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Question:Rent鈥橰 Cars is a multisite car rental company in the city. It is trying out a new 鈥渞eturn the car to the location most convenient for you鈥 policy to improve customer service. But this means that the company has to constantly move cars around the city to maintain the required levels of vehicle availability. The supply and demand for economy cars, and the total cost of moving these vehicles between sites, are shown below.

a. Find the solution that minimizes moving costs using Microsoft Excel.

b. What would you have to do to the costs to assure that A always sends a car to D as part of the optimal solution?

Short Answer

Expert verified

Answer

An optimal solution is a type of feasible solution in which the objective reaches its minimum or the maximum value that is either profit or loss.

Step by step solution

01

(a) Calculate the moving costs

The transport cost of the firm can be shown in the given chart:

Formula to calculate the minimized costs

Minimize (Z)=xyCyi=0,j=0i=3,j=4

Where Cy is the transportation cost from location I to j

Xy is the no. of vehicles moving from location I to j

02

Prepare the constraints

Supply constraints:

X11+X12+X13+X14= 50

X21+X22+X23+X24 = 40

X31+X32+X33+X34 = 75

Demand constraints:

X11+X21+X31 = 50

X12+X22+X32 = 60

X13+X23+X33 = 25

X14+X24+X34 = 30

03

Now solve the equation in Excel as explained below

On Excel, the result will look like this,

Therefore, from the above calculation, we can conclude that the minimum moving costis $720.

04

To assure the cost as a part of an optimum solution

From the above calculation, it is clear that about 25 cars moved from location A to D at a cost of $9. To ensure that location A always sends a car to location D, in order to minimize the total moving cost.

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