Hw# 6 roblem Problem 1 A company is considering hiring people for four types of

Question

Hw# 6 roblem Problem 1 A company is considering hiring people for four types of jobs. Five persons are applied to perform the four jobs. The time it takes each person to perform each job is given in Table 1. Table 1 Time(hours) Job 1Job 2 Job 3 Job 4 23 erson 1 24 19 Person 2 Person 3 Person 4 19 29 21 35 31 31 26 25 27 3 32 16 32 Person 5 25 28 NoteDashes ndicates person camot do particular job. Use excel to determine the assignment of persons to jobs that minimizes the total time required to perform four jobs. a) b) Draw the problem. c) Formulate the problem.

Explanation / Answer

The boxes in green, are decision variables
The boxes in blue are constrains
The boxes in orange is the objective function

The formulation:

The solution:

Job 1 Job 2 Job 3 Job 4 P 1 24 19 35 23 P 2 19 31 26 P 3 29 25 31 32 P 4 21 27 16 P 5 25 28 32 Dec var (0/1) Job 1 Job 2 Job 3 Job 4 One person one job P 1 0 1 0 0 =SUM(B8:E8) <= 1 P 2 1 0 0 =SUM(B9:E9) <= 1 P 3 0 0 0 0 =SUM(B10:E10) <= 1 P 4 0 0 1 =SUM(B11:E11) <= 1 P 5 0 1 0 =SUM(B12:E12) <= 1 Each job done =SUM(B8:B12) =SUM(C8:C12) =SUM(D8:D12) =SUM(E8:E12) >= >= >= >= 1 1 1 1 Total time =SUMPRODUCT(B2:E6,B8:E12) Minimize Objective function

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