# An Economic Model for Shipping and Disposal of Waste

1080 Words Jan 15th, 2018 4 Pages
The objective is to determine whether it is more cost effective to ship directly from the plants to the waste disposal sites, or if using intermediate points is the least expensive option.

Z represents the cost.
Xij, represents the quantity of waste transported from the i-th plant (where i=1,2,3,4,5,6) to the j-th waste disposal site (where j= A,B,C).
The linear programming model for this problem is:
Minimize Z=\$12X1A+15X1B+17X1C+14X2A+9X2B+10X2C+13X3A+20X3B+11X3C + 17X4A+16X4B+19X4C+7X5A+14X5B+12X5C+22X6A+16X6B+18X6C
With supply constraints:
X1A+X1B+X1C = 35
X2A+X2B+X2C = 26
X3A+X3B+X3C = 42
X4A+X4B+X4C = 53
X5A+X5B+X5C = 29
X6A+X6B+X6C = 38
X1A+X2A+X3A+X4A+X5A+X6A <= 65
X1B+X2B+X3B+X4B+X5B+X6B <= 80
X1C+X2C+X3C+X4C+X5C+X6C <= 105
Xij >= 0, i=1,2,3,4,5,6; j=A,B,C In this case, the total demand is 65 + 80 + 105 = 250
Total Supply is 35 + 26 + 42 + 53 + 29 + 38 = 223

It is clear that demand is higher than supply. Since demand is greater than supply, the demand constraints will be less than or equal to in the equation. Using solver in Excel, we can complete the spreadsheet. We find that the optimal solution is:

The minimum cost is then calculated:
Z = 12X1A+15X1B+17X1C+14X2A+9X2B+10X2C+13X3A+20X3B+11X3C + 17X4A+16X4B+19X4C+7X5A+14X5B+12X5C+22X6A+16X6B+18X6C =

\$12*35+\$10*26+\$11*42+\$17*1+\$16*52+\$7*29+\$16*28+\$18*10 = \$2,822

A…