How the structure of precedence constraints may change the complexity class of scheduling problems

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. We also show that there still are many very exciting challenges in this research area

A Note on NP-Hardness of Preemptive Mean Flow-Time Scheduling for Parallel Machines

In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, D\"urr, Kravchenko and Sourd, the authors claimed to prove strong NP-hardness of the scheduling problem $P|pmtn,r_j|\sum C_j$, namely multiprocessor preemptive scheduling where the objective is to minimize the mean flow time. We point out a serious error in their proof and give a new proof of strong NP-hardness for this problem

METHODS FOR THE SHIFT DESIGN AND PERSONNEL TASK SCHEDULING PROBLEM

Colloque avec actes et comité de lecture. internationale.International audienceThis paper introduces an overview of the methods that have been used in the literature to solve the Shift Design and Personnel Task Scheduling Problem with Equity. Basically, this problem aims at designing a schedule while assigning fixed tasks, that cannot be preempted, to an heterogeneous workforce. Such problem may occur in several contexts, where industrial activity requires a sharp and efficient management of workers. In this paper, we focus on the particular case of a company specialized in drug evaluation. This company is facing a scheduling problem that may be modelized as a Shift Design and Personnel Task Scheduling Problem with Equity. Based on realistic instances of this particular problem, we compare the relative performances of the different methods considered: A two-phase method, a constraint-based approach and a large neighborhood search derived from the constraint-based model

A two-phase method for the Shift Design and Personnel Task Scheduling Problem with Equity objective

International audienceIn this paper, we study the Shift Design and Personnel Task Scheduling Problem with Equity objective (SDPTSP-E), initially introduced in [11]. This problem consists in designing the shifts of workers and assigning a set of tasks to quali ed workers, so as to maximise the equity between workers. We propose a natural two-phase approach consisting in rst designing shifts and then assigning tasks to workers, and we iterate between these two phases to improve solutions. We compare our experimental results with existing literature and show that our approach outperforms previous known results

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

International audienceWe 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

Tabu search and lower bound for an industrial complex shop scheduling problem

International audienceThis paper deals with an industrial shop scheduling problem that arises in a metal goods production group. The scheduling problem can be seen as a multi-mode job shop with assembly. Jobs have additional constraints such as release date, due date and sequence-dependent setup times. The aim of the decision-makers is to minimize the maximum lateness. This article introduces a tabu search procedure to solve the whole problem and a valid lower bound used to evaluate the tabu search procedure

Approximation results for the two machine cross-docking problem

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

International audienceIn 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|∑T j and P|r j ,p j =p,pmtn|∑T j are NP -Hard. We give a counter-example to their proofs, letting the complexity of these two problems open

Dimensionnement d'équipe pour la réalisation d'étude de produits pharmaceutiques

National audienceLe problème connu sous le nom de Shift Design and Personnel Task Scheduling Problem with Equity (SDPTSP-E) est un problème de création d'horaires de travail pour couvrir une charge prédéfinie. Les tâches à réaliser ont des dates d'exécution fixées et correspondent à un besoin en compétence. On doit donc affecter des horaires de travail à chaque employé afin de couvrir cette demande, dans le respect des contraintes légales et organisationnelles. Une méthode de résolution efficace est introduite dans [1]. Elle est actuellement utilisée dans un logiciel de gestion propriétaire d'une entreprise de tests pharmaceutiques. Il peut cependant arriver que la charge de travail soit trop importante pour être couverte par l'équipe permanente. Dans ce cas, il est prévu de faire appel à des intérimaires sur une période de durée définie. Cette période peut être augmentée afin de décharger l'équipe qui a d'autres activités en parallèle. L'objectif de cette étude est de montrer comment l'approche proposée permet au décideur de simuler différents scenarii. Cela permet tout d'abord de cibler les périodes qui ne peuvent être entièrement couvertes et sur lesquels il est obligatoire de faire des recrutements. Par la suite, il est possible de reconstruire un emploi du temps qui couvre la totalité des tâches à réaliser, en fonction des employés additionnels et des périodes qui leur sont affectées. On pourra ainsi évaluer la qualité des plannings obtenus pour le personnel, en termes d'équité, mais également le coût des emplois supplémentaires qui sont ainsi mieux maitrisés. [1] A large neighborhood search for the Shift Design Personnel Task Scheduling Problem with Equity Lapègue T., Prot D., Bellenguez-Morineau O. 6th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2013), Belgium (2013) [hal-00859182 - version 1

A constraint-based approach for the Shift Design Personnel Task Scheduling Problem with Equity

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