The Days On Days Off Scheduling Problem

TL;DR

This paper analyzes a specific personnel scheduling problem with constraints on work and days off, proving its NP-completeness and offering efficient algorithms for certain cases.

Contribution

It proves the NP-completeness of a scheduling variant and classifies its special cases, providing algorithms for feasible schedule computation.

Findings

The scheduling problem is NP-complete.

Certain simplified cases are polynomial-time solvable.

Efficient algorithms are provided for feasible schedule construction.

Abstract

Personnel scheduling problems have received considerable academic attention due to their relevance in various real-world applications. These problems involve preparing feasible schedules for an organization's employees and often account for factors such as qualifications of workers and holiday requests, resulting in complex constraints. While certain versions of the personnel rostering problem are widely acknowledged as NP-hard, there is limited theoretical analysis specific to many of its variants. Many studies simply assert the NP-hardness of the general problem without investigating whether the specific cases they address inherit this computational complexity. In this paper, we examine a variant of the personnel scheduling problems, which involves scheduling a homogeneous workforce subject to constraints concerning both the total number and the number of consecutive work days and days off. This problem was claimed to be NP-complete by [Brunner+2013]. In this paper, we prove its NP-completeness and investigate how the combination of constraints contributes to this complexity. Furthermore, we analyze various special cases that arise from the omission of certain parameters, classifying them as either NP-complete or polynomial-time solvable. For the latter, we provide easy-to-implement and efficient algorithms to not only determine feasibility, but also compute a corresponding schedule.