Modélisation et évaluation des performances d'un système hybride fabrication réutilisation en logistique inverse

Abstract

Our work is the study of stochastic optimal control problems involved in inventory management of manufacturing systems. In practice, these systems are often subject to random phenomena that result in significant effects on the evolution of their behaviour. We first consider, in the forward direction of logistic, a production system consisting of a machine producing a single product type. The machine has a finite capacity and is assumed reliable. We consider that the customer's demand can fluctuate over time. Subsequently, we will integrate, in the opposite direction of the basic production environment, reverse logistics to take into account the return of random products. In this case, the system consists of two reliable machines with a finite capacity and producing the same type of product. The objective of this study is to determine optimum strategies for production planning in order to meet a stochastic demand of customer and manage inventory at lowest cost. A twolevel hierarchical control model is developed by applying the stochastic optimal control theory based on Pontryagin's maximum principle. In the first level of the proposed hierarchy, a stochastic linear-quadratic optimal control problem is formulated to optimally determine the target values of the state and control variables. In the second level, a recursive optimization control problem (predictive control) is presented in order to minimize the square deviation from nominal trajectories (problem of trajectory tracking). The optimal solution is obtained numerically by the Euler-Maruyama scheme. Numerical examples and sensitivity analysis are presented to illustrate the effectiveness and quality of the proposed approach.

Date	11 Jan 2012
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Jean-Pierre Kenné (Supervisor) & Ali Gharbi (Co-supervisor)