Assignment #4: Case Problem “Stateline Shipping and Transport Company”
Assignment #4: Case Problem “Stateline Shipping and Transport Company”
1) This transportation model problem consists of 18 decision variables, representing the number of barrels of wastes product transported from each of the 6 plants to each of the 3 waste disposal sites: [pic]= Number of Barrels transported per week from plant ‘i’ to the j-th waste disposal site, where i = 1, 2, 3, 4, 5, 6 and j = A, B, C.
The objective function is to minimize the total transportation cost for all shipments. So the objective function is the sum of the individual shipping costs from each plant to each waste disposal site:
Minimize Z = 12[pic]+ 15[pic]+ 17[pic]+ 14[pic]+ 9[pic]+ 10[pic]+ 13[pic]+ 20[pic] +11[pic] +17[pic] +16[pic] +19[pic] +7[pic] +14[pic] +12[pic] +22[pic] +16[pic] +18[pic]
Let’s assume the constraints are the number of barrels of wastes available per week at each plant and the number of barrels of wastes contained at each waste disposal site. Therefore there are 9 constraints- one for each plant supply and one for each waste disposal site’s demand.
The six supply constraints are: [pic]+ [pic]+ [pic] = 35 [pic]+ [pic]+ [pic] = 26 [pic]+ [pic] +[pic] = 42 [pic] + [pic] +[pic] = 53 [pic] +[pic] +[pic] = 29 [pic] + [pic] +[pic] = 38
For example, let’s say the supply constraint [pic]+ [pic]+ [pic] = 35 represents the number of barrels transported from the plant Kingsport to all the three waste disposal sites. The amount transported from Kingsport is limited to the 35 barrels available.
The three demand constraints are: [pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic] ≤ 65 [pic]+ [pic]+ [pic]+ [pic]+[pic] +[pic] ≤ 80 [pic]+ [pic]+[pic]+ [pic]+[pic] +[pic] ≤ 105 Here the demand constraint [pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic] ≤ 65 represents the number of barrels transported to the waste disposal site Whitewater from all the six plants. The barrel of wastes that can accommodate in the waste disposal site Whitewater is limited to 65 barrels.
1) This transportation model problem consists of 18 decision variables, representing the number of barrels of wastes product transported from each of the 6 plants to each of the 3 waste disposal sites: [pic]= Number of Barrels transported per week from plant ‘i’ to the j-th waste disposal site, where i = 1, 2, 3, 4, 5, 6 and j = A, B, C.
The objective function is to minimize the total transportation cost for all shipments. So the objective function is the sum of the individual shipping costs from each plant to each waste disposal site:
Minimize Z = 12[pic]+ 15[pic]+ 17[pic]+ 14[pic]+ 9[pic]+ 10[pic]+ 13[pic]+ 20[pic] +11[pic] +17[pic] +16[pic] +19[pic] +7[pic] +14[pic] +12[pic] +22[pic] +16[pic] +18[pic]
Let’s assume the constraints are the number of barrels of wastes available per week at each plant and the number of barrels of wastes contained at each waste disposal site. Therefore there are 9 constraints- one for each plant supply and one for each waste disposal site’s demand.
The six supply constraints are: [pic]+ [pic]+ [pic] = 35 [pic]+ [pic]+ [pic] = 26 [pic]+ [pic] +[pic] = 42 [pic] + [pic] +[pic] = 53 [pic] +[pic] +[pic] = 29 [pic] + [pic] +[pic] = 38
For example, let’s say the supply constraint [pic]+ [pic]+ [pic] = 35 represents the number of barrels transported from the plant Kingsport to all the three waste disposal sites. The amount transported from Kingsport is limited to the 35 barrels available.
The three demand constraints are: [pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic] ≤ 65 [pic]+ [pic]+ [pic]+ [pic]+[pic] +[pic] ≤ 80 [pic]+ [pic]+[pic]+ [pic]+[pic] +[pic] ≤ 105 Here the demand constraint [pic]+ [pic]+ [pic]+[pic]+ [pic]+[pic] ≤ 65 represents the number of barrels transported to the waste disposal site Whitewater from all the six plants. The barrel of wastes that can accommodate in the waste disposal site Whitewater is limited to 65 barrels.