Question

There are four resources and four jobs to be done. Assume there must be one-to one matching between jobs and resources. The time required for each resource to do each job is as follows: Job (Bour) source ABcD What is the optimal assignment of resources to jobs? O 1 to A 2 to C:3 to 8:4 to D O 1 to B: 2 to D:3 to C: 4 to A O 1 to C;2 to B:3 to A 4 to D O 1 to D:2 to B: 3 to C: 4 to A O 1 to A; 2 to C: 3 to D: 4 to B

Answer 1

Using Solver:

Minimize Resources Constraints Used Sign Available 4 Resources 4 10 12 13

Solver Parameters Set Objective: 0: O Min Value Of: ах By Changing Variable Cells: $C$2:$F$5 Subject to the Constraints: $C$2:$F$5integer $1$10 $K$10 Add Change Delete $1$12 $K$12 $I$7 $K$7 Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Minimize = SUMPRODUCT(C2:F5,C8:F11)

Constraints:

1: SUM(C2:F2) = 1

2: SUM(C3:F3) = 1

3: SUM(C4:F4) = 1

4: SUM(C5:F5) = 1

A: SUM(C2:C5) = 1

B: SUM(D2:D5) = 1

C: SUM(E2:E5) = 1

D: SUM(F2:F5) = 1

On Solving:

1 = A

2 = C

3 = D

4 = B