A Model for Shipping Waste for Stateline Shipping and Transport Company

3718 Words Feb 1st, 2018 15 Pages
The six pants and their capacity for wastes generated are shown below. Also shown are the three waste disposal sites and their demand requirements.
Plants
Supply (barrels)
1. Kingsport
35
2. Danville
26
3. Macon
42
4. Selma
53
5. Columbus
29
6. Allentown
38
Waste Disposal Sites
Demand (barrels)
A. Whitewater
65
B. Los Canos
80
C. Duras
105
Shown below are the shipping costs ($/bbl) from each waste disposal site to each plants.
Plants
Waste Disposal Sites
A. Whitewater
B. Los Canos
C. Duras
1. Kingsport
$12
$15
$17
2. Danville
14
9
10
3. Macon
13
20
11
4. Selma
17
16
19
5. Columbus
7
14
12
6. Allentown
22
16
18

Mathematical Formulation
The objective of the problem is to develop a shipping schedule that minimizes the total cost of transportation. The objective function Z represents the cost. In this transportation model the decision variables, Xij, represent 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 can be written as follows. minimize…