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Week 4

Week 4

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Student’s Name

Professor Name

Course Code

Date

Network diagram

Client

Consultant

A

B

C

D

Alfred

100

125

115

100

Barbara

110

135

115

110

Charlie

155

140

140

130

1) Develop a network representation of the problem. You may reference the Network Diagram Template.

A

180 HRS

Charlie

140 HOURS

Barbara

160 HOURS

Alfred

160 HOURS

100

B

75 HRS

125

D

85 HRS

115

110 100135

C

100 HRS

110115

155140

140

130

2. Formulate the problem as a linear program; with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing.

Linear Program

Max. 100*HAA+ 125*HAB + 115*HAC+ 100*HAD+ 120*HBA+ 135*HBB+ 115*HBC+ 120*HBD+ 155* HCA+ 150*HCB+ 140*HCC+ 130*HCD

Constraints;

HAA+ HAB+ HAC+ HAD≤ 160 HBA+ HBB+ HBC+ HBD≤ 160 HCA+ HCB+ HCC+ HCD≤ 140 HAA+ HBA+ HCA≤ 180 HAB+HBB+ HCB≤75HAC+ HBC+ HCC≤ 100 HAD+ HBD+ HCD≤ 85; HAA≥ 0; HAB≥ 0; HAC≥ 0; HAD≥ 0; HBA≥ 0; HBB≥ 0; HBC≥ 0; HBD≥ 0; HCA≥ 0; HCB≥ 0; HCC≥ 0; HCD≥ 0;

LINGO CODE:

MAX= (100 *HAA) + (125 *HAB) + (115 *HAC) + (100 *HAD) + (120 *HBA) + (135 *HBB) + (115 *HBC) + (120 *HBD) + (155* HCA) + (150 *HCB) + (140 *HCC) + (130 *HCD);HAA +HAB+ HAC + HAD <= + 160; HBA + HBB + HBC + HBD <= 160; HCA + HCB + HCC + HCD <= 140; HAA + HBA + HCA <= 180; HAB HBB + HCB <=75;HAC + HBC + HCC <= 100; HAD + HBD + HCD <= 85; HAA >=0; HAB >=0; HAC >=0; HAD >=0; HBA >=0; HBB >=0; HBC >=0; HBD >=0; HCA >=0; HCB >=0; HCC >=0; HCD >=0 CITATION And17 \p 1` \l 1033 (Anderson, Sweeney and Williams 1`);

Schedule

Client

Consultant

A

B

C

D

Alfred

-

40

100

-

Barbara

40

35

-

85

Charlie

140

-

-

-

Billing

Client

Consultant

A

B

C

D

Alfred

-

200

500

-

Barbara

250

350

-

450

Charlie

450

-

-

-

Works Cited

BIBLIOGRAPHY Anderson, David R., et al. An Introduction to Management Science: Quantitative Approaches to Decision ... New York: Cengage learning, 2017.

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