Operations Research2080.25 marksNumerical: Assignment problem cost minimizationFormulation of assignment problems
There are three jobs P, Q and R to be completed on four machines A, B, C and D. The costs of performing the different jobs on machines are given below. Assign the jobs to different machines to minimize the total cost of performing the jobs on machines.
There are three jobs P, Q and R to be completed on four machines A, B, C and D. The costs of performing the different jobs on machines are given below. Assign the jobs to different machines to minimize the total cost of performing the jobs on machines.
$$\begin{array}{|c|c|c|c|c|}\hline \text{Jobs/Machines} & A & B & C & D \ \hline P & 90 & 120 & 140 & 160 \ Q & 40 & 65 & 85 & 95 \ R & 50 & 75 & 95 & 110 \ \hline \end{array}$$
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Cost matrix (3 jobs × 4 machines): Jobs/Machines A B C D --------------- P 90 120 140 160 Q 40 65 85 95 R 50 75 95 110 - 3 jobs (P, Q, R), 4 machines (A, B, C, D) - Objective: minimize total cost. More machines than jobs, so add a dummy job S with all zero costs: A B C D --------------- P 90 120 ...