An automatic constructive matheuristic for the shift minimization personnel task scheduling problem

Abstract

The shift minimization personnel task scheduling problem is an NP-complete optimization problem that concerns the assignment of tasks to multi-skilled employees with a view to minimize the total number of assigned employees. Recent literature indicates that hybrid methods which combine exact and heuristic techniques such as matheuristics are efficient as regards to generating high quality solutions. The present work employs a constructive matheuristic (CMH): a decomposition-based method where sub-problems are solved to optimality using exact techniques. The optimal solutions of subproblems are subsequently utilized to construct a feasible solution for the entire problem. Based on the study, a time-based CMH has been developed which, for the first time, solves all the difficult instances introduced by Smet et al. (2014) to optimality. In addition, an automated CMH algorithm that utilizes instance-specific problem features has also been developed that produces high quality solutions over all current benchmark instances.

A Successful Three-Phase Metaheuristic for the Shift Minimization Personal Task Scheduling Problem

“…e five other methods use commercial MILP solvers as part of the solution process: S14 [19], FL13 [14], B15 [15], R18 [17], and C20 [18]. Table 5 shows the detailed results.…”

“…Chirayil Chandrasekharan et al [18] noted that FL instances were unavailable when S14 method was published and that a summary of the S14 results was obtained upon request. e authors provided us the instance-specific results of the S14 method for FL instances.…”

“…erefore, we speculate that these two instances might be such that the lower bound value is not the optimum value. Note that the instances were also unsolved by the Chirayil Chandrasekharan et al method in [18]. e KEB instances are easy to solve.…”

“…e authors stated that even though they proved interesting theoretical results, their methods fulfilled the expectations practically by easily surpassing other comparable exact methods. Chirayil Chandrasekharan et al [18] improved the metaheuristic introduced in [12] and presented a decomposition-based method where subproblems are solved to optimality using exact techniques. e optimal solutions of subproblems are subsequently utilized to construct a feasible solution for the entire problem.…”

The Extended Shift Minimization Personnel Task Scheduling Problem

“…The number of shifts denotes the known optimum value for the SMPTSP, i.e. the minimum number of shifts derived from the recent paper by Chandrasekharan et al [21]. The @AVG measure indicates the estimated average number of tasks per non-empty shift, i.e.…”