / p) 5.00(1 400 /2000)
D 100000
(b) There are approximately N == = 16.33 cycles per year.
Q 6123.7
(c) The maximum inventory is Q 1 d = 6123.7 1 400 = 4899 units; average
p 2000
inventory is 4899 / 2 = 2449.5 units. (d) Annual inventory management costs are 16.33 x 750+ 2449.5 x 5 = $12,247.45+$12,247.45 = $24,494.90 (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} Huckaby Motor Services, Inc. rebuilds small electrical items such as motors, alternators, and transformers, all using a certain type of copper wire. The firm's demand for this wire is approximately normal, averaging 20 spools per week, with a standard deviation of 6 spools per week. Cost per spool is $24; ordering costs are $25 per order; inventory handling cost is $4.00 per spool per year. Acquisition lead time is four weeks. The company works 50, 5-day weeks per year. 1. a. What is the optimal size of an order, if minimization of inventory system cost is the objective? 2. b. What are the safety stock and reorder point if the desired service level is 90%? Demand is 20 x 50 = 1000 spools per year
*
2 20 50 25
a. Q = = 111.8 . Huckaby should order 112 spools at one time.
4
b. SS =1.29 6
4 = 15.48 or about 16 spools. The ROP is thus 20 4 + 16 = 96 spools.
(Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} Demand for ice cream at the Ouachita Dairy can be approximated by a normal distribution with a mean of 47 gallons per day and a standard deviation of 8 gallons per day. The new management desires a service level of 95%. Lead time is four days; the dairy is open seven days a week. What reorder point would be consistent with the desired service level? SS = 1.65 8
4 = 26.4 gallons; and ROP = 47* 4 + 26.4 = 214.4 gallons.
(Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
136. The Winfield Distributing Company has maintained an 80% service level policy for inventory of string trimmers. Mean demand during the reorder period is 170 trimmers, and the standard deviation is 60 trimmers. The annual cost of carrying one trimmer in inventory is $6. The area sales people have recently told Winfield's management that they could expect a $400 improvement in profit (based on current figures of cost per trimmer) if the service level were increased to 99%. Is it worthwhile for Winfield to make this change? This is solved with a cost comparison: total costs status quo compared to total costs at higher service, as amended by the increased profit. First calculate their safety stock. SS = 0.84 60 = 50.4 trimmers at $6 each, this safety stock policy costs about $302.40. At a service level of 99%, the safety stock rises to 2.33 60 = 139.8, which will cost $838.80. The added cost is $536.40, which is more than the added profit, so Winfield should not increase its service level. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 137. Daily demand for a product is normally distributed with a mean of 150 units and a standard deviation of 15 units. The firm currently uses a reorder point system, and seeks a 75% service level during the lead time of 6 days. 1. a. What safety stock is appropriate for the firm? 2. b. What is the reorder point? SS = 0.67 15
6 = 24.6; ROP = 150 6 + 24.6 = 924.6
(Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
138. Daily demand for a product is normally distributed with a mean of 200 units and a standard deviation of 20 units. The firm currently uses a reorder point system, with a lead time of 4 days. 1. a. What safety stock provides a 50% service level? 2. b. What safety stock provides a 90% service level? 3. c. What safety stock provides a 99% service level? Standard deviation during lead time is 20
4 = 40 units. Z is 0 for 50% service level, 1.29
for 90%, and 2.33 for 99%. The resulting safety stocks are 0, 51.6, and 93.2. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 139. Average daily demand for a product is normally distributed with a mean of 5 units and a standard deviation of 1 unit. Lead time is fixed at four days. 1. a. What is the reorder point if there is no safety stock? 2. b. What is the reorder point if the service level is 80 percent? 3. c. How much more safety stock is required if the service level is raised from 80 percent to 90 percent? This problem requires formula 12-15, since demand is variable but lead time is constant.
1. (a) With no safety stock, the reorder point is D x L = 5 x 4 = 20 units.
2. (b) For 80 percent service level, z is 0.85. The reorder point is ROP = D L + z d LT = 5 4 + 0.851 4 = 20 + 1.7 = 21.7 . Safety stock is 1.7 units. 3. (c) At 90 percent service, z=1.29. Safety stock is 1.29*1* 4 = 2.58 , an increase of about
0.9 units. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 140. Average daily demand for a product is normally distributed with a mean of 20 units and a standard deviation of 3 units. Lead time is fixed at 25 days. What reorder point provides for a service level of 95 percent? This problem requires formula 12-15, since demand is variable but lead time is constant. For 95 percent service level, z is 1.65.
ROP = D L + z d
LT = 20 25 + 1.65 3
25 = 500 + 24.75 = 524.75
(Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
141. A product has a reorder point of 110 units, and is ordered four times a year. The following table shows the historical distribution of demand values observed during the reorder period.
a. b. c. d.
Demand Probability 100 .3 110 .4 120 .2 130 .1 Managers have noted that stockouts occur 30 percent of the time with this policy, and question whether a change in inventory policy, to include some safety stock, might be an improvement. The managers realize that any safety stock would increase the service level, but are worried about the increased costs of carrying the safety stock. Currently, stockouts are valued at $20 per unit per occurrence, while inventory carrying costs are $10 per unit per year. What is your advice? Do higher levels of safety stock add to total costs, or not? What level of safety stock is best? Action Safety stock cost Stockout cost Total cost ROP=110 (SS=0) 0 = $0 .2 x 10 x 20 x 4 = $160 .1 x 20 x 20 x 4 = $160 $0 $320 $320 ROP=120 (SS=10) 10 x $10 = $100 .1 x 10 x 20 x 4 = $80 $100 $80 $180 ROP=130 (SS=20) 20 x $10 = $200 0 = $0
$200 $0 $200 The cheapest inventory policy has 10 units of safety stock. The managers should not be concerned about carrying cost only, but should consider that, while carrying costs rise, stockout costs fall. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills}
142. Demand for a product is approximately normal, averaging 5 units per day with a standard deviation of 1 unit per day. Lead time for this product is approximately normal, averaging 10 days with a standard deviation of 3 days. What reorder point provides a service level of 90 percent? This problem requires formula (12-17), since both demand and lead time are variable. The value of z that corresponds to 90 percent service is 1.29. DLT =
10 1 + 5 3 =
2 2 2
235 = 15.33
ROP = 5 10 +1.29 15.33 = 50 +19.78 = 69.78
(Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 143. A product has a reorder point of 260 units, and is ordered ten times a year. The following table shows the historical distribution of demand values observed during the reorder period.
a. b. c. d. e.
Demand Probability 240 .1 250 .2 260 .4 270 .2 280 .1 Currently, stockouts are valued at $5 per unit per occurrence, while inventory carrying costs are $2 per unit per year. Should the firm add safety stock? If so, how much safety stock should be added? Action Safety stock cost Stockout cost Total cost ROP=260 (SS=0) 0 = $0 .2 x 10 x 5 x10 = $100 .1 x 20 x 5 x10 = $100 $0 $200 $200 ROP=270 (SS=10) 10 x $2 = ROP=280 (SS=20) 20 x $2 = $20 .1 x 10 x 5 x10 = $50 $20 $50 $70 $40 0 = $0
$40 $0 $40 The current policy is not the cheapest inventory policy for this product. The cheapest inventory policy has a reorder point of 280, so the firm should add 20 units of safety stock. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 144. Demand for a product is relatively constant at five units per day. Lead time for this product is normally distributed with a mean of ten days and a standard deviation of three days.
1. a. What reorder point provides a 50 percent service level? 2. b. What reorder point provides a 90 percent service level? 3. c. If the lead time standard deviation can be reduced from 3 days to 1, what reorder point
now provides 90 percent service? How much is safety stock reduced by this change? This problem requires formula 12-16 since demand is constant but lead time is variable. 1. (a) There is no safety stock; the reorder point is 5 x 10 = 50 units;
2. (b) The value of z corresponding to 90 percent service is 1.29. ROP = D L + z D LT = 5 10 + 1.29 5 3 = 50 + 19.35 = 69.35 3. (c) ROP = 5 10 + 1.29 5 1 = 50 + 6.45 = 56.45 ; safety stock has decreased by 12.9
units. (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 145. A product has variable demand and constant lead time. Currently this product is managed by a fixed-period inventory system, for which the review period is one week. Lead time is four weeks. Annually about 5,200 units of this product are sold. The current target inventory is 500 units. Today is review day; 75 units are on the shelves, and orders placed at previous reviews in the amount of 110, 60, and 30 have not yet been received. There are no backorders. 1. a. How much is the firm allowing for safety stock in this case? 2. b. What should be the order amount this week?
1. (a) Since demand averages 100 units per week, expected demand is 4 x 100 = 400 units. The
target value of 500 implies that safety stock is 100 units. 2. (b) Q = Target On-hand Pending + Backorders = 500 - 75 (110 + 60 + 30) + 0 = 225 (Probabilistic models and safety stock, moderate) {AACSB: Analytic Skills} 146. 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. 1. a. What is the EOQ at the current behavior? 2. b. What is the annual total cost, including product cost, of continuing their current behavior? 3. c. What are the annual total costs, if they accept either of the proposed discounts? 4. d. At the cheapest of the total costs, are carrying costs equal to ordering costs? Explain.
*
2 720 6
(a) Q = = 41.57 or 42 units at a time.
.2 25 720 41.57 1. (b) TC = 720 25 + 6 + .2 25 = 18000 + 103.92 + 103.92 = $18,207.85 2. 41.57 2 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. 3. (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 Range 11-59 $25 Range 260179$24.5 Range 3 179+ $24
Q* (Square root formOrder Quantity Holding cost Setup cost Product cost Total cost, Tc
ula) 41.5741.57 103.92103.9318,000.00$18,207.8 5
41.99 60
42.43 180
72 147 24 432 17,280 $17,736 17,640 $17,859
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 147. 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
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. Range 3 Range 4
Q* (Square root formula) 1805.788 2013.468 Order Quantity 1805.788 5000 Holding cost $415.33 $925.00 Setup cost $415.33 $150.00 Unit costs $23,000.00 $18,500.00 Total cost, Tc $23,830.66 $19,575.00 (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 148. 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 1. a. How many should she order at one time? 2. b. How many times per year will she replenish her inventory of this material? 3. c. What will be the total annual inventory costs associated with this material?
1. 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?
2.
*
2 150 42
4. a. Q = = 56.12 . She should order 56 units at a time. 4 150 1. b. N == 2.67 She should place about 2.67 orders per year. 2. c. The inventory costs are $112 for holding and $112 for ordering, or $224 total. 3. d. At the lower value for H, the EOQ will be doubled to 112.25.
(Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
56.12
149. 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
1. 2. 3. 4.
a. What is the optimal behavior? b. Does the firm take advantage of the lowest price available? Explain. 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. Range 1 Range 2 Range 3
Q* (Square root formula) 1032.796 1032.796 1032.796 Order Quantity 1032.796 1500 5000 Holding cost $1,549.19 $2,250.00 $7,500.00 Setup cost $1,549.19 $1,066.67 $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 (Inventory models for independent demand, moderate) {AACSB: Analytic Skills} 150. 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. 1. a. How many pounds should Groundz order at a time? 2. b. What is total annual cost (excluding item cost) of managing this item on a cost-minimizing basis? 3. c. In pursuing lowest annual total cost, how many orders should Groundz place annually? 4. d. How many days will there be between orders (assume 310 operating days) if Groundz practices EOQ behavior?
*
2 4 52 8
= 8 . Groundz should order 8 pounds per order.
a. Q =
1 52 4 52 8
b. TC = 8 + 1 52 = 208 + 208 = 416 . The firm will spend $416 annually.
82 4 52 1. c. N == 26 . Groundz should order 26 times per year. 2. d. Days between orders will be 310/26 or approximately every 12 working days. (Inventory
models for independent demand, moderate) {AACSB: Analytic Skills}
8
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. 1. a. What is the cost minimizing size of the manufacturing batch? 2. b. What is the total cost of this solution? The cost-minimizing batch size is Q =
*
2 60000 300
= 3000 crates. This will cost
4 60000 3000 300 + 4 = 6000 + 6000 = $12,000 per year in inventory management costs. 3000 2 (Inventory models for independent demand, moderate) {AACSB: Analytic Skills}
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?
*
2 300 12 120
Order size is Q =
= 157.12 or 157; 35 300 12 157.12
annual inventory costs are 120 + 35 = 2749.55 + 2749.55 = $5,499.10 .
157.12 2 (Inventory models for independent demand, moderate)
{AACSB: Analytic Skills} 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? Start with the economic order quantity model, and solve for S.
70 = 2(340)S becomes S = 70 2 = $14.41
2
22 340 (Inventory models for independent demand, difficult) {AACSB: Analytic
Skills}
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. 1. a. What is the optimal order size? 2. b. What is the optimal number of orders per year? 3. c. What is the optimal number of days between orders? 1. d. What is the annual inventory cost?
2.
*
2 145 25
4. a. The optimal order size is Q = = 19.04 , or approximately 19 units. 20 1. b. The optimal number of orders per year is N = 145 / 19.04 = 7.62 or 8 orders. 2. c. The optimal number of days between orders is 350/7.62 = 45.9 days. 145 19.04 3. d. The annual inventory cost is 25 + 20 = 190.39 + 190.39 = $380.78 . 19.04 2 (Inventory models for independent demand, difficult) {AACSB: Analytic Skills} 155. 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.
2400 600 200 TC 2400 = 8 1 + 1= 1208;TC 600 = 8 4 + 1= 322;TC 200 = 8 12 + 1= 196 2 22
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.
(Inventory models for independent demand, difficult) {AACSB: Analytic Skills} 156. 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? 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. (Inventory models for independent demand, difficult) {AACSB: Analytic Skills}
MGT 301: Operations Management Name: Alban Mariau Fall 2008 Instructor: Kurt Haskell 2/33 94% Quiz: Chapter 12 Due: Tuesday: Dec 2, 11:59 PM 1. A major challenge in inventory management is to maintain a balance between inventory investment and customer service. True False 2. Which item to order and with which supplier the order should be placed are the two fundamental issues in inventory management. True False 3. One function of inventory is to take advantage of quantity discounts. True False 4. Work-in-process inventory is devoted to maintenance, repair, and operations.
True False 5. In ABC analysis, "A" Items are the most tightly controlled. True False 6. ABC analysis is based on the presumption that carefully controlling all items is necessary to produce important inventory savings. True False 7. Cycle counting is an inventory control technique exclusively used for cyclical items. True False 8. One advantage of cycle counting is that it maintains accurate inventory records. True False 9. In cycle counting, the frequency of item counting and stock verification usually varies from item to item depending upon the item's classification. True False 10. Retail inventory that is unaccounted for between receipt and time of sale is known as shrinkage. True False 11. The demand for automobiles would be considered an independent demand. True False 12. Insurance and taxes on inventory are part of the costs known as setup or ordering costs. True False 13. If setup costs are reduced by substantial reductions in setup time, the production order quantity is also reduced. True False 14. The reorder point is the inventory level at which action is taken to replenish the stocked item. True False 15. In the quantity discount model, the cost of acquiring goods (product cost) is not a factor in determining lot size. True False 16. Units of safety stock are additions to the reorder point that allow for variability in the rate of demand, the length of lead time, or both. True False 17. Which of the following statements regarding Amazon.com is false? a. The company was opened by Jeff Bezos in 1995. b. The company was founded as, and still is, a "virtual retailer" with no inventory. c. The company is now a world-class leader in warehouse management and automation. d. The company uses both United Parcel Service and the U.S. Postal Service as shippers. e. Amazon obtains its competitive advantage through inventory management. 18. Which of the following is a function of inventory? a. to decouple or separate parts of the production process b. to decouple the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers c. to take advantage of quantity discounts d. to hedge against inflation e. All of the above are functions of inventory. 19. Which of the following would not generally be a motive for a firm to hold inventories? a. to decouple or separate parts of the production process b. to provide a stock of goods that will provide a selection for customers c. to take advantage of quantity discounts d. to minimize holding costs e. All of the above are functions of inventory. 20. Which of the following is not one of the four main types of inventory?
a. raw material inventory b. work-in-process inventory c. maintenance/repair/operating supply inventory d. safety stock inventory e. All of these are main types of inventory. 21. Which of the following statements about ABC analysis is false? a. ABC analysis is based on the presumption that controlling the few most important items produces the vast majority of inventory savings. b. In ABC analysis, "A" Items are tightly controlled, have accurate records, and receive regular review by major decision makers. c. In ABC analysis, "C" Items have minimal records, periodic review, and simple controls. d. ABC analysis is based on the presumption that all items must be tightly controlled to produce important cost savings. e. All of the above statements are true. 22. All of the following statements about ABC analysis are true except a. inventory may be categorized by measures other than dollar volume b. it categorizes on-hand inventory into three groups based on annual dollar volume c. it is an application of the Pareto principle d. it states that all items require the same degree of control e. it states that there are the critical few and the trivial many inventory items 23. ABC analysis is based upon the principle that a. all items in inventory must be monitored very closely b. there are usually a few critical items, and many items which are less critical c. an item is critical if its usage is high d. more time should be spent on class C items because there are more of them e. an item is critical if its unit price is high 24. Cycle counting a. is a process by which inventory records are verified once a year b. provides a measure of inventory accuracy c. provides a measure of inventory turnover d. assumes that all inventory records must be verified with the same frequency e. assumes that the most frequently used items must be counted more frequently 25. The two most basic inventory questions answered by the typical inventory model are a. timing and cost of orders b. quantity and cost of orders c. timing and quantity of orders d. order quantity and service level e. ordering cost and carrying cost 26. Among the advantages of cycle counting is that it a. makes the annual physical inventory more acceptable to management b. does not require the detailed records necessary when annual physical inventory is used c. does not require highly trained people d. allows more rapid identification of errors and consequent remedial action than is possible with annual physical inventory e. does not need to be performed for less expensive items 27. Which of the following are elements of inventory holding costs? a. housing costs b. material handling costs c. investment costs d. pilferage, scrap, and obsolescence
e. All of the above are elements of inventory holding cost. 28. Which category of inventory holding costs is much higher than average for rapid-change industries such as PCs and cell phones? a. housing costs b. material handling costs c. labor cost d. parts cost e. pilferage, scrap, and obsolescence 29. The purpose of safety stock is to a. replace failed units with good ones b. eliminate the possibility of a stockout c. eliminate the likelihood of a stockout due to erroneous inventory tally d. control the likelihood of a stockout due to the variability of demand during lead time e. protect the firm from a sudden decrease in demand 30. Raw Material inventory is material that is usually purchased, but has yet to enter the manufacturing process. 31. ABC analysis is a method for dividing on-hand inventory into three classifications based on annual dollar volume. 32. Cycle Counting is a continuing reconciliation of inventory with inventory records. 33. Shrinkage is the time between placement and receipt of an order. Lead time