Algorithms for large scale Shift Minimisation Personnel Task Scheduling Problems

In this paper we introduce the Personnel Task Scheduling Problem (PTSP) and provide solution algorithms for a variant of this problem known as the Shift Minimisation Personnel Task Scheduling Problem (SMPTSP). The PTSP is a problem in which a set of tasks with fixed start and finish times have to be allocated to a heterogenous workforce. Personnel work in shifts with fixed start and end times and have skills that enable them to perform some, but not all tasks. In other words, some personnel are qualified to only perform a subset of all tasks. The objective is to minimise the overall cost of personnel required to perform the given set of tasks. In this paper we introduce a special case in which the only cost incurred is due to the number of personnel (shifts) that are used. This variant of the PTSP is referred to as the Shift Minimisation Personnel Task Scheduling Problem (SMPTSP). While our motivation is a real‐life Personnel Task Scheduling Problem, the formulation may also be applied to machine shop scheduling. We review the existing literature, provide mathematical formulations, and develop a heuristic approach for the SMPTSP.