Encyclopedie de la recherche sur l'aluminium au Quebec - Edition 2014 | Page 72
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Stochastic TRANSFORMATION AND APPLICATIONS
TRANSFORMATION ET APPLICATIONS // models and numerical solutions for
manufacturing/remanufacturing systems with
applications to the printer cartridge industry
APPLICATION DES MODÈLES STOCHASTIQUES ET DES MÉTHODES NUMÉRIQUES POUR L'OPTIMISATION DU « MANUFACTURING »
ET DE « REMANUFACTURING » : APPLICATION AU RECYCLAGE DES CARTOUCHES D'ENCRE POUR IMPRIMANTES
Application des modèles stochastiques et des méthodes
STOCHASTIC MODELS AND NUMERICAL SOLUTIONS FOR MANUFACTURING/REMANUFACTURING
numériques au cas des entreprises de récyclage des
SYSTEMS WITH APPLICATIONS TO THEcartouches d’encre pour imprimantes
PRINTER CATRIDGE INDUSTRY
Kouedeu Annie Francie1, Songmene Victor1, Kenné Jean-Pierre1
Dejax Pierre2 et Polotski Vladimir1
1
Université du Québec / École de Technologie Supérieure, ÉTS
2 École des Mines de Nantes / LUNAM / IRCCyN
1. Introduction
5. Methodology
Increasing attention is being paid to reverse logistics both by industry and academia.
Traditionally, remanufacturing has been used within the sole domain of the automotive and
aeronautical sectors. In recent decades, it has spread to other sectors as well. In this paper,
we will focus on the case of printer cartridges.
A more general structure of manufacturing/remanufacturing systems as depicted in below
figure is often associated with different dynamic blocks involving random and exogenous
events. Thus, the control problem can be very complex. Hence, it is important to develop
mathematical models capable of handling random events in the context of complex
production systems.
6. Results (next)
The corresponding HJB equations as in Kouedeu et al. (2014) are :
g ( , x , x )
v( , x1 , x2 ) (u1 u2 d ) v( , x1)
1 2
x1
B
(u ,u ) ( )
v( , x2 )
1 2
(r u2 disp)
x2
min
Production rate of M1 at mode 1
v , x1, x2
Using Kushner methods approach (Kushner (1992)), we have:
2. Goal of the Control Problem
The goal of the control problem concerns the minimization
of a cost function which penalizes the presence of waiting
customers, the inventory of finished parts, and the
inventory of parts returned from customers.
h
(u u d ) v ( x1 h1 , x2 , ) Ind u1 u2 d 0
h
g ( , x1 , x2 ) v ( x1 , x2 , ) 1 2
h
h1
v ( x1 h1 , x2 , ) Ind u1 u2 d 0
h
(r u2 disp ) v ( x1 , x2 h2 , ) Ind r u2 disp 0
h
h2
v ( x1 , x2 h2 , ) Ind r u2 disp 0
h
v , x1 , x2
min h
( u1 ,u2 ) ( )
u1 u2 d c r u2 disp
h1
h2
0.4
U
0.3
0.2
0.1
2
1.5
0
1
0.5
h
Vi ( x1 , x2 ,1)
Returned products
Serviceable
inventory
Disposal
Ramanufacturing
Factory
(M2)
x2(t)
u2(t)
x1(t)
min
Demand
(Customers)
• mode 2
Manufacturing
Factory
(M1)
i
1
2
i
Forward
Backward
Vi h ( x , x , 2)
1
MRC (Manufacturing Remanufacturing Company ):
European leader in compatible consumables for inkjet,
laser, fax and impact printing.
2
min
u1
20 countries, 25 industrial and commercial sites, 2 000 employees.
Pierre Dejax
École des Mines de Nantes,
LUNAM, IRCCyN
h
(u1 d ) v ( x1 H