Odile Bellenguez-Morineau

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.

Branch-and-price approach for the multi-skill project scheduling problem

This work introduces a procedure to solve the multi-skill project scheduling problem (MSPSP) (Néron and Baptista, International symposium on combinatorial, optimization (CO’2002), 2002). The MSPSP mixes both the classical resource constrained project scheduling problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project, composed of a set of activities. In addition, precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present a column generation approach embedded within a branch-and-price (B&P) procedure that considers a given activity and time-based decomposition approach. Obtained results show that the proposed B&P procedure is able to reach optimal solutions for several small and medium sized instances in an acceptable computational time. Furthermore, some previously open instances were optimally solved.

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.

Integrated Column Generation and Lagrangian Relaxation Approach for the Multi-Skill Project Scheduling Problem

This chapter introduces a procedure to solve the Multi-Skill Project Scheduling Problem. The problem combines both the classical Resource-Constrained Project Scheduling Problem and the multi-purpose machine model. The aim is to find a schedule that minimizes the completion time (makespan) of a project composed of a set of activities. Precedence relations and resources constraints are considered. In this problem, resources are staff members that master several skills. Thus, a given number of workers must be assigned to perform each skill required by an activity. Practical applications include the construction of buildings, as well as production and software development planning. We present an approach that integrates the utilization of Lagrangian relaxation and column generation for obtaining strong makespan lower bounds. Finally, we present the corresponding obtained results.

Performance evaluation of holonic control of a switch arrival system

The application of holonic paradigm to the hybrid control system class is a promising way to give flexibility to the control of such systems, leading to new industrial intelligent processes. However, there is a need for performance evaluation of such solutions in order to give them credit among the multiple formalisms used in the literature. This article aims at evaluating the optimality and stability of the holonic control of a switch arrival system, a classical system from the literature where a unique server has to switch between leaking tanks full of fluids before they get empty. Optimality is evaluated compared to a scheduling algorithm aimed at minimizing the number of switches of the server while respecting the constraints. Stability is evaluated through a stochastic simulation run aiming at finding cyclic behavior of the control in a whole set of random initial configurations. The results tend to show a good overall performance of the control, especially considering the algorithms used are quite simple, thus could be made better and enhance the performance.

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

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

\mathcal{NP}

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

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

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