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

Exercise 10

The port of Lajitas has three loading docks. The distance (in meters) between the loading docks is given in the following table:
Three tankers currently at sea are coming into Lajitas. It is necessary to assign a dock for each tanker. Also, only one tanker can anchor in a given dock. Currently, ships 2 and 3 are empty and have no cargo. However, ship 1 has cargo that must be loaded onto the other two ships. The number of tons that must be transferred are as follows:
Formulate and solve with Excel Solver or LINGO an optimization problem that will assign ships to docks so that the product of tonnage moved times distance is minimized. ( Hints: This problem is an extension of the assignment problem introduced in Chapter 6. Also, be careful with the objective function. Only include the nonzero terms. Each of the 12 nonzero terms in the objective function is a quadratic term, or the product of two variables.) There are 12 nonzero terms in the objective function.
This problem formulation is an example of a quadratic assignment problem. The quadratic assignment problem is a powerful model. It is used in a number of facility location problems and components on circuit boards. It is also used to assign jets to gates at airports to minimize product of passengers and distance walked.