Question

The Hyundai dealer at Muscat needs to decide on how to ship new automobiles from two ports (Sohar and Muscat) to four of their agencies in Muscat, Sohar, Nizwa and Salalah. The following table summarizes the transportation costs incurred per automobile (in OMR).
Muscat Sohar Nizwa Salalah Capacity
Muscat 20 80 60 150 200
Sohar 70 20 50 200 100
Demand 100 80 40 60

a. Formulate a linear program to determine the least costly shipping plan. Clearly define the decision variables and the objective. (2)
b. Use an appropriate software to solve the linear program. Summarize the shipping plan and the total cost. (2)
c. The company is in the process of determining their orders of new automobiles for the coming year. Would you recommend keeping the same numbers arriving at each port (200 for Muscat and 100 for Sohar)? Justify your answer. (1)
d. All four agencies expressed interest in increasing their demand for new cars; however, the company can only accommodate one demand increase, which agency would you recommend? Justify your answer. (1)

Answer 1

a.

Given problem
	Muscat	Sohar	Nizwa	Salalah	Dummy	Capacity
Muscat	20	80	60	150	N	200
Sohar	70	20	50	200	N	100
Demand	100	80	40	60	20	300/300

Note: In order to solve the problem, the total demand and supply shall be equal. Therefore a dummy column is inserted with N cost and balance demand (20)

b)

Allocation using Vogels approximation method
	Muscat	Sohar	Nizwa	Salalah	Dummy	Capacity
Muscat	100	0	20	60	20	200
Sohar	0	80	20	0	0	100
Demand	100	80	40	60	20	300/300

Note: To obtain optimal allocation under Vogels method, perform following steps

Calculate row and column poenalties by taking differences between least value and next hoghest value in repective row and column

Select the row/column with high row penalty and make allocation on least cost cell

Delete the row that satisfie supply/demand

Repeat until entire supply demand is satisfied

c)

Yes. Since there is an unutilised capacity of 20 cars it is sufficient to keep the same numbers. If the demand is more than 300 then the capacity shall be increased.

d)

Muscat agency should be recommended because the cost of transportation is 20, but the capacity not met by this agency is 100 cars which is allocated to other agencies where the transportation cost is more.