We propose an effective improvement of the well-known Jackson's preemptive schedule lower bound for the single machine scheduling problem with heads and tails. The semi-preemptive scheduling concept roughly consists in reducing the preemption impact by constraining some particular job parts to be processed in reduced time intervals. The impact of semi-preemptive scheduling is twofold: it yields a lower bound which dominates the preemptive one, and enables more effective adjustments of the heads and tails.

A branch-and-bound algorithm is devised to determine the optimal attack strategy to disconnect a network where the objective is to minimize the expected attacking cost. The attacker cannot launch an attack if its cost is beyond his available budget or its probability of success falls below a threshold level. The proposed branch-and-bound algorithm includes, among other features, a dynamic programming-based lower bound as well as a preprocessing algorithm which aims at identifying unattackable links and removing irrelevant ones.

In this paper, we address the problem of two-machine flowshop scheduling problem with sequence independent setup times to minimize the total completion time. We propose five new polynomial lower bounds. Computational results based on randomly generated data show that our proposed lower bounds consistently outperform those of the literature.

The contribution of this paper to the job shop related literature is twofold. First, we provide an efficient way forf solving the job shop scheduling problem with release dates, delivery times and delayed precedence constraints. It is shown that the latter problem is equivalent to a classical job shop with precedence constraints. Second, an effective extension of the standard single machine-based relaxation scheme is derived.

We consider the problem of minimizing makespan on identical parallel machines subject to release dates and delivery times. We present several new feasibility tests and adjustment techniques that consistently improve the classical energetic reasoning approach. Computational results carried out on a set of hard instances provide strong evidence that the performance of a state-of-the-art exact branch-and-bound algorithm is substantially improved through embedding the proposed enhanced energetic reasoning.

We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is NPNP-hard in the strong sense. We show that the worst-case performance of Jackson's 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 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.

We 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 NP -hard problem. Among other features, our algorithm is based on the exact solution of identical parallel machine scheduling problems with heads and tails.

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.