Tanguy Lapègue

A constraint-based approach for the shift design personnel task scheduling problem with equity

Abstract This paper presents an industrial problem which arises in a company specialized in drug evaluation and pharmacology research. The aim is to build employee timetables covering the demand given by a set of fixed tasks. The optimality criterion concerns the equity of the workload sharing. A solution to this problem is the assignment of all tasks whose resulting working shifts respect tasks requirements as well as legal and organizational constraints. Scheduling problems usually consider a fixed set of shifts which have to be assigned to a given number of employees whereas in our problem shifts are not fixed and are deduced from the task assignment. In the following, we refer to this problem as the shift-design personnel task scheduling problem with an equity criterion (SDPTSP-E), in reference to the shift minimization personnel task scheduling problem (SMPTSP). Even if the SDPTSP-E is related to several problems, none of them allow to grasp its full complexity. Consequently, we propose a dedicated method based on constraint programming. Several branching and exploration strategies are proposed and tested.

A two-phase method for the shift design and personnel task scheduling problem with equity objective

In this paper, we study the Shift Design and Personnel Task Scheduling Problem with Equity objective, initially introduced by Lapègue, Bellenguez-Morineau and Prot (“A Constraint-based Approach for the Shift Design Personnal Task Scheduling Problem with Equity”, Computers and Operations Research 40 (10): 2450–2465). This problem, arising in the company Biotrial, consists in designing the shifts of employees and assigning a set of tasks to qualified employees, so as to maximise the equity between employees. We propose a natural two-phase approach consisting in first designing shifts and then assigning tasks to employees, and we iterate between these two phases to improve solutions. We compare our experimental results with existing approaches and show that our approach outperforms previous known results.

Filtering AtMostNValue with difference constraints: application to the shift minimisation personnel task scheduling problem

The problem of minimising the number of distinct values among a set of variables subject to difference constraints occurs in many real-life contexts. This is the case of the Shift Minimisation Personnel Task Scheduling Problem, introduced by Krishnamoorthy et al., which is used as a case study all along this paper. Constraint-Programming enables to formulate this problem easily, through several AllDifferent constraints and a single AtMostNValue constraint. However, the independence of these constraints results in a poor lower bounding, hence a difficulty to prove optimality. This paper introduces a formalism to describe a family of propagators for AtMostNValue. In particular, we provide simple but significant improvement of the state-of-the-art AtMostNValue propagator of Bessiere et al., to filter the conjunction of an AtMostNValue constraint and disequalities. In addition, we provide an original search strategy which relies on constraint reification. Extensive experiments show that our contribution significantly improves a straightforward model, so that it competes with the best known approaches from Operational Research.