6. A software development company wants to assign 4 software engineers to four p
ID: 447408 • Letter: 6
Question
6. A software development company wants to assign 4 software engineers to four projects. The estimated time of completion (in days) of each project by each software engineer is given in the following table.
Project 1 Project 2 Project 3 Project 4
___________________________________________________________
Software Engineer A 28 25 20 18
Software Engineer B 40 32 - 44
Software Engineer C 36 27 19 25
Software Engineer D 30 25 15 22
___________________________________________________________
Software engineer B cannot be assigned to project 3 because he does not have enough training to do that project. The company wants project 1 to be assigned to software engineer C or software engineer D. The objective is to minimize the total time of completion of all four projects.
For this assignment problem:
(a) Define the decision variables.
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Explanation / Answer
a) As B dont have expertise on Project 3. Only 3 options are available for Engineer B. ( Project 1,2 or 4).Again one more constraint from company side as they wanted to give Project 1 to either Engineer D or C. So project 2 or 4 can be assigned to Engineer B. In project 4 , Engineer B is taking maximum time for completition. As our objective is to optimise the total time taken for the completion of the project finally Project 2 can be assigned to Engineer B. Decision variables are majorly the factors which decide the allocation of project.
b: Objective function is to optimise the total time taken for the project.
c. Engineer D can do project 1 as D is comparitively taking less time compare to C in doing project 1.Engineer C can be assigned to Project 3.and finally the vacant slot of project 4 can be assigned to Engineer A.
Constraints are Project C and Engineer B , Engineer C or D to Project 1.
Final allocation:
Engineer A will do Project 4, Engineer B will do Project 2, Engineer C will do project 3, Engineer D will do project Project 1.
Total time taken for completion ( Objective function): 18+32+19+30= 99 days.
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