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This study considers the shift minimization personnel task scheduling problem, which is to assign a set of tasks with fixed start and finish times to a minimum number of workers from a heterogeneous workforce. An effective lower bounding procedure based on solving a new integer programming model of the problem is proposed for the problem. An extensive computational study on benchmark data sets reveals that the proposed lower bounding procedure outperforms those existing in the literature and consistently and rapidly yields high quality lower bounds that are necessary for the decision makers to assess the quality of the obtained schedules.

The Shift Minimization Personnel Task Scheduling Problem: An Effective Lower Bounding Procedure