Stateline Shipping and Transport Company Math 540 Assignment 4
1.) The model transportation problem consists of 18 decision variables which are the number of barrels of wastes transported from each of the six plants to each of the three waste disposal sites.
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:
The constraints in the model are the number of barrels of wastes available per week at each plant and the number of barrels of wastes that are able to go to each waste disposal site. There are nine constraints and they include one for each plant supply and one for each waste disposal site’s demand.
The six supply constraints are:
X1A+X1B+X1C | = 35 |
X2A+X2B+X2C | = 26 |
X3A+X3B+X3C | = 42 |
X4A+X4B+X4C | = 53 |
X5A+X5B+X5C | = 29 |
X6A+X6B+X6C | = 38 |
The supply constraints symbolize the number of barrels transported from the plants to the three waste disposal sites.
The three demand constraints are:
X1A+X2A+X3A+X4A+X5A+X6A | <= 65 |
X1B+X2B+X3B+X4B+X5B+X6B | <= 80 |
X1C+X2C+X3C+X4C+X5C+X6C | <= 105 |
The demand constraints symbolize the number of barrels transported to the waste disposal sites from the six plants. The barrels of waste are limited to what the different sites can handle. The demand constraints are <= inequalities because the total demand exceeds the total supply.
The linear programming model for the transportation problem is summarized as the following:...