Modelling Of Engineering Management Systems

A company is managing a number of projects (as shown below) producing similar items:

 

Project #

# of items likely to be Sold (AED)

Project 1

40,000

Project 2

60,000

Project 3

30,000

Project 4

20,000

Project 5

50,000

Project 6

36,000

Project 7

50,000

Project 8

100,000

Project 9

40,000

Project 10

60,000

 

Three people (Ahmed , Sara and Mourad) are to work on a given project once it accepted. The 3 people has limited time available to work on projects.

 

Person

Time

Ahmed

120 days

Sara

80

Mourad

80

 

The time to complete the study of the project by the three Ahmed, Sara and Moura is given below

Project

Modelling Of Engineering Management Systems

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Ahmed

Sara

Mourad

Project 1

60 days

80

Not needed

Project 2

32

48

Not needed

Project 3

48

Not needed

60

Project 4

40

Not needed

48

Project 5

20

Not needed

32

Project 6

Cannot do

Not needed

28

Project 7

Cannot do

48

52

Project 8

Cannot do

56

60

Project 9

80

64

60

Project 10

Cannot do

100

72

 

 

Explanation of the above table:  If project 1 is assigned, it would mean that it requires 60 days from Ahmed, 80 days from Sara and Mourad is not needed.

 

Other constraints:

 

1.    The company cannot go with more than 2 projects from Projects 5 , 4 and 3.

 

2.    The company must not execute more than one project from projects 8 and 7.

 

3.    The company should do either project 1 or 2 but not both (exclusive or). 

 

4.    At least two people should be assigned to each project. This rule is not applied necessarily to project 6.  

 

 

The objective is to maximize the # of items that can be sold. 

 

Discuss and conduct analysis

 

1)    Write the linear program and solve it without the four constraints.

2)    Write the linear program and solve it including the four constraints.

 

3)    If it is profitable, whether Sara can be moved to other project(s) and offer her 24 more days (explain).

 

4)    Use solver table to carry an appropriate sensitivity analysis.    

 

 

 

 


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