Solving the general employee scheduling problem

doi:10.1016/j.cor.2019.104794

Computers & Operations Research

Volume 113, January 2020, 104794

https://doi.org/10.1016/j.cor.2019.104794 Get rights and content

Highlights

•
Framework covers a wide range of different employee scheduling problems.
•
Reuse moves and algorithms for new problems with minimum adaptation effort.
•
Extensible way to include different constraints in employee scheduling.
•
Improved results for some benchmark instances.

Abstract

In many professions the demand for work requires employees to work in different shifts to cover varying requirements including areas like health care, protection services, transportation, manufacturing or call centers. However, there are many constraints that need to be satisfied in order to create feasible schedules. The demands can be specified in various ways, different legal requirements need to be respected and employee satisfaction has to be taken into account. Therefore, automated solutions are mandatory to stay competitive. However, even then it is often hard to provide good solutions in reasonable time as many of the problems are NP-hard.

While not each problem will require the whole set of available restrictions, it is cumbersome to develop a new specification format and corresponding solver for each problem. Often these can not be well applied to similar problems differing in some requirements. On the other hand it is a challenging task to provide a general formulation and solution methods that can solve large integrated problems, as even several sub-problems on their own are known to be NP-hard.

Therefore a new framework is proposed for the general employee scheduling problem that allows the implementation of various heuristic algorithms and their application to a wide range of problems. This is realized by proposing a unified handling of constraints and the possibility to implement various moves that can be reused across different algorithms. Further, a new search method is developed and implemented in the framework.

In order to show the applicability to a wide range of problems, we take different problems from literature that cover different types of demand and constraints, translate their instances to our formulation and apply our solver to those instances as well as our own instances with good results. For one problem class our framework could obtain better solutions for several benchmark instances.

Introduction

In many professions the demand for work requires employees to work in different shifts to cover varying requirements including areas like health care, protection services, transportation, manufacturing or call centers. However, this problem can come in many shapes (Ernst, Jiang, Krishnamoorthy, Sier, 2004, Van den Bergh, Belin, De Bruecker, Demeulemeester, De Boeck, 2013). The demand might be to assign employees to certain shifts that are already fixed like in nurse rostering. It might also be necessary to design shifts in a way that there is always a certain number of employees present. Sometimes tasks are given and the shifts have to be designed to cover these tasks.

On the other hand shifts can not be assigned freely. Legal requirements can be very strict in demanding times between shifts, certain patterns or sequences of shifts or days off that are required or forbidden and much more. Employees might have different contracts that might specify very differing requirements for each employee. On some occasions it might also be necessary to schedule breaks as well in order to guarantee that still enough employees are available for duty.

Further, the employees themselves often specify their own requests like days they would like to have on or off, shifts they want to avoid or other employees they want to work with or avoid. There might also be measurements of fairness between employees that need to be considered. In order to increase employee satisfaction it is important to include such wishes as well.

To reduce cost and maximize effectiveness, companies want to find schedules that cover all the demands in an effective way. Ineffective scheduling might require the hiring of temporary employees increasing the cost, while schedules that do not respect all the legal constraints can lead to penalties and employee dissatisfaction. Not only is it increasingly difficult to generate schedules by hand for more employees and more requirements, it is also very time consuming. Therefore, automated solutions are mandatory to stay competitive. However, even then it is often hard to provide good solutions in reasonable time as many of the problems are NP-hard.

While not each problem will require the whole set of available restrictions, it is cumbersome to develop a new specification and corresponding solver for each version. Often these can not be well applied to similar problems differing in some requirements. Therefore, it would be highly beneficial to have a framework suitable for application on various problems without the need to design a new formulation from scratch. On the other hand it is a challenging task to provide a general formulation and solution methods that can solve large integrated problems, as even several sub-problems on their own are known to be NP-hard.

The main contribution of this paper is a new framework allowing the implementation of various heuristic solvers for different kinds of problems specified in our formulation while increasing reusability and easy adaptation to new problem variants. Researchers have proposed general heuristic frameworks such as hyperheuristics (Burke et al., 2013), but to the best of our knowledge a framework for generalized employee scheduling problems does not exist yet.

A new approach based on Simulated Annealing is implemented in our framework and applied to various benchmark instances from literature for comparison as well as to instances from a new instance generator. The instances from literature cover nurse rostering (Curtois, 2017) as well as different problems involving tasks from Smet et al. (2016) and Lapgue et al. (2013).

The remainder of this paper is organized as follows. In Section 2 an overview of related work in employee scheduling is presented. In Section 3 the problem definition is presented. Section 4 explains the structure of the framework and its components. In Section 5 the evaluation of the framework on the generated instances and the instances from literature is presented. Section 6 provides a summary and an outlook for possible future work.

Section snippets

Related work

Many different versions of employee scheduling problems have been described in the past. Already in Glover and McMillan (1986) an informal description of the General Employee Scheduling (GES) Problem was provided, giving rise to the identification of several common notions in all problems of this kind.

Several reviews of different problem versions are available. In the review on staff scheduling and rostering in Ernst et al. (2004) several modules in the rostering process are identified. The

Problem definition and specification format

In General Employee Scheduling a wide range of different constraints needs to be considered to allow the specification of different requirements without the need to introduce a new problem formulation for each variant of the problem.

Based on the analysis of various employee scheduling problems in literature, a new specification format was developed (Kletzander et al., 2017) that supports a wide range of problems using different demand specifications and different types of definitions,

Solver framework

As the domain of employee scheduling can include a large range of constraints and combine various different aspects of scheduling, it would be highly beneficial to have a general framework that can be applied to a wide range of different employee scheduling problems. Therefore, the main goal is to provide a framework for the implementation of solvers that can be used to solve different problems specified in the GES format. This section describes the main components and structure of the newly

Evaluation

For the evaluation of the framework several different problems from literature as well as some instances from our new instance generator are used. While it would be possible to develop specific algorithms for each problem that are specialized to the demands and constraints of the particular problem, we want to show the wide applicability by applying the same Simulated Annealing algorithm presented before to all problems. This highlights the adaptability of the framework to different problems as

Conclusion

This paper proposed a new framework for general employee scheduling that allows independent handling of various constraints in a unified way, promoting easy addition or change of constraints. A common way of implementing and handling moves was provided that allows easy integration of new moves as well as their reusability across different algorithms. A new general purpose simulated annealing algorithm and a set of moves were implemented in the framework.

To evaluate the generality of our

Acknowledgments

This work was supported by the Austrian Science Fund (FWF): P24814-N23. The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged.

References (27)

P. Brucker et al.
Personnel scheduling: models and complexity
Eur. J. Operat. Res.
(2011)
E.K. Burke et al.
New approaches to nurse rostering benchmark instances
Eur. J. Operat. Res.
(2014)
P. De Bruecker et al.
Workforce planning incorporating skills: state of the art
Eur. J. Operat. Res.
(2015)
A. Ernst et al.
Staff scheduling and rostering: a review of applications, methods and models
Eur. J. Operat. Res.
(2004)
F. Hutter et al.
Sequential model-based optimization for general algorithm configuration
J.S. Loucks et al.
Tour scheduling and task assignment of a heterogeneous work force: a heuristic approach
Decis. Sci.
(1991)
P. Smet et al.
The shift minimisation personnel task scheduling problem: a new hybrid approach and computational insights
Omega
(2014)
H.K. Alfares
Survey, categorization, and comparison of recent tour scheduling literature
Ann. Operat. Res.
(2004)
A. Beer et al.
An AI-based break-scheduling system for supervisory personnel
IEEE Intell. Syst.
(2010)
E.K. Burke et al.
The state of the art of nurse rostering
J. Schedul.
(2004)

E.K. Burke et al.

Hyper-heuristics: a survey of the state of the art

JORS

(2013)

Curtois, T., 2017. Employee shift scheduling benchmark data sets. http://www.schedulingbenchmarks.org/. Accessed:...

T. Curtois et al.

Computational results on new staff scheduling benchmark instances

Technical Report

(2014)

Cited by (26)

Integrated task scheduling and personnel rostering of airports ground staff: A case study
2024, Expert Systems with Applications
In dealing with personnel management in companies, two fundamental planning issues have to be handled: staff rostering and activities assignment. These two problems have historically been treated separately, in a sequential way; however, it is evident how strongly they are tied to each other and that solution quality inevitably drops if this connection is not taken into proper account. For this reason, also taking advantage of the massive recent advances in software and hardware technologies, the integrated task scheduling and personnel rostering problem (TSPR) has been formalized along with suitable algorithmic approaches to tackle both planning stages altogether. In this paper, we describe how the peculiar and complex case of airport ground staff was handled in a scenario defined by real-world data from a large airport in Italy. Specifically, we show that the problem can be cast into a mixed integer linear programming model. We then show that, to make the problem computationally tractable, the introduction within the model of a set of suitable valid inequalities is crucial. Indeed, as opposed to the base model from the literature, the novel, improved formulation allowed to effectively obtain near-optimal solutions in reasonable time even for the considered large-scale and real-world scenario.
Workforce scheduling approaches for supporting human-centered algorithmic management in manufacturing: A systematic literature review and a conceptual optimization model
2024, Procedia Computer Science
Workforce scheduling is becoming increasingly complex and time-consuming as the number of influencing factors increases. Intelligent, algorithmic optimization approaches can support managers in mastering this complex task. Since workforce scheduling influences key elements of work design, it has the potential to promote human-centered work design and thus, e.g., reduce stress and increase job satisfaction. This paper presents a literature review of various factors considered by existing algorithmic scheduling approaches in manufacturing environments. The identified factors are classified based on the dimensions of human-centered work design. The results show that the identified approaches integrate various aspects that can support human-centered workforce scheduling. However, usually only specific aspects are considered (e.g. learning effects) and certain dimensions are not considered at all (e.g. feedback). In order to exploit the potentials of algorithmic management for the design of humane work, an exemplary optimization model is presented and discussed.
Optimization of the integrated problem of employee timetabling and job shop scheduling
2022, Computers and Operations Research
Citation Excerpt :
Other algorithms, that are inspired from biological processes, can also be applied to the ETP, such as the particle swarm optimization (Günther and Nissen, 2010), memetic algorithms (Landa-Silva and Obit, 2009), ant colony optimization (Gutjahr and Rauner, 2007), the artificial immune system (Maenhout and Vanhoucke, 2013), and harmony search (Hadwan et al., 2013). Recently, Kletzander and Musliu (2020) proposed a new framework for the general employee scheduling problem, to implement various heuristic algorithms and to address a wide range of cases. Their framework proposes a unified handling of constraints, promoting easy addition or change of constraints.
This paper deals with a real manufacturing scheduling problem that is particularly encountered in the tannery industries. This problem often integrates employee timetabling and production scheduling. The employee timetabling problem is addressed in the context of skill requirements and under availability and legislative constraints. The production scheduling is considered as a re-entrant hybrid job-shop problem with time lags and sequence dependent setup times, under machine availability constraints. The objective is to minimize the labor cost, while respecting a maximum makespan and a maximum tardiness constraints. Two different models and exact resolution methods are proposed, using Mixed Integer Linear Programming (MILP) and Constraint Programming (CP). Numerical experimentations are conducted to compare and evaluate their performances, based on randomly generated instances. The results show that the CP model is slower than the MILP model in terms of finding optimal solutions for large instances, but is more efficient in generating feasible solutions. Thus, providing a feasible initial solution to the MILP model using the CP model is a promising hybrid approach to reduce the computational time.
Modeling employee flexible work scheduling as a classification problem
2021, Procedia Computer Science
Many organizations have adapted flexible working arrangements during COVID19 pandemic because of restrictions on the number of employees required on site at any time. Unfortunately, current employee scheduling methods are more suited for compressed working arrangements. The problem of automating compressed employee scheduling has been studied by many researchers and is widely adopted by many organizations in an attempt to achieve high quality scheduling. During process of employee scheduling many constraints may have to be considered and may require negotiating a large dimension of constraints like in flexible working. These constraints make scheduling a challenging task in these working arrangements. Most scheduling algorithms are modeled as constraint optimization problems and suited for compressed work but for flexible working with large constraint dimensions, achieving accurate scheduling is even more challenging. In this research, we propose a machine learning approach that takes advantage of mining user-defined constraints or soft constraints and transform employee scheduling into a classification problem. We propose automatically extracting employee personal schedules like calendars in order to extract their availability. We then show how to use the extracted knowledge in a multi-label classification approach in order to generate a schedule for faculty staff in a University that supports flexible working. We show that the results of this approach are comparable to that of a constraint satisfaction and optimization method that is commonly used in literature. Results show that our approach achieved accuracy of 93.1% of satisfying constraints as compared to 92.7% of a common constraint programming approach.
A hybrid fix-and-optimize and simulated annealing approaches for nurse rostering problem
2020, Computers and Industrial Engineering
Citation Excerpt :
In a recent survey paper, Erhard, Schoenfelder, Fügener, and Brunner (2018) provide a review on physician scheduling problem. Very recently, Kletzander and Musliu (2020) propose a new framework for general employee scheduling that allows independent handling of various constraints in a unified way. Table 1 represents a comprehensive summary of studies in the NRP field in the last several decades.
The Nurse Rostering Problem (NRP) is a complex scheduling problem in which nurses must be assigned to shifts according to a set of constraints. The NRP is difficult to solve to optimality due to its combinatorial structure. In this paper, we propose a hybrid solution algorithm that combines Mixed Integer Programming (MIP) based heuristics—namely Fix-and-Relax (F&R) and Fix-and-Optimize (F&O)—and Simulated Annealing (SA) to solve the NRP. In MIP-based heuristics, a problem is decomposed into a set of smaller problems and each problem is iteratively solved to optimality. In the hybrid approach, high-quality initial solutions are obtained via the F&R algorithm and fed to the SA part of the algorithm. When solutions can no longer be improved, the F&O algorithm is inserted into the SA algorithm. This enables the hybrid algorithm to diversify the search space and provide better solutions. To assess the quality and efficiency of the hybrid approach, we use 24 publicly available test instances recently introduced in literature in the field. Computational results show that the hybrid method outperforms other advanced solution techniques in most of the test data and seven new best-known results are reported.
A fast-flexible strategy based approach to solving employee scheduling problem considering soft work time
2024, Scientific Reports

View all citing articles on Scopus

View full text

Solving the general employee scheduling problem

Highlights

Abstract

Introduction

Section snippets

Related work

Problem definition and specification format

Solver framework

Evaluation

Conclusion

Acknowledgments

Eur. J. Operat. Res.

Eur. J. Operat. Res.

Eur. J. Operat. Res.

Eur. J. Operat. Res.

Decis. Sci.

Omega

Survey, categorization, and comparison of recent tour scheduling literature

Ann. Operat. Res.

An AI-based break-scheduling system for supervisory personnel

IEEE Intell. Syst.

The state of the art of nurse rostering

J. Schedul.

Hyper-heuristics: a survey of the state of the art

JORS

Computational results on new staff scheduling benchmark instances

Technical Report