Design of demand driven return supply chain for hightech products
Jalal Ashayeri^{1}, Gülfem Tuzkaya^{2}
^{1}Tilburg University (THE NETHERLANDS), ^{2}Yildiz Technical University (TURKEY)
Received June 2010
Accepted September 2011
Ashayeri, J.; & Tuzkaya, G. (2011). Design of demand driven return supply chain for hightech products. Journal of Industrial Engineering and Management, 4(3), 481503. http://dx.doi.org/10.3926/jiem.2011.v4n3.481503

Abstract:
Purpose: The purpose of this study is to design a responsive network for aftersale services of hightech products.
Design/methodology/approach: Analytic Hierarchy Process (AHP) and weighted maxmin approach are integrated to solve a fuzzy goal programming model.
Findings: Uncertainty is an important characteristic of reverse logistics networks, and the level of uncertainty increases with the decrease of the products’ lifecycle.
Research limitations/implications: Some of the objective functions of our model are simplified to deal with nonlinearities.
Practical implications: Designing aftersale services networks for hightech products is an overwhelming task, especially when the external environment is characterized by high levels of uncertainty and dynamism. This study presents a comprehensive modeling approach to simplify this task.
Originality/value: Consideration of multiple objectives is rare in reverse logistics network design literature. Although the number of multiobjective reverse logistics network design studies has been increasing in recent years, the last two objective of our model is unique to this research area.
Keywords: aftersale services, reserve logistics, AHP, weighted maxmin approach, fuzzy goalprogramming

1 Introduction
The worldwide hightech products market is one of the most dynamic industrial segments. Hightech supply chains, particularly the electronics, operate at one hand directly with consumers and on other hand with the industrial markets. For both markets, responsiveness in forward and reverse chains is a prerequisite. With sharp decline in the profit margins, the aftersales services and activities to support consumers and the product disposal have become not only a source of profit but also a key differentiation for customer satisfaction. Here, we describe some of the return flow challenges in the hightech supply chain of business to consumer (B2C) nature and make suggestions for improving the longterm return network design decisions. These flows are mainly warranty and service returns. After sales returns are endemic in hightech, with rates as high as 20% in some sectors (Thrikutam & Kumar, 2004) and the industry global nature requires many hightech supply chain examine carefully their Return Supply Chain flows (RSC) (Cheng & Lee, 2010). Also from the economic point of view, according to the Bundschuh and Dezvane (2003), after sales services market has been found to be up to four or five times larger than the market for new products.
In general, the RSC network design challenges are: (a) customer related, these are usually related to customer return order cycle time (on time to request) and flexibility and adaptability of return/repair operations to the changing market requirements; (b) cost related, this requires maintaining cheapest cost solution while customer service is not endangered; and finally (c) asset related, here the idea is to better utilize the fixed assets in order to meet financial requirements. Currently, all three are priorities for hightech RSC.
The shortlife cycle of products due to high level of technical and market uncertainties; rapidly declining prices (D’Cruz, 2010); and rapid technological obsolescence (White et al., 2003) all have an amplifying effect on the uncertainties and degree of returns. Therefore, repair centers are increasingly “demand driven”. Under such circumstances, minimal inventories of components and parts are maintained and most of it is circulating, thus the increasing importance of the location and transport component in RSC network design decisions. The operational management of such a system relies heavily on warehousing management capabilities, advanced information systems, and repair process activities to insure that parts and/or products are delivered to repair centers when required (on demand) and repaired products are sent back to consumers within the requested leadtime (on time).
Summarizing the situation, the design of RSC is rather involved multiobjective problem. The return responsiveness not only impacts the customer satisfaction but also on the increased forward demand. This responsiveness is a function of the size, location, and utilization of collection and repair centers. For example, the likely exponential increase in return demand in the early phase of product introduction, requires proximity of collection centers to the market regions, so that a pool of returned products are quickly checked and dispatched to repaircenters. The proper sizing and a balanced utilization of repair centers would avoid bottlenecks and impact the speed of the return flow. Therefore, the RSC design is a strategic decision.
Major hightech chains have restructured their RSC strategies through the introduction of outsourcing the return flow and services, centralized (outsourced) repair centers with a number of collection centers, see for example Cheng and Lee (2010). Centralization is not always best solution; it might reduce the overall costs but not necessarily increase the responsiveness and demand driven nature of repair centers. The multiechelon and the multiobjective nature of RSC design problem is mostly overlooked in the process of outsourcing. And the thirdparty providers usually focus on optimizing own entire activities, rather than a particular client. Therefore, analyzing such a problem is important to the companies owning own RSC and those that have subcontracted it as a mean to measure the subcontractor’s performance.
The problem of locating return centers has attracted considerable attention of the academicians and practitioners recently. When the current literature investigated, it can be concluded that most of the RSC network design problems are modeled in deterministic environment (Srivastava, 2008; Yongsheng & Shouyang, 2008; Beamon & Fernandes, 2004; Pishvaee et al., 2010). However, the uncertain nature of the reverse logistics environment has not been considered very often until now. As Qin and Ji (2010) suggest, uncertainty is one of the characteristics of logistics networks with product recovery. Earlier Lee and Dong (2009) stated that it would be useful to have a comprehensive quantitative study concerning the impact of uncertainty on recovery network design and the appropriateness of traditional approaches for capturing this element. Even though some common denominators can be found, the uncertainties of the design environment vary from one case to another case. Demand (or quantity) uncertainty Zhang et al. (2010), Xiao et al. (2010), Qin and Ji (2010), Amaro and BarbosoPovoa (2009), Lee and Dong (2009), Chouinard et al. (2008), ElSayed et al. (2010), Salema et al. (2007), Biehl et al. (2007), quality uncertainty (Qin & Ji, 2010 ; Chouinard et al., 2008) price uncertainty (Amaro & BarbosoPovoa, 2009), lead times or timing uncertainty (Lieckens & Vandaele, 2007; Biehl et al., 2007) are some of the investigated uncertainty dimensions of return networks. The modelling efforts to include these uncertainty dimensions vary. Here we have highlighted a few approaches along with the type of uncertainties considered (Table 1).
As can be seen from Table 1, consideration of uncertainty in the RSC literature is relatively new and the number of papers has been increasing in the recent years. Under the category of robust optimization, Realff et al. (2000) propose a model trying to minimize the maximum deviation of the performance of the network from the optimal performance under a number of different return scenarios for used carpet RSC. A supplementary study was proposed by Realff et al. (2004) utilizing robust optimization where demand decays with distance from collection centers. Hong et al. (2006) propose a scenario based robust optimization model for supporting strategic escrap reverse production infrastructure design decisions under uncertainty.


Utilized Techniques 



Robust Optimization 
Stochastic Programming 
Fuzzy Programming 
Others 
Uncertainty Dimension 
Time 
 
 
 
Lieckens & Vandaele (2007) 
Quality 
 
Listes & Dekker (2005) 
 
 

Quantity 
Realff et al. (2000) Realff et al. (2004) Hong et al. (2006) 
Listes & Dekker (2005) Listes (2007) ElSayed et al. (2010) Chouinard et al. (2008) Lee & Dong (2009) 
Qin & Ji (2010) Zhang et al. (2010) 
Biehl et al. (2007) Salema et al. (2007) Amaro & BarbosaPovoa (2009) 
Table 1. RSC network design literature overview
As a second category stochastic programming is also used to cope with the uncertainty inherent to RSC systems. Listes and Dekker (2005) propose a stochastic programming based approach by which a deterministic location model for product recovery network design may be extended to explicitly account for the uncertainties. The objective of the proposed model is net revenue maximization and the uncertainties on the amount and quality of the returned flows are taken into account. Listes (2007) presents a generic stochastic model for the design of networks comprising both supply and return channels organized in a closed loop system. The proposed model accounts for a number of scenarios which may be constructed based on critical levels of design parameters such as demand and return. The objective of the model is net profit maximization and demandreturn volume uncertainties are taken into account. ElSayed et al. (2010) propose multiperiod multiechelon forwardreverse logistic network design under risk model. The problem is formulated in a stochastic mixedinteger linear programming decision making form as a multistage stochastic program. The objective of the model is to maximize the total expected profit and demand uncertainty is taken into account. Chouinard et al. (2008) suggest a stochastic programming model to study the impacts of random factors related to the recovery, processing and demand volumes on the design of supply loops. Their solution approach is based on the sample average approximation with use of Monte Carlo simulation method. The objective of their model is cost minimization and recovery, processing and demand volume uncertainties are taken into account. Lee and Dong (2009) offer a dynamic location allocation model to cope with the factors may vary over time. The proposed model is a two stage stochastic programming model by which a deterministic model for multiperiod RSC network design can be extended to account for the uncertainties. The objective of the model is to minimize the total investment and operational costs in the dynamic logistics network. Demand of forward products and the supply of returned products at customers are uncertain.
The third category of papers utilizes fuzzy programming and some other related techniques to handle the uncertainty of RSCs. Among those we can refer to Qin and Ji (2010) and Zhang et al. (2010). They use fuzzy programming to design the product recovery networks. In these studies the volume of returned products are considered as uncertain data.
The fourth category of papers includes a variety of approaches. Lieckens and Vandaele (2007) propose a RSC network design model with stochastic lead times. The model is a mixed integer nonlinear programming model with the combination of queuing model. Biehl et al. (2007) simulate a carpet RSC and use a designed experiment to analyze the impact of the system design factors as well as environmental factors impacting the operational performance of the RSC considering highly variable return flows. Salema et al. (2007) propose a generalized model where capacity limits, multiproduct management and uncertainty on product demands and returns are considered. They develop a mixed integer formulation and solve it using standard branch and bound technique. A similar technique is also used by Amaro and BarbosaPovoa (2010). They propose a multiperiod planning model where the supply chain operational decisions impacts on supply, production, transportation and distribution are measured for given horizon with different demand and price per period.
Numerous papers on forward and a few on reverse supply chain considering network location design are surveyed by Zanjirani Farahani et al. (2010). They made a very detailed review of the literature on multicriteria facility location. There is however very limited number of papers taking into account simultaneously the uncertainties related to return quantity, quality, and the leadtime.
This paper is organized as follows: In Section 2, we brief the return chains network design of hightech products. In this section we present the modeling approach. Section 3 presents a fuzzy based multiobjective linear programming solution methodology to solve the problem. Section 4 briefs numerical results. Finally, in Section 5 conclusions are drawn.
2 Return Supply Chain Network Design: Modeling Approach
Uncertainty degrees and types depend on the case understudy, for example, in some cases; expected return volume variation may be relatively small for the products with relatively long lifecycles. Such uncertainties can be studied through sensitivity analyses. For hightech products however return volume is unknown, in general. This return behavior can be easily formulated as different fuzzy sets. Uncertainty can be included in the modeling process in different ways. Ilgin and Gupta (2010) suggest robust optimization and stochastic programming are the most popular techniques implemented to handle uncertainty in RSC network design.
We proposed a MultiObjective Linear Programming (MOLP) modeling approach based consultation with the experts and related literature, especially, Tuzkaya et al. (2011), Du and Evans (2008), Pishvaee et al. (2010), Chan et al. (2005) and Altiparmak et al. (2006). Our approach, for the most part, provides a mean to make more strategic decision. It addresses the design aspect of the distribution channel, i.e., the establishments of the distribution network and its associated flows. The proposed RSC network model consists of customers, Collection Centers (CC), Repair Centers (RC) and potential flows among them. Based on the customer calls, products are collected by the CC considering the maximum service coverage area constraint. From CC, returned products are being pooled and sent to the nearest RC considering its capacity constraint. In the RCs, returned products are inspected and classified according to repair needs: (i) products which have important defects are rejected, then new products are dispatched to customers or they are reimbursed in full. The rejected products are transported to a disposal center, (ii) products which have slight repair needs (iii) products which have important repair needs with additional repair times and repair costs.
Some assumptions are made as follows:
· It’s assumed that spare parts required for the repairable products with relatively more repair needs are brought from manufacturing facilities based on the demand. The replenishment time including the transportation times and repair times are given and known.
· Each customer is assumed to be a group of customers located in close vicinity.
· Transportation costs between a disposal center and RCs are assumed to be included in the disposal costs.
· The total of rejected and repairable products percentages (with slight and important repair needs) is equal to one.
· New product cost for returned products that cannot be repaired (rejected) is a function of collection center from which the products comes and subject to dependencies like currency rate and tax rate.
Return volume from customers, and objective functions’ values are considered as fuzzy values. Indices, parameters, decision variables and the details of the model are given as follows:
Indices
m Index for customers
i Index for collection centers (CCs)
j Index for repair centers (RCs)
Parameters
D_{m} 
Total return volume per year of customer m 
d_{mi} 
Distance between customer m and CC_{i} 
d_{ij} 
Distance between CC_{i} and RC_{j} 
tc 
Unit transportation cost for returns 
dpc 
Unit disposal cost for rejected products 
t_{mi} 
Transportation time between customer m and CC_{i} 
t_{ij} 
Transportation time between CC_{i} and RC_{j} 
t_{INS} 
Total inspection and classification time in RCs 
t_{SRN} 
Repair time for products with slight repair needs 
t_{IRN} 
Part replenishment and repair times for products with important repair needs 
t_{EXP} 
Customer expectation on service time (or promised service time to the customers with guarantee contract) 
Cap_{i} 
Total capacity of CC_{i} per year 
Cap_{j} 
Total capacity of RC_{j} per year 
R_{i} 
Renting cost of CC_{i} per year 
C_{ESTj} 
Establishment cost of RC_{j} 
A_{j} 
The weight of RC_{j} obtained via Analytical Hierarchy Process (AHP) 
C_{insj} 
Unit inspection and classification cost in the RC_{j} 
B_{REJ} 
Percentage of rejected products in RCs 
B_{SRN} 
Percentage of repairable products with slight repair needs 
B_{IRN} 
Percentage of repairable products with important repair needs 
L 
Arbitrarily set large number 
C_{NPi} 
New product costs in CC_{i }for the returned products that cannot be repaired (rejected) 
C_{SRNj} 
Repair costs for products which has slight repair needs and can be repaired in RCs 
C_{IRNj} 
Repair costs for products which has important repair needs in RCs 
_{ }_{ }
Variables
Y_{i} 
Renting decision of CC_{i } 
Z_{j } 
Establishment decision of RC_{j }

Y_{mi} 
Assignment decision of customer m to CC_{i} 
Z_{ij} 
Assignment decision of CC_{i} to RC_{j} 
X_{mi} 
Total return volume coming from customer m to CC_{i} 
X_{ij} 
Total return volume coming from CC_{i} to RC_{j} 
Four objectives are considered in the proposed RSC network design model: (1) cost minimization (2) maximization of weighted assignments to RCs, (3) minimization of tardiness in the customer service (4) maximization of average capacity utilization levels.
First objective (OF1): net cost minimization
The first objective function is cost minimization (Equation 1). This function includes transportation cost, CC renting cost, RC establishment cost, inspectionclassificationoverhauling cost, new product costs for rejected repairs, repairing costs in RCs.

(1) 
The components of the first objective function can be explained as below.
The total transportation costs from customers to the CCs, from the CCs to the RCs can be represented as Equations 23, respectively.

(2) 

(3) 
Total renting or annuity costs for selected CCs can be represented as Equation 4.

(4) 
Establishment costs of the RCs can be represented as Equation 5.

(5) 
Total inspection, classification costs in RCs can be represented as Equation 6.

(6) 
Total costs of rejected products (new products need to be given to the customers and disposal needs for the rejected ones) can be represented as Equation 7.

(7) 
Total cost of products needed slight repairing (slight repair needs can be solved in RCs) as Equation 8.

(8) 
Total cost of products needed important repairing as Equation 9.

(9) 
Second objective (OF2): maximization of weighted product volume assigned from CCs to RCs
The second objective function is the maximization of the weighted product volume assigned from CCs to RCs (Equation 10). Here, the weighting for the qualitative factors is realized for RCs via AHP.

(10) 
Third objective function (OF3): total tardiness minimization
The third objective function is the minimization of the total tardiness from the customers expected service time (i.e. promised service time in guarantee contract) (Equation 11).

(11) 
Fourth objective function (OF4): equity on capacity utilization
With the fourth objective function, total average capacity utilization levels of RCs are tried to be maximized (Equation 12).

(12) 
Constraints
Equations 13 guarantee that each customer’s demand is satisfied.

(13) 
Equations 14 secure only when CC is opened, a customer can be assigned to this CC.

(14) 
Equations 15 permit customer flow volume to CC only if the customer is assigned to CC.

(15) 
Equations 16 guarantee that the incoming product volume of the CC is equal to the outgoing product volume of that CC.

(16) 
Equations 17 ensure that a CC cannot be assigned to this RC if this RC is not established.

(17) 
Equations 18 represent that if a CC is not assigned to a RC, an assignment product volume does not occur.

(18) 
Equations 19 guarantee that each customer is assigned to only one CC, Equations 20 assure that each CC is assigned to only one RC.

(19) 

(20) 
Equations 21 and 22 are the capacity constraints of the CC_{i }and the RC_{j} , respectively.

(21) 

(22) 
Equations 2324 represent nonnegativity constraints.

(23) 

(24) 
Equations 25 represent binary variables.

(25) 
3 Methodology
An integrated Analytical Hierarchy Process (AHP) and weighted maxmin approach is utilized in this study. Objective function and repair center weights are calculated via AHP. Using these weights and input data, Fuzzy Goal Programming (FGP) model is solved via weighted maxmin approach.
3.1 AHP approach for objective functions and repair centers evaluations
In order to calculate the objective function weights, AHP approach is utilized (Saaty, 1980). Our four objectives weights are calculated via pair wise comparisons with respect to their contribution to the main objective (to find best RSC network for the decision makers (DM)).
Repair centers’ weights are calculated considering the criteria obtained from Tuzkaya and Gülsün (2008), Tuzkaya, Gülsün and Önsel (2011). The evaluation criteria are transportation, environmental, socialpolitical, economical and technical. Similar to objective function weighting, for this purpose the DM preferences for pairwise comparison are solicited.
3.2 Weighted maxmin method
In this study, we utilized the FGP approach of Lin (2004). A FGP model with m goal can be represented as in Equation 26:
(26) 
where x is an nvector with components x_{1}, x_{2}, …, x_{n} and are system constraints in vector notation. Since all objectives might not be achieved simultaneously under the system constraints, the decision maker may define a lower tolerance limit and a membership function for each objective to determine the achieved level of that objective.
In the FGP model (Equation 27), objective functions can be weighted considering their relative importance to the achievement of the main aim which is to find best network design for the after sale services. With the weighted objective functions, Equation 26 can be converted to Equation 27, as a one objective linear model with the weighted maxmin approach (Lin, 2004; Kongar & Gupta, 2006). In this equation, lambda is the satisfaction degree of decision makers with the objective functions’ obtained values.

(27) 
Figure 1. Linear membership functions for minimization (a) and maximization (b) objectives
If the objective functions (ax)_{i}, i=1,2,…,m, are expressed as fuzzy sets whose membership functions increase linearly from 0 to 1 (Amid et al., 2011), membership function for a minimization objective (Figure 1a) can be expressed as in Equation 28.

(28) 
Membership function for a maximization objective (Figure 1b) can be expressed as in Equation 29.

(29) 
Adapted from Liang (2006, 2009), we can summarize our solution methodology as follows.
Step 1. Formulate the original fuzzy MOLP model,
Step 2. Specify the best (g_{ib}) and worst (g_{iw}) objective values for each objective i. In this study, best objective values are found solving the model for each objective separately. The worst values are obtained between solutions of calculating other objective values in the one objective solution,
Step 3. Specify the degree of membership f_{i}((ax)_{i}) for each objective i,
Step 4. To convert the FGP approach to an equivalent linear programming model, introduce the auxiliary variable lambda,
Step 5. Calculate the weight of objective functions and repair centers using AHP,
Step 6. Solve the linear programming model.
4 Numerical Results
In this study, a hypothetical case of a LCDmonitor return supply chain network design is solved. In this example, for the after sales services we consider twenty customers clusters, four collection centers, three repair centers. Input data related with distances, transportation times between nodes and demand of customers for one planning period, yearly rental costs of collection centers and establishment costs of repair centers are shown in Table 2. Unit inspection costs for RC1, RC2 and RC3 are 5, 5.5 and 6 Euros, respectively; new product costs from CC1, CC2, CC3 and CC4 are 1500, 1550, 1570 and 1530 Euros, respectively. The product costs are assumed to include disposal cost for the rejected returns. Repair costs for the products which need slightly repairs in RC1, RC2, RC4 are 30, 50, 35 Euros, respectively. Repair costs for the products which need important repairs in RC1, RC2, RC4 are 200, 230, 210 Euros, respectively. The percentages of returns which are rejected, need slightly repair, and important repair are 5%, 70% and 25% respectively. Capacities of CC1, CC2, CC3, CC4, RC1, RC2, RC3 are 25000, 25000, 25000, 25000, 20000, 30000 and 40000 units, respectively. Arbitrarily set large number L is taken as 5000000.
Objective functions are evaluated via AHP and their weights are obtained as 0.56 for OF1, 0.06 for OF2, 0.12 for OF3 and 0.26 for OF4. Additionally, repair centers are evaluated via AHP and their weights (these weights are used as A_{j} parameters of the second objective function) are obtained as 0.61 for RC1, 0.21 for RC2 and 0.18 for RC3.
Although distances between nodes have an important effect on return times, they are also assumed to be influenced by the road conditions and transportation types. Hence, vehicle transportation times per km are not same for the every route.
4.1 Analyses and Discussion
To construct the membership functions of objective functions, first the model is solved separately for each objective. By doing this, best values are obtained. Secondly, objective function values are obtained for the other objectives’ global solutions. Between these values, the worst one for each objective is the objective’s worst value. These results are summarized as in Table 3.
After constructing the membership functions, problem is solved with integrated AHPweighted maxmin approach via Lingo 9.0 solver program. Obtained results are summarized in Tables 4, 5, 6, 7, 8 and 9 for different objective function weight combinations. First objective weight combination is W= (0.56, 0.06, 0.12, 0.26) and these weights are the results of AHP and DM preferences. In this weight combination, all collection centers are supposed to be rented (Table 4, 5 and 6). However, with the change in the objective function weight combinations, those assignment volumes are observed to be changed. As an example, while weight of OF1 is decreasing, the assignment volume to CC3 is increasing since the rental cost of this collection center is the most expensive one and the assigned volume is low when total cost is important.
When repair center’s assignments are considered, it is observed that first two repair centers are decided to be opened for all objective function weight combinations (Table 7, 8 and 9). Also, while the second objective function’s weight is increasing, the assignment volume of RC1 is increasing similarly. It is an expected situation, since the second objective is the weighted assignment maximization to the repair centers and the RC1 has the biggest weight between the others. All these analyses show the sensitivity of the model to the parameter changes.

Distance (km) 


Distance (km) 
Transportation time (hr) 


CC1 
CC2 
CC3 
CC4 
Demand (unit/year) 

CC1 
CC2 
CC3 
CC4 

CC1 
CC2 
CC3 
CC4 

C1 
321 
250 
528 
225 
3585 
RC1 
151 
269 
307 
288 
C1 
5.35 
3.57 
7.04 
5 

C2 
313 
213 
335 
445 
548 
RC2 
100 
219 
258 
437 
C2 
5.22 
3.04 
5.58 
4.68 

C3 
318 
338 
503 
113 
768 
RC3 
271 
409 
275 
495 
C3 
5.3 
4.83 
8.38 
1.19 

C4 
319 
254 
508 
596 
705 

Transportation time (hr) 
C4 
3.99 
3.63 
8.47 
6.27 

C5 
332 
476 
424 
225 
731 

CC1 
CC2 
CC3 
CC4 
C5 
4.15 
7.93 
8.48 
2.37 

C6 
273 
416 
364 
185 
1306 
RC1 
1.68 
2.99 
3.41 
4.11 
C6 
3.41 
6.93 
7.28 
3.08 

C7 
293 
422 
455 
126 
4008 
RC2 
1.43 
3.13 
4.3 
7.28 
C7 
3.66 
4.96 
9.1 
2.1 

C8 
282 
423 
371 
173 
2004 
RC3 
3.61 
5.45 
3.67 
8.25 
C8 
5.64 
4.98 
4.12 
2.88 

C9 
130 
130 
149 
372 
1702 

Rental cost (€/year) 
C9 
2.6 
1.53 
1.66 
9.3 

C10 
99 
143 
170 
288 
3676 
CC1 
35000 
C10 
1.98 
1.68 
1.89 
7.2 

C11 
93 
235 
106 
328 
1411 
CC2 
50000 
C11 
1.03 
4.7 
1.06 
8.2 

C12 
86 
147 
166 
289 
3125 
CC3 
30000 
C12 
0.96 
2.94 
1.66 
7.23 

C13 
120 
145 
168 
287 
964 
CC4 
35000 
C13 
1.33 
2.9 
1.68 
4.42 

C14 
100 
151 
207 
288 
9106 

Establishment costs (€) 
C14 
2.5 
3.02 
2.07 
4.43 

C15 
251 
160 
410 
339 
2100 
RC1 
4000000 
C15 
6.28 
5.33 
4.1 
5.22 

C16 
250 
120 
371 
320 
755 
RC2 
5000000 
C16 
6.25 
4 
6.18 
4.92 

C17 
266 
128 
379 
367 
386 
RC3 
5500000 
C17 
6.65 
4.27 
6.32 
6.12 

C18 
246 
95 
366 
399 
2053 





C18 
4.1 
1.27 
6.1 
6.65 

C19 
174 
29 
263 
355 
2835 





C19 
2.9 
0.39 
5.84 
5.92 

C20 
193 
45 
270 
346 
6020 





C20 
3.22 
0.6 
6 
5.77 

Table 2. Input data for the hightech after sale services network design problem
Objective function type 
Minimization 
Maximization 
Minimization 
Maximization 

OF1 
OF2 
OF3 
OF4 
OF1 (ax)_{1} (Euros) 
61,198,930 (best value) 
18,021 
3,450,535 
0.6411 
OF2 (ax)_{2} (units) 
86,135,632 (worst value) 
18,093 (best value) 
3,652,103 
0.6421 
OF3 (ax)_{3} (hours) 
68,891,111 
17,837 (worst value) 
3,426,533 (best value) 
0.6298 (worst value) 
OF4 (ax)_{4} (units) 
83,997,935 
18,093 
3,659,867 (worst value) 
0.6421 (best value) 
Multiobjective solution 
73,221,000 
17,851 
3,685,762 
0.6387 
Table 3. Best and worst values for objective functions
Objective function weights obtained via AHP W=(0.56, 0.06, 0.12, 0.26) 


CC1 
CC2 
CC3 
CC4 
TOTAL 
C 1 



3585 
3585 
C 2 
548 



548 
C 3 
768 



768 
C 4 
705 



705 
C 5 


731 

731 
C 6 



1306 
1306 
C 7 



4008 
4008 
C 8 
2004 



2004 
C 9 



1702 
1702 
C 10 



3676 
3676 
C 11 



1411 
1411 
C 12 



3125 
3125 
C 13 
964 



964 
C 14 
9106 



9106 
C 15 

2100 


2100 
C 16 

755 


755 
C 17 

386 


386 
C 18 
2053 



2053 
C 19 


2835 

2835 
C 20 

6200 


6020 
TOTAL 
15380 
9261 
3566 
19581 
47788 
Table 4. Flows between customers and collection centers. Objective function weights obtained via AHP
Equal objective function weights W=(0.25, 0.25, 0.25, 0.25) 


CC1 
CC2 
CC3 
CC4 
TOTAL 
C 1 



3585 
3585 
C 2 
548 



548 
C 3 
768 



768 
C 4 

705 


705 
C 5 


731 

731 
C 6 



1306 
1306 
C 7 



4008 
4008 
C 8 
2004 



2004 
C 9 



1702 
1702 
C 10 



3676 
3676 
C 11 



1411 
1411 
C 12 



3125 
3125 
C 13 



964 
964 
C 14 
9106 



9106 
C 15 

2100 


2100 
C 16 
755 



755 
C 17 

386 


386 
C 18 
2053 



2053 
C 19 

2835 


2835 
C 20 


6020 

6020 
TOTAL 
15234 
6026 
6751 
19777 
47788 
Table 5. Flows between customers and collection centers. Equal objective function weights
Reverse objective function weights of AHP results W=(0.06, 0.56, 0.22, 0.12) 


CC1 
CC2 
CC3 
CC4 
TOTAL 
C 1 
3585 



3585 
C 2 


548 

548 
C 3 
768 



768 
C 4 

705 


705 
C 5 

731 


731 
C 6 

1306 


1306 
C 7 


4008 

4008 
C 8 
2004 



2004 
C 9 
1702 



1702 
C 10 



3676 
3676 
C 11 

1411 


1411 
C 12 

3125 


3125 
C 13 

964 


964 
C 14 
9106 



9106 
C 15 



2100 
2100 
C 16 



755 
755 
C 17 

386 


386 
C 18 

2053 


2053 
C 19 
2835 



2835 
C 20 


6020 

6020 
TOTAL 
20000 
10681 
10576 
6531 
47788 
Table 6. Flows between customers and collection centers. Reserve objective function weights of AHP results
Objective function weights obtained via AHP W=(0.56, 0.06, 0.12, 0.26) 


CC1 
CC2 
CC3 
CC4 
TOTAL 
RC1 



19581 
19581 
RC2 
15380 
9261 
3566 

28207 
RC3 




0 
TOTAL 
15380 
9261 
3566 
19581 
47788 
Table 7. Flows between collection centers and repair centers. Objective function weights via AHP
Equal objective function weights W=(0.25, 0.25, 0.25, 0.25) 


CC1 
CC2 
CC3 
CC4 
TOTAL 
RC1 



19777 
19777 
RC2 
15234 
6026 
6751 

28011 
RC3 




0 
TOTAL 
15234 
6026 
6751 
19777 
47788 
Table 8. Flows between collection centers and repair centers. Equal objective function weights
Reverse objective function weights of AHP results W=(0.06, 0.56, 0.22, 0.12) 


CC1 
CC2 
CC3 
CC4 
TOTAL 
RC1 
20000 



20000 
RC2 

10681 
10576 
6531 
27788 
RC3 




0 
TOTAL 
20000 
10681 
10576 
6531 
47788 
Table 9. Flows between collection centers and repair centers. Reserve objective function weights of AHP results
In Table 10, overall satisfaction degrees, membership function and objective function values for different weight combinations are presented. Membership function value of OF4 is more than 0.81 for all combinations because capacity levels of RCs are not very limited and satisfaction of this objective function is easier considering the others. However, for all the other objective functions, it can be noted that their weights are almost directly affect their membership function values.

Objective function weights obtained via AHP W=(0.56, 0.06, 0.12, 0.26) 
Equal objective function weights W=(0.25, 0.25, 0.25, 0.25) 
Reverse objective function weights of AHP results W=(0.06, 0.56, 0.22, 0.12) 
lambda 
0.90 
1.43 
1.78 
mu_{1}((ax)_{1}) 
0.51 
0.36 
0.11 
(ax)_{1}(Euros) 
73462800 
77165840 
83268770.00 
mu_{2}((ax)_{2}) 
0.35 
0.65 
1.00 
(ax)_{2} (units) 
17927.01 
18004.80 
18093.31 
mu_{3}((ax)_{3}) 
0.11 
0.36 
0.46 
(ax)_{3} (hours) 
3686145 
3743545 
3767263.00 
mu_{4}((ax)_{4}) 
0.81 
0.90 
1 
(ax)_{4} (units) 
0.64 
0.64 
0.64 
Table 10. Overall satisfaction degrees, membership function and objective functions' values for different weight combinations
5 Conclusions
In this study after sale services RSC for hightech industry is investigated. After detailed literature and field analyses, uncertainties inherent to the hightech returns, the multiobjective structure of the network design was presented. The main uncertainties are taken into account and a FGP model is developed. This model is converted to an equivalent linear programming model using weighted maxmin approach. Objective functions and repair facility location alternatives are evaluated via AHP approach. A compromise solution is obtained with the utilized weighted maxmin approach.
The model is in development phase. Considering the need for solution simplicity; some assumptions are made especially related to the third and fourth objectives. For example, regardless of number of opened facilities, average capacity utilization is considered in the fourth objective to avoid nonlinearities. Such simplify assumption must be relaxed and a new formulation is needed.
With utilization of weighted maxmin approach, the main aim is to maximize the value of the worst objective. This approach may cause loses about some improvement potentials for the other objective functions. The solution methodology can be more effective with a two phase approach in which a weighted average operator can be utilized in the second phase. With the improved model and twophase approach, there might be a need to employ a metaheuristic.
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