Minimizing waste transportation costs using linear programming

¶ … plants; let I be the number of plants on location. Thus, i=1,2,3,4,5,6

There are three (3) waste disposable sites; let j be the number of waste disposable sites. Thus, j = 1, 2, 3

Now, there is going to be a shipping schedule to transport wastes from plant I to disposable site j depending on the total cost of transportation. The goal is to minimize this cost.

Total cost of transportation can be denoted by Z. As the objective function to be minimized and let X the amount of waste to be transported from I to j.

Thus we have X11, X12, X13, X21, X22, X23, X31, X32, X33, X41, X42, X43, X51, X52, X53, X61, X62 and X63.

Given the cost of shipping from each plant to each waste disposable site, Z can be defined as:

Z = 12 X11 + 15 X12 + 17 X13 + 14 X21 + 9 X22 + 10 X23 + 13 X31 + 20 X32 + 11 X33 + 17 X41+ 16 X42 + 19 X43 + 7 X51 + 14 X52+ 12 X53 + 22 X61 + 16 X62 + 18 X63.

Give the total amount of waste generated each week at each site, we set constraints on Z. as:

X11 + X12 + X13 = 35

X21 + X22 + X23 = 26

X31 + X32 + X33 = 42

X41 + X42 + X43 = 53

X51 + X52 + X53 = 29

X61 + X62 + X63 = 38

9) The maximum amount of waste each site can contain each is given as:

X11 + X21+ X31+X41 + X51 + X61 ? 65

X12 + X22+ X32+X42 + X52 + X62 ? 80

X13 + X23+ X33+X43 + X53 + X63 ? 105

Part 1:

NB: Click on the excel object sheet below and scroll up and/or down to view all numbers

The results from excel show that to minimize direct shipment costs,

(1) Kingport plant has to dispose 35 bbl of waste to Whitewater

(2) Danville plant has to dispose 26 bbl of waste to Duras.

(3) Macon plant has to dispose 42 bbl of waste to Duras.

(4) Selma plant has to dispose 1 bbl of waste to White water and 52 bbl to Los Canos

(5) Columbus plant has to dispose 29 bbl of waste to Whitewater

(6) Allentown plant has to dispose 28 bbl of waste to Los Canos and 10 bbl to Duras

The total minimum cost involved in shipping waste directly from the 6 plants to the 3 waste disposable sites is $2,822.

Part 2:

NB: Click on the excel object sheet below and scroll up and/or down to view all numbers

The results from excel show that to minimize transshipment costs,

(1) Kingport plant has to drop off 19 bbl of its of waste at Macon and ship 16 bbl directly to Los Canos

(2) Danville plant has to dispose 26 bbl of waste directly to Duras.

(3) Macon plant has to dispose (42bbl + 17 bbl +19bbl=78bbl) of waste directly to Duras.

(4) Selma plant has to drop off 17 1 bbl of waste at Macon and drop off 52 bbl at Columbus without shipping directly to any of the disposable sites

(5) Columbus plant has to dispose (29bbl + 36 bbl) of waste directly to Whitewater