Integer programming models for hierarchical workforce scheduling problems including excess off-days and idle labour times

The decision problem considered in this paper is a hierarchical workforce scheduling problem in which a higher qualified worker can substitute for a lower qualified one, but not vice versa, labour requirements may vary, and each worker must receive n off-days a week. Within this context, five mathematical models are discussed. The first two of these five models are previously published. Both of them are for the case where the work is indivisible. The remaining three models are developed by the authors of this paper. One of these new models is for the case where the work is indivisible and the other two are for the case where the work is divisible. The three new models are proposed with the purpose of removing the shortcomings of the previously published two models. All of the five models are applied on the same illustrative example. Additionally, a total of 108 test problems are solved within the context of two computational experiments.