SOLUTION MANUAL FOR y t y t
MatchingSupplywith DemandAn Introduction to OperationsManagement,5th EditionCachon
yt yt yt yt yt yt yt yt yt yt yt
Chapter 2-19
yt yt
Chapter 2 yt
The Process View of the Organization
yt yt yt yt yt
Q2.1 Dell yt
The following steps refer directlyto Exhibit 2.1. yt yt yt yt yt yt yt
#1:For2001,wefindinDell’s10-k: Inventory=$400(inmillion) yt yt yt yt yt yt yt y t yt yt yt yt
#2: For 2001, we find in Dell’s 10-k: COGS =$26,442(in million)
yt yt yt yt yt yt yt y t yt yt yt yt
26,442$/year
#3:Inventory turns= =66.105turnsperyear 400$
yt yt yt
yt y t yt yt yt yt yt yt yt
40% per year
#4: Per unit Inventory cost = =0.605%per year
y t y t
yt yt yt y t
y t yt yt yt
66.105 per year y t y t
Q2.2. Airline yt
Weuse Little’slawto computethe flow time, sinceweknow both the flow rate as well as the
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
inventory level: yt yt
FlowTime=Inventory/FlowRate=35passengers/255passengersper hour =0.137hours yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
=8.24minutes yt yt
Q2.3 Inventory Cost
yt yt
(a) Sales=$60,000,000per year/$2000per unit =30,000unitssoldper year yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Inventory =$20,000,000/$1000 per unit = 20,000 units in inventory
yt yt yt yt yt yt yt yt yt yt yt yt
Flow Time = Inventory/Flow Rate = 20,000/30,000 per year = 2/3 year =8 months Turns=
y t yt yt yt y t yt yt yt yt y t y t y t yt yt yt yt y t yt yt yt yt
1/FlowTime=1/(2/3year)=1.5 turns per year
yt yt yt yt yt yt yt yt yt yt yt y t y t
Note: we can also get this number directlyby writing: yt yt yt yt yt yt yt yt yt y t Inventoryturns = COGS/Inventory yt yt yt yt yt
(b) Cost of Inventory: 25%per year/1.5turns =16.66%. For a $1000 product, this would yt yt y t yt yt yt yt yt yt yt yt y t y t yt yt
make an absolute inventory cost of $166.66. yt yt yt yt yt yt y t yt
Q2.4. Apparel Retailing
yt yt
(a) Revenue of $100Mimplies COGS of $50M (because of the 100% markup). yt y t yt yt yt y t y t yt yt yt yt
Turns = COGS/ Inventory = $50M/$5M =10 . y t y t yt y t y t yt y t yt yt
(b) The inventory cost, given 10 turns, is 40%/10 = 4%. For a 30$ item, the inventory cost yt yt yt yt yt yt y t yt yt yt yt yt y t y t yt yt yt
is 0.4$30 = $1.20 per unit . yt y t yt yt yt yt yt yt
Q2.5. La Villa yt yt
(a) Flow Rate = Inventory/ Flow Time =1200 skiers/10 days =120 skiers per day y t y t y t yt yt y t y t yt yt yt yt y t yt y t y t y t
(b) Last year: on anygiven day, 10% (1 of 10) of skiers are on their first dayof skiing yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
© McGrawHill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
McGraw Hill LLC. yt yt yt
, This year: on any given day, 20% (1 of 5) of skiers are on their first dayof skiing
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Average amount spent in local restaurants (per skier) yt yt yt yt yt yt yt
Last year =0.1$50+0.9$30=$32 This yt yt yt yt yt yt yt yt
year =0.2$50+0.8$30=$34
yt yt yt yt yt yt yt
%change=($34−$32)/$32=6.25%increase
yt yt yt yt yt yt yt yt yt
Q2.6. Highway
yt
We look at 1 mile of highwayasour process. Sincethe speed is 60 miles per hour, it takes a car 1
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
minute to travel through the process (flow time).
yt yt yt yt yt yt yt yt
Thereare24 carson ¼ of a mile,i.e. there are 96 carson the 1 mile stretch (inventory). Inventory
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
= Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Q2.7. Strohrmann Baking
yt yt
Thebreadneedsto be in theoven for 12 minutes (flowtime). We want to produce at a flow rate of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
4000 breads per hour, or 4000/60 = 66.66 breads per minute.
yt yt yt yt yt y t yt yt y t yt yt
Inventory= Flow Rate * Flow Time: Inventory= 66.66 breads per minute* 12 minutes Thus, yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Inventory = 800 breads, which is the required size of the oven.
yt yt yt yt yt yt yt yt yt yt yt yt
Q2.8. Mt Kinley Consulting
yt yt yt
Wehave the following information available from the question:
yt yt yt yt yt yt yt yt
Level Inventory(number of consultants at yt yt yt yt Flow Time (time spent at that yt yt yt yt yt
that level) yt level)
Associate 200 4 years yt
Manager 60 6 years yt
Partner 20 10 years yt
(a) We can use Little’s law to find the flow rate for associate consultants: Inventory = Flow
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate is 50
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
consultants per year, which need to be recruited to keep the firm in its current size (note:
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
while thereare also 50 consultants leavingthe associate level,this says nothing about how
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
many of them are dismissed vs how many of them are promoted to Manager level).
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(b) We can perform a similar analysis at the manager level, which indicates that the flow rate
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
there is 10 consultants. In order to have 10 consultants as a flow rate at the manager level,
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
we need to promote 10 associates to manager level (remember, the firm is not recruiting to
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
the higher ranks from the outside). Hence, every year, we dismiss 40 associates and
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
promote10 associates to the manager level(the odds at that level are 20%)
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
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yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
McGraw Hill LLC. yt yt yt
, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained via the
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
same calculations as before). Thus, from the 10 manager cases we evaluate every year, 8 are
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
dismissed and 2 are promoted to partner (the oddsat that level aretherebyalso 20%).
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
In order to find the odds of a new hire to become partner, we need to multiply the promotion
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
probabilities:0.2*0.2 = 0.04. Thus, a new hire has a4% chance of makingit to partner.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Q2.9. Major US Retailers
yt yt yt
a. Product stays on average for31.9 days in Costco’s inventory yt yt yt yt yt yt yt yt yt
b. Costco has for a $5 product an inventorycost of $0.1311 which compares to a yt yt yt yt yt yt yt yt yt yt yt yt yt yt
$0.2049 atWal-Mart y t yt
Q2.10. McDonald’s yt
a. Inventoryturnsfor McDonald’s were 92.3. They were 30.05 for Wendy’s. yt yt yt yt yt yt yt yt yt yt
b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about yt yt yt yt yt yt yt yt yt yt yt yt yt
$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. yt yt yt yt yt yt yt yt yt yt yt yt y t yt
Q2.11. BCH yt
I=400associates,T=2years. R=I/T=400associates/2yrs=200associates/yr.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Q2.12. Kroger yt
Turns = R / I =76858/ 6244 =12.3 yt yt yt yt y t yt yt yt yt
Matching Supplywith Demand:AnIntroduction to Operations Management 5e yt yt yt yt yt yt yt yt yt
SolutionstoChapterProblems yt yt yt
Chapter 3 yt yt
Understanding the Supply Process: Evaluating Process Capacity yt yt yt yt yt yt
Q3.1 Process Analysis with One Flow Unit
yt yt yt yt yt yt
(a) Capacity of the three resources in units per hour are 602 /10 =12 , 601/ 6 =10; 603 yt yt yt yt yt yt yt yt yt y t yt yt yt y t yt yt yt
/16=11.25.The bottleneck is the resource with the lowest capacity, which is resource 2.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(b) The process capacity is the capacityof the bottleneck, which is 10units/hr.
yt yt yt yt yt yt yt yt yt yt y t yt yt
(c) If demand =8 units/hr, then the process is demand constrained and the flow rate is
y t y t y t yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
8units/hr yt
(d) Utilization=FlowRate/Capacity.Forthethreeresourcestheyare 8/12, 8/10,and yt yt yt yt yt yt yt yt yt yt yt yt y t yt yt yt y t yt yt yt yt
8/11.25. yt yt
© McGrawHill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
McGraw Hill LLC. yt yt yt
, Q3.2 Process Analysis with Multiple Flow Units
yt yt yt yt yt yt
a) Bottleneck is resource 3 because it has the highest implied utilization of 125%. The demands yt yt yt yt yt yt yt yt yt yt yt yt yt yt
per hour of the three products are 40/8=5 , 50/8=6.25and 60/8=7.5. The
yt yt yt yt yt yt yt y t yt yt yt yt y t yt yt yt yt yt y t yt yt yt yt y t y t
total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 = yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
resource 1’s utilization is 93.75 /120 = 0.78. Utilization at the other resources are
yt yt yt yt y t yt yt yt yt yt yt yt yt yt
similarly evaluated. yt yt
b) The capacity of resource 3 is 60/15 = 4 units per hour. Given the ratio of units produced must yt yt yt yt yt y t
yt yt yt yt y t
yt yt yt yt yt yt yt yt
be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units/hrof B and
yt yt yt yt yt yt yt yt yt yt y t
yt yt y t
yt y t
yt yt yt yt
yt yt
6units/hrofC. yt yt yt yt
yt
Q3.3. Cranberry yt
Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per hour. yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens while trucks
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour = 400
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(a) 200 barrels yt
(b) From 2pm onwards, no additionalcranberries are received. Inventorygets depletedat a rate of 100
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at which
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
time all waiting cranberries can be stored in the bins (no more truck waiting)
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(c) It will take another2 hours until all the bins are empty
yt yt yt yt yt yt yt yt yt yt yt
(d) Since the seasonal workers only start at 10:00am, the first 4 hours of the day we accumulate 4hours
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
* 50barrels per hour = 200 barrels. For the remaining time that we receive incoming cranberries,
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
our processing rate is higher (125 barrels per hour). Thus, inventory only accumulates at a rate of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
25 (150-125 barrels per hour). Given that this happens over 4 hours, we get another 100 barrels in
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
inventory. At 2pm, we thereby have 300 barrels in inventory. After 2pm, we receive no further
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
cranberries, yet we initially process cranberries at a rate of 125 barrels per hour. Thus, it only takes
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
100barrels/125barrels/hour =0.8hours =48minutes
y t yt yt yt yt yt yt yt yt yt
until all bins areempty. From then, we need another 2h until the bins are empty.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Q3.4. Western Pennsylvania Milk yt yt yt
We start the daywith 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
gallons, yetwe ship 10,000 gallons. Thus inventoryisdepleted at a rate of 5000 gallons per hour, which
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to wait. This
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
situation gets worse and worse and by 6pm (last client arrives), we are short 25,000 gallons.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(a) 1pm
(b) Clients will stop waitingwhen we have worked off our 25,000 gallon backlogthat we are facing yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will stop waiting at
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
11pm (after 5 more hours).
yt yt yt yt yt
(c) At 6pm, we have a backlog of 25,000 gallons, which is equivalent to 20 trucks
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(d) The waiting time is the areain the triangle yt yt yt yt yt yt yt yt
© McGrawHill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
McGraw Hill LLC. yt yt yt
MatchingSupplywith DemandAn Introduction to OperationsManagement,5th EditionCachon
yt yt yt yt yt yt yt yt yt yt yt
Chapter 2-19
yt yt
Chapter 2 yt
The Process View of the Organization
yt yt yt yt yt
Q2.1 Dell yt
The following steps refer directlyto Exhibit 2.1. yt yt yt yt yt yt yt
#1:For2001,wefindinDell’s10-k: Inventory=$400(inmillion) yt yt yt yt yt yt yt y t yt yt yt yt
#2: For 2001, we find in Dell’s 10-k: COGS =$26,442(in million)
yt yt yt yt yt yt yt y t yt yt yt yt
26,442$/year
#3:Inventory turns= =66.105turnsperyear 400$
yt yt yt
yt y t yt yt yt yt yt yt yt
40% per year
#4: Per unit Inventory cost = =0.605%per year
y t y t
yt yt yt y t
y t yt yt yt
66.105 per year y t y t
Q2.2. Airline yt
Weuse Little’slawto computethe flow time, sinceweknow both the flow rate as well as the
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
inventory level: yt yt
FlowTime=Inventory/FlowRate=35passengers/255passengersper hour =0.137hours yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
=8.24minutes yt yt
Q2.3 Inventory Cost
yt yt
(a) Sales=$60,000,000per year/$2000per unit =30,000unitssoldper year yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Inventory =$20,000,000/$1000 per unit = 20,000 units in inventory
yt yt yt yt yt yt yt yt yt yt yt yt
Flow Time = Inventory/Flow Rate = 20,000/30,000 per year = 2/3 year =8 months Turns=
y t yt yt yt y t yt yt yt yt y t y t y t yt yt yt yt y t yt yt yt yt
1/FlowTime=1/(2/3year)=1.5 turns per year
yt yt yt yt yt yt yt yt yt yt yt y t y t
Note: we can also get this number directlyby writing: yt yt yt yt yt yt yt yt yt y t Inventoryturns = COGS/Inventory yt yt yt yt yt
(b) Cost of Inventory: 25%per year/1.5turns =16.66%. For a $1000 product, this would yt yt y t yt yt yt yt yt yt yt yt y t y t yt yt
make an absolute inventory cost of $166.66. yt yt yt yt yt yt y t yt
Q2.4. Apparel Retailing
yt yt
(a) Revenue of $100Mimplies COGS of $50M (because of the 100% markup). yt y t yt yt yt y t y t yt yt yt yt
Turns = COGS/ Inventory = $50M/$5M =10 . y t y t yt y t y t yt y t yt yt
(b) The inventory cost, given 10 turns, is 40%/10 = 4%. For a 30$ item, the inventory cost yt yt yt yt yt yt y t yt yt yt yt yt y t y t yt yt yt
is 0.4$30 = $1.20 per unit . yt y t yt yt yt yt yt yt
Q2.5. La Villa yt yt
(a) Flow Rate = Inventory/ Flow Time =1200 skiers/10 days =120 skiers per day y t y t y t yt yt y t y t yt yt yt yt y t yt y t y t y t
(b) Last year: on anygiven day, 10% (1 of 10) of skiers are on their first dayof skiing yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
© McGrawHill LLC. All rights reserved. No reproduction or distribution without the prior written consent of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
McGraw Hill LLC. yt yt yt
, This year: on any given day, 20% (1 of 5) of skiers are on their first dayof skiing
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Average amount spent in local restaurants (per skier) yt yt yt yt yt yt yt
Last year =0.1$50+0.9$30=$32 This yt yt yt yt yt yt yt yt
year =0.2$50+0.8$30=$34
yt yt yt yt yt yt yt
%change=($34−$32)/$32=6.25%increase
yt yt yt yt yt yt yt yt yt
Q2.6. Highway
yt
We look at 1 mile of highwayasour process. Sincethe speed is 60 miles per hour, it takes a car 1
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
minute to travel through the process (flow time).
yt yt yt yt yt yt yt yt
Thereare24 carson ¼ of a mile,i.e. there are 96 carson the 1 mile stretch (inventory). Inventory
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
= Flow Rate * Flow Time: 96 cars = Flow Rate * 1 minute
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Thus, the Flow Rate is 96 cars per minute, corresponding to 96*60 = 5760 cars per hour.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Q2.7. Strohrmann Baking
yt yt
Thebreadneedsto be in theoven for 12 minutes (flowtime). We want to produce at a flow rate of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
4000 breads per hour, or 4000/60 = 66.66 breads per minute.
yt yt yt yt yt y t yt yt y t yt yt
Inventory= Flow Rate * Flow Time: Inventory= 66.66 breads per minute* 12 minutes Thus, yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Inventory = 800 breads, which is the required size of the oven.
yt yt yt yt yt yt yt yt yt yt yt yt
Q2.8. Mt Kinley Consulting
yt yt yt
Wehave the following information available from the question:
yt yt yt yt yt yt yt yt
Level Inventory(number of consultants at yt yt yt yt Flow Time (time spent at that yt yt yt yt yt
that level) yt level)
Associate 200 4 years yt
Manager 60 6 years yt
Partner 20 10 years yt
(a) We can use Little’s law to find the flow rate for associate consultants: Inventory = Flow
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Rate * Flow Time; 200 consultants = Flow Rate * 4 years; thus, the flow rate is 50
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
consultants per year, which need to be recruited to keep the firm in its current size (note:
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
while thereare also 50 consultants leavingthe 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).
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(b) We can perform a similar analysis at the manager level, which indicates that the flow rate
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
there is 10 consultants. In order to have 10 consultants as a flow rate at the manager level,
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
we need to promote 10 associates to manager level (remember, the firm is not recruiting to
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
the higher ranks from the outside). Hence, every year, we dismiss 40 associates and
yt yt yt yt yt yt yt yt yt yt yt yt yt yt
promote10 associates to the manager level(the odds at that level are 20%)
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, Now, consider the partner level. The flow rate there is 2 consultants per year (obtained via the
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
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 oddsat that level aretherebyalso 20%).
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
In order to find the odds of a new hire to become partner, we need to multiply the promotion
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
probabilities:0.2*0.2 = 0.04. Thus, a new hire has a4% chance of makingit to partner.
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Q2.9. Major US Retailers
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a. Product stays on average for31.9 days in Costco’s inventory yt yt yt yt yt yt yt yt yt
b. Costco has for a $5 product an inventorycost of $0.1311 which compares to a yt yt yt yt yt yt yt yt yt yt yt yt yt yt
$0.2049 atWal-Mart y t yt
Q2.10. McDonald’s yt
a. Inventoryturnsfor McDonald’s were 92.3. They were 30.05 for Wendy’s. yt yt yt yt yt yt yt yt yt yt
b. McDonald’s has per unit inventory costs of 0.32%, which for a 3$ meal about yt yt yt yt yt yt yt yt yt yt yt yt yt
$0.00975. That compares to 0.998% at Wendy’s where the cost per meal is $0.0299. yt yt yt yt yt yt yt yt yt yt yt yt y t yt
Q2.11. BCH yt
I=400associates,T=2years. R=I/T=400associates/2yrs=200associates/yr.
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Q2.12. Kroger yt
Turns = R / I =76858/ 6244 =12.3 yt yt yt yt y t yt yt yt yt
Matching Supplywith Demand:AnIntroduction to Operations Management 5e yt yt yt yt yt yt yt yt yt
SolutionstoChapterProblems yt yt yt
Chapter 3 yt yt
Understanding the Supply Process: Evaluating Process Capacity yt yt yt yt yt yt
Q3.1 Process Analysis with One Flow Unit
yt yt yt yt yt yt
(a) Capacity of the three resources in units per hour are 602 /10 =12 , 601/ 6 =10; 603 yt yt yt yt yt yt yt yt yt y t yt yt yt y t yt yt yt
/16=11.25.The bottleneck is the resource with the lowest capacity, which is resource 2.
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(b) The process capacity is the capacityof the bottleneck, which is 10units/hr.
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(c) If demand =8 units/hr, then the process is demand constrained and the flow rate is
y t y t y t yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
8units/hr yt
(d) Utilization=FlowRate/Capacity.Forthethreeresourcestheyare 8/12, 8/10,and yt yt yt yt yt yt yt yt yt yt yt yt y t yt yt yt y t yt yt yt yt
8/11.25. yt yt
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, Q3.2 Process Analysis with Multiple Flow Units
yt yt yt yt yt yt
a) Bottleneck is resource 3 because it has the highest implied utilization of 125%. The demands yt yt yt yt yt yt yt yt yt yt yt yt yt yt
per hour of the three products are 40/8=5 , 50/8=6.25and 60/8=7.5. The
yt yt yt yt yt yt yt y t yt yt yt yt y t yt yt yt yt yt y t yt yt yt yt y t y t
total minutes of work demanded per hour at resource 1 is 5 × 5 + 6.25 * 5 + 7.5 * 5 = yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
93.75. Two workers at resource 1 produce 2 * 60 = 120 min of work per hour. So yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
resource 1’s utilization is 93.75 /120 = 0.78. Utilization at the other resources are
yt yt yt yt y t yt yt yt yt yt yt yt yt yt
similarly evaluated. yt yt
b) The capacity of resource 3 is 60/15 = 4 units per hour. Given the ratio of units produced must yt yt yt yt yt y t
yt yt yt yt y t
yt yt yt yt yt yt yt yt
be 4 to 5 to 6, the process can produce 4 units/ hr of A, 5 units/hrof B and
yt yt yt yt yt yt yt yt yt yt y t
yt yt y t
yt y t
yt yt yt yt
yt yt
6units/hrofC. yt yt yt yt
yt
Q3.3. Cranberry yt
Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per hour. yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Thus, inventory accumulates at a rate of 150-100 = 50 barrels per hour. This happens while trucks
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour = 400
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barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(a) 200 barrels yt
(b) From 2pm onwards, no additionalcranberries are received. Inventorygets depletedat a rate of 100
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barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at which
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
time all waiting cranberries can be stored in the bins (no more truck waiting)
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(c) It will take another2 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 4hours
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
* 50barrels per hour = 200 barrels. For the remaining time that we receive incoming cranberries,
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
our processing rate is higher (125 barrels per hour). Thus, inventory only accumulates at a rate of
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
25 (150-125 barrels per hour). Given that this happens over 4 hours, we get another 100 barrels in
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inventory. At 2pm, we thereby have 300 barrels in inventory. After 2pm, we receive no further
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
cranberries, yet we initially process cranberries at a rate of 125 barrels per hour. Thus, it only takes
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
100barrels/125barrels/hour =0.8hours =48minutes
y t yt yt yt yt yt yt yt yt yt
until all bins areempty. From then, we need another 2h until the bins are empty.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
Q3.4. Western Pennsylvania Milk yt yt yt
We start the daywith 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
gallons, yetwe ship 10,000 gallons. Thus inventoryisdepleted at a rate of 5000 gallons per hour, which
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
leaves us without milk after 5 hours (at 1pm). From then onwards, clients will have to wait. This
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
situation gets worse and worse and by 6pm (last client arrives), we are short 25,000 gallons.
yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
(a) 1pm
(b) Clients will stop waitingwhen we have worked off our 25,000 gallon backlogthat we are facing yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt yt
at 6pm. Since we are doing this at a rate of 5,000 gallon per hour, clients will stop waiting at
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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 areain the triangle yt yt yt yt yt yt yt yt
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McGraw Hill LLC. yt yt yt
