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

1. Formulate a linear program to determine the least costly shipping plan. Clearly define the decision variables and the objective. (2)
2. Use an appropriate software to solve the linear program. Summarize the shipping plan and the total cost. (2)
3. 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)

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

Answer 1

The decision variables are:

x_MM = # of orders from Muscat to Muscat

x_MSO = # of orders from Muscat to Sohar

x_MN = # of orders from Muscat to Nizwa

x_MSA = # of orders from Muscat to Salalah

x_SM = # of orders from Sohar to Muscat

x_SSO = # of orders from Sohar to Sohar

x_SN = # of orders from Sohar to Nizwa

x_SSA = # of orders from Sohar to Salalah

The objective function is:

Min = 20x_MM + 80x_MSO + 60x_MN + 150x_MSA + 70x_SM + 20x_SSO + 50x_SN + 200x_SSA

The Shipping plan is:

	Muscat	Sohar	Nizwa	Salalah	Capacity
Muscat	100	0	20	60	180
Sohar	0	80	20	0	100
Demand	100	80	40	60

The total cost is:

Total Cost

14800

From the output, we can say that the company should change the orders for Muscat ti 180 and Sohar should be the same as 100.

The demand should be increased for Muscat as it has the highest number of orders.