solver rich a

8/2/2019 Solver Rich A

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A company has to transport its product from 3 plants to 3 distribution centres. The

availability and demand for units of products, with unit transportation costs in rupees

are given below. Find the optimal transport pattern.

Plant Distribution Centre AvailabilityD1 D2 D3

P1 16 19 12 140P2 12 13 19 160P3 14 28 8 120Demand 100 150 170

Solution :

Using Solver

Step 1 - Enter the data in excel

D1 D2 D3Availability

P1 16 19 12 140

P2 12 13 19 160

P3 14 28 8 120demand 100 150 170

Step 2 copy and paste the data once again below the sheet


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Step 3 - enter the objective function value ( sumproduct of B2:D4,B12:D14)

the sumproduct refers to the sum of the digits times the product of the digits


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Step 4: make one more column and row titled as total and insert the sum formular

in f2 as =sum(b2:d2) and drag it from F2 to F4

Step 5


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Same as above now enter the sum product in the row column and drag the cell till d6

Step 6 delete the cells from B2 to D4 ( marked yellow for your reference )


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These cells constitute the variable cells in solver ( in other words solver will enter

the values in these cells and such that the total does not exceed availability or

demand or as specified by us)

Step 7 go to data and click on solver the dialog box should open as shown


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Step 8 enter the cell b8 as the target cell


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Step 9 since it is a minimization problem ( reducing transportation costs) click on

min


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Step 10 click on box below changing cells and select the blank variable cells

( marked yellow )

Step 11 click on the add button ( a dialog box showing add constraint will open up)


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Step 12 now click on cell reference and select the total column (f2:f4)

since the total cannot exceed availability we have to click less than or equal to from

the drop down box next to the cell reference (


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Step 13 - same as above you have to do the same for the row column total

Remember in this case the total should be equal to demand ( as in the problem we

have to ensure that the demand is fully met)

Click OK

Step 14 click on options tick on assume linear model and assume nonnegative

and click ok


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Step 15

Click solve and tick on keep solver equation ( default )

Click on answer, sensitivity and limits in the reports column


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Step 16 click Ok and you can see the optimum transportation cost at Rs.5070 and

also each of the allocations of demand being matched to the availability ( viz

B2,C3,D4,D2,B3)

( as pointed out above this is the sumproduct of 90x 16 + 10 x12 + 150 x 13 + 50 x

12 + 120 x 8)


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