Approximation algorithms for scheduling with a limited number of communications

International audienceWe consider the case of a UET tree and an unlimited number of processors. We give a 2-approximation algorithm for minimizing the total number of communications, when there are no communication delays. This algorithm allows us to design a 6-approximation algorithm for the makespan minimization problem when there are unit length communication delays and the processors are interconnected by a single bus. Finally, we compare our 6-approximation algorithm with other algorithms by simulations. We show that its mean performance is regular (around 1.25) and we explain, for certain cases, the performance of these algorithms by considering some parameters of the problem

Idempotent version of the Fréchet contingency array problem

International audienceIn this paper we study the idempotent version of the so-called Fréchet correlation array problem. The problem is studied using an algebraic approach. The major result is that there exists a unique upper bound and several lower bounds. The formula for the upper bound is given. An algorithm is proposed to compute one lower bound. Another algorithm is provided to compute all lower bounds, but the number of lower bounds may be a very large number. Note that all these results are only based on the distributive lattice property of the idempotent algebraic structure

Single-machine scheduling with time window-dependent processing times

International audienceIn the one-machine scheduling problems analysed in this paper, the processing time of a job depends on the time at which the job is started. More precisely, the horizon is divided into time windows and with each one a coefficient is associated that is used to determine the actual processing time of a job starting in it. Two models are introduced, and one of them has direct connections with models considered in previous papers on scheduling problems with time-dependent processing times. Various computational complexity results are presented for the makespan criterion, which show that the problem is NP-hard, even with two time windows. Solving procedures are also proposed for some special cases

Scheduling with unit processing and communication times on a ring network: Approximation results

International audienceWe consider the problem of scheduling UET-UCT task graphs on a ring network of m processors, in order to minimize the makespan. We show that no polynomial-time algorithm with relative performance better than 4/3 can exist in that case (unless P=NP), and prove that the relative performance g of the general list scheduling algorithm proposed by Rayward-Smith is such that [radicm]leg lap-1 + 3/8m -1/2m, for m even

Modelling and Solving a Practical Flexible Job-Shop Scheduling Problem with Blocking Constraints

International audienceThis paper aims at presenting the study of a practical job-shop scheduling problem we modelled and solved when helping a company to design a new production workshop. The main characteristics of the problem are that some resources are flexible, and blocking constraints have to be taken into account. The problem and the motivations for solving it are detailed. The modelling of the problem and the proposed resolution approach, a genetic algorithm, are described. Numerical experiments on real data are presented and analysed. We also show how these results were used to support choices in the design of the workshop

A Branch-and-Price algorithm to minimize the maximum lateness on a batch processing machine

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