introduction• We are making an operations Research project using Linear Programming to take decision what type of UPS we have to make more which utilize our full resources and will help to increase our profit.
Basically we have four type of UPS 400VOLT, 875 VOLT, 1025 VOLT,1550 VOLTwe have to use 1 battery in 400 VOLT UPS, 2 Battery in 875 VOLT UPS,3 Battery in 1025VOLT UPS, 4 Battery in 1550VOLT UPS. From theavailable battery (i.e.- 950)we have to use 2 Plug Socket in 400 VOLT UPS, 2 Plug Socket in 875VOLT UPS, 3 Plug Socket in 1025VOLT UPS, 4 Plug Socket in 1550VOLTUPS. From the available Plug Socket (i.e.- 1150)we have to use 1 Fuse in 400 VOLT UPS, 1 Fuse in 875 VOLT UPS, 2Fuse in 1025VOLT UPS, 3 Fuse in 1550VOLT UPS. From the availableFuse (i.e.- 300)we have to use 1 trans farmer in 400 VOLT UPS, 1 Trans farmer in 875VOLT UPS, 2 Trans farmer in 1025VOLT UPS, 3 Trans farmer in1550VOLT UPS. From the available Trans farmer (i.e.- 550)
• We have gaining unit profit Rs 200 for 400VOLT UPS, Rs 250 for 875VOLT UPS, Rs 350 for 1025 VOLT UPS, Rs 500 for 1550 VOLT UPS
Constraint and Objective FunctionBy the above Data Our Constraint is :-1X 2X1 3X3 4X4 <=9502X 2X 3X3 4X4 <=11501X 1X 2X3 2X4 <=3001X 1X 2X3 3X4 <=550(Objective Function)Z=200X+250X2+350X3+500X4
Senstivity ReportMicrosoft Excel 14.0 Sensitivity ReportWorksheet: [Book1]Sheet1Report Created: 29-May-12 10:01:09 AMVariable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $E$4 objective function 0 -50 200 50 1E+30 $F$4 objective function 300 0 250 1E+30 0 $G$4 objective function 0 -150 350 150 1E+30 $H$4 objective function 0 0 500 0 1E+30Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $I$8 Bettery constraint used 600 0 950 1E+30 350 $I$9 plug socket used 600 0 1150 1E+30 550 $I$10 fuse used 300 250 300 175 300 $I$11 transfamer used 300 0 550 1E+30 250
Interpretation• According to Sensitivity Report:-• In Constraint View:-• Battery, Plug Socket, Transfarmer have ‘0’ shadow Price that’s mean these are not Binding. We increase these constraint up to ‘1E+30’ as (allowance increase is 1E+30) . They will not effect the optimum solution because they have slack value( resource that are unused):- 350 for Battery,550 for Plug Socket,250 for Transfarmer.
• If we talk about Wire than it is not binding its shadow price is 250.• It’s Allowable increase is 175 so we increase the use of wire up to 140. After increasing of 140 it will effect the optimum solution with 250/unit.• It’s Allowable Decrease is 300 so We can Decrease it up to 300 after that it will effect the optimum solution.
Variable Cell:-Reduced CostThe amount an objective function coefficent must change before wewould make any of the product.or, the amount the profit would change if you made at least one unit ofthe product x200 was not a high enough profit on 400VOLT UPS to make any. Itsprofit must increase to 200+50or 250 before we would make 400VOLTUPS . [ reduced cost is -50 . till 50 unit cost is valid after this we cannotsay.For Product X3 1025VOLT UPS )= profit must increase to 350+150=500 [ reduced cost is -150 . till 150 unit cost is valid after this we cannotsay.We are already making 875VOLT UPS , so their reduced costs are 0.