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SP23: BUSINESS ANALYTICS & MODELING: 20646, Fall 2022 Consider the following set of activities

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SP23: BUSINESS ANALYTICS & MODELING: 20646, Fall 2022

Consider the following set of activities.

Activity Time Required  Predecessor Activities

A             6              —

B             3              A

C             6              B

D             7              B

E              10           C

F              7              C, D

G             7              D

H             2              E, F, G

(a)

Draw the CPM network for this problem.

 

A graph with 8 nodes and 10 directed arcs is shown.

Node A is connected by a directed arc to node B.

Node B is connected by directed arcs to nodes C, D, and F.

Node C is connected by a directed arc to node E.

Node D is connected by a directed arc to node G.

Node E is connected by a directed arc to node H.

Node F is connected by directed arcs to nodes E and G.

Node G is connected by a directed arc to node H.

No directed arcs come from node H.

 

A graph with 8 nodes and 10 directed arcs is shown.

Node A is connected by a directed arc to node B.

Node B is connected by directed arcs to nodes C and D.

Node C is connected by directed arcs to nodes E and F.

Node D is connected by directed arcs to nodes F and G.

Node E is connected by a directed arc to node H.

Node F is connected by a directed arc to node H.

Node G is connected by a directed arc to node H.

No directed arcs come from node H.

 

A graph with 8 nodes and 10 directed arcs is shown.

Node A is connected by directed arcs to nodes B, C, and E.

Node B is connected by a directed arc to node D.

Node C is connected by a directed arc to node F.

Node D is connected by a directed arc to node G.

Node E is connected by directed arcs to nodes D and F.

Node F is connected by a directed arc to node G.

Node G is connected by a directed arc to node H.

No directed arcs come from node H.

 

A graph with 8 nodes and 10 directed arcs is shown.

Node A is connected by directed arcs to nodes B and C.

Node B is connected by directed arcs to nodes D and E.

Node C is connected by directed arcs to nodes E and F.

Node D is connected by a directed arc to node G.

Node E is connected by a directed arc to node G.

Node F is connected by a directed arc to node G.

Node G is connected by a directed arc to node H.

No directed arcs come from node H.

 

(b)

Identify each path through the network and its expected length (the total time spent performing the activities on the path). (Enter your paths as comma-separated lists of the activities A, B, ..., H in the order of their completion. Enter your paths in alphabetical order from top to bottom; for example, the path A, B, C would come a row before A, B, D.)

Path       Expected Length

               

               

               

               

(c)

What is the critical path? (Enter your answer as a comma-separated list of the activities A, B, ..., H in the order of their completion.)

 

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2.

[–/6 Points]

 

DETAILS

RAGSMDA9 15.E.012.

 

MY NOTES

 

ASK YOUR TEACHER

 

PRACTICE ANOTHER

A software company is moving its helpdesk operations center from Newark, New Jersey to Plano, Texas. Some of its employees will be moved to Plano and others will be terminated and replaced by new workers in Texas. The activities that must be carried out to implement the move are summarized in the following table.

Activity Description         Predecessors     Weeks

A             Revise organizational structure  —           4

B             Select new office location            —           3

C             Determine personnel requirements       A             3

D             Design new call center   B, C        3

E              Renovate office space   D             9

F              Select employees to move          C             2

G             Hire new employees      F              3

H             Set up new administrative systems         A             4

I               Move office equipment and records       F              2

J              Train new employees    E, G, H, I               3

(a)

Draw the CPM network for this problem.

 

A graph with 11 nodes and 14 directed arcs is shown.

Node Start is connected by directed arcs to nodes A and B.

Node A is connected by directed arcs to nodes C and H.

Node B is connected by a directed arc to node D.

Node C is connected by directed arcs to nodes D and F.

Node D is connected by a directed arc to node E.

Node E is connected by a directed arc to node J.

Node F is connected by directed arcs to nodes G and I.

Node G is connected by a directed arc to node J.

Node H is connected by a directed arc to node J.

Node I is connected by a directed arc to node J.

No directed arcs come from node J.

 

A graph with 11 nodes and 14 directed arcs is shown.

Node Start is connected by directed arcs to nodes A and B.

Node A is connected by a directed arc to node C.

Node B is connected by a directed arc to node D.

Node C is connected by a directed arc to node F.

Node D is connected by directed arcs to nodes C, E, and H.

Node E is connected by directed arcs to nodes I and J.

Node F is connected by a directed arc to node G.

Node G is connected by a directed arc to node J.

Node H is connected by a directed arc to node F.

Node I is connected by a directed arc to node G.

No directed arcs come from node J.

 

A graph with 11 nodes and 14 directed arcs is shown.

Node Start is connected by directed arcs to nodes A and B.

Node A is connected by a directed arc to node C.

Node B is connected by directed arcs to nodes D and H.

Node C is connected by a directed arc to node F.

Node D is connected by directed arcs to nodes C and E.

Node E is connected by directed arcs to nodes I and J.

Node F is connected by a directed arc to node G.

Node G is connected by a directed arc to node J.

Node H is connected by a directed arc to node G.

Node I is connected by a directed arc to node G.

No directed arcs come from node J.

 

A graph with 11 nodes and 14 directed arcs is shown.

Node Start is connected by directed arcs to nodes A and B.

Node A is connected by a directed arc to node C.

Node B is connected by a directed arc to node D.

Node C is connected by directed arcs to nodes D, F and H.

Node D is connected by a directed arc to node E.

Node E is connected by a directed arc to node J.

Node F is connected by directed arcs to nodes G and I.

Node G is connected by a directed arc to node J.

Node H is connected by a directed arc to node E.

Node I is connected by a directed arc to node J.

No directed arcs come from node J.

 

(b)

Create a spreadsheet to calculate and summarize the earliest and latest start and finish times (in weeks), the slack for each activity, and the critical activities.

Activity EST         EFT         LST         LFT         Slack      Critical?

A            

 

---Select---

B            

 

---Select---

C            

 

---Select---

D            

 

---Select---

E             

 

---Select---

F             

 

---Select---

G            

 

---Select---

H            

 

---Select---

I              

 

---Select---

J             

 

---Select---

(c)

What is the least amount of time (in weeks) required to complete the project?

 weeks

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3.

[–/6 Points]

 

DETAILS

RAGSMDA9 15.E.009.

 

MY NOTES

 

ASK YOUR TEACHER

 

PRACTICE ANOTHER

Consider the following set of activities:

Activity Days Required   Predecessor Activity

A             3              —

B             4              A

C             3              A

D             3              A

E              3              D

F              3              B

G             6              B

H             4              F, C, E

I               5              G, H

J              4              F, C, E

K             2              D

L              7              I, J, K

The following data summarizes the per-day cost of crashing these activities.

Activity Crash Cost per Day          Maximum Crash Days

A             $50         2

B             $60         3

C             $57         1

D             $45         2

E              $25         2

F              $30         2

G             $65         5

H             $55         2

I               $28         4

J              $33         3

K             $40         1

L              $37         2

Create an LP model to determine the least costly way of crashing the project to complete it within 20 days. By how much should each activity be crashed? (Let CA, CB, ..., CL be the number of days each activity is crashed. Restrict your answers to whole days.)

(CA, CB, CC, CD, CE, CF, CG, CH, CI, CJ, CK, CL) =

 

 

 

 

What is the total crashing cost (in dollars)?

$

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4.

[–/6 Points]

 

DETAILS

RAGSMDA9 15.E.015.

 

MY NOTES

 

ASK YOUR TEACHER

 

PRACTICE ANOTHER

The activities required to service a car at Zippy-Lube can be viewed as a mini-project as summarized in the following table.

Time Required

Activity Description         Predecessor Activity       Min        Most Likely         Max

A             Drain oil                —           2              3.3          4.6

B             Replace filter     A             1              4              7

C             Refill oil B, E         1              2.3          3.6

D             Check tires          —           2              3              4

E              Wash windows D             2              3              5

F              Fill fluids               E              2              3              4

G             Final test              C, F         0.5          0.8          1.1

The variability in the time required to perform each activity is due to the different types, sizes, and condition of the cars to be serviced.

(a)

Draw the activity network for this problem.

 

A graph with 8 nodes and 9 directed arcs is shown.

Node Start is connected by directed arcs to nodes A and D.

Node A is connected by a directed arc to node B.

Node B is connected by a directed arc to node C.

Node C is connected by a directed arc to node G.

Node D is connected by a directed arc to node E.

Node E is connected by directed arcs to nodes B and F.

Node F is connected by a directed arc to node G.

No directed arcs come from node G.

 

A graph with 8 nodes and 9 directed arcs is shown.

Node Start is connected by directed arcs to nodes A and D.

Node A is connected by a directed arc to node B.

Node B is connected by a directed arc to node C.

Node C is connected by a directed arc to node G.

Node D is connected by a directed arc to node E.

Node E is connected by directed arcs to nodes C and F.

Node F is connected by a directed arc to node G.

No directed arcs come from node G.

 

A graph with 8 nodes and 9 directed arcs is shown.

Node A is connected by directed arcs to nodes B and D.

Node B is connected by a directed arc to node C.

Node C is connected by a directed arc to node G.

Node D is connected by a directed arc to node E.

Node E is connected by directed arcs to nodes C and F.

Node F is connected by a directed arc to node Finish.

Node G is connected by a directed arc to node Finish.

No directed arcs come from node Finish.

 

A graph with 8 nodes and 9 directed arcs is shown.

Node A is connected by directed arcs to nodes B and D.

Node B is connected by a directed arc to node C.

Node C is connected by a directed arc to node G.

Node D is connected by a directed arc to node E.

Node E is connected by directed arcs to nodes F and G.

Node F is connected by a directed arc to node Finish.

Node G is connected by a directed arc to node Finish.

No directed arcs come from node Finish.

 

(b)

Use PERT to identify the expected time and variance for each activity. (Round your expected times to two decimal places and your variances to four decimal places.)

Activity Expected Time  Variance

A            

B            

C            

D            

E             

F             

G            

(c)

What is the critical path? (Enter your answer as a comma-separated list of the activities A, B, ..., G in the order of their completion. Include artificial Start or Finish activities in your list as needed.)

 

What is the expected time of the critical path? (Round your answer to two decimal places.)

What is the variance of the critical path? (Round your answer to four decimal places.)