Frédéric Dugardin

New multi-objective method to solve reentrant hybrid flow shop scheduling problem

This paper focuses on the multi-objective resolution of a reentrant hybrid flow shop scheduling problem (RHFS). In our case the two objectives are: the maximization of the utilization rate of the bottleneck and the minimization of the maximum completion time. This problem is solved with a new multi-objective genetic algorithm called L-NSGA which uses the Lorenz dominance relationship. The results of L-NSGA are compared with NSGA2, SPEA2 and an exact method. A stochastic model of the system is proposed and used with a discrete event simulation module. A test protocol is applied to compare the four methods on various configurations of the problem. The comparison is established using two standard multi-objective metrics. The Lorenz dominance relationship provides a stronger selection than the Pareto dominance and gives better results than the latter. The computational tests show that L-NSGA provides better solutions than NSGA2 and SPEA2; moreover, its solutions are closer to the optimal front. The efficiency of our method is verified in an industrial field-experiment.

Hybrid Job Shop and parallel machine scheduling problems: minimization of total tardiness criterion

Scheduling is a scientific domain concerning the allocation of limited tasks over time. The goal of scheduling is to maximize (or minimize) different criteria of a facility as makespan, occupation rate of a machine, total tardiness ... In this area, scientific community usually group the problem with, on one hand the system studied, defining the number of machines (one machine, parallel machine), the shop type (as Job shop, Open shop or Flow shop), the job characteristics (as pre-emption allowed or not, equal processing times or not) and so on. On the other hand scientists create these categories with the definition of objective function (it can be single criterion or multiple criteria). The main goal of this chapter is to present model and solution method for the total tardiness criterion concerning the Hybrid Job Shop (HJS) and Parallel Machine (PM) Scheduling Problem. The total tardiness criterion seems to be the crux of the piece in a society where service levels become the central interest. Indeed, nowadays a product often undergoes different steps and then traverses different structures along the supply chain, this involve in general a due date at each step. This can be minimized as a single objective or as a part of a multiobjective case. On the other hand, the structure of a hybrid job shop consists in two types of stages with single and parallel machines. That is why we propose to point out the parallel machine PM problem domain which can be used to solve the hybrid job shop scheduling system. This hybrid characteristic of a job shop is very common in industry because of two major factors: at first some operations are longer than other ones and secondly flexible factory. Indeed, if some operations too long; they can be accelerated by technical engineering but if it is not possible they must be parallelized to avoid bottlenecks. Another potential cause is the flexible factory: if a factory does many different jobs these jobs can perhaps pass through a central operation and so the latter must increase his efficiency. This work is organized as follow: firstly a state of the art concerning PM is realized. The latter leads us to a the HJS problem where we summarize a state of the art on the minimization of the total tardiness and in a second step we present several results concerning efficient heuristic methods to solve the Hybrid Job Shop problem such as Genetic Algorithm or Ant Colony System algorithm. We also deal with multi-objective

Multiobjective scheduling of a reentrant hybrid flowshop

This paper deals with the multiobjective scheduling of a two stages reentrant hybrid flow shop. The system studied here is reentrant: jobs have to be processed more than once at each stage which is made of several identical parallel machines. Furthermore, the sequence is the same on each stage. In this study the two objectives are the minimization of both the maximum completion time and the sum of the tardiness. Two evolutionary algorithms are proposed : our Lorenz-Non dominated Sorting Genetic Algorithm (L-NSGA) and the Strength Pareto Evolutionary Algorithm version 2 (SPEA2). Several configurations of the system are tested and the results of the two algorithms are compared with the Pareto optimal front with respect to two different measures. The results show that our L-NSGA is more efficient than SPEA2 in 81% of the configurations. Furthermore the L-NSGA reaches optimal solutions for some instances.

Forecasting the Emergency Department Patients Flow

Emergency department (ED) have become the patient’s main point of entrance in modern hospitals causing it frequent overcrowding, thus hospital managers are increasingly paying attention to the ED in order to provide better quality service for patients. One of the key elements for a good management strategy is demand forecasting. In this case, forecasting patients flow, which will help decision makers to optimize human (doctors, nurses…) and material(beds, boxs…) resources allocation. The main interest of this research is forecasting daily attendance at an emergency department. The study was conducted on the Emergency Department of Troyes city hospital center, France, in which we propose a new practical ED patients classification that consolidate the CCMU and GEMSA categories into one category and innovative time-series based models to forecast long and short term daily attendance. The models we developed for this case study shows very good performances (up to 91,24 % for the annual Total flow forecast) and robustness to epidemic periods.

Fuzzy Project Scheduling

This book lights out the different improvement of the recent history of fuzzy logic. The present chapter deals with the connections that exist between fuzzy logic and production scheduling.

FLC-archive to solve multiobjective reentrant hybride flowshop scheduling problem

This article deals with the multiobjective reentrant hybrid flowshop scheduling problem. In the latter several tasks has to be processed in a system and the special feature here is that they must be processed several times on each machines. The system is composed of multiple stages which contain parallel identical machines. Since the tasks must reenter the system at the end of the normal process they create conflict with the following tasks. This problem is NP-Hard and we have developped a metaheuristics to solve it. The latter is an evolutionary algorithm based on the well known SPEA2 mechanism. This algorithm has a Fuzzy-Logic Controller to adapt mutation and crossover probability of generation t with respect to the structure of the population in previous generations (t −1) and (t −2). The two objectives are the makespan and the total tardiness minimization. In this works we compare the classic SPEA2 and the latter improved by FLC (so called FLC-archive). These two algorithms are tested on multiple instances adapted from the literature. Finally the comparisons of the results obtained by the algorithms are done with two different multi-objectives measures.

Buffers sizing in assembly lines using a Lorenz multiobjective ant colony optimization algorithm

In this paper, a new multiobjective resolution approach is proposed for solving buffers sizing problems in assembly lines. The considered problem consists of sizing the buffers between the different stations in a line taking in consideration that the size of each buffer is bounded by a lower and an upper value. Two objectives are taken in consideration: the maximization of the throughput rate and the minimization of the total size of the buffers. The resolution method is based on a multiobjective ant colony algorithm but using the Lorenz dominance instead of the well-known Pareto dominance relationship. The Lorenz dominance relationship provides a better domination area by rejecting the solutions founded on the extreme sides of the Pareto front. The obtained results are compared with those of a classical Multiobjective Ant Colony Optimization Algorithm. For that purpose, three different measuring criteria are applied. The numerical results show the advantages and the efficiency of the Lorenz dominance.

Open shop scheduling problem with a multi-skills resource constraint: a genetic algorithm and an ant colony optimisation approach

The continuous evolution of manufacturing environments leads to a more efficient production process that controls an increasing number of parameters. Production resources usually represent an important constraint in a manufacturing activity, specially talking about the management of human resources and their skills. In order to study the impact of this subject, this paper considers an open shop scheduling problem based on a mechanical production workshop to minimise the total flow time including a multi-skill resource constraint. Then, we count with a number of workers that have a versatility to carry out different tasks, and according to their assignment a schedule is generated. In that way, we have formulated the problem as a linear as and a non-linear mathematical model which applies the classic scheduling constraints, adding some different resources constraints related to personnel staff competences and their availability to execute one task. In addition, we introduce a genetic algorithm and an ant colony optimisation (ACO) method to solve large size problems. Finally, the best method (ACO) has been used to solve a real industrial case that is presented at the end.

Méthodes multi-objectifs pour l’ordonnancement de lignes réentrantes

This article presents the scheduling of a reentrant maintenance line with parallel machine stages. In this study the system is composed of machines with their upstream buffer and are modeled by queuing system. The criteria are the maximization of the utilization rate of the bottleneck and the minimization of the mean cycle time of the products. We present the results obtained by a multi-objective ant colony algorithm with local search (MOACS-LS), which are compared with the results obtained by one of the most competitive genetic algorithm called Non-dominated Sorting Genetic Algorithm version 2 (NSGA2). This two metaheuristics are coupled with a discrete event simulation module. Our results are compared with an industrial solution.

Non-dominated Sorting Genetic Algorithms for a Multi-objective Resource Constraint Project Scheduling Problem

Abstract The resource constraint project scheduling problem (RCPSP) has attracted growing attention since the last decades. Precedence constraints are considered as well as resources with limited capacities. During the project, the same resource can be required by several in-process jobs and it is compulsory to ensure that the consumptions do not exceed the limited capacities. In this paper, several criteria are involved, namely makespan, total job tardiness, and workload balancing level. Our problem is firstly solved by the non-dominated sorting genetic algorithm-II (NSGAII) as well as the recently proposed NSGAIII. Giving emphasis to the selection procedure, we apply both the traditional Pareto dominance and the less documented Lorenz dominance into the niching mechanism of NSGAIII. Hence, we adopt and modify L-NSGAII to our problem and propose L-NSGAIII by integrating the notion of Lorenz dominance. Our methods are tested by 1350 randomly generated instances, considering problems with 30–150 jobs and different configurations of resources and due dates. Hypervolume and C-metric are considered to evaluate the results. The Lorenz dominance leads the population more toward the ideal point. As experiments show, it allows improving the original NSGA approach.