Chapter 16 Service Levels and Lead Times in Supply Exam Prep

Matching Supply with Demand: An Introduction to Operations Management, 4e (Cachon)

Chapter 16 Service Levels and Lead Times in Supply Chains:

The Order-up-to Inventory Model

[The following information applies to questions 1-4.]

Jim is a CFO of a mid-sized construction company. One of his key tasks is to ensure that the company has sufficient cash to pay its daily and hourly workers who are hired whenever the need arises. The company operates all 365 days a year, and Jim estimates that on any day his payroll is normally distributed with mean $25,000 and standard deviation $7,000. Jim manages his cash reserves using the order-up-to model: each morning he places an order for cash with the bank, and the armored vehicle arrives 2 days later with the money. It is the company's policy to pay all workers on the same day, but in rare cases when the company runs out of cash, it pays workers as soon as possible while increasing their paycheck by 1% for each day of delay. For each dollar carried, the company incurs 15% cost annually, which includes the cost of capital and insurance.

1) What is the profit-maximizing order-up-to level for cash?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

2) Suppose Jim is interested in ensuring that the company immediately satisfies all employee salary requirements with a 95% probability. What is the corresponding order-up-to level?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

3) Suppose Jim uses the order-up-to level of $150,000. One of these days the armored car is robbed. What is the probability that more than $30,000 is stolen?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

4) To reduce lines and move payroll closer to workers, Jim considers opening another payroll office. Exactly half of the workers will receive payments at one office, and the other half will receive payments at the other office. What will be the coefficient of variation of daily demand for cash at each of these offices?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

[The following information applies to questions 5-7.]

Supreme Cola is a supplier of fountain equipment to restaurants, bars, and cafeterias. The fountain equipment is manufactured at their York PA plant site. A national distribution center (DC) for the fountain equipment is also maintained adjacent to the plant. Supreme has one common platform design to which they add various features and accessories to create 10 different product options. The lead time for manufacturing and delivering a batch of products to the distribution center is 2 weeks. They review inventory and order weekly.

For product ACola, Supreme uses a normal distribution with mean 25 and standard deviation 20 to model weekly demand. Demands across weeks are independent. ACola sells for $15,000, and they enjoy a 50% gross margin. The annual holding cost for inventory in the DC is 25% of the product's cost. In the event that a customer order cannot be filled from the warehouse due to an out-of-stock situation, Supreme expedites the manufacture and delivery of the item. It estimates that such expediting increases their cost by $770 per unit.

5) What order-up-to level should Supreme choose to minimize their inventory for ACola while achieving at least a 99.25% in-stock probability?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

6) Suppose Supreme wants to minimize its holding and backorder (i.e., expediting) costs for ACola. What stockout probability should they target? Assume 52 weeks per year.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

7) Supreme uses an order-up-to policy with a base stock level equal to 250 for ACola. What is the probability that Supreme will have more than 40 units on order of that product at the start of any given week?

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Analytical Thinking

Blooms: Analyze

8) An industrial company requires argon gas cylinders for its work. Weekly demand is normally distributed with a mean of 35 and a standard deviation of 15. Demands are independent across weeks. Orders are placed weekly and the lead time to receive an order is 1 week. They want to hold enough cylinders to ensure a 99.75% in-stock probability. If they use an order-up-to model, what base stock level should they implement? (Do not round to an integer value, i.e., leave your response in decimal form.)

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Analytical Thinking

Blooms: Analyze

[The following information applies to questions 9-11.]

Radio Shack sells a 32GB flash drive. Weekly demand for the 32GB flash drive in one of their stores is Poisson distributed with a mean of 1.25. The store places orders weekly, and there is a one-week lead time to receive orders.

9) On average, how many units will the store have on order?

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Knowledge Application

Blooms: Apply

10) Suppose that they have 5.5 units of this flash drive on average in inventory in the store. What are the annual turns of this item in this store? Assume 52 weeks per year.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

11) Suppose they operate with a base stock level of 4. What in-stock probability would they achieve?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

12) Radio Shack sells the same 32GB flash drive on their e-commerce site which has a single distribution center. Daily demand at their e-commerce DC is forecasted to be normally distributed with a mean of 150 and a standard deviation of 75. The lead time to receive a replenishment at the distribution center from their supplier is 2 days. They review their inventory and place orders every two days, on the same day that they receive deliveries of new inventory. They operate 7 days a week. If they were to implement an order-up-to model, what base stock level should they choose for the DC if they want to achieve a 99.3% in-stock probability? (Leave your answer in decimal form, i.e., no need to round to an integer value.)

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

13) A retailer uses the order-up-to model to manage inventory of an item in a store. The lead time for replenishment is 4 weeks, and they can place orders weekly. Weekly demand is Poisson with mean 0.10 units. Their base stock level is 5, and unfilled demand is backordered. What is the coefficient of variation of their orders?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

[The following information applies to questions 14-18.]

A large toy company Müttel currently allows toy retailers to place orders with delivery in 2 weeks. The Gigantic Pocket Monster (Gipokmon) is a new toy that Müttel has introduced. Müttel charges a wholesale price of $10 for the Gipokmon. The manager of a small boutique toy retail company, TOYS-are-MINE, plans to sell the toy for $20 and incurs a holding cost of $0.1 per toy, per week. At this price, demand per week for the toy at one of their stores is estimated to be Poisson distributed with a mean of 1.5 units. Assume that the backorder cost is equal to the product's retail margin. Assume TOYS-are-MINE uses the order-up-to model to plan orders and deliveries to this store.

14) Suppose TOYS-are-MINE uses an order-up-to level of 10. After receiving their delivery for this week, they have 2 units on-hand. Last week's order was for 5 units. How many units will they order this week?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

15) Suppose they use an order-up-to level of 10 for this store. On average, how many units will this store have on-order?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

16) Given their cost and price for the Gipokmon, what is the optimal in-stock probability that TOYS-are-MINE should target?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

17) Suppose an order-up-to level of 5 is established. What is the resulting in-stock probability?

Difficulty: 3 Hard

Topic: Performance Measures

AACSB: Knowledge Application

Blooms: Apply

18) Suppose an order-up-to level of 3 is established. What would be the expected end-of-period on-hand inventory of Gipokmons?

Difficulty: 3 Hard

Topic: The End-of-Period Inventory

AACSB: Analytical Thinking

Blooms: Analyze

19) Locus Computer, based in California, is planning to manufacture its entry into the tablet space, the Lpad, in Taiwan. One option is to ship Lpads via ocean carrier. It is estimated that the lead time will be 2.5 months. Alternatively, the company can use air shipments which only have a lead time of 1/4 months. Annual holding costs are estimated to be 30% of the value of the product. As a percentage of the value of the product, how much would air shipments save in holding costs if you only consider pipeline inventory and ignore the cost of air shipments?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

[The following information applies to questions 20-21.]

Timbuk2 Inc. manufactures over 100,000 different versions of a messenger bag (illustrated on the right). Suppose Timbuk2 implements an order-up-to model to manage its inventory of a particular plastic buckle. The lead time to receive these buckles is three weeks. Demand is approximately normally distributed with a mean of 2,300 units per week and a standard deviation of 1,300. Each week's demand is independent of the demand in the other weeks.

20) What is the order-up-to level that achieves a target in-stock probability of 99.6%?

Difficulty: 3 Hard

Topic: Choosing an Order-up-to Level to Meet a Service Target

AACSB: Analytical Thinking

Blooms: Analyze

21) Suppose Timbuk2 operates with an order-up-to level of 16,000. At the start of a week (before shipments are received for that week, before an order is placed that week and before any demand occurs), what is the probability there is at least 3,500 units on order?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

[The following information applies to questions 22-25.]

Craig is a self-proclaimed movie buff who uses WebFlix, an Internet DVD rental service, to satisfy his movie needs. Craig watches movies in the evening and mails movies back the following morning. Upon receipt of a DVD, WebFlix mails Craig a new movie. To make sure that new movies are mailed to him without delays, Craig maintains a very long list of movies he desires to watch in his WebFlix account. It takes 4 days on average for Craig to receive a new movie from the moment he mails the previous movie. (For example, he receives Friday afternoon the replacement for a movie he mailed Monday morning.) Craig's daily thirst for movies is Poisson-distributed with mean 0.5. If on a given day, Craig is unable to watch the number of movies he desires because they are not available, then he watches them as soon as they become available.

22) Suppose Craig uses a rental plan allowing him to have up to 5 DVDs at home or in the mail at any point in time. What is the probability that, on a given day, Craig cannot satisfy his movie-watching needs?

Difficulty: 3 Hard

Topic: Performance Measures

AACSB: Knowledge Application

Blooms: Apply

23) How many DVDs, on average, does Craig have in the mail (on the way to or from WebFlix)?

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Knowledge Application

Blooms: Apply

24) Craig decides that his current plan is too expensive, so he switches to the cheaper plan that only allows him to have up to 4 DVDs at home or in the mail. On average, how many movies does Craig have at the end of the day at his home that he hasn't watched?

Difficulty: 3 Hard

Topic: Performance Measures

AACSB: Analytical Thinking

Blooms: Analyze

25) Instead of an ad hoc way of deciding which plan to buy, Craig decides that he would like to be able to fulfill all of his moving watching needs in a month with at least an 80% probability while minimizing his monthly fee (fees are increasing in the number of DVDs held). In this case, how many DVDs should Craig's plan allow him to have?

Difficulty: 3 Hard

Topic: Performance Measures

AACSB: Knowledge Application

Blooms: Apply

26) For products with slow-moving demand, e.g., 1 unit per week, the Poisson distribution is likely to be a better model for demand than the normal distribution because (choose the best answer)

A) the Poisson's standard deviation is equal to the square root of its mean.

B) the normal distribution does not allow the freedom to choose any standard deviation for any given mean.

C) the Poisson distribution is a continuous distribution.

D) only the standard normal distribution would apply in this setting.

E) the Poisson distribution does not assign any probability to negative outcomes.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Evaluate

27) A retailer is considering two possible definitions of "in-stock":

(I) A product is in-stock if it has at least one unit on-hand at the end of the day.

(II) A product is in-stock if it has satisfied all demand during a day.

For a given order-up-to level, which definition yields the higher in-stock probability?

A) Definition I, because if one unit is on-hand, then all demand must have been satisfied.

B) Definition II, because the firm is more likely to satisfy all demand than to end the day with one unit on hand.

C) Definition II, because if all demand is satisfied, then there must be some inventory left over.

D) Either one is possible because it will depend on the particular order-up-to policy chosen, the distribution function of demand, and the lead time.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Analyze

28) A firm manages its inventory with an order-up-to model. Each period is one day, the lead time is 2 days, the base stock level is 10 and their inventory position at the start of a day (before they submit an order for that day) is -4. Which of the following is definitely true?

A) Demand was 4 units yesterday.

B) Demand was 10 units yesterday.

C) There are 4 units backordered.

D) There are 14 units on-order before they order today.

E) After today's order there will be 14 units on-order.

F) They will receive more inventory today.

G) None of the above.

Difficulty: 3 Hard

Topic: Performance Measures

AACSB: Reflective Thinking

Blooms: Analyze

29) A firm uses the order-up-to model to manage its inventory. It wants to increase its in-stock probability while decreasing its holding costs (i.e., reduce its average inventory). Which of the following will help to achieve this goal? (Consider each one on its own.)

(i) Decrease the lead time.

(ii) Increase the base stock level.

(iii) Increase the average quantity on-order.

A) Only (i)

B) Only (ii)

C) Only (iii)

D) (i) and (ii)

E) (i) and (iii)

F) (ii) and (iii)

G) Any of them will help (that is (i), (ii) or (iii).

H) None of them will help.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Evaluate

30) A firm implements the order-up-to model with weekly ordering. In week 11 they observe that demand is much lower than expected demand. At the start of week 12 (before they order), they decide to lower their forecast of mean demand per week while keeping the standard deviation the same as well as the target in-stock probability. Their order in week 12 will:

A) be less than the demand they observed in week 11.

B) equal to the demand they observed in week 11.

C) be greater than the demand they observed in week 11, but less than their updated expected demand.

D) be greater than their updated expected demand.

E) equal to their updated expected demand over their lead time plus one period.

F) none of the above.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Analyze

31) Assume a firm implements an order-up-to inventory model with an order-up-to level of 10. The lead time is 5 time periods, demand is normally distributed, and the target fill rate is 95%. Suppose the order has just been placed. Which of the following is definitely not true?

A) The last order was 12.

B) The backorder in the previous period was 14.

C) There are 11 units in on-hand inventory.

D) Demand in the previous period was 71.

E) There are 12 units in the pipeline, and 2 units are backordered.

F) There are 8 units on-hand and 2 units in the pipeline.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Analyze

32) Suppose inventory is managed using the order-up-to model. Your inventory position is 20 and demand in the last period was 10. Your optimal order quantity is 10 units. Your target in-stock probability is

A) 95%

B) 96%

C) 97%

D) 98%

E) 99%

F) Could be any of the above a-e.

G) Cannot be any of the above a-e.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Analytical Thinking

Blooms: Analyze

33) Suppose you are managing inventory using the order-up-to model, the order-up-to quantity is 10 and you have already received several replenishments. Which of the following statements is definitely false?

A) On-order inventory is 9.

B) Inventory position is 9.

C) Backorder is 11.

D) On-hand inventory is 11.

E) Inventory position is -11.

F) Pipeline inventory is 11.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

34) Suppose the order-up-to model is used. The probability that you end any given period with no on-hand inventory equals

A) the in-stock probability.

B) the critical ratio.

C) lost sales.

D) the gross margin.

E) the ratio of inventory turns to days-of-supply.

F) none of the above.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

35) A firm sells a product whose demand over the next couple years will be stable so the order-up-to model is used to manage its inventory. When the demand uncertainty is small (for example, the weekly demand has a mean of 100 and a standard deviation of 5), the main benefit of reducing the lead time is

A) to do more lead time pooling.

B) to reduce the expected on-hand inventory at the end of every period.

C) to enable us to use the reactive capacity.

D) to reduce the pipeline stock.

E) none of the above.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Analyze

36) In the order-up-to model, assume that the mean of demand in a period remains the same and the order-up-to level is kept at a constant level. If the demand uncertainty (the standard deviation of demand in each period) increases,

A) the expected inventory at the end of each period would increase.

B) the expected inventory at the end of each period would decrease.

C) the expected inventory at the end of each period would remain unchanged.

D) the expected inventory at the end of each period may go up or down.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Analyze

37) Suppose the order-up-to model is used to manage inventories. The firm is planning changes that will reduce the lead time to receive replenishments, but the firm is also planning on making its assortment more "fashionable," which essentially means that forecast uncertainty is likely to rise for all products. What can be said about the likely change in the firm's on-order inventory?

A) It will surely decrease.

B) It will remain the same.

C) It will surely increase.

D) More information is needed to determine the impact of these changes.

Difficulty: 3 Hard

Topic: Choosing Demand Distributions

AACSB: Reflective Thinking

Blooms: Evaluate

38) Suppose in the order-up-to model the target in-stock probability is 0.95 and demand across periods are independent and normally distributed. If the lead time is doubled but the target in-stock probability remains 0.95, what happens to the order up-to level?

A) It more than doubles (increases by more than a factor of 2).

B) It doubles (increases exactly by a factor of 2).

C) It increases, but by less than a factor of 2.

D) It decreases.

E) The answer cannot be determined with the given information.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Analytical Thinking

Blooms: Analyze

39) In the order-up-to model the standard deviation of orders

A) is higher than the standard deviation of demand.

B) is lower than the standard deviation of demand.

C) is equal to the standard deviation of demand.

D) cannot be compared to the standard deviation of demand.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

40) In the order-up-to model, what is the relationship between lead time and inventory turns?

A) Higher lead time leads to higher turns.

B) Higher lead time leads to lower turns.

C) Higher lead time leads to higher turns only if the in-stock probability is greater than 50%.

D) Higher lead time leads to lower turns only if the in-stock probability is greater than 50%.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

41) Regarding the performance of the order-up-to model, if the order-up-to level is always chosen to minimize the sum of the expected holding and backorder costs, then as the lead time decreases

A) pipeline inventory as a percentage of total inventory increases.

B) pipeline inventory as a percentage of total inventory decreases.

C) the optimal in-stock probability increases.

D) the optimal in-stock probability decreases.

E) none of the above.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

42) Suppose inventory is managed using the order-up-to model. Which of the following actions will certainly lead to a higher order-up-to level? In all cases assume the characteristics of the demand process do not change.

A. Increase in the target in-stock probability (for the same lead time).

B. Decrease the target stock-out probability (for the same lead time).

C. Increase in the lead time (for the same service level).

A) A only.

B) B only.

C) C only.

D) A and B.

E) B and C.

F) A and C.

G) A, B and C.

H) None of the above.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

43) Ana Litic, a new supply chain manager at HP, decides to check some data on the supply chains she manages. She discovers that HP's in-transit inventory of printers between Vancouver, WA and its Asian DC has increased from two quarters ago. However, the distribution of demand at the Asian DC has not changed over this period of time. Ana knows that the Asian DC manager is controlling inventory to achieve a fixed in-stock probability target, so she is happy to see that indeed the in-stock at the Asian DC has also not deviated off the target. Ana wonders what has happened to the Asian DC's average inventory. What is she likely to discover regarding the Asian DC's on-hand inventory?

A) On-hand inventory has not changed because the in-stock probability has not changed at the Asian DC.

B) On-hand inventory has increased because the lead time from Vancouver WA to the Asian DC must have increased.

C) On-hand inventory has not changed because average demand has not changed at the Asian DC.

D) On-hand inventory has decreased because the variability of demand must have decreased.

E) It is not possible to predict what Ana is likely to observe with respect to the change in on-hand inventory, i.e., it could be lower, higher, or unchanged.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze

44) Assuming that the order-up-to level stays constant, which of the following statements is true about the order-up-to model?

A) As the lead time increases, the on-hand inventory increases, but the pipeline inventory remains the same.

B) As the demand uncertainty (measured by σ) increases, both on-hand inventory and pipeline inventory increase.

C) When the mean demand increases, both on-hand inventory and pipeline inventory remain the same.

D) As the demand uncertainty (measured by σ) increases, on-hand inventory decreases, but the pipeline inventory remains the same.

E) None of the above.

Difficulty: 3 Hard

Topic: The Order-up-to Model Design and Implementation

AACSB: Reflective Thinking

Blooms: Analyze