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Texas A&M University College of Engineering

Unbalanced supplies and demands, assignments

Posted on July 27, 2021 by Abigail Stason

For the job assignment table, determine who should be assigned to each job.

  Bill Joe Sam Emily
Survey 10 12 2 6
Design 14 10 3 8
Inspect 20 8 5 10
Manage 22 7 7 7

Min Z = 10BS + 14BD + 20BI + 22BM + 12JS + 10JD + 8JI + 7JM +  2SS + 3SD + 5SI + 7SM +

                                6ES + 8ED + 10EI + 7EM

ST           BS + JS + SS + ES = 1

                BD + JD + SD + ED = 1

                BI + JI + SI + EI = 1

                BM + JM + SM + EM = 1

                BS + BD + BI + BM = 1

                JS + JD + JI + JM = 1

                SS + SD + SI + SM = 1

                ES + ED + EI + EM = 1

For the job assignment table, determine who should be assigned to each job.

  Bill Joe Sam Emily
Survey 10 12 2 6
Design 14 10 3 8
Inspect 20 8 5 10

Min Z = 10BS + 14BD + 20BI + 12JS + 10JD + 8JI +  2SS + 3SD + 5SI + 6ES + 8ED + 10EI

ST           BS + JS + SS + ES = 1

                BD + JD + SD + ED = 1

                BI + JI + SI + EI = 1

                BS + BD + BI <= 1

                JS + JD + JI <= 1

                SS + SD + SI <= 1

                ES + ED + EI < = 1

For the job assignment table, determine who should be assigned to each job.

  Bill Joe Sam
Survey 10 12 2
Design 14 10 3
Inspect 20 8 5
Manage 22 7 7

Min Z = 10BS + 14BD + 20BI + 22BM + 12JS + 10JD + 8JI + 7JM +  2SS + 3SD + 5SI + 7SM

ST           BS + JS + SS <= 1

                BD + JD + SD <= 1

                BI + JI + SI <= 1

                BM + JM + JM <= 1

                BS + BD + BI + BM = 1

                JS + JD + JI + JM = 1

                SS + SD + SI + SM = 1

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