Please only do 5-10 . You do not need to do problems 5-8 and 5-9, but problem 5-
ID: 365334 • Letter: P
Question
Please only do 5-10 . You do not need to do problems 5-8 and 5-9, but problem 5-10 asks you to refer to problem 5.8. please solve using VAM method
5-8. Three refineries with daily capacities of 6, 5, and 8 million gallons, respectively, supply three distribution areas with daily demands of 4,8, and 7 million gallons, respectively Gasoline is transported to the three distribution areas through a network of pipelines. The transportation cost is 10 cents per 1000 gallons per pipeline mile. Table 5.26 gives the mileage between the refineries and the distribution areas. Refinery 1 is not connected to distribution area 3. (a) Construct the associated transportation model (b) Determine the optimum shipping schedule in the network. 5-9. In Problem 5-8, suppose that the capacity of refinery 3 is 6 million gallons only and that distribution area 1 must receive all its demand. Additionally, any shortages at areas 2 and 3 will incur a penalty of 5 cents per gallon (a) Formulate the problem as a transportation model. (b) Determine the optimum shipping schedule. 5-10. In Problem 5-8, suppose that the daily demand at area 3 drops to 4 million gallons. Surplus production at refineries 1 and 2 is diverted to other distribution areas by truck The transportation cost per 100 gallons is $1.50 from refinery 1 and $2.20 from refinery 2. Refinery 3 can divert its surplus production to other chemical processes within the plant (a) Formulate the problem as a transportation model. (b) Determine the optimum shipping schedule TABLE 5.26 Mileage Chart for Problem 5-8 Distribution area Refinery 1 120 Refinery 2 300 Refinery 3 200 180 100 250 80 120Explanation / Answer
As mentioned in the question, formulation and solution is required as per the transportation model.
Therefore, Decision variables are defined as Xij representing the quantity to be transported from ith refinery to jth area.
Cij represents the per unit cost of transportation from ith refinery to jth area. It is mentioned that transportation cost is cents 10 per 1000 gallons per mile and distances between the refineries and areas are given.
Therefore, Cij matrix in terms of cost ($) per 1000 gallons is as follows:
Availabilities and demands are given in terms of million gallons, needs to be converted into 1000 gallons.
Formulation of problem 5.8 is as follows for the excel solver.
Please note in order to avoid supply from Refiney 1 to Area 3, very high cost coefficient is considered.
Optimal solution with sensitivity analysis is as follows:
Modified problem
in problem 5-8, suppose that the daily demand at area 3 drops to 4 million gallons. Surplus production at refineries 1 and 2 is diverted to other distribution areas by truck. The transportation cost per 100 gallons is $1.50 from refinery 1 and $2.20 from refinery 2. Refinery 3 can divert its surplus production to other chemical processes within the plant.
Solution as per excel solver
Refinery 3 may uses the balance 3 million inside the plant.
Area1 Area2 Area3 Refinery1 12 18 '--- Refinery2 30 10 8 Refinery3 20 25 12