Question: Linear Optimization Problem - Assign 5 Objects to 5 People Five people (A, B, C, D, and E) would like to have one of five objects.

Question:

Linear Optimization Problem - Assign 5 Objects to 5 People

Five people (A, B, C, D, and E) would like to have one of five objects. The store wants to make sure each person has an object and that each object goes to one person. The objects are numbered from 1 to 5, and each individual ranks the objects in order of preference (with '1' being the most preferred, and '5' the least preferred rank). This information is organized in the matrix below, where each row denotes a person and each column denotes a object.

Form a linear optimization so that each person gets as close as possible to their top ranking.

 (a)  Formulate this as an integer linear programming problem. Clearly specify the decision variables, the objective function and the constraints.