Optimisation des stratégies de fabrication et de réutilisation de l'aluminium en logistique inverse

Abstract

The present work deals with the problem of optimal stochastic control of an aluminum recycling unit in reverse logistics. The unit considered is in an open loop, that is to say, dissociated from the direct supply line and assimilated to a machine producing a single type of product (M1P1) subject to random failures and repairs. The unit is fueled at a constant rate of return of end-of-life aluminum products and must satisfy a constant rate customer demand. Faced with this random unavailability of the machine, the need to satisfy the customer demand, it is imperative to set up an optimal policy of production to be able to supplement customer demand. In our work, we also consider the case of the random return rate in order to get closer to industrial reality. The objective of this study is to propose an optimal production policy that will minimize the sum of holding and backlog costs for remanufacturing products. The decision variables are the production rate of the unit and the disposal rate of returned products. The disposal of the returned products from the recycling unit integrates the burial of the returned products, the sending of returned products to subcontracting. The optimality conditions of the problem has been developed using homogeneous Markov chains (constant transition rate) and led to the Hamilton-Jacobi Bellman equations. Given the non-existence of the analytical methods for solving the obtained equations, a numerical method based on the approach of Kushner and Dupuis (1992) was used and we obtained an optimal Hedging Point Policy type. Considering the fact that, there is no functional relationship between the performance criterion of the model studied and the independent variables in a general case, we have combined the analytical approach with simulation, experimental plans and Analysis of variance (ANOVA) to allow us to determine the factors that influence the response significantly, to estimate a correlation between the response and these significant factors and to identify the optimal values of the variables that minimize the costs. The results obtained showed that the production policy depends on the level of inventory of returns and the finished products available. These results obtained were validated by a sensitivity analysis.

Date	11 May 2017
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Jean-Pierre Kenné (Supervisor) & Victor Songmene (Co-supervisor)