Solution Manual for Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon

SOLUTION MANUAL FOR b b




Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon
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Chapter 2-19
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Chapter 2 b




The Process View of the Organization
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Q2.1 Dell b




The following steps refer directly to Exhibit 2.1. b b b b b b b




#1:For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
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#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
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26,442$/ year
#3: Inventory turns = = 66.105 turns per year 400$
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b b b b b b b b b




40% per year
#4: Per unit Inventory cost = = 0.605% per year
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b b b b b b b b



66.105 per year b b




Q2.2. Airline b




We use Little’s law to compute the flow time, since we know both the flow rate as well as the
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inventory level:
b b




Flow Time = Inventory/Flow Rate =35 passengers/255 passengers per hour =0.137 hours
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= 8.24 minutes b b




Q2.3 Inventory Cost
b b




(a) Sales= $60,000,000 per year/$2000 per unit =30,000 units sold per year b b b b b b b b b b b b b b




Inventory = $20,000,000/$1000 per unit = 20,000 units in inventory
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Flow Time = Inventory/ Flow Rate = 20,000/30,000 per year = 2/3 year = 8 months Turns =
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1/Flow Time =1/(2/3 year) =1.5 turns per year
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Note: we can also get this number directly by writing: b b b b b b b b b b Inventory turns = COGS/ Inventory b b b b b




(b) Cost of Inventory: 25% per year/1.5 turns =16.66%. For a $1000 product, this would
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make an absolute inventory cost of $166.66.
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Q2.4. Apparel Retailing
b b




(a) Revenue of $100Mimplies COGS of $50M (because of the 100% markup). b b b b b b b b b b b




Turns = COGS/ Inventory = $50M/$5M =10 . b b b b b b b b b




(b) The inventory cost, given 10 turns, is 40%/10 = 4% . For a 30$ item, the inventory cost
b b b b b b b b b b b b b b b b b




is 0.4$30 = $1.20 per unit . b b b b b b b b




Q2.5. La Villa b b




(a) Flow Rate = Inventory/ Flow Time =1200 skiers /10 days = 120 skiers per day b b b b b b b b b b b b b b b b




(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing b b b b b b b b b b b b b b b b b b




© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
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McGraw Hill LLC. b b b

, This year: on any given day, 20% (1 of 5) of skiers are on their first day of skiing
b b b b b b b b b b b b b b b b b b




Average amount spent in local restaurants (per skier) b b b b b b b




Last year = 0.1$50+0.9$30 = $32 This
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year = 0.2$50+0.8$30 =$34
b b b b b b b




%change =($34−$32)/$32 =6.25%increase
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Q2.6. Highway
b




We look at 1 mile of highway as our process. Since the speed is 60 miles per hour, it takes a car
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1 minute to travel through the process (flow time).
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There are 24 cars on ¼ of a mile, i.e. there are 96 cars on the 1 mile stretch (inventory).
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Inventory = Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
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Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
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Q2.7. Strohrmann Baking
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The bread needs to be in the oven for 12 minutes (flow time). We want to produce at a flow rate
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of 4000 breads per hour, or 4000/60 = 66.66 breads per minute.
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Inventory = Flow Rate * Flow Time: Inventory = 66.66 breads per minute* 12 minutes Thus,
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Inventory = 800 breads, which is the required size of the oven.
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Q2.8. Mt Kinley Consulting
b b b




We have the following information available from the question:
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Level Inventory (number of consultants at b b b b Flow Time (time spent at that b b b b b




that level) b level)
Associate 200 4 years b




Manager 60 6 years b




Partner 20 10 years b




(a) We can use Little’s law to find the flow rate for associate consultants: Inventory = Flow
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Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate is 50
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consultants per year, which need to be recruited to keep the firm in its current size (note:
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while there are also 50 consultants leaving the associate level, this says nothing about how
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many of them are dismissed vs how many of them are promoted to Manager level).
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(b) We can perform a similar analysis at the manager level, which indicates that the flow rate
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there is 10 consultants. In order to have 10 consultants as a flow rate at the manager level,
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we need to promote 10 associates to manager level (remember, the firm is not recruiting
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to the higher ranks from the outside). Hence, every year, we dismiss 40 associates and
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promote 10 associates to the manager level (the odds at that level are 20%)
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© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
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McGraw Hill LLC. b b b

, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained via the
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same calculations as before). Thus, from the 10 manager cases we evaluate every year, 8 are
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dismissed and 2 are promoted to partner (the odds at that level are thereby also 20%).
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In order to find the odds of a new hire to become partner, we need to multiply the promotion
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probabilities: 0.2*0.2 = 0.04. Thus, a new hire has a 4% chance of making it to partner.
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Q2.9. Major US Retailers
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a. Product stays on average for 31.9 days in Costco’s inventory b b b b b b b b b




b. Costco has for a $5 product an inventory cost of $0.1311 which compares to a b b b b b b b b b b b b b b




$0.2049 atWal-Mart b b




Q2.10. McDonald’sb




a. Inventory turns for McDonald’s were 92.3. They were 30.05 for Wendy’s. b b b b b b b b b b




b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about b b b b b b b b b b b b b




$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. b b b b b b b b b b b b b b




Q2.11. BCH b




I=400associates, T=2years. R = I/T = 400associates/2 yrs = 200associates/ yr.
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Q2.12. Kroger b




Turns = R / I = 76858/ 6244 =12.3 b b b b b b b b b




Matching Supply with Demand: An Introduction to Operations Management 5e
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Solutionsto ChapterProblems b b b




Chapter 3 b b




Understanding the Supply Process: Evaluating Process Capacity b b b b b b




Q3.1 Process Analysis with One Flow Unit
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(a) Capacity of the three resources in units per hour are 602 /10 =12 , 601/ 6 =10; 603
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/16 =11.25 . The bottleneck is the resource with the lowest capacity, which is resource
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2. b




(b) The process capacity is the capacity of the bottleneck, which is 10 units/hr.
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(c) If demand =8 units / hr , then the process is demand constrained and the flow rate is
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8 units/hr b




(d) Utilization = Flow Rate / Capacity.For the three resources they are 8/12, 8/10, and b b b b b b b b b b b b b b b b b b b b b




8/11.25. b b




© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
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McGraw Hill LLC. b b b

, Q3.2 Process Analysis with Multiple Flow Units
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a) Bottleneck is resource 3 because it has the highest implied utilization of 125%. The demands b b b b b b b b b b b b b b




per hour of the three products are 40/8 = 5 , 50/8= 6.25and 60/8 = 7.5. The
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total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 =
b b b b b b b b b b b b b b b b b b b b b b




93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So b b b b b b b b b b b b b b b b b




resource 1’s utilization is 93.75 /120 = 0.78. Utilization at the other resources are
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similarly evaluated. b b




b) The capacity of resource 3 is 60 /15 = 4 units per hour. Given the ratio of units produced must
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be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units/ hr of B and
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6units/hrof C. b b b b b




Q3.3. Cranberry b




Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per
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hour. Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens while
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trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour =
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400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.
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(a) 200 barrels b




(b) From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a rate of
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100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at
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which time all waiting cranberries can be stored in the bins (no more truck waiting)
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(c) It will take another 2 hours until all the bins are empty
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(d) Since the seasonal workers only start at 10:00am, the first 4 hours of the day we accumulate
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4hours * 50barrels per hour = 200 barrels. For the remaining time that we receive incoming
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cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only
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accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4 hours, we
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get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in inventory. After
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2pm, we receive no further cranberries, yet we initially process cranberries at a rate of 125 barrels
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per hour. Thus, it only takes 100 barrels/125 barrels/hour = 0.8hours = 48 minutes
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until all bins are empty. From then, we need another 2h until the bins are empty.
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Q3.4. Western Pennsylvania Milk
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We start the day with 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000
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gallons, yet we ship 10,000 gallons. Thus inventory is depleted at a rate of 5000 gallons per hour,
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which leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to wait.
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This situation gets worse and worse and by 6pm (last client arrives), we are short 25,000 gallons.
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(a) 1pm
(b) Clients will stop waiting when we have worked off our 25,000 gallon backlog that we are
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facing at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will stop
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waiting at 11pm (after 5 more hours).
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(c) At 6pm, we have a backlog of 25,000 gallons, which is equivalent to 20 trucks
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(d) The waiting time is the area in the triangle
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© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
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McGraw Hill LLC. b b b