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

Methods to solve multi-skill project scheduling problem

International audienceThis is a summary of the author's PhD thesis supervised by P. Martineau and E. Néron and defended on 28 November 2006 at the Université François-Rabelais de Tours. The thesis is written in French, and is available upon request from the author. This work deals with the problem of scheduling a project. The activities of this project requires skills that may not be mastered by all persons involved. First of all, the problem is defined in the introduction part. Then we propose different methods to solve it: lower bounds in part 2, different heuristics and meta-heuristics in part 3, and finally a branch-and-bound procedure in the last part

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

Complexity of parallel scheduling unit-time jobs with in-tree precedence constraints while minimizing the mean flow time

This paper deals with a particular scheduling problem. We consider unit-time jobs and in-tree precedence constraints while minimizing the mean flow time. This problem is observed as P |p j = 1, in-tree| C j with the use of the 3-filed notation. To the best of our knowledge, its complexity is still open. Through a reduction from 3-Partition, we show that this problem is N P-complete

The Complexity of Parallel Machine Scheduling of Unit-Processing-Time Jobs under Level-Order Precedence Constraints

International audienc