Operations Research course Math473-2022-3 Q4:Inspection Problem A company has two grades of inspections 1& 2 to undertak

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Operations Research Course Math473 2022 3 Q4 Inspection Problem A Company Has Two Grades Of Inspections 1 2 To Undertak 1 (73.74 KiB) Viewed 33 times

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Operations Research Course Math473 2022 3 Q4 Inspection Problem A Company Has Two Grades Of Inspections 1 2 To Undertak 2 (73.54 KiB) Viewed 33 times

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Operations Research course Math473-2022-3 Q4:Inspection Problem A company has two grades of inspections 1& 2 to undertake quality control inspection. At least 1,500 pieces must be inspected in 8 hour per day. Grade 1 inspector can check 50 pieces in an hour with an accuracy of 98%. Grade 2 inspector can check 40 pieces in an hour with an accuracy of 95%. Wages of grade 1 inspector are Rs. 10 per hour while those of grade 2 inspector are Rs. 8 per hour. Any error made by an inspector costs Rs. 6 in grade 1 and Rs. 5 in grade 2 to the company if there are in all. In the company there are at most 10 inspectors in grade 1 and 15 inspectors in grade 2. Let X1 and X2 denote the number of grade 1 and grade 2 inspectors that may be assigned the job of quality control inspection. Find the optimal assignment of inspectors that minimizes the daily inspection cost. inspection inspectors wages per hour Error cost per hour number of Pieces per hour number of inspectors per hour grade 1 10 2% 10 12 grade 2 12 5% 15 10 total 1500
Solution Formulation of L.P model: Let x1 and x2 denote the number of gradel and gradell inspectors that may be assigned the job of quality control inspection. The objective is to minimize the daily cost of inspection. Now the company has to incur two types of costs:wages paid to the inspectors and the cost of their inspection errors. The cost of a grade I inspector/hour is Rs.(5+3x0.04x20)=Rs.7.40 Similarly,cost of a gradell inspector/hour is Rs.(4+3x0.08x14)=Rs.7.36. :. The objective function is minimize Constraints are on the number of gradel inspectors:=x1<10, on the number of gradell inspectors:=x2<15, on the number of pieces to be inspected daily:20x8x1 +14x8x221,500 Z=8(7.40x1+7.36x2)=59.20x1+58.88x2. or 160x1+112x2≥1,500, where x1,x220