Procedia - Social and Behavioral Sciences 109 ( 2014 ) 1110 – 1115
1877-0428 © 2014 The Authors. Published by Elsevier Ltd.
Selection and peer review under responsibility of Organizing Committee of BEM 2013. doi: 10.1016/j.sbspro.2013.12.596
ScienceDirect
2
ndWorld Conference On Business, Economics And Management- WCBEM 2013
Open loop reverse supply chain network design
Seval Ene
a*, Nursel Öztürk
ba Uludag University, Faculty of Enginnering and Architecture, Industrial Engineering Department, Bursa 16059, Turkey b Uludag University, Faculty of Enginnering and Architecture, Industrial Engineering Department, Bursa 16059, Turkey
Abstract
Reverse supply chain management is a significant issue for sustainable economy, product recovery and green thinking. The purpose of this study is to contribute product recovery management by designing open loop reverse supply chain network. The main difference between open loop and closed loop reverse supply chain is in returning of used products. In a closed loop reverse supply chain, used products are generally returned to original producers. But in an open loop reverse supply chain, used products are not returned to original producers, outsider firms recover them. This paper presents a mathematical model for multi stage and multi period reverse supply chain network, which maximizes total profit of the network. The proposed model determines facility locations and material flows between stages in each period. Numerical experiments showed the applicability and efficiency of the model.
1. Introduction
In recent years, the importance of reverse supply chain management is increased with growing environmental and social concerns, environmental regulations and increase in end-of-life products. Consequently there has been an increasing amount of research on the intersection between supply chain management and environmental factors (Jabali et al. 2012).
Guide and Van Wassenhove (2002) defined reverse supply chain as a series of activities required to retrieve used products from customers and either dispose of them or reuse them, and reverse supply chain management as the field that studies how to manage those activities effectively and efficiently. A reverse supply chain can be either a closed-loop system or an open-loop system. In a closed- loop reverse supply chain, products or materials are often returned to the original producers. In an open-loop reverse supply chain, products are not returned to the original producers, recovered by outsider firms (Gou et al. 2008). To manage reverse supply chain efficiently, network design is a critical issue. Network design problem consists of determining number and location of facilities and establishing material flows between facilities.
Alumur et al. (2012) proposed a mixed integer linear programming model that maximizes reverse logistics network profit. Salema et al. (2010) proposed a multi-period and multi-product network model for the simultaneous
* Corresponding Author: Seval Ene. Tel.: +90-224-2942-078 E-mail address: [email protected]
Keywords: Supply chain management, open loop system, product recovery, network design, mathematical programming
© 2014 The Authors. Published by Elsevier Ltd.
Selection and peer review under responsibility of Organizing Committee of BEM 2013.
Open access under CC BY-NC-ND license.
design and planning of supply chains with reverse flows. Mutha and Pokarel (2009) developed a mathematical model for reverse logistics network of product returns. The model makes decision on location, number, capacity of storing, reprocessing, remanufacturing facilities and allocation of material flows between them considering all network costs. Lee and Dong (2009) proposed two phase stochastic programming model for reverse logistics operations. Pisvaee et al. (2010) developed a mixed integer linear programming model to minimize transportation and fixed opening costs in a multi stage reverse logistics network. The network includes, customer, collection/inspection, recovery and disposal stages and is designed for one product type.
In this paper a mathematical model for open loop reverse supply chain network design problem is proposed. Open loop reverse supply chain network design problem is defined as planning of collecting used products from customers and shipping them to reprocessing center for refurbishing, repair and reprocessing; to recycling center for material recovery; to disposal center for disposing. Based on the proposed model facility locations and material flows between them can be determined.
2. Problem definition
The structure of the proposed multi stage, multi period open loop reverse supply chain designed for collecting used products from customers and transporting them to capacitated reprocessing, recycling and disposal centers is illustrated in Figure 1. Used products, collected from customers, will be inspected at collection center and classified into three groups according to their quality levels: reusable, rocevarable and disposal. Reusable products will be transported to reprocessing center, recoverable products will be transported to recycling center and unrecoverable products will be transported to disposal center. Reprocessed products will be transported to secondhand market for selling. Recycled products will be transported to manufacturing facility as raw material.
Figure1. Structure of the proposed open loop reverse supply chain network
3. Mathematical formulation
The mixed integer linear programming model, proposed for network design, determines the location and number of collection and reprocessing centers, and allocates material flow between customers, collection, reprocessing, recycling and disposal centers. The sets, decision variables, parameters and constraints used in the model are defined as follows:
Indices:
i=1,2,3,…..,I set of customers
j=1,2,3,…..,J set of collection points
k=1,2,3,….,K set of reprocessing center points
l=1,2,3,…..,L set of recycling center points Customers Collection Points Reprocessing Centers Recycling Centers Disposal Centers Manufacturing Facility Secondhand Market
m=1,2,3,…,M set of disposal center points t=1,2,3,...,T set of periods Decision Variables: ⎩ ⎨ ⎧ = otherwise 0 location at opens point collection a if 1 j aj ⎩ ⎨ ⎧ = otherwise 0 location at operates center ng reprocessi a if 1 k bk ijt
x Amount of product shipped from customer i to collection point j in period t
jkt
y Amount of product shipped from collection point j to reprocessing center k in period t jlt
z Amount of product shipped from collection point j to recycling center l in period t
jmt
w Amount of product shipped from collection point j to disposal center m in period t
Parameters:
1
j
c
Fixed cost of opening collection point at location j2
k
c Fixed cost of opening reprocessing center at location k
1
j
cap Capacity of the collection point j
2
k
cap Capacity of the reprocessing center k
3
l
cap
Capacity of the recycling center l4
m
cap Capacity of the disposal center m
1
ij
ct Unit transportation cost from customer i to collection point j
2
jk
ct Unit transportation cost from collection point j to reprocessing center k
3
jl
ct Unit transportation cost from collection point j to recycling center l
4
jm
ct Unit transportation cost from collection point j to disposal center m
cd Unit disposal cost
1
r
Unit revenue gained in reprocessed productsr2 unit revenue gained in recycled products
di demand of customer i 1
k Rate of product shipped to reprocessing center 2
k Rate of product shipped to recycling center 3
k Rate of product shipped to disposal center
Considering the notation described above, open loop reverse supply chain network design problem can be formulated as follows:
Objective Function:
∑
∑∑
∑∑∑
∑∑∑
∑∑∑
∑∑∑
∑
∑
∑∑∑
∑∑∑
= = = = = = = = = = = = = = = = = = = = = = = − − − − − − − + = J j J j M m T t jmt M m T t jm jmt J j L l T t jl jlt J j K k T t jk jkt I i J j T t ij ijt k K k k j J j j J j K k T t jkt J j L l T t jlt cd w ct w ct z ct y ct x c b c a r y r z z 1 1 1 1 1 1 4 1 1 1 3 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 max (1) Constraints: it J j ijt d x =∑
=1 t i, ∀ (2) j j I i ijt cap a x 1 1 ≤∑
=∀
j,
t
(3) k k J j jkt capb y 2 1 ≤∑
=∀
k,
t
(4) 3 1 l J j jlt cap z ≤∑
=t
l,
∀
(5) 4 1 m J j jmt cap w ≤∑
=∀
m,
t
(6) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =∑∑
∑∑
= = = = J j I i ijt J j K k jkt k x y 1 1 1 1 1∀
t
(7) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =∑∑
∑∑
= = = = J j I i ijt J j L l jlt k x z 1 1 1 1 2∀
t
(8) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =∑∑
∑∑
= = = = J j I i ijt J j M m jmt k x w 1 1 1 1 3∀
t
(9)∑
∑
∑
∑
= = = = + + = M m jmt L l jlt K k jkt I i ijt y z w x 1 1 1 1∀
j,
t
(10) 0 , , , jkt jlt jmt ≥ ijt y z w x (11){ }
0,1 , k∈ j b a (12)Objective function (1) maximizes total profit of the network. Constraint 2 specifies that demand of all customers must be satisfied in each period. Constraint 3 ensures that in each period total product shipped to opened collection center can not exceed the capacity of the center. Constraint 4 states that total product shipped to opened reprocessing center in each period can not exceed the capacity of the center. Constraints 5 and 6 ensures that total product shipped to recycling and disposal centers can not exceed their capacities in each period. Constraints 7, 8 and 9 states returned product rates shipped from collection centers to reprocessing, recycling and disposal centers respectively for each period. Constraint 10 satisfies flow balance at collection centers in each period. Constraint 11 specifies that decision variables x, y, z, w must be greater than 0. Constraint 12 states that decision variables a, b must be 1 or 0.
4. Computational results
To illustrate applicability of the model and to evaluate the performance of the model 5 problem sets are generated. These test problems are composed changing the number of customer, collection, reprocessing, recycling, disposal center and time periods.The characterisrics of 5 test problems are shown in Table 1.
Table 1. Characteristics of test problems Problem
Set Number of Customers Number of Collection Centers Number of Reprocessing Centers Number of Recycling Centers Number of
Disposal Centers Time Periods Number of 1 5 3 2 2 2 1 2 10 5 3 3 3 3 3 25 12 7 5 5 3 4 50 25 10 8 8 3 5 100 40 15 10 10 5
The proposed model is solved optimally with MPL - Gurobi solver. The model, determined optimum number and location of collection and reprocessing centers and optimum material flow between customers, collection, reprocessing, recycling and disposal centers. All experiments are performed on a Intel Core i7 2640QM 2.20 GHz computer with 8 GB RAM. Optimum results of the test problems are presented in Table 2.
Table 2. Computational results of test problems Problem
Set Objective Function Value Iteration Number CPU Time(s) 1 -19315 15 0,03 2 -11336 96 0,06 3 258782 645 0,37 4 856015 1156 1,33 5 1012138 5059 2,98
It can be concluded from the results that when number of returned products and time periods increases, total profit of the network increases. In that case it is clearly undertstood from the obtained results that companies should provide suitable incentives in a planning period to customers or retailers for increasing number of returned used products.
5. Conclusions
Network design is one of the most important planning activities in supply chain management. Furthermore, in recent years, reverse supply chain operations has a gaining and critical value for researchers and companies with extending environmental regulations of product recovery. This paper presents a mixed integer linear programming model for an open loop multi stage multi period reverse supply chain network design. The model is validated with different problem sets. Obtained results showed the applicability and efficiency of the model. The model proposed in this study is a strategic decision making tool for reverse supply chain network design problem of any product type.
References
Jabali, O., Van Woensel, T. & Kok, A.G. (2012). Analysis of travel times and CO2 emissions in time-dependent vehicle routing. Production and
Operations Management, 21, 1060-1074.
Guide Jr, V. D. R. & Van Wassenhove, L. N. (2002). The reverse supply chain. Harvard Business Review, 80, 25–26.
Gou, Q., Liang, L., Huang, Z. & Xu, C. (2008). A joint inventory model for an open loop reverse supply chain. International Journal of Production Economics, 116, 28-42.
Alumur, S. A., Nickel, S., Saldanha-da-Gama F. & Verter, V. (2012). Multi-period reverse logistics network design. European Journal of Operational Research, 220, 67-78.
Salema, M.I.G., Barbosa-Povoa, A.P. & Novais, A.Q. (2010). Simultaneous design and planning of supply chains with reverse flows: A generic modelling framework. European Journal of Operational Research, 203, 336-349.
Mutha, A. & Pokharel, S. (2009). Strategic network design for reverse logistics and remanufacturing using new and old product modules. Computers & Industrial Engineering, 56, 334-346.
Lee, D.H. & Dong, M. (2009). Dynamic network design for reverse logistics operations under uncertainty. Transportation Research Part E, 45,61-71
Pishvaee, M. S., Kianfar, K. & Karimi, B. (2010). Reverse logistics network design using simulated annealing. International Journal of Advanced Manufacturing Technology, 47, 269-281.
