The Multicommodity Multiperiod Assignment Problem 11: Theoretical Results
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The multiperiod assignment problem is an important specialization of the three dimensional assignment problem, which is a generalization of the classical (two dimensional) assignment problem. This model describes the optimization problem of assigning people to activities (jobs) over several time periods. In the most general case, there is a cost of assigning a person to an activity in each time period, and a cost of transferring a person from one activity in each period to another activity in the following period. The number of time periods is not restricted to equal the number of persons and activities. We focus on the special characteristics and properties of noninteger solutions to the linear programming relaxation of the multicommodity, multiperiod assignment problem. The propositions highlight special conditions that must be present for any solution to the problem to be fractional, basic and fesible.