Integer programming approach for a class of staff scheduling problems — Schedule optimization and parameter estimation

This paper introduces an integer programming approach for a class of staff scheduling problems which is applicable for various kinds of the problems by both adopting an optimization model and parameter estimation techniques based on a mathematical programming formulation. For a work in which a staff must change or rotate shifts, generally, a responsible personnel (e.g., a manager) makes a schedule (e.g., a dairy or a weekly staff assignment) in a manual way based on some experiences. It is very hard, however, to generate not only a good schedule but also a feasible one, due to several kinds of constraints and requirements should be satisfied. Here, it is the case that the constraints are not be completely clear because these have no evident boundary, which makes the scheduling problems more difficult. In this paper, first, the staff scheduling problem is formally described in a rather generalized form to apply a wide range of work types, and is formulated as a integer programming model. In this formulation, so many parameters concerning the desires of workers as well as the conditions on works are included. Then, some ways of identifying the parameters is investigated by utilizing the available information acquired extraction from the past staff schedules and listening from managers. In the case that the setting of the parameters is not suitable, a good schedule or even a practical schedule can not be obtained through the integer programming model. With respect to this point, some computational examples have been done in order to examine the reliability of the way of setting parameters as well as the model of optimizing schedule. Through the result of computational examples, the effectiveness and the potential of the proposed approach are confirmed.