Anis Gharbi

Optimal Scheduling of a Two-stage Hybrid Flow Shop

AbstractWe present an exact branch-and-bound algorithm for the two-stage hybrid flow shop problem with multiple identical machines in each stage. The objective is to schedule a set of jobs so as to minimize the makespan. This is the first exact procedure which has been specifically designed for this strongly

Fast lifting procedures for the bin packing problem

\mathcal{NP}

Lower Bounds for Scheduling on Identical Parallel Machines with Heads and Tails

-hard problem. Among other features, our algorithm is based on the exact solution of identical parallel machine scheduling problems with heads and tails. We report the results of extensive computational experiments on instances which show that the proposed algorithm solves large-scale instances in moderate CPU time.

The two-machine flowshop scheduling problem with sequence-independent setup times: New lower bounding strategies

We address the problem of minimizing makespan on identical parallel machines. We propose new lower bounding strategies and heuristics for this fundamental scheduling problem. The lower bounds are based on the so-called lifting procedure. In addition, two optimization-based heuristics are proposed. These heuristics require iteratively solving a subset-sum problem. We present the results of computational experiments that provide strong evidence that the new proposed lower and upper bounds consistently outperform the best bounds from the literature.

Energetic reasoning revisited: application to parallel machine scheduling

In this paper, we investigate fast lower bounds for the deterministic one-dimensional bin packing problem. We present two variants of a general lifting procedure which aims at systematically tightening a given lower bound. We describe several enhancements which improve the efficiency of the proposed procedure. Extensive numerical experiments show that the proposed lifting procedures consistently improve lower bounds from the literature.

Jackson's semi-preemptive scheduling on a single machine

Abstract We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is NP -hard in the strong sense. We show that the worst-case performance of Jacksons algorithm is improved by using a preprocessing algorithm, and we propose an approximate decomposition algorithm which requires iteratively solving a sequence of two-machine problems. We present the results of an extensive computational study on large instances with up to 2000 jobs and 100 machines which show that the proposed heuristic is fast and yields in most cases schedules with relative deviation from a lower bound less than 0.2%.

Polynomial Lower Bounds for the Two-Machine Flowshop Problem with Sequence-Independent Setup Times

In this paper, we investigate new lower bounds for the P|rj,qj|Cmax scheduling problem. A new bin packing based lower bound, as well as several new lifting procedures are derived for this strongly NP -hard problem. Extensive numerical experiments show that the proposed lower bounds consistently outperform the best existing ones.

Scheduling IT Staff at a Bank: A Mathematical Programming Approach

The two-machine flowshop environment with sequence-independent setup times has been intensely investigated both from theoretical and practical perspectives in the scheduling literature. Nevertheless, very scant attention has been devoted to deriving effective lower bounding strategies. In this paper, we propose new lower bounds for the total completion time minimization criterion. These bounds are based on three relaxation schemes, namely the waiting time-based relaxation scheme, the single machine-based relaxation scheme, and the Lagrangian relaxation scheme. Extensive computational study carried on instances with up to 500 jobs reveals that embedding the waiting time-based bounding strategy within the Lagrangian relaxation framework yields the best performance while requiring negligible CPU time.