Deliveries optimization by exploiting production traceability information

International audienceThe recent product traceability requirements, particularly in food production chains, demonstrate an industrial need to improve traceability systems. Having real-time access to traceability information allows its exploitation, which is the aim of this work. In this paper the problem of minimizing the cost of products recall is treated. First the raw material dispersion problem is analyzed, in order to determine a risk level criterion or "production criticality". This criterion is used subsequently to optimize deliveries dispatch with the purpose of minimizing the number of batch recalls in case of crisis. This is achieved by implementing decision-making aid tools based on operational research and artificial intelligence

Graphes d'événements stochastiques : temps de cycle moyen et marquage

Dans ce papier, nous considérons un type particulier de réseaux de Petri appelé graphes d'événements temporisés. Nous examinons le cas où les temps de franchissement sont aléatoires et bornés. Le but est d'obtenir un temps de cycle moyen aussi petit que possible en utilisant un nombre donné de jetons. Nous montrons que sous certaines conditions, la diminution la plus importante du temps de cycle moyen est obtenue lorsqu'on ajoute un jeton dans le circuit élémentaire qui a le temps de cycle moyen le plus grand. Nous illustrons ce résultat avec un exemple

New performance bounds and asymptotic properties of stochastic timed event graphs

This paper addresses the performance evaluation and asymptotic properties of stochastic timed event graphs. The transition firing times are generated by random variables with general distribution. New upper bounds of the average cycle time are obtained by applying large deviation theory. Asymptotic properties with respect to the net structure, the transition firing times and the initial marking are then established on the basis of these new bounds and the existing ones. We propose in particular sufficient conditions under which the average cycle time tends to a finite positive value as the number of transitions tends to infinity. The convergence of the average cycle time, when the variances of the average cycle time, when the variances of the firing times decrease, is established. We also prove that, by putting enough tokens in all places, it is always possible to approach as close as possible to the minimum average cycle time which is equal to the maximum of the average transition firing times. Applications to manufacturing systems are presented. We prove in particular a conjecture which claims that the throughput rate of a transfer line decreases to a positive value when the number of machines increases

Continuous Approach of Scheduling Problems Based on Petri Nets

Scheduling a manufacturing system is usually an NP-hard problem. This means that only heuristic algorithms can be used to provide near-optimal schedules. In this paper, we show that a manufacturing system can be modelled using a particular type of Petri net, called Controllable-Output nets, or CO nets for short. These Petri net models are then used to introduce a two-stage scheduling algorithm for large horizon problems. The first stage consists of distributing the workload among the resources. The second stage derives a schedule from the resource workload. The deterministic case is considered. Numerical result are proposed

Optimality condition decomposition approach to distributed model predictive control

International audienceThis paper presents a new methodology for distributed model predictive control of large-scale systems. The methodology involves two distinct stages, i.e., the decomposition of large-scale systems into subsystems and the design of subsystem controllers. Two procedures are used: in the first stage, the structure of the Karush-Kuhn-Tucker matrix resulting from the necessary optimality conditions is exploited to yield a decomposition of the large-scale system into several subsystems. In the second stage, a particular technique, the so-called optimality condition decomposition makes it possible to synthesize distributed coordinated subcontrollers thus achieving an optimal distributed control of the large-scale system. The convergence of the proposed approach is stated

Optimization of the number of transportation devices in a flexible manufacturing system using event graphs

An important step when designing a Flexible Manufacturing System (FMS) using Automated Guided Vehicles (AGVs) is the definition of the number of AGVs to be used in order to reach a given productivity. A way to define this number is to consider several scenari, to define the minimal number of AGVs required by each scenario, and to keep the maximal of these numbers. In this paper, we propose a Branch and Bound (B&B) approach to define the minimal number of AGVs require for a scenario. This approach is based on an Event Graph (EG) formulation

On Unrelated Machine Scheduling with Precedence Constraints

In this paper, we consider the problem of scheduling tasks on unrelated parallel machines. Precedence constraints exist between the tasks, but their number is limited compared with the number of tasks. We propose a number of heuristics in order to find near-optimal solutions to the problem. Empirical results show that the heuristics are able to find very good approximate solutions

Stochastic timed event graphs : bounds, cycle time reachability and marking optimization

This paper addresses the performance evaluation and optimization of stochastic timed event graphs. The transitions firing times of such a timed event graph are random variables with general distribution. We first establish an upper bound and a lower bound for the average cycle time of the timed event graph. We prove that any cycle time greater than the greatest mean transition firing time can be reached by putting enough tokens in each place. The necessary and sufficient condition of the reachability of the greatest mean firing time is established. We then address the marking optimization problem which consists in obtaining a given cycle time while minimizing a linear criterion depending on the initial marking

Marking optimization of stochastic timed event graphs using IPA

This paper addresses the marking optimization of stochastic timed event graphs. The transition firing times are generated by random variables with general distributions. The marking optimization problem consists of obtaining a given cycle time while minimizing a p-invariant criterion. Some important properties have been established. In particular, the average cycle time is shown to be non-increasing with respect to the initial marking while the p-invariant criterion is non-decreasing. We further prove that the criterion value of the optimal solution is non-increasing in transition firing times in stochastic ordering's sense. Based on some existing lower bounds and upper bounds of the average cycle time, we show that the p-invariant criterion reaches its minimum when the firing times become deterministic and we establish the reachability conditions of a given cycle time. We also propose a heuristic algorithm. It starts from the optimal solution to the deterministic case and iteratively adds tokens to adequate places as long as the given cycle time is not obtained. Infinitesimal perturbation analysis of the average cycle time with respect to the transition firing times is used to identify the adequate places in which the new tokens are added. Numerical results show that the heuristic algorithm provides near optimal solutions