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

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.