Review MT2

7/23/2019 Review MT2

1/33

Review for Midterm 2

OPSM 301


2/33

Practice Problems

Problem 1:

A major drug store chain wishes to build a new warehouse to serve the whole

Midwest. At the moment, it is looking at three possible locations. The factors,

weights, and ratings being considered are given below:

RatingsFactor eights !eoria "es Moines #hicago

$earness to markets %& ' ( )

*abor cost ) + + '

Taes -) + ($earness to suppliers -& -& / -&

hich cit0 should the0 choose1


3/33

Practice Problems

Problem 1:

A major drug store chain wishes to build a new warehouse to serve the whole

Midwest. At the moment, it is looking at three possible locations. The factors,

weights, and ratings being considered are given below:

RatingsFactor eights !eoria "es Moines #hicago

$earness to markets %& ' ( )

*abor cost ) + + '

Taes -) + ($earness to suppliers -& -& / -&

hich cit0 should the0 choose1

2ased upon the weights and rating,

"es Moines should be chosen.

eighted Ratings!eoria "es Moines #hicago

+& -'& -&&

'& '& %&

-%& -3) -&)-&& /& -&&

Total 3'& 3() 3%)


4/33

Problem 2:

2alfour4s is considering building a plant in one of three possible locations.

The0 have estimated the following parameters for each location:

Practice Problems

*ocation Fied #ost 5ariable #ost

aco, Teas 63&&,&&& 6).()

Tijuana, Meico 6+&&,&&& 6%.()

Fa0etteville, Arkansas 6-&&,&&& 6+.&&

For what unit sales volume should the0 choose each location1


5/33

Problem 2:



Practice Problems


aco, Teas 63&&,&&& 6).()




Transition between aco and Tijuana

3&&,&&& 7 ).()x8 +&&,&&& 7 %.()x

3x8 )&&,&&&

x8 -//,&&&

Transition between aco and Fa0etteville

3&&,&&& 7 ).()x8 -&&,&&& 7 +.&&x

%.%)x8 %&&,&&&

x8 ++,+++


6/33

Problem 2:



Practice Problems


aco, Teas 63&&,&&& 6).()




Transition between aco and Tijuana

3&&,&&& 7 ).()x8 +&&,&&& 7 %.()x

3x8 )&&,&&&

x8 -//,&&&

Transition between aco and Fa0etteville

3&&,&&& 7 ).()x8 -&&,&&& 7 +.&&x

%.%)x8 %&&,&&&

x8 ++,+++

Locate in Fayetteville


7/33

Practice Problems

Problem 3:

9ur main distribution center in !hoeni, A is due to be replaced with a

much larger, more modern facilit0 that can handle the tremendous needs

that have developed with the cit04s growth. Fresh produce travels to the

seven store locations several times a da0 making site selection critical forefficient distribution. ;sing the data in the following table, determine the

map coordinates for the proposed new distribution center.


8/33

Practice Problems

Problem 3:9ur main distribution center in !hoeni, A is due to be replaced with a





Truck Round Trips

per "a0

Mesa =-&, )> 3

?lendale =3, +> 3

#amelback =', (> %

/

Apache @unction =-3, 3> )

3!ima =), )> -&


9/33

Practice Problems

Problem 3:9ur main distribution center in !hoeni, A is due to be replaced with a





Truck Round Trips

per "a0

Mesa =-&, )> 3

?lendale =3, +> 3

#amelback =', (> %

/

Apache @unction =-3, 3> )

3!ima =), )> -&

Cx8 8 8 (.(=-&3> 7 =33> 7 ='%> 7 =-)/> 7 =-3)> 7 =-3> 7 =)-&>

3 7 3 7 % 7 / 7 ) 7 3 7 -&

%))

3%

Cy8 8 8 /./=)3> 7 =+3> 7 =(%> 7 =-&/> 7 =3)> 7 =-%3> 7 =)-&>

3 7 3 7 % 7 / 7 ) 7 3 7 -&

%-'

3%


10/33

Practice ProblemsProblem 4:

@ohn ?alt


11/33


@ohn ?alt


12/33


Assume that in !roblem - the demand at each warehouse is increased b0

' units. $ow how man0 units should be shipped from each factor0 to each

warehouse1

arehouse B- arehouse B% arehouse B3

!lant A 6' 6% 63!lant 2 63 6% 6-


13/33


Assume that in !roblem - the demand at each warehouse is increased b0

' units. $ow how man0 units should be shipped from each factor0 to each

warehouse1

arehouse B- arehouse B% arehouse B3

!lant A 6' 6% 63!lant 2 63 6% 6-


14/33

Practice Problems

Problem 6:hat are the appropriate A2#

groups of inventor0 items1


15/33

Practice Problems



A2# Anal0sis

!ercent of


16/33

Practice Problems



A2# Anal0sis

!ercent of


17/33

Practice Problems

Problem 7:

Assume 0ou have a product with the following parameters:

Annual "emand 8 3/& units

Colding cost per 0ear 8 6-.&& per unit

9rder cost 8 6-&& per orderhat is the G9D for this product1


18/33

Practice Problems

Problem 7:

Assume 0ou have a product with the following parameters:

Annual "emand 8 3/& units

Colding cost per 0ear 8 6-.&& per unit

9rder cost 8 6-&& per orderhat is the G9D for this product1

EOQ8 8 8

% "emand 9rder #ost

Colding #ost

% 3/& -&&

-

(%&&& 8 %/+.33 items


19/33

Practice Problems

Problem 8:?iven the data from !roblem (, and assuming a 3&&Hda0 work 0ear, how

man0 orders should be processed per 0ear1 hat is the epected time

between orders1


20/33

Practice Problems

Problem 8:?iven the data from !roblem 3, and assuming a 3&&Hda0 work 0ear, how

man0 orders should be processed per 0ear1 hat is the epected time

between orders1

N8 8 8 -.3' orders per 0ear"emand

Q

3/&

%/+

T8 8 8 %%' da0s between ordersorking da0s

Gpected number of orders

3&&

-.3'


21/33

Practice Problems

Problem 9:hat is the total cost for the inventor0 polic0 used in !roblem (1


22/33

Practice Problems

Problem 9:hat is the total cost for the inventor0 polic0 used in !roblem (1

TC8 7"emand 9rder #ostQ

Duantit0 of Etems Colding #ost%

8 7 8 -3' 7 -3' 8 6%/+3/& -&&

%/+

%/+ -

%


23/33

Practice Problems

Problem 10:*itel0 #orp sells -,3)& of its special decorator light switch per 0ear and

places orders for 3&& of these switches at a time. Assuming no safet0

stocks, *itel0 estimates a )&I chance of no shortages in each c0cle and

the probabilit0 of shortages of ), -&, and -) units as &.%, &.-), and &.-)respectivel0. The carr0ing cost per unit per 0ear is calculated as 6) and the

stockout cost is estimated at 6/ =63 lost profit per switch and another 63

loss of goodwill or future sales>. hat level of safet0 stock should *itel0

use for this product1 =#onsider safet0 stock of &, ), -&, and -) units.>


24/33

Practice Problems

Problem 10:*itel0 #orp sells -,3)& of its special decorator light switch per 0ear and

places orders for 3&& of these switches at a time. Assuming no safet0

stocks, *itel0 estimates a )&I chance of no shortages in each c0cle and

the probabilit0 of shortages of ), -&, and -) units as &.%, &.-), and &.-)respectivel0. The carr0ing cost per unit per 0ear is calculated as 6) and the

stockout cost is estimated at 6/ =63 lost profit per switch and another 63

loss of goodwill or future sales>. hat level of safet0 stock should *itel0

use for this product1 =#onsider safet0 stock of &, ), -&, and -) units.>


25/33

Practice Problems

Problem 11:!resume that *itel0 carries a modern white kitchen ceiling lamp that is

Kuite popular. The anticipated demand during leadHtime can be

approimated b0 a normal curve having a mean of -+& units and a

standard deviation of '& units. hat safet0 stock should *itel0 carr0 toachieve a )I service level1


26/33

Practice Problems

Problem 11:!resume that *itel0 carries a modern white kitchen ceiling lamp that is

Kuite popular. The anticipated demand during leadHtime can be

approimated b0 a normal curve having a mean of -+& units and a

standard deviation of '& units. hat safet0 stock should *itel0 carr0 toachieve a )I service level1

To find the safet0 stock for a )I service level it is necessar0 to

calculate the )th percentile on the normal curve. ;sing the standard

$ormal table from the tet, we find the value for &.) is -./)standard units. The safet0 stock is then given b0:

=-./) '&> 7 -+& 8 // 7 -+& 8 %'/ #eiling *amps


27/33


A new shopping mall is considering setting up an information desk manned

b0 one emplo0ee. 2ased upon information obtained from similar information

desks, it is believed that people will arrive at the desk at a rate of %& per hour.

Et takes an average of % minutes to answer a Kuestion. Et is assumed that the

arrivals follow a !oisson distribution and answer times are eponentiall0distributed.


28/33







a. Find the probabilit0 that the emplo0ee is idle.

b. Find the proportion of the time that the emplo0ee is

bus0.

c. Find the average number of people receiving andwaiting to receive some information.

d. Find the average number of people waiting in line to

get some information.

e. Find the average time a person seeking information

spends in the s0stem.f. Find the epected time a person spends just waiting

in line to have a Kuestion answered =time in the

Kueue>.


29/33







a. Find the probabilit0 that the emplo0ee is idle.

b. Find the proportion of the time that the emplo0ee is

bus0.

c. Find the average number of people receiving andwaiting to receive some information.

d. Find the average number of people waiting in line to

get some information.

e. Find the average time a person seeking information

spends in the s0stem.f. Find the epected time a person spends just waiting

in line to have a Kuestion answered =time in the

Kueue>.

a. P&8 - L J8 - L %& J 3& 8 &.3333I

b. p8 J8 &.////I

c. Ls8 J = L> 8 %& J =3& L %&> 8 % people

d. Lq8 %J=L > 8 %&%J 3&=3& L %&> 8 -.33 people

e. Ws8 - J = L> 8 - J =3& L %&> 8 &.-& hours

f. Wq8 J=L > 8 %& J 3&=3& L %&> 8 &.&//(hours


30/33


Assume that the information desk emplo0ee in !roblem -% earns 6) per

hour. The cost of waiting time, in terms of customer unhappiness with the

mall, is 6-% per hour of time spentwaitingin line. Find the total epected

costs over an +Hhour da0.


31/33


Assume that the information desk emplo0ee in !roblem - earns 6) per hour.

The cost of waiting time, in terms of customer unhappiness with the mall, is

6-% per hour of time spentwaitingin line. Find the total epected costs over

an +Hhour da0.

From the solution to !roblem -%:

The average person waits &.&//( hours and there are

-/& =%& arrivals + hours> arrivals per da0.

Therefore: Total waiting time 8 -/& &.&//( 8 -&./( hours

Total cost for waiting 8 Total waiting time #ost per hour 8

-&./( 6-% 8 6-%+ per da0.


32/33


Three students arrive per minute at a coffee machine that dispenses eactl0

four cups per minute at a constant rate. "escribe the s0stem parameters.


33/33


Three students arrive per minute at a coffee machine that dispenses eactl0

four cups per minute at a constant rate. "escribe the s0stem parameters.

Lq8 8 -.-%) people in the Kueue on average

Wq8 8 &.3() minutes in the Kueue waiting

Ls8 Lq7 8 -.+( people in the s0stem

Ws8 Wq7 8 &./%) minutes in the s0stem

%

%=L >

%=L >

-

Documents

Review MT2