Damien Prot

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.

New complexity results for parallel identical machine scheduling problems with preemption, release dates and regular criteria

In this paper, we are interested in parallel identical machine scheduling problems with preemption and release dates in case of a regular criterion to be minimized. We show that solutions having a permutation flow shop structure are dominant if there exists an optimal solution with completion times scheduled in the same order as the release dates, or if there is no release date. We also prove that, for a subclass of these problems, the completion times of all jobs can be ordered in an optimal solution. Using these two results, we provide new results on polynomially solvable problems and hence refine the boundary between P and NP for these problems.

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.

A 4D-sequencing approach for air traffic management

The current air traffic system is forecasted to face strong challenges due to the continuous increase in air traffic demand. Hence, there is a need for new types of organization permitting a more efficient air traffic management, with both a high capacity and a high level of safety, and possibly with a reduced environmental impact. In this article, we study a holistic approach, consisting in designing across Europe a very organized air traffic system, as opposed to free flight, to reduce costs while maintaining safety.

Using graph concepts to assess the feasibility of a sequenced air traffic flow with low conflict rate

In this paper, we propose to study feasibility issues of a new air traffic paradigm. In this paradigm, aircraft are following immaterial moving points in such a way that no conflict (or at most few) occurs between aircraft. We provide lower and upper bounds on the maximum density of a solution. In particular, we characterize the density of the solution according to the colorability of an auxiliary graph, modelling the potential conflicts between moving points.

A note on the paper Minimizing total tardiness on parallel machines with preemptions by Kravchenko and Werner (2012)

In this note, we point out two major errors in the paper “Minimizing total tardiness on parallel machines with preemptions” by Kravchenko and Werner (2012). More precisely, they claimed to have proved that both problems P|pmtn|∑Tj and P|rj,pj=p,pmtn|∑Tj are

Approximations for the Two-Machine Cross-Docking Flow Shop Problem

\mathcal{NP}

A survey on how the structure of precedence constraints may change the complexity class of scheduling problems

-Hard. We give a counter-example to their proofs, letting the complexity of these two problems open.

Complexity of a one-to-one meeting scheduling problem with two types of actors

We consider in this article the Two-Machine Cross-Docking Flow Shop Problem, which is a special case of scheduling with typed tasks, where we have two types of tasks and one machine per type. Precedence constraints exist between tasks, but only from a task of the first type to a task of the second type. The precedence relation is thus a directed bipartite graph. Minimizing the makespan is strongly NP-hard even with unit processing times, but any greedy method yields a 2-approximation solution. In this paper, we are interested in establishing new approximability results for this problem. More specifically, we investigate three directions: list scheduling algorithms based on the relaxation of the resources, the decomposition of the problem according to the connected components of the precedence graph, and finally the search of the induced balanced subgraph with a bounded degree.

A note on

This survey aims to demonstrate that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed, many problems can be