An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 19

Morley Company is attempting to determine the best location for a new machine in an existing layout of three machines. The existing machines are located at the following x 1 , x 2 coordinates on the shop floor:
a. Develop a goal programming model that can he solved to minimize the total distance of the new machine from the three existing machines. The distance is to be measured rectangularly. For example, if the location of the new machine is ( x 1 = 3, x 2 = 5), it is considered to be a distance of Hint : In the goal programming formulation, let
x 1 = first coordinate of the new machine location
x 2 = second coordinate of the new machine location = amount by which the x 1 coordinate of the new machine exceeds the x 1 coordinate of machine i ( i = 1, 2, 3) = amount by which the x 1 coordinate of machine i exceeds the x 1 coordinate of the new machine ( i = 1, 2, 3) = amount by which the x 2 coordinate of the new machine exceeds the x 2 coordinate of machine i ( i = 1, 2, 3) = amount by which the x 2 coordinate of machine exceeds the x 2 coordinate of the new machine ( i = 1, 2, 3)b. What is the optimal location for the new machine?