Mohamed Haouari

Discrepancy search for the flexible job shop scheduling problem

The flexible job shop scheduling problem (FJSP) is a generalization of the classical job shop problem in which each operation must be processed on a given machine chosen among a finite subset of candidate machines. The aim is to find an allocation for each operation and to define the sequence of operations on each machine, so that the resulting schedule has a minimal completion time. We propose a variant of the climbing discrepancy search approach for solving this problem. We also present various neighborhood structures related to assignment and sequencing problems. We report the results of extensive computational experiments carried out on well-known benchmarks for flexible job shop scheduling. The results demonstrate that the proposed approach outperforms the best-known algorithms for the FJSP on some types of benchmarks and remains comparable with them on other ones.

Integrated Airline Schedule Design and Fleet Assignment: Polyhedral Analysis and Benders' Decomposition Approach

The main airline operations consist of schedule planning, fleet assignment, aircraft routing, and crew scheduling. To improve profitability, we present in this paper an integrated fleet assignment model with schedule planning by simultaneously considering optional flight legs to select along with the assignment of aircraft types to all scheduled legs. In addition, we consider itinerary-based demands for multiple fare classes. A polyhedral analysis is conducted of the proposed mixed-integer programming model to tighten its representation via several classes of valid inequalities. Solution approaches are developed by applying Benders decomposition method to the resulting lifted model, and computational results are presented using real data obtained from a major U.S. airline to demonstrate the efficacy of the proposed procedures.

An optimization-based heuristic for the robotic cell problem

This study investigates an optimization-based heuristic for the robotic cell problem. This problem arises in automated cells and is a complex flow shop problem with a single transportation robot and a blocking constraint. We propose an approximate decomposition algorithm. The proposed approach breaks the problem into two scheduling problems that are solved sequentially: a flow shop problem with additional constraints (blocking and transportation times) and a single machine problem with precedence constraints, time lags, and setup times. For each of these problems, we propose an exact branch-and-bound algorithm. Also, we describe a genetic algorithm that includes, as a mutation operator, a local search procedure. We report the results of a computational study that provides evidence that the proposed optimization-based approach delivers high-quality solutions and consistently outperforms the genetic algorithm. However, the genetic algorithm delivers reasonably good solutions while requiring significantly shorter CPU times.

Exact approaches for integrated aircraft fleeting and routing at TunisAir

We describe models and exact solutions approaches for an integrated aircraft fleeting and routing problem arising at TunisAir. Given a schedule of flights to be flown, the problem consists of determining a minimum cost route assignment for each aircraft so as to cover each flight by exactly one aircraft while satisfying maintenance activity constraints. We investigate two tailored approaches for this problem: Benders decomposition and branch-and-price. Computational experiments conducted on real-data provide evidence that the branch-and-price approach outperforms the Benders decomposition approach and delivers optimal solutions within moderate CPU times. On the other hand, the Benders algorithm yields very quickly high quality near-optimal solutions.

Algorithmic expedients for the Prize Collecting Steiner Tree Problem

This paper investigates the Prize Collecting Steiner Tree Problem (PCSTP) on a graph, which is a generalization of the well-known Steiner tree problem. Given a root node, edge costs, node prizes and penalties, as well as a preset quota, the PCSTP seeks to find a subtree that includes the root node and collects a total prize not smaller than the specified quota, while minimizing the sum of the total edge costs of the tree plus the penalties associated with the nodes that are not included in the subtree. For this challenging network design problem that arises in telecommunication settings, we present two valid 0-1 programming formulations and use them to develop preprocessing procedures for reducing the graph size. Also, we design an optimization-based heuristic that requires solving a PCSTP on a specific tree-subgraph. Although, this latter special case is shown to be NP-hard, it is effectively solvable in pseudo-polynomial time. The worst-case performance of the proposed heuristic is also investigated. In addition, we describe new valid inequalities for the PCSTP and embed all the aforementioned constructs in an exact row-generation approach. Our computational study reveals that the proposed approach can solve relatively large-scale PCSTP instances having up to 1000 nodes to optimality.

Bounding strategies for the hybrid flow shop scheduling problem

In this paper, we investigate new lower and upper bounds for the multiple-center hybrid flow shop scheduling problem. We propose a family of center-based lower bounds as well as a destructive lower bound that is based on the concept of revised energetic reasoning. Also, we describe an optimization-based heuristic that requires iteratively solving a sequence of parallel machine problems with heads and tails. We present the results of extensive computational experiments that provide evidence that the proposed bounding procedures consistently improve the best existing ones.

Enhanced energetic reasoning-based lower bounds for the resource constrained project scheduling problem

We present new and effective lower bounds for the resource constrained project scheduling problem. This problem is widely known to be notoriously difficult to solve due to the lack of lower bounds that are both tight and fast. In this paper, we propose several new lower bounds that are based on the concept of energetic reasoning. A major contribution of this work is to investigate several enhanced new feasibility tests that prove useful for deriving new lower bounds that consistently outperform the classical energetic reasoning-based lower bound. In particular, we present the results of a comprehensive computational study, carried out on 1560 benchmark instances, that provides strong evidence that a deceptively simple dual feasible function-based lower bound is highly competitive with a state-of-the-art lower bound while being extremely fast. Furthermore, we found that an effective shaving procedure enables to derive an excellent lower bound that often outperforms the best bound from the literature while being significantly simpler. Highlights? We present three classes of lower bounds that are based on the concept of energetic reasoning. ? The first class includes bounds that are based on the so-called revisited energetic reasoning. ? The second class includes bounds that are based on the concept of reduced instances. ? Finally, the last class of bounds are based on discrete dual feasible functions. ? Our computational results provide evidence that a deceptively simple DFF-based lower bound is effective.

Exact Solution Methods for a Generalized Assignment Problem with Location/Allocation Considerations

We investigate modeling approaches and exact solution methods for a generalized assignment problem with location/allocation (GAPLA) considerations. In contrast with classical generalized assignment problems, each knapsack in GAPLA is discretized into consecutive segments having different levels of attractiveness. To maximize a total reward function, the decision maker decides not only about item knapsack assignments, but also the specific location of items within their assigned knapsacks and their total space allocation within prespecified lower and upper bounds. Mathematical programming formulations are developed for single and multiple knapsack variants of this problem along with valid inequalities, preprocessing routines, and model enhancements. Further, a branch-and-price algorithm is devised for a set partitioning reformulation of GAPLA, and is demonstrated to yield substantial computational savings over solving the original formulation using branch-and-bound/cut solvers such as CPLEX over challengin...