Optimisation hybride par colonies de fourmis pour le problème de découpe à deux dimensions

Nous nous intéressons dans cet article au problème de découpe guillotine en deux dimensions noté 2BP/O/G. Il s'agit de découper un certain nombre de pièces rectangulaires dans un ensemble de plaques de matière première, elles même rectangulaires et identiques. Celles-ci sont disponibles en quantité illimitée. L'objectif est de minimiser le nombre de plaques utilisées pour satisfaire la demande, en appliquant une succession de coupes, dites guillotines, allant de bout en bout. Nous proposons une approche de résolution combinant l'optimisation par colonies de fourmis (ACO) et l'heuristique SHF-FF de Ben Messaoud et al. [2] pour résoudre ce problème NP-difficile

A Petri-Net-Based Scheduling Strategy for Dual-Arm Cluster Tools With Wafer Revisiting

International audienceThere are wafer fabrication processes in cluster tools that require wafer revisiting. The adoption of a swap strategy for such tools forms a 3-wafer cyclic (3-WC) period with three wafers completed in each period. It has been shown that, by such a scheduling strategy, the minimal cycle time cannot be reached for some cases. This raises a question of whether there is a scheduling method such that the performance can be improved. To answer this question, a dual-arm cluster tool with wafer revisiting is modeled by a Petri net. Based on the model, the dynamical behavior of the process is analyzed. Then, a 2-wafer cyclic (2-WC) scheduling strategy is revealed for the first time. Cycle time analysis is conducted for the proposed strategy to evaluate its performance. It shows that, for some cases, the performance obtained by a 2-WC schedule is better than that obtained by any existing 3-WC ones. Thus, they can be used to complement each other in scheduling dual-arm cluster tools with wafer revisiting. Illustrative examples are given

Scheduling to minimize over-regular criteria

In this paper,we define a new class of scheduling criteria called over-regular criteria. This class is a subclass of regular criteria. We analyze the properties of scheduling problems with over-regular criteria. In the literature a lot of effort has been made to solve specific problems, these properties, however, are applicable to several scheduling problems. Using these properties and proving additional specific ones, we propose a procedure to solve the scheduling problem to minimize total tardiness with generalized due dates. This latter problem particularly arises in maintenance departments where maintained parts are interchangeable. Computational results are also reported

Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level. Document type: Articl

Linearization and Decomposition Methods for Large Scale Stochastic Inventory Routing Problem with Service Level Constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, for a depot to determine delivery volumes to its customers in each period, and vehicle routes to distribute the delivery volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicles if necessary. The objective of the problem is to minimize the total inventory and transportation cost while some constraints are given to satisfy other criteria, such as the service level to limit the stockout probability at each customer and the service level to limit the overfilling probability of the warehouse of each customer. In order to tackle the SIRPSD with notorious computational complexity, we propose for it an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model can be found by the approach, and then be used to construct a near optimal solution of the SIRPSD. Numerical examples show that, for an instance of the problem with 200 customers and 5 periods that contains about 400 thousands decision variables where half of them are integer, our approach can obtain high quality near optimal solutions with a reasonable computational time on an ordinary PC

Vérification de la consistance et de la conservation de Petri

Les réseaux de Petri sont un outil performant pour concevoir, modéliser, analyser et évaluer les systèmes a événements discrets. Dans ce rapport, nous étudions des propriétés structurelles importantes des réseaux de Petri utilises en gestion de production : la consistance et la conservation. Nous mettons en évidence une condition nécessaire et suffisante simple pour vérifier la consistance et la conservation. Cette condition permet de diminuer la dimension du problème. Nous dégageons des conditions suffisantes dans des cas particuliers. Nous proposons en outre un algorithme pour vérifier ces deux propriétés dans le cas général

Single machine scheduling with chain structured precedence constraints and minimal and maximal separation times

We consider a single machine scheduling problem. This problem has been solved for a medical laboratory. It comprises not only chain-structured precedence constraints, but also minimal and maximal times separating successive jobs in the same chain. The criterion to be minimized is the makespan. This problem arises particularly in systems where chemical processes are involved. Consider a chemical plant in which every chemical process is a sequence of chemical reactions the duration of which is upper and lower bounded. Between two successive chemical reactions which are performed in different locations, a transportation system such as robot is used to carry the product from place to place. In this kind of plant, jobs are transportation operations and production processes can be modeled as chains. Therefore the problem studied in this paper is of practical importance. We first prove that the problem is NP-complete. As a consequence, we propose heuristics for large size problems and a branch and bound based algorithm for small size problems. Computational results are reported

Single machine scheduling problems with release dates

The single machine scheduling problems have been extensively studied with various criteria to be optimized and under various assumptions. In this work, we review some results obtained recently in the case of different release dates. Most problems with different release dates are NP-hard. Some researchers have proved some dominance properties or sufficient conditions for local optimality which lead to an optimal schedule in some specificic cases. We present some properties or conditions for two regular criteria, total tardiness and total flow time

Minimisation de la somme des retards pour les problèmes d'ordonnancement à une machine

Dans cet article, nous démontrons un théorème qui présente une condition suffisante d'optimalité locale pour le problème d'ordonnancement du type n/1/ri/\sumTi. Cette condition nous permet de définir un nouveau sous-ensemble dominant de solutions pour ce problème qui est NP-difficile. Nous utilisons les résultats obtenus pour construire un algorithme approché polynômial et donnons une majoration de l'erreur commise par cet algorithme dans le pire des cas