The shift minimisation personnel task scheduling problem: A new hybrid approach and computational insights

Abstract

Assigning scheduled tasks to a multi-skilled workforce is a known NP-complete problem with many applications in health care, services, logistics and manufacturing. Optimising the use and composition of costly and scarce resources such as staff has major implications on any organisation's health. The present paper introduces a new, versatile two-phase matheuristic approach to the shift minimisation personnel task scheduling problem, which considers assigning tasks to a set of multi-skilled employees, whose working times have been determined beforehand. Computational results show that the new hybrid method is capable of finding, for the first time, optimal solutions for all benchmark instances from the literature, in very limited computation time. The influence of a set of problem instance features on the performance of different algorithms is investigated in order to discover what makes particular problem instances harder than others. These insights are useful when deciding on organisational policies to better manage various operational aspects related to workforce. The empirical hardness results enable to generate hard problem instances. A set of new challenging instances is now available to the academic community.

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

“…We use F to denote the lower bounds obtained by solving the F model to optimality, CP to denote the lower bounds obtained by the constraint programming approach of Fages and Lapegue (2013), CLB to denote the lower bound of Smet et al (2014), RF' and RF to denote the lower bounds obtained by solving the proposed RF' and RF models, respectively. Krishnamoorthy et al (2012) b Smet et al (2014) c Fages and Lapegue (2013) d Each worker can perform a certain percent of all tasks on average.…”

“…Each worker can perform a set of tasks with one task at a time only if those tasks' start and finish times fit those of the worker and the worker has the required qualifications to perform those tasks. Each task has to be performed by one of the eligible workers without interruption.The SMPTSP, a strongly NP-hard problem (Kroon et al, 1997), has been studied by Krishnamoorthy et al (2012), Smet and Berghe (2012), Smet et al (2014), Fages andLapegue (2013), andLin andYing (2014). Krishnamoorthy et al (2012) proposed Lagrangian relaxation-based upper and lower bounding procedures using a mixed integer programming (MIP) model of the problem (see Section 1) and assessed the performance of these procedures on a data set of 137 instances, referred to as KEB instances, which they generated considering real-life applications.…”

“…Their heuristic yielded solutions that deviate on average 0.56% from the optimal values. Smet et al (2014) proposed a two-phase heuristic composed of a construction heuristic in the first phase and a local branchingbased improvement heuristic in the second phase. The two-phase heuristic managed to solve all KEB instances optimally within a short time.…”

Heuristic decomposition approaches for an integrated task scheduling and personnel rostering problem

“…Krishnamoorthy et al (2012) introduce a problem in which tasks, fixed in time, are assigned to multi-skilled employees whose working times are predetermined. Alternative algorithms for this problem are discussed by Baatar et al (2015); Smet et al (2014). The objective is to minimise the total number of employees.…”

“…The horizontal decomposition algorithm is based on the constructive matheuristic introduced by Smet et al (2014) which sequentially solves subproblems consisting of b employees. The employees in each subproblem are selected randomly without taking into account any instance-specific information.…”