SOLUTION MANUAL FOR jj jj
Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon
jj jj jj jj jj jj jj jj jj jj jj
Chapter 2-19
jj jj
Chapter 2 jj
The Process View of the Organization
jj jj jj jj jj
Q2.1 Dell jj
The following steps refer directly to Exhibit 2.1.
jj jj jj jj jj jj jj
#1: For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
jj jj jj jj jj jj jj jj jj jj jj jj
#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
jj jj jj jj jj jj jj j j jj jj jj jj
26,442$/ year
#3: Inventory turns 66.105 turns per year 400$
j jj jj
jj jj jj jj jj jj jj jj jj
40% per year
0.605% per year
jj jj
#4: Per unit Inventory cost jj jj jj j j jj jj jj
jj
66.105 per jj
year jj
Q2.2. Airline jj
We use Little’s law to compute the flow time, since we know both the flow rate as well
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
as the inventory level:
jj jj jj jj
Flow Time Inventory/Flow Rate 35 passengers/255 passengers per hour 0.137 hours
jj jj jj j jj jj j j j j jj jj jj j jj
8.24 minutes jj jj
Q2.3 Inventory Cost
jj jj
(a) Sales $60,000,000 per year/$2000 per unit 30,000 units sold per year j j j jj j j jj jj jj j j j jj jj
Inventory $20,000,000 /$1000 per unit 20,000 units in inventory
jj jj jj j j jj jj jj jj jj jj jj
Flow Time Inventory/ Flow Rate 20,000/30,000 per year 2/3 year 8 months
jj jj jj jj jj jj jj j j jj j j jj jj j j jj jj jj jj
Turns 1/Flow Time 1/(2/3 year) 1.5 turns per year
jj jj j j jj jj j j j jj jj j jj jj jj
Note: we can also get this number directly by writing:
jj jj jj jj jj jj jj jj jj j j Inventory jjturns jj jjCOGS/j jjInventory
(b) Cost of Inventory: 25% per year/1.5 turns 16.66%. For a $1000 product, this
jj jj j j jj jj j jj jj j jj jj j j j j jj
would make an absolute inventory cost of $166.66.
jj jj jj jj jj jj jj j j j
Q2.4. Apparel Retailing
jj jj
(a) Revenue of $100M implies COGS of $50M (because of the 100% markup). jj j j j jj jj j j j j jj jj jj jj
Turns COGS/ Inventory $50M/ $5M 10 . jj jj jj jj jj j jj j jj
(b) The inventory cost, given 10 turns, is 40%/10 4% . For a 30$ item, the
jj jj jj jj jj jj j j jj jj jj jj jj j j j j jj
inventory cost is 0.4$30 $1.20 per unit .
jj jj jj j j j jj jj jj jj jj
Q2.5. La Villa jj jj
(a) Flow Rate Inventory / Flow Time 1200 skiers /10 days 120 skiers per day jj jj jj j jj jj jj j jj jj jj jj jj jj j j j j
(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
, This year: on any given day, 20% (1 of 5) of skiers are on their first day of skiing
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Average amount spent in local restaurants (per skier) jj jj jj jj jj jj jj
Last year 0.1$500.9$30 $32
jj jj jj j j jj j
This year 0.2$500.8$30 $34
jj jj jj jj j j jj j
% change ($34$32)/$32 6.25% increase
j jj j j j j jj j j
Q2.6. Highway
jj
We look at 1 mile of highway as our process. Since the speed is 60 miles per hour, it
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
takes a car 1 minute to travel through the process (flow time).
jj jj jj jj jj jj jj jj jj jj jj jj
There are 24 cars on ¼ of a mile, i.e. there are 96 cars on the 1 mile stretch (inventory).
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Inventory = Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Q2.7. Strohrmann Baking
jj jj
The bread needs to be in the oven for 12 minutes (flow time). We want to produce at a
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
flow rate of 4000 breads per hour, or 4000/60 = 66.66 breads per minute.
jj jj jj jj jj jj jj jj j j jj jj j j jj jj
Inventory = Flow Rate * Flow Time: Inventory = 66.66 breads per minute* 12 minutes
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Thus, Inventory = 800 breads, which is the required size of the oven.
jj jj jj jj jj jj jj jj jj jj jj jj jj
Q2.8. Mt Kinley Consulting
jj jj jj
We have the following information available from the question:
jj jj jj jj jj jj jj jj
Level Inventory (number of consultants at jj jj jj jj Flow Time (time spent at that jj jj jj jj jj
that level) jj level)
Associate 200 4 years jj
Manager 60 6 years jj
Partner 20 10 years jj
(a) We can use Little’s law to find the flow rate for associate consultants: Inventory =
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Flow Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
is 50 consultants per year, which need to be recruited to keep the firm in its current
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
size (note: while there are also 50 consultants leaving the associate level, this says
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
nothing about how many of them are dismissed vs how many of them are promoted
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
to Manager level).
jj jj jj
(b) We can perform a similar analysis at the manager level, which indicates that the
jj jj jj jj jj jj jj jj jj jj jj jj jj
flow rate there is 10 consultants. In order to have 10 consultants as a flow rate at the
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
manager level, we need to promote 10 associates to manager level (remember, the
jj jj jj jj jj jj jj jj jj jj jj jj jj
firm is not recruiting to the higher ranks from the outside). Hence, every year, we
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
dismiss 40 associates and promote 10 associates to the manager level (the odds at that
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
level are 20%)
jj jj jj
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
via the same calculations as before). Thus, from the 10 manager cases we evaluate every
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
year, 8 are dismissed and 2 are promoted to partner (the odds at that level are thereby also
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
20%).
jj
In order to find the odds of a new hire to become partner, we need to multiply the
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
promotion probabilities: 0.2*0.2 = 0.04. Thus, a new hire has a 4% chance of making it to
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
partner.
jj
Q2.9. Major US Retailers
jj jj jj
a. Product stays on average for 31.9 days in Costco’s inventory jj jj jj jj jj jj jj jj jj
b. Costco has for a $5 product an inventory cost of $0.1311 which compares to a jj jj jj jj jj jj jj jj jj jj jj jj jj jj
$0.2049 at Wal-Mart jj jj
Q2.10. McDonald’s jj
a. Inventory turns for McDonald’s were 92.3. They were 30.05 for Wendy’s. jj jj jj jj jj jj jj jj jj jj
b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about jj jj jj jj jj jj jj jj jj jj jj jj jj
$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. jj jj jj jj jj jj jj jj jj jj jj jj j j j
Q2.11. BCH jj
I = 400 associates, T = 2 years. R I/T 400 associates/2 yrs 200 associates/ yr .
j j j jj j j j jj jj j j j jj jj j j j jj jj jj j j j j
Q2.12. Kroger jj
Turns R / I 76858/ 6244 12.3 jj jj jj jj jj jj j jj jj
Matching Supply with Demand: An Introduction to Operations Management
jj jj jj jj jj jj jj jj
5e jj
Solutions to Chapter Problems jj jj jj
Chapter 3 jj jj
Understanding the Supply Process: Evaluating Process Capacity jj jj jj jj jj jj
Q3.1 Process Analysis with One Flow Unit
jj jj jj jj jj jj
(a) Capacity of the three resources in units per hour are 602 /10 12 , 601/ 6 10;
jj jj jj jj jj jj jj jj jj j j jj jj jj j j jj jj
603 /16 11.25 . The bottleneck is the resource with the lowest capacity, which is
jj j j j jj jj jj jj jj jj jj jj jj jj jj
resource 2. jj jj
(b) The process capacity is the capacity of the bottleneck, which is 10 units/hr .
jj jj jj jj jj jj jj jj jj jj jj jj j
(c) If demand 8 units / hr , then the process is demand constrained and the flow rate is
jj jj jj j jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
8 units/hr jj
(d) Utilization = Flow Rate / Capacity. For the three resources they are 8/12, 8/10 , and
jj jj jj jj jj j jj jj jj jj jj jj jj j j j jj j j j jj
8/11.25. j j
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
, Q3.2 Process Analysis with Multiple Flow Units
jj jj jj jj jj jj
a) Bottleneck is resource 3 because it has the highest implied utilization of 125%. The jj jj jj jj jj jj jj jj jj jj jj jj jj
demands per hour of the three products are 5 , 6.25 and 7.5.
jj jj jj jj jj jj jj jj j j j j jj jj j j j j jj jj j j j j j jj jj j j
The j j
total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 =
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
resource 1’s utilization is 93.75 /120 0.78. Utilization at the other resources
jj jj jj jj j j j jj jj jj jj jj jj jj
are similarly evaluated.jj jj jj
b) The capacity of resource 3 is 60 /15 4 units per hour. Given the ratio of units
jj jj jj jj jj j j j jj jj jj j j jj jj jj jj jj jj
produced must be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units / hr of
jj jj jj jj jj jj jj jj jj jj jj jj j j jj jj j j jj j j jj j jj jj
B and jj jj
6 units/hrof C. j j j j jj
Q3.3. Cranberry jj
Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
per hour. Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
while trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
per hour = 400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
are in trucks.
jj jj jj
(a) 200 barrels jj
(b) From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a rate
jj jj jj jj jj jj jj jj jj jj jj jj jj
of 100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
barrels, at which time all waiting cranberries can be stored in the bins (no more truck
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
waiting)
jj
(c) It will take another 2 hours until all the bins are empty
jj jj jj jj jj jj jj jj jj jj jj
(d) Since the seasonal workers only start at 10:00am, the first 4 hours of the day we accumulate
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
4hours * 50barrels per hour = 200 barrels. For the remaining time that we receive incoming
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only
jj jj jj jj jj jj jj jj jj jj jj jj jj
accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
hours, we get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
inventory. After 2pm, we receive no further cranberries, yet we initially process cranberries
jj jj jj jj jj jj jj jj jj jj jj jj jj
at a rate of 125 barrels per hour. Thus, it only takes 100 barrels/125 barrels/hour 0.8 hours
jj jj jj jj jj jj jj jj jj jj jj jj jj jj j jj jj jj jj jj
48 minutes
jj jj
until all bins are empty. From then, we need another 2h until the bins are empty.
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Q3.4. Western Pennsylvania Milk
jj jj jj
We start the day with 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
gallons, yet we ship 10,000 gallons. Thus inventory is depleted at a rate of 5000 gallons per hour,
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
which leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
wait. This situation gets worse and worse and by 6pm (last client arrives), we are short 25,000
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
gallons.
jj
(a) 1pm
(b) Clients will stop waiting when we have worked off our 25,000 gallon backlog that we are
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
facing at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
stop waiting at 11pm (after 5 more hours).
jj jj jj jj jj jj jj jj
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
Matching Supply with Demand An Introduction to Operations Management, 5th Edition Cachon
jj jj jj jj jj jj jj jj jj jj jj
Chapter 2-19
jj jj
Chapter 2 jj
The Process View of the Organization
jj jj jj jj jj
Q2.1 Dell jj
The following steps refer directly to Exhibit 2.1.
jj jj jj jj jj jj jj
#1: For 2001, we find in Dell’s 10-k: Inventory = $400 (in million)
jj jj jj jj jj jj jj jj jj jj jj jj
#2: For 2001, we find in Dell’s 10-k: COGS = $26,442 (in million)
jj jj jj jj jj jj jj j j jj jj jj jj
26,442$/ year
#3: Inventory turns 66.105 turns per year 400$
j jj jj
jj jj jj jj jj jj jj jj jj
40% per year
0.605% per year
jj jj
#4: Per unit Inventory cost jj jj jj j j jj jj jj
jj
66.105 per jj
year jj
Q2.2. Airline jj
We use Little’s law to compute the flow time, since we know both the flow rate as well
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
as the inventory level:
jj jj jj jj
Flow Time Inventory/Flow Rate 35 passengers/255 passengers per hour 0.137 hours
jj jj jj j jj jj j j j j jj jj jj j jj
8.24 minutes jj jj
Q2.3 Inventory Cost
jj jj
(a) Sales $60,000,000 per year/$2000 per unit 30,000 units sold per year j j j jj j j jj jj jj j j j jj jj
Inventory $20,000,000 /$1000 per unit 20,000 units in inventory
jj jj jj j j jj jj jj jj jj jj jj
Flow Time Inventory/ Flow Rate 20,000/30,000 per year 2/3 year 8 months
jj jj jj jj jj jj jj j j jj j j jj jj j j jj jj jj jj
Turns 1/Flow Time 1/(2/3 year) 1.5 turns per year
jj jj j j jj jj j j j jj jj j jj jj jj
Note: we can also get this number directly by writing:
jj jj jj jj jj jj jj jj jj j j Inventory jjturns jj jjCOGS/j jjInventory
(b) Cost of Inventory: 25% per year/1.5 turns 16.66%. For a $1000 product, this
jj jj j j jj jj j jj jj j jj jj j j j j jj
would make an absolute inventory cost of $166.66.
jj jj jj jj jj jj jj j j j
Q2.4. Apparel Retailing
jj jj
(a) Revenue of $100M implies COGS of $50M (because of the 100% markup). jj j j j jj jj j j j j jj jj jj jj
Turns COGS/ Inventory $50M/ $5M 10 . jj jj jj jj jj j jj j jj
(b) The inventory cost, given 10 turns, is 40%/10 4% . For a 30$ item, the
jj jj jj jj jj jj j j jj jj jj jj jj j j j j jj
inventory cost is 0.4$30 $1.20 per unit .
jj jj jj j j j jj jj jj jj jj
Q2.5. La Villa jj jj
(a) Flow Rate Inventory / Flow Time 1200 skiers /10 days 120 skiers per day jj jj jj j jj jj jj j jj jj jj jj jj jj j j j j
(b) Last year: on any given day, 10% (1 of 10) of skiers are on their first day of skiing
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
, This year: on any given day, 20% (1 of 5) of skiers are on their first day of skiing
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Average amount spent in local restaurants (per skier) jj jj jj jj jj jj jj
Last year 0.1$500.9$30 $32
jj jj jj j j jj j
This year 0.2$500.8$30 $34
jj jj jj jj j j jj j
% change ($34$32)/$32 6.25% increase
j jj j j j j jj j j
Q2.6. Highway
jj
We look at 1 mile of highway as our process. Since the speed is 60 miles per hour, it
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
takes a car 1 minute to travel through the process (flow time).
jj jj jj jj jj jj jj jj jj jj jj jj
There are 24 cars on ¼ of a mile, i.e. there are 96 cars on the 1 mile stretch (inventory).
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Inventory = Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Q2.7. Strohrmann Baking
jj jj
The bread needs to be in the oven for 12 minutes (flow time). We want to produce at a
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
flow rate of 4000 breads per hour, or 4000/60 = 66.66 breads per minute.
jj jj jj jj jj jj jj jj j j jj jj j j jj jj
Inventory = Flow Rate * Flow Time: Inventory = 66.66 breads per minute* 12 minutes
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Thus, Inventory = 800 breads, which is the required size of the oven.
jj jj jj jj jj jj jj jj jj jj jj jj jj
Q2.8. Mt Kinley Consulting
jj jj jj
We have the following information available from the question:
jj jj jj jj jj jj jj jj
Level Inventory (number of consultants at jj jj jj jj Flow Time (time spent at that jj jj jj jj jj
that level) jj level)
Associate 200 4 years jj
Manager 60 6 years jj
Partner 20 10 years jj
(a) We can use Little’s law to find the flow rate for associate consultants: Inventory =
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
Flow Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
is 50 consultants per year, which need to be recruited to keep the firm in its current
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
size (note: while there are also 50 consultants leaving the associate level, this says
jj jj jj jj jj jj jj jj jj jj jj jj jj jj
nothing about how many of them are dismissed vs how many of them are promoted
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
to Manager level).
jj jj jj
(b) We can perform a similar analysis at the manager level, which indicates that the
jj jj jj jj jj jj jj jj jj jj jj jj jj
flow rate there is 10 consultants. In order to have 10 consultants as a flow rate at the
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
manager level, we need to promote 10 associates to manager level (remember, the
jj jj jj jj jj jj jj jj jj jj jj jj jj
firm is not recruiting to the higher ranks from the outside). Hence, every year, we
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dismiss 40 associates and promote 10 associates to the manager level (the odds at that
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level are 20%)
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of McGraw Hill LLC. jj jj jj jj
, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained
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via the same calculations as before). Thus, from the 10 manager cases we evaluate every
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year, 8 are dismissed and 2 are promoted to partner (the odds at that level are thereby also
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20%).
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In order to find the odds of a new hire to become partner, we need to multiply the
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promotion probabilities: 0.2*0.2 = 0.04. Thus, a new hire has a 4% chance of making it to
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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 jj jj jj jj jj jj jj jj jj
b. Costco has for a $5 product an inventory cost of $0.1311 which compares to a jj jj jj jj jj jj jj jj jj jj jj jj jj jj
$0.2049 at Wal-Mart jj jj
Q2.10. McDonald’s jj
a. Inventory turns for McDonald’s were 92.3. They were 30.05 for Wendy’s. jj jj jj jj jj jj jj jj jj jj
b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about jj jj jj jj jj jj jj jj jj jj jj jj jj
$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. jj jj jj jj jj jj jj jj jj jj jj jj j j j
Q2.11. BCH jj
I = 400 associates, T = 2 years. R I/T 400 associates/2 yrs 200 associates/ yr .
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Q2.12. Kroger jj
Turns R / I 76858/ 6244 12.3 jj jj jj jj jj jj j jj jj
Matching Supply with Demand: An Introduction to Operations Management
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5e jj
Solutions to Chapter Problems jj jj jj
Chapter 3 jj jj
Understanding the Supply Process: Evaluating Process Capacity jj jj jj jj jj jj
Q3.1 Process Analysis with One Flow Unit
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(a) Capacity of the three resources in units per hour are 602 /10 12 , 601/ 6 10;
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603 /16 11.25 . The bottleneck is the resource with the lowest capacity, which is
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resource 2. jj jj
(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 jj
(d) Utilization = Flow Rate / Capacity. For the three resources they are 8/12, 8/10 , and
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8/11.25. j j
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jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
, 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 jj jj jj jj jj jj jj jj jj jj jj jj jj
demands per hour of the three products are 5 , 6.25 and 7.5.
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The j j
total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 =
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
resource 1’s utilization is 93.75 /120 0.78. Utilization at the other resources
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are similarly evaluated.jj jj jj
b) The capacity of resource 3 is 60 /15 4 units per hour. Given the ratio of units
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produced must be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units / hr of
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B and jj jj
6 units/hrof C. j j j j jj
Q3.3. Cranberry jj
Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels
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per hour. Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens
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while trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels
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per hour = 400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels
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are in trucks.
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(a) 200 barrels jj
(b) From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a rate
jj jj jj jj jj jj jj jj jj jj jj jj jj
of 100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
barrels, at which time all waiting cranberries can be stored in the bins (no more truck
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
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
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
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
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
hours, we get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
inventory. After 2pm, we receive no further cranberries, yet we initially process cranberries
jj jj jj jj jj jj jj jj jj jj jj jj jj
at a rate of 125 barrels per hour. Thus, it only takes 100 barrels/125 barrels/hour 0.8 hours
jj jj jj jj jj jj jj jj jj jj jj jj jj jj j jj jj jj jj jj
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
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wait. This situation gets worse and worse and by 6pm (last client arrives), we are short 25,000
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
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
jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
stop waiting at 11pm (after 5 more hours).
jj jj jj jj jj jj jj jj
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jj jj jj jj jj jj jj jj jj jj jj jj jj jj jj
of McGraw Hill LLC. jj jj jj jj
