The multicommodity multiperiod assignment problem I:A specialized branch and bound algorithm

Abstract

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 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 present an integer, multiperiod, multicommodity network flow model formulation of the multiperiod assignment problem, we develop a specialized branch and bound algorithm that exploits the multicommodity structure of the model. We report favorable computational results of an implementation of the algorithm, and compare them to those of a commercial mixed-integer, linear programming code.