Staff Scheduling Problem Research Articles

On the trade-off between staff-decomposed and activity-decomposed column generation for a staff scheduling problem

In this paper a comparison is made between two decomposition techniques to solve a staff scheduling problem with column generation. In the first approach, decomposition takes place on the staff members, whereas in the second approach decomposition takes place on the activities that have to be performed by the staff members. The resulting master LP is respectively a set partitioning problem and a capacitated multi-commodity flow problem. Both approaches have been implemented in a branch-and-price algorithm. We show a trade-off between modeling power and computation times of both techniques.

Exact and heuristic methodologies for scheduling in hospitals: problems, formulations and algorithms

This text summarizes the PhD thesis defended by the author in January 2006 under the supervision of Professor Erik Demeulemeester at the Katholieke Universiteit Leuven. The thesis is written in English and is available from the author’s website (http://www.econ.kuleuven.be/jeroen.belien). In this research we propose a number of exact and heuristic algorithms for various scheduling problems encountered in hospitals. The emphasis lies on the design of new methodologies as well as on the applicability of the algorithms in real-life environments. The main contributions include a new decomposition approach for a particular class of staff scheduling problems, an extensive study of master surgery scheduling algorithms that aim at leveling the resultant bed occupancy and an innovative method for integrating nurse and surgery scheduling.

Modeling staff scheduling problems. A tutorial

This tutorial gives an introduction to staff scheduling problems. It is meant to be especially accessible for non-initiated people to help them with the analysis and modeling of staff scheduling problems.

An Implicit Tour Scheduling Model with Applications in Healthcare

Motivated by difficult staff scheduling problems arising in healthcare institutions, we have developed an implicit tour scheduling model which includes full and part-time tour types as well as intra-tour start time flexibility. Potential benefits of intra-tour start time flexibility are demonstrated through a computational experiment. The model has been embedded in a decision support system at a large tertiary care hospital and has been used in numerous studies to help estimate staffing needs and to analyze the impact of scheduling policies and practices.

A Polyhedral Approach for the Staff Rostering Problem

In this paper we formulate and efficiently solve staff scheduling problems for large organizations that provide continuous services to customers. We describe an integer programming approach for a class of such problems, where solutions have to obey a number of constraints related to workload balancing, shift compatibility, and distribution of days off. The formulation of the constraints is general and can be extended to different personnel management problems where staff members must cover shifts, and management must assign a fixed number of days off per week. The model maximizes staff satisfaction, expressed by positive weights for pairs of shifts in consecutive days. We consider the associated polytope and study its structure, determining some classes of inequalities that are facet inducing for special subproblems and other valid classes. We also identify a particular subproblem whose solution can be used to determine strong cuts for the complete problem. In addition, we design special branching rules that break the symmetries that arise in the solution space and have a large impact in the efficiency of the method. The validity of this approach has been ascertained by extensive computational tests; moreover, the operations research (OR) department of an airline has implemented the method to solve ground staff management problems.

Models and algorithms for a staff scheduling problem

We present mathematical models and solution algorithms for a family of staff scheduling problems arising in real life applications. In these problems, the daily assignments to be performed are given and the durations (in days) of the working and rest periods for each employee in the planning horizon are specified in advance, whereas the sequence in which these working and rest periods occur, as well as the daily assignment for each working period, have to be determined. The main objective is the minimization of the number of employees needed to perform all daily assignments in the horizon. We decompose the problem into two steps: the definition of the sequence of working and rest periods (called pattern) for each employee, and the definition of the daily assignment to be performed in each working period by each employee. The first step is formulated as a covering problem for which we present alternative ILP models and exact enumerative algorithms based on these models. Practical experience shows that the best approach is based on the model in which variables are associated with feasible patterns and generated either by dynamic programming or by solving another ILP. The second step is stated as a feasibility problem solved heuristically through a sequence of transportation problems. Although in general this procedure may not find a solution (even if one exists), we present sufficient conditions under which our approach is guaranteed to succeed. We also propose an iterative heuristic algorithm to handle the case in which no feasible solution is found in the second step. We present computational results on real life instances associated with an emergency call center. The proposed approach is able to determine the optimal solution of instances involving up to several hundred employees and a working period of up to 6 months.

Staff Scheduling for Inbound Call and Customer Contact Centers

The staff scheduling problem is a critical problem in the call center (or, more generally, customer contact center) industry. This article describes DIRECTOR, a staff scheduling system for contact centers. DIRECTOR is a constraint-based system that uses AI search techniques to generate schedules that satisfy and optimize a wide range of constraints and service-quality metrics. DIRECTOR has successfully been deployed at more than 800 contact centers, with significant measurable benefits, some of which are documented in case studies included in this article.

Modeling and algorithmic development of a staff scheduling problem

The problem of scheduling workers at a hub of a trucking system for the stripping and loading of the trucks and the determination of the optimal number of workers is a difficult problem. The trucks arrive at the facility at different (but known) times and may have their own scheduled departure times. This problem is like a set partitioning problem but with a side constraint pertaining to the dynamic arrival of the trucks. We develop a procedure to solve this problem that is based on the column generation technique, and the solution of a set covering problem to obtain the integer solution. The performance of the procedure is demonstrated by applying it to the real-life data obtained from a trucking company. Its effectiveness is illustrated by comparing it with a lower bound and a well-known heuristic procedure.

A genetic algorithm for scheduling staff of mixed skills under multi-criteria

We consider the problem of scheduling staff with mixed skills. We formulate the problem as a multi-criteria optimization model, where the primary objective is to minimize the total cost for assigning staff to meet the manpower demands over time, the secondary objective is to seek a solution with the maximum surplus of staff among the solutions with almost same level of assigning cost, and the tertiary objective is to reduce the variation of staff surplus over different scheduling periods. This is a new model to handle the staff scheduling problem, which is motivated by the operational requirements in some local service organizations. We propose a new genetic algorithm (GA) to solve the problem. The proposed GA differs from traditional GAs in the following components: (1) it performs its parent selection by using a ranking scheme that considers successively the three criteria; (2) it uses a multi-point crossover operator based on the hamming distance between schedules; and (3) it adopts a heuristic to resolve the problem of infeasibility created by crossover operations. Computational results are reported, which show the effectiveness of the proposed approach in finding desirable solutions.

Algorithms for handling soft constraints and their applications to staff scheduling problems

Algorithms for handling soft constraints and their applications to staff scheduling problems

Tabu search in audit scheduling

The problem of audit staff scheduling normally involves auditors with varying efficiencies, and several audit engagements with varying requirements and at different locations. The task of scheduling auditors to the audit tasks becomes more complicated if the scheduler has to accommodate the many real life considerations. The problem, regardless of its size or complexity, has been formulated as a (0–1) integer program. However, the large number of variables and constraints in such a formulation makes the use of exact optimization methods impractical. In this paper, we present a heuristic procedure based on tabu search (TS) and intelligent memory structures for solving this problem. The TS method starts with a feasible schedule generated by a greedy forward dispatching procedure, then through a series of intensification and diversification steps it improves on the initial schedule. The improvement in the value of the objective function is observed interactively. The search can be terminated as the improvement in the value of the objective function stabilizes. Application of the TS method to different audit scheduling problems has led to a consistent and significant improvement in the value of the cost minimization objective function.

A simulated annealing approach to the cyclic staff-scheduling problem

This article presents the application of a simulated annealing heuristic to an NP-complete cyclic staff-scheduling problem. The new heuristic is compared to branch-and-bound integer programming algorithms, as well as construction and linear programming-based heuristics. It is designed for use in a continuously operating scheduling environment with the objective of minimizing the number of employees necessary to satisfy forecast demand. The results indicate that the simulated annealing-based method tends to dominate the branch-and-bound algorithms and the other heuristics in terms of solution quality. Moreover, the annealing algorithm exhibited rapid convergence to a low-cost solution. The simulated annealing heuristic is executed in a single program and does not require mathematical programming software. © 1993 John Wiley & Sons, Inc.

Multiproject staff scheduling with variable resource constraints

An analytical approach and a PC software based solution are presented to a project management problem, in which multiple resources must be allocated to perform both routine tasks and a set of projects with varying levels of priority. The performance of a priority-based decision rule was tested on this project management problem. The model was able to provide division-level management with an effective tool for staff workload planning and program management. A sequential, iterative approach is developed and used to test and evaluate alternative PC commercial software on a set of projects and evolving criteria. A PC commercial software package, with associated heuristics, is demonstrated to provide useful results to multiproject staff scheduling problems in an actual organization.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An integrated approach for manpower planning in the service sector

The manpower planning problem receives considerable attention by the management of service organizations because they are typically labor intensive. Not only must optimal staff sizes be determined over an extended horizon, but optimal staff schedules which assign labor to tours of duty and specific tasks, given the available staff size, must also be found. Adding to the complexity arising from the interrelatedness of the staff-sizing and staff-scheduling problems is the existence of the conflicting multiple objectives of minimizing costs and maximizing customer service. The few methodologies reported in the literature which treat the complete manpower planning problem as stated above have several shortcomings. Some techniques place a severe strain on computational capabilities. Also, these methods confound the specification of the goal levels with the analysis of the relative goal weightings. Often the specification of the desired goal levels is made at a different level in the organizational hierarchy than the specification of the relative importance of the various goals. This paper suggests an approach which overcomes these shortcomings. The methodology utilizes a simulation model with an imbedded heuristic procedure for the staff-scheduling problem to identify realistic aggregate staff-size goals to be used in a multiple-objective staff-sizing model. The methodology is applied to the manpower planning problem of a large sectional center post office and the managerial benefits are discussed.

A Guaranteed-Accuracy Round-off Algorithm for Cyclic Scheduling and Set Covering

The problem of cyclic staff scheduling is solved by a linear programming round-off heuristic for which a bound on the absolute error is established. The quality of the bound is independent of the resource requirements. Moreover, the quality of the bound improves as the matrix of resource availability approximates the property of consecutive ones. The appropriateness of the heuristic is further established by showing that cyclic staff scheduling is NP-complete.