Djamal Rebaine

Flow shop vs. permutation shop with time delays

This paper considers the evaluation of the worst-case performance ratio between the best solution of the flow shop problem and the permutation flow shop with time delays considerations. It is observed that, even in the restricted case of two machines and unit execution time operations, the two models may generate different optimal values for the makespan. More specifically, it is shown that, in the two-machine case, the performance ratio between the best permutation schedule and the best flow shop schedule is bounded by 2. When the operations of the n jobs are restricted to be unit execution time, this ratio is reduced to (2-(3/n+2)) for the two-machine case, and is m for the m-machine case.

Scheduling identical parallel machines and operators within a period based changing mode

This article addresses the problem of scheduling n non-preemptive jobs on m identical parallel machines with @w operators to minimize the makespan. The number of operators is less than the number of machines. As a result, it may happen that an operator has to supervise simultaneously several machines. This in turn has an impact on the job processing times as they become a function of the operators modus operandi. In this paper we consider the case where each modus operandi can only be changed at the end of a given period, i.e., a period based changing mode. We present heuristic algorithms to solve this problem. An experimental study is conducted to evaluate the performance of these heuristics in the average case, and a worst case analysis is presented for one of them.

Improving the migrating birds optimization metaheuristic for the permutation flow shop with sequence-dependent set-up times

Abstract This paper addresses the problem of scheduling a set of independent jobs with set-up times on a set of machines in a permutation flow shop environment. A metaheuristic known as the Migrating Birds Optimization (MBO) is adapted for the minimization of the makespan. Two versions of the algorithm are presented. The first is a basic MBO and the second introduces additional features. An extensive computational study is conducted to analyse the efficiency of the two methods on a benchmark of instances that can be found in Sistemas de Optimizacion Aplicada (http://soa.iti.es/problem-instances). The second version outperforms by far the first one. Moreover, the results that are produced by the latter show that it is suitable for solving real-world scheduling problems.

Polynomial time algorithms for the UET permutation flowshop problem with time delays

This paper addresses the problem of scheduling a set of n unit execution time (UET) jobs on an m-permutation flowshop with arbitrary time delays, so as to minimize the makespan criterion. A polynomial time algorithm is exhibited for the three-machine and four-machine cases, respectively.

A branch and bound algorithm for the two-machine flowshop problem with unit-time operations and time delays

In this paper we consider the problem of scheduling, on a two-machine flowshop, a set of unit-time operations subject to time delays with respect to the makespan. This problem is known to be \hbox{

The two-machine open-shop problem with unit-time operations and time delays to minimize the makespan

{\cal NP}

Analysis of heuristics for the UET two-machine flow shop problem with time delays

}-hard in the strong sense. We propose an algorithm based on a branch and bound enumeration scheme. This algorithm includes the implementation of new lower and upper bound procedures, and dominance rules. A computer simulation to measure the performance of the algorithm is provided for a wide range of test problems.

Scheduling the two-machine open shop problem under resource constraints for setting the jobs

This paper addresses the problem of scheduling unit-time operations with integral and non-negative time delay considerations on a two-machine open-shop environment. The criterion to minimize is the makespan. Two well solvable cases and two approximation algorithms, with their worst-case analyses, are presented.

Optimality of HLF for scheduling divide-and-conquer UET task graphs on identical parallel processors

The problem of minimising the overall completion time for the two-machine flow shop problem with unit execution time (UET) tasks and arbitrary time delays is known to be unary NP-hard. Two heuristic algorithms to solve this problem along with their worst-case analyses are presented. We also discuss computational experiments we conducted to study the average-case performance of these two heuristics using simulation and statistical sampling methods.

FPTAS for the two identical parallel machine problem with a single operator under the free changing mode

This paper addresses the problem of open shop scheduling on two machines with resources constraints. In the context of our study, in order to be executed, a job requires first, for its preparation for a given period of time, a number of resources which cannot exceed a given resource capacity. Then, it goes onto its execution while the resources allocated to it become available again. We seek a schedule that minimizes the makespan. We first prove the