Eric Sanlaville

Machine scheduling with availability constraints

Abstract. We will give a survey on results related to scheduling problems where machines are not continuously available for processing. We will deal with single and multi machine problems and analyze their complexity. We survey NP-hardness results, polynomial optimization and approximation algorithms. We also distinguish between on-line and off-line formulations of the problems. Results are concerned with criteria on completion times and due dates.

Flexibility and Robustness in Scheduling

Preface. Chapter 1. Introduction to Flexibility and Robustness in Scheduling (Jean-Charles Billaut, Aziz Moukrim an Eric Sanlaville). Chapter 2. Robustness in Operations Research and Decision Aiding (Bernard Roy). Chapter 3. The Robustness of Multi-Purpose Machines Workshop Configuration (Marie-Laure Espinouse, Mireille Jacomino and Andre Rossi). Chapter 4. Sensitivity Analysis for One and m Machines (Amine Mahjoub, Aziz Moukrim, Christophe Rapine and Eric Sanlaville). Chapter 5. Service Level in Scheduling (Stephane Dauzere-Peres, Philippe Castagliola and Chams Lahlou). Chapter 6. Metaheuristics for Robust Planning and Scheduling (Marc Sevaux, Kenneth Sorensen and Yann Le Quere). Chapter 7. Metaheuristics and Performance Evaluation Models for the Stochastic Permutation Flow-Shop Scheduling Problem (Michel Gourgand, Nathalie Grangeon and Sylvie Norre). Chapter 8. Resource Allocation for the Construction of Robust Project Schedules (Christian Artigues, Roel Leus and Willy Herroelen). Chapter 9. Constraint-based Approaches for Robust Scheduling (Cyril Briand, Marie-Jose Huguet, Hoang Trung La and Pierre Lopez). Chapter 10. Scheduling Operation Groups: A Multicriteria Approach to Provide Sequential Flexibility (Carl Esswein, Jean-Charles Billaut and Christian Artigues). Chapter 11. A Flexible Proactive-Reactive Approach: The Case of an Assembly Workshop (Mohamed Ali Aloulou and Marie-Claude Portmann). Chapter 12. Stabilization for Parallel Applications (Amine Mahjoub, Jonathan E. Pecero Sanchez and Denis Trystram). Chapter 13. Contribution to a Proactive/Reactive Control of Time Critical Systems (Pascal Aygalinc, Soizick Calvez and Patrice Bonhomme). Chapter 14. Small Perturbations on Some NP-Complete Scheduling Problems (Christophe Picouleau). List of Authors. Index.

Linear programming based algorithms for preemptive and non-preemptive RCPSP

Abstract In this paper, the RCPSP (resource constrained project scheduling problem) is solved using a linear programming model. Each activity may or may not be preemptive. Each variable is associated to a subset of independent activities (antichains). The properties of the model are first investigated. In particular, conditions are given that allow a solution of the linear program to be a feasible schedule. From these properties, an algorithm based on neighbourhood search is derived. One neighbour solution is obtained through one Simplex pivoting, if this pivoting preserves feasibility. Methods to get out of local minima are provided. The solving methods are tested on the PSPLIB instances in a preemptive setting and prove efficient. They are used when preemption is forbidden with less success, and this difference is discussed.

Preemptive scheduling with variable profile, precedence constraints and due dates

Abstract This paper is concerned with the problem of scheduling preemptive tasks subject to precedence constraints in order to minimize the maximum lateness and the makespan. The number of available parallel processors is allowed to vary in time. It is shown that when an earliest due date first algorithm provides an optimal nonpreemptive schedule for unit-execution-time (UET) tasks, the preemptive priority scheduling algorithm, referred to as smallest laxity first, provides an optimal preemptive schedule for real-execution-time (RET) tasks. When the objective is to minimize the makespan, we get the same kind of result between highest level first schedules solving nonpreemptive tasks with UET and the longest remaining path first schedule for the corresponding preemptive scheduling problem with RET tasks. These results are applied to four specific profile scheduling problems and new optimality results are obtained.

Nearly on line scheduling of preemptive independent tasks

Abstract We discuss the problem of scheduling preemptive independent tasks, subject to release dates and due dates, on identical processors, so as to minimize the maximum lateness. This problem was solved by a polynomial flow based algorithm, but the major drawback of this approach is its off-line character. We study a priority algorithm, the equivalent of a list scheduling method in the non-preemptive case, in which tasks are ordered according to their due dates. This algorithm is nearly on-line and of low complexity. It builds an optimal schedule when the release dates are equal. In the general case, it provides an absolute performance guarantee. These results hold when the number of available machines is allowed to vary with time in a zigzag way (the number of machines is either K , or K − 1).

Partitioning Problems in Cluster Analysis: A Review of Mathematical Programming Approaches

Three main mathematical programming approaches have been followed to design exact algorithms for partitioning problems in cluster analysis: cutting-planes, branch-and-bound and recently, column generation combined with integer programming. These approaches are reviewed and evaluated, using two versions of the clique partitioning problem for illustration.

Sensitivity analysis of tree scheduling on two machines with communication delays

Abstract This paper presents a sensitivity analysis for the problem of scheduling trees with communication delays on two identical processors, to minimize the makespan. Tasks are supposed to have unit execution time ( uet ), and the values associated to communication delays are supposed unknown before the execution. The paper compares the optimal makespans with and without communication delays. The results are used to obtain sensitivity bounds for algorithms providing optimal schedules for graphs with unit execution and communication times ( uect ). The notion of processor-ordered schedules, for two-processor systems, is introduced. It describes schedules in which all communications are oriented from one processor to the other. It is shown that these schedules are dominant for unit delays, for zero delays, but not for delays of less than or equal to one. We establish that algorithms building optimal processor-ordered schedules for uect graphs admit an absolute sensitivity bound equal to the difference between the maximum and the minimum actual communication delays: ω−ω ∗ ⩽ c − c . This bound is tight.

Stochastic Scheduling with Variable Profile and Precedence Constraints

In this paper, we consider the stochastic profile scheduling problem of a partially ordered set of tasks on uniform processors. The set of available processors varies in time. The running times of the tasks are independent random variables with exponential distributions. We obtain a sufficient condition under which a list policy stochastically minimizes the makespan within the class of preemptive policies. This result allows us to obtain a simple optimal policy when the partial order is an interval order, an in-forest, or an out-forest.

Computing a lower approximation of the compulsory part of a task with varying duration and varying resource consumption

This paper considers a generalisation of the classical RCPSP problem: the resource consumption of each task is continuously varying over time and the duration and the start of each task may vary within real intervals. A first contribution is a general model for describing the resource consumption of a task over time. This model is justified when considering continuously divisible resources. The second contribution is the computation of the compulsory part or core time of such a task. The compulsory part gives the tasks resource consumption common to all feasible schedules. Hence, it can be used in a global resolution process such as constraint programming or branch and bound approaches. The presented polynomial algorithms use only two particular schedules of that task.

The Basic Cyclic Scheduling Model For Robotic Flow Shops

Abstract This paper analyzes the productivity of a robotic production cell, functioning under a repetitive robot move cycle. The cell is composed of m machines and one or several robot arms. Identical or different parts are entering the cell during a robot cycle. The problem of cycle time evaluation is shown to be an instance of the basic cyclic scheduling problem. Thus, several powerful results previously developed in the cyclic scheduling context are used to analyze our problem. We propose a O(q · m3) algorithm to compute the cycle time. The algorithm is first introduced for one-robot cells and then extended to multi-robot cells. A dynamic programming algorithm is used to find the optimal robot move cycle, that is, the cycle with minimum cycle time. Numerical results highlight the efficiency of cycle time evaluation methods and their potential practical utility in finding the optimal robot move cycle.