A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system

A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system

Accepted Manuscript A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system Baigang Du, Shunsheng Guo, Xiaoron...

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Accepted Manuscript A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system Baigang Du, Shunsheng Guo, Xiaorong Huang, Yibing Li, Jun Guo PII: DOI: Reference:

S0957-4174(15)00079-2 http://dx.doi.org/10.1016/j.eswa.2015.01.056 ESWA 9836

To appear in:

Expert Systems with Applications

Please cite this article as: Du, B., Guo, S., Huang, X., Li, Y., Guo, J., A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system, Expert Systems with Applications (2015), doi: http:// dx.doi.org/10.1016/j.eswa.2015.01.056

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A Pareto supplier selection algorithm for minimum the life cycle cost of complex product system Baigang Dua,*, Shunsheng Guoa, Xiaorong Huangb, Yibing Lia, Jun Guoa a

School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China School of Management & Economics, Hubei Polytechnic University, Huangshi 435003, China

b

([email protected], [email protected], [email protected], [email protected], [email protected]) *

Corresponding author. Tel.: +86 027 87857811. E-mail address: [email protected] (Baigang Du).

Abstract: Supplier selection has significant impact on life cycle cost of complex product system (CoPS). In this paper, a new variant of supplier selection problem named life cycle supplier selection of CoPS (LSS&CoPS) problem is addressed. There are three kinds of choices for a manufacturer to complete a CoPS: self-made, purchasing the finished component and outsourcing. Different selection not only results in difference of procurement cost of CoPS, but also results in reliability changing after it delivered to customer which greatly influences the operating cost in CoPS’s lifecycle. However, the minimizing of two objectives is mutually conflicted. This paper presents a bi-objective LSS&CoPS model which considering operating stage of CoPS to balance the procurement cost and operating cost. Moreover, a hybridization of Pareto Genetic Algorithm (PGA) with multi-intersection and similarity crossover (MSC) strategy is proposed to solve the bi-objective problem. Also, a dual-chromosome is used to represent the variable-length chromosome. Finally, a cement equipment supplier optimal in a cement equipment enterprise is provided. Example indicates that the procurement cost and operating cost have been optimized, yields a Pareto optimal solution of supplier schema for project managers to make-decision and decrease the life cycle cost of CoPS. Additionally, the results show that the proposed approach is more preferably in Pareto optimal solution searching.

Keywords: Supplier selection, Complex product system, Pareto optimal, Hybrid genetic algorithm, Life cycle cost

1. Introduction Supplier selection has always been considered as a key factor within purchasing and supply management (Luo et al. 2009; Hsu et al. 2009).The procurement of materials and components plays an important role in many respects for CoPS project, such as project approval and deliver, project schedule, project profitability and product service life (Aghai et al. 2014; Humphreys et al. 2007). For technological system high in complexity and value, CoPS is produced as customized, one-off or small batched capital goods items and capital goods acquired through business-to-business (B2B) transactions, having higher unit costs than commodity products, which are often mass-produced (Hobday 1998). The components of CoPS are typically tailor-made to suit the buyer's requirements, whereas commodity products generally consist of standardized or modular components (Dedehayir, Nokelainen and Mäkinen 2014). CoPS is likely to demonstrate complex component interfaces within a hierarchical system structure (Shibata 2009), in contrast to commodity products, which tend toward simpler interfaces and a simpler architectural structure. The life cycle of CoPS is longer 1

than commodity products (Dedehayir, Nokelainen and Mäkinen 2014). Further, supplier selection occupied a core position in the life cycle of CoPS, so as to guarantee the reliability and service life of CoPS with lower cost (Sheikhalishahi and Torabi 2014). In traditional procurement activities, procurement decision maker mainly influenced by the quoted price of different suppliers (Zhang et al. 2011; Li, Murat, and Huang 2009; Jacek et al. 2014). Meanwhile, components quality is ensured by the initial qualified suppliers but not considering the influence of operating cost in the life cycle. For a CoPS, the complexity of components set a higher demand for supplier selection with less expensive cost and reliability requirements (Yu and Wong 2015). Price-based purchase may lead to increase the operating cost of CoPS which has increased customer’s unnecessary expenses and reduced the reputation of CoPS manufacturing enterprise (Wang et al. 2014). Currently, intelligent decision procurement with considering operating cost in life cycle is far more concern. Therefore, the existing problems in supplier selection for CoPS can be summarized into following aspects. (1) Price-based strategy. Price-based strategy tends to one-shot cooperation and not uses the historical transaction information of different suppliers effectively. It cannot be enhancing CoPS’s quality. Choosing the lowest cost component is not benefit for decreasing the life cycle cost. Therefore, price-based purchase strategy cannot be guaranteed to reduce CoPS’s cost in the whole life cycle. (2) Limited considering phase. Traditional procurement is limited within CoPS manufacturing enterprise and not expanded to permeate in CoPS’s life cycle. In addition, it only focused on procurement cost optimization for manufacturing enterprise but ignored the operating cost optimization for CoPS’s life cycle. In terms of the problems mentioned above, motivations of the research can be concluded as follows: (1) Propose a multi-objective supplier selection model to handling the life cycle cost of CoPS in different phases. (2) Develop techniques to solve the proposed supplier selection model, where the Pareto-optimal searching in supplier space is NP hard problem. Therefore, the paper contributed a richer LSS&CoPS model, which considering procurement cost and operating cost in the life cycle. The model mainly focuses on supplier selection which simultaneously minimum procurement cost and operating cost when CoPS delivers to customer. Two objectives (procurement cost and operating cost) are mutually conflicted. Improving one objective will compromise another. For bi-objective optimization problem, it is desirable for Pareto optimal values to be evenly distributed in Pareto-optimal solution set, rather than converged in a single region of Pareto front (Wang et al. 2013). Drawing upon this, it used Pareto optimal set to solve bi-objective optimization employing a hybridization of PGA and MSC strategy. The remainder of this paper is organized as follows. In the next section, the relevant literature related to supplier selection of CoPS manufacturing is reviewed. Problem description and mathematic model of supplier optimal selection are developed in Section 3. Section 4 details the proposed hybridization of PGA with MSC strategy to approximate Pareto optimal solutions. A case study of supplier selection for cement equipment in a cement equipment enterprise is demonstrated in Section 5 and conclusions are given in Section 6.

2

2. Literature review In recent years, many attempts have been published to develop and optimize supplier selection models. These studies encompass the wide scope of models ranged from simple linear single product deterministic problems to complex non-linear multi-product stochastic ones. Chai, Liu, and Ngai (2013) presented a general review of supplier selection models to support the development of richer supplier selection models. Traditionally, the focus of supplier selection is usually on a deterministic model with single objective or multi-objective in supply chain management. For example, Latha Shankar et al. (2013) used swarm intelligence based Multi-objective Hybrid Particle Swarm Optimization algorithm (MOHPSO) with non-dominated sorting method to achieve bi-objective optimization of minimizing total cost and maximizing fill rate in a supply chain design. Deng et al. (2014) investigated an integrated supplier selection model simultaneously considering suppliers of sourcing components in a product line. Wang and Li (2014) applied Nash bargaining game DEA model to consider the competition between suppliers with common weights comparing to traditional DEA method with various weights. Sheikhalishahi and Torabi (2014) addressed the maintenance supplier selection problem for a manufacturer to decide the purchasing of different replaceable parts for equipment’s maintenance. Zeydan, Çolpan and Çobanoğlu (2011) proposed an approach considers both qualitative and quantitative variables in evaluating performance for supplier selection to reduced product life cycle cost. Mahapatra, Das and Narasimhan (2012) used a contingent theory for supplier management in product life cycle to choose optimal suppliers. Abdallah et al. (2012) established supplier estimation model of product life cycle cost from an environmental perspective. Liu and Hipel (2012) proposed a hierarchical decision model to select the optimal quality control strategies among various suppliers in producing a complex product. Aksoy and Öztürk (2011) used a neural network for selecting the most appropriate suppliers to solve the complex product configuration in JIT environment. Yeh and Chuang (2011) introduced green appraisal score into the framework of supplier selection criteria and used multi-objective genetic algorithm to find the Pareto-optimal solutions. Zhang et al. (2013) used a Pareto genetic algorithm to solve the green partner selection problem with green criteria of carbon emission and lead content in manufacturing production. Abdollahi et al.

(2015) used an integrated approach of analytical network process (ANP) and data envelopment analysis (DEA) with considering product-related and organization-related characteristics to select lean and agile suppliers. Moncayo-Martínez and Recio (2014) proposed a Pareto-antcolony algorithm to minimize the cost of goods sold (CoGS) and the lead time (LT) in an assembly supply chain. The use of uncertainty and risk in supplier selection models is a natural extension of a deterministic approach because all the model parameters, in practice, are not certain. This consideration results in the more realistic problems. In this matter, a number of researchers present comprehensive supplier selection models using stochastic and risk control approach. Wu et al. (2013) developed a stochastic fuzzy multi-objective programming model for risk supplier selection in presence of both random uncertainty and fuzzy uncertainty. Bandyopadhyay and Bhattacharya (2013) proposed a modified NSGA-II with a fuzzy variable crossover algorithm to minimize the value of total cost and bullwhip effect in a bi-objective supplier selection problem. Kar (2014) proposed a group decision support approach for the supplier selection by integrating fuzzy AHP for group decision making. Lee et al. (2015) provided a decision support system to quantify the importance of the 3

agility criterion for supplier selection. The proposed system used a fuzzy analytic hierarchy process (fuzzy AHP) and fuzzy technique for order of preference by similarity to ideal solution (fuzzy TOPSIS) to determine the weights of multi-criteria. Chai and Ngai (2014) proposed a soft decision model involving multiple stakeholders and multiple perspectives to perform theoretical decision modeling using interval and hesitant fuzzy methodology for strategic supplier selection in uncertain decision environments. Bilsel and Ravindran (2011) presented a multi-objective stochastic sequential supplier allocation model to help in supplier selection under uncertainty. Fallah-Tafti et al. (2014) proposed a novel interactive possibilistic approach based on STEP method to minimize total costs, maximize suppliers’ ranks and minimize total delivery time of products in closed-loop supply chain network design under uncertainty. Guo et al. (2014) used a semi-fuzzy support vector domain description (semi-fuzzy SVDD) method to determine the select group of suppliers. Chen et al. (2013) established the optimal cost-sharing model with Nash equilibrium and Stackelberg equilibrium to analyze cooperation status between the manufacturer and suppliers for complex equipment under grey information. Huang and Goetschalckx (2014) proposed a robust supply chain model which simultaneously considering the efficiency and the risk of Pareto-optimal solutions. Kannan et al. (2013) presented an integrated approach of fuzzy multi attribute utility theory with quality control, capacity, and other objectives for rating and selecting the best green suppliers according to economic and environmental criteria. To structure the literature review of supplier selection problem and to show difference of this paper form others, a systematic state-of-the-art to review the existing works on the supplier selection problem corresponding to Table 2 and 3 in terms of type, features, objectives and solutions of approach. The codes of these tables are given in Table 1. As shown in Tables, a large part of papers is deterministic with optimization of multi-objective Pareto supplier selection, a smaller part is associated with stochastic and uncertain conditions, a few papers optimize supply chain with multi-period of product life cycle, and a very little research addresses the supplier selection problem of CoPS. Although a number of researches are performed in supplier selection area, but to the best of knowledge, there is no study that addresses the issues of supplier selection with bi-objective of procurement cost and operating cost in context of CoPS’s life cycle with changing reliability. The relevant Tables show the distinctiveness of this paper from others in the literature. Table 1 Classification codes of reviewed works Category

Detail

Code

Type of models (ToMs)

Deterministic

DT

Stochastic

ST

Features of model (FoMs)

Product Multi-product

MPs

Single-product

SPs

Participant Suppliers

Ss

Production plants

PPs

Distribution centers

DCs

Lifecycle Multi-period

MP

Single-period

SP

Environment factor

EF

4

Objectives of model (OoMs)

Solutions of model (SoMs)

Risk factor

RF

Complex product system

CoPS

Cost/price

CP

Quality/ Acceptance

QA

Responsiveness/service

RS

Reliability/risk

RR

Flexibility/agility

FA

Intelligence algorithm

IA

Game theory

GT

Linear programming

LP

Fuzzy approach

FP

Tabel 2 Type and Features of models ToMs Reference

DT

FoMs ST

Product MPs

Latha Shankar et al. (2013) Deng et al. (2014) Wang and Li (2014) Sheikhalishahi and Torabi (2014)

× × × ×

Zeydan, Çolpan and Çobanoğlu (2011) Mahapatra, Das and Narasimhan (2012) Abdallah et al. (2012) Liu and Hipel (2012) Aksoy and Öztürk (2011)

× × × × ×

Yeh and Chuang (2011) Zhang et al. (2013) Abdollahi et al. (2015) Moncayo-Martínez and Recio (2014) Wu et al. (2013)

× × × ×

Participant

Lifecycle

SPs

Ss

PPs

DCs

MP

×

×

×

×

× × × × × × × × ×

×

×

× ×

× × ×

×

× × ×

×

Bandyopadhyay and Bhattacharya (2013) Kar (2014) Lee et al. (2015) Chai and Ngai (2014) Bilsel and Ravindran (2011) Fallah-Tafti et al. (2014)

× × × × × ×

× × × × × ×

× × × × × ×

Guo et al. (2014) Chen et al. (2013) Huang and Goetschalckx (2014) Kannan et al. (2013) This paper

× × × × ×

× ×

× × × × ×

×

× × × × × × ×

× ×

× × × ×

×

×

× × × ×

×

×

Table 3 Objectives and Solutions of models Reference

OoMs CP

Latha Shankar et al. (2013) Deng et al. (2014) Wang and Li (2014)

× ×

Sheikhalishahi and Torabi (2014) Zeydan, Çolpan and Çobanoğlu (2011) Mahapatra, Das and Narasimhan (2012)

×

SoMs

QA

RS

×

× × ×

RR

×

5

× ×

FA

IA

GT

LP

FP

× × × ×

×

CoPS

×

× × × × ×

×

RF

× ×

× × × × ×

×

EF

SP

× ×

×

Abdallah et al. (2012)

×

×

×

Liu and Hipel (2012) Aksoy and Öztürk (2011) Yeh and Chuang (2011) Zhang et al. (2013) Abdollahi et al. (2015) Moncayo-Martínez and Recio (2014)

× × × ×

×

×

×

Wu et al. (2013) Bandyopadhyay and Bhattacharya (2013) Kar (2014) Lee et al. (2015) Chai and Ngai (2014)

× × × × ×

Bilsel and Ravindran (2011) Fallah-Tafti et al. (2014) Guo et al. (2014) Chen et al. (2013) Huang and Goetschalckx (2014)

× × × × ×

Kannan et al. (2013) This paper

× ×

× × × ×

× ×

× × ×

×

× ×

×

× ×

×

× × × ×

× × × × × × × × × ×

×

× × ×

× × × ×

×

×

×

×

× ×

×

3. Problem definition and modeling 3.1. Typical manufacturing process of CoPS CoPS’s manufacturing is based on the requirements of customer and the basic flow can be shown in Fig. 1. The bid of marketing department plays a leading role in the process of manufacturing enterprise. The project is established with customer requirements and then transmitted to product design department so as to carry out a series of production activities. The mainly processes are listed below. (1) Firstly, the design activities have been carried out by design department with the inputs of customer requirements for output, service life, working time and condition, etc. Moreover, the manufacturing processes are in parallel with design processes. (2) Secondly, the drawing information is delivered to technical department for technical preparation which is mainly divided into two parts, the first part is material information for purchasing department and the other is manufacturing information for production department. (3) Thirdly, according to the above information, purchasing department prepares the procurement of raw materials and components. Synchronously, production department generates the master production scheduling, outsourcing or production plan to finished product. In the process of procurement and production activities, a series of logistics which including inbound and outbound of materials and finished product have a close relationship with transportation department. (4) Finally, delivery preparation is carried out according to the packing list provided by technical department. The CoPS is delivered to customer by ocean shipping or land transport when the project is finished. Moreover, the maintenance of CoPS is assisted by manufacturing enterprise.

6

Fig. 1. The manufacturing process of CoPS

3.2. Life cycle oriented manufacturing process According to the typical manufacturing process described in Section 3.1 and the literature definition of CoPS (Hobday 1998; Dedehayir, Nokelainen and Mäkinen 2014), this paper summarized the characteristics of CoPS into four major aspects with motivations of optimal supplier selection, as shown in Table 4. Table 4 Motivations of the LSS&CoPS model. Characteristics High value

Motivations The high value is not only reflected in the high benefits for CoPS created, but also the high production costs of CoPS, so the optimal supplier selection is valuable for a manufacturer.

Customized

The customized CoPS cannot be manufactured in mass production system as a result of the limitations of manufacturing capacity and project duration. Self-made or outsourcing becomes an alternative choice for a manufacturer to finish components of CoPS.

Complex

The CoPS has a highly complex of multi-level BOM structure with many processes,

structure

materials and components requirements. So, it needs more suppliers to support for the processes, materials and components in demand, while the cost and quality of processes, materials and components different suppliers provided are various.

Long lifespan

The CoPS’s higher reliability is a guarantee of long lifespan to decrease the fault and improve productivity.

As shown in Table 4, there are interactions in the effects of the four characteristics for CoPS. The complexity of CoPS’s structure is expected to increase with highly customized requirements. The value will be increased with more revenue the CoPS created for longer lifespan, as well as more production costs the 7

manufacturer spend on manufacturing process, purchasing materials and components to guarantee higher reliability of CoPS. The manufacturing process, raw materials and components procurement plays an important role in

many respects such as the timeliness, economy and reliability of CoPS. Therefore, the influence of selected suppliers on costs is not isolated and it is necessary to research the supplier selection with the viewpoint of CoPS’s life cycle, so as to decrease the life cycle cost. The CoPS’s life cycle cost refers to the cost which taken into account the whole life cycle from the product bidding to the end of recycling. More importantly, the component procurement and manufacturing process determined the quality and reliability of CoPS, and then indirectly influenced the operating cost. An interview has been undertaken with purchasing managers in a cement equipment company located in Tianjin of China (http://www.sinoma-tec.com.cn/en/default.aspx) to comprehend the component’s purchasing criteria of CoPS. In a procurement process, they first get the price of required processes, materials and components from different suppliers and then select the lower price supplier. But a problem they faced is that chosen processes, materials and components with lower price will probably be caused more equipment faults, directly increased the maintenance cost in operating phase of CoPS and decreased the corporate reputation. Generally, the processes, materials and components with higher price have a higher reliability assurance. With regard to customers, getting the higher reliability will be benefit for reducing operating cost because of lower maintenance rate. However, the procurement cost will be significantly increased if the higher price processes, materials and components are selected. Therefore, the purchasing managers are forced to make a choice between price and reliability among various suppliers for CoPS. That is the trade-off between procurement cost and operating cost. In this paper, an improved process with life cycle objectives is proposed to provide a feasible optimization and control method for procurement and manufacturing, as shown in Fig. 2. All procurement and manufacturing activities are beginning with customer order, and it considers not only the basic procurement objectives (procurement cost, etc.), but also the life cycle objectives (operating cost, etc.). Therefore, in the life cycle perspective, procurement and manufacturing has not only controlled the procurement cost, but also take into account the CoPS’s life cycle cost.

8

Fig. 2. The life cycle oriented manufacturing process

3.3. Assumptions of the optimization model Drawing upon the above analysis, two objectives with constraint satisfaction in the life cycle (i.e., procurement cost and operating cost) are employed as the objective functions of Pareto optimization method. In terms of the fact that minimization of procurement cost is not synonymous with operating cost, decision-makers can choose proper suppliers from Pareto optimal solution set to achieve different business purposes. Some assumptions have been made in order to strengthen modeling ability of the proposed LSS&CoPS model, as follows.  CoPS including multiple key components and their combined reliability determined CoPS’s reliability.  CoPS preventive maintenances have been taken at fixed intervals, T,2T,…, and the reliability is assumed to be invariable during each interval. Each change of equipment reliability is assumed to take place at the end of the interval, exactly before the preventive maintenance moment.  CoPS has been made by outsourcing manufacturers, material suppliers and equipment manufacturing enterprise itself. Three groups are described as component suppliers which collaboratively to complete a key component.  The component is composed of different material through multiple processing procedures.  There exists no resource shortage during the procurement and manufacturing process.  Manufacturing capacity of each outsourcing manufacturer and equipment manufacturing enterprise are evaluated.  The settlement of manufacturing and transportation are based on project quantity. Before formulating a mathematical model of the problem, the notations used throughout the remainder of 9

this paper is define in Table 5. Table 5 Model parameters notations. Parameters

Description

Parameters

The number of key components in CoPS

N

Mi

Description The

number

of

material

in

component i, for i=1,2,…,N Xi

The decision variable for component i to

Qi

purchase finished product or materials , for i=1,2,…,N;

X i ={0,1}

The project quantity of component i, for i=1,2,…,N

X i =0

,where

represents purchase materials, otherwise finished product Pi

The manufacturing process number of

Sic

component i, for i=1,2,…,N

The

number

provide

of

suppliers

component

i,

to for

i=1,2,…,N S

m ij

The number of suppliers to

provide

S

p ik

The

number

of

outsourcing

material j for component i, for i=1,2,…, N;

manufacturers to provide process k

j=1,2,…, M i

for component i, for i=1,2,…,N ; k=1,2,…, Pi

Nic

The required number of component i, for

N ijm

The

required

number

of

material j for component i, for

i=1,2,…, N

i=1,2,…, N; j=1,2,…, M i U

c iα

The unit price for supplier α to provide component i, for i=1,2,…,N; α=1,2,…, S

U

m ij β

c i

The unit price for supplier β to provide material j for component i, for

i=1,2,…,N;

j=1,2,…, M i ;

β=1,2,…, S ij

m

U ikpγ

The unit price for supplier γ to provide

Wikpγ

The correction factor of

U ikpγ

process k for component i per ton, for

which represents the difficulty of

i=1,2,…,N; k=1,2,…, Pi ; γ=1,2,…, S

process k for component i, for

p ik

Wikpγ ≥ 1

Tiαc

The transport price for supplier α to deliver

Tijmβ

The transport price for supplier β

component per ton, for i=1,2,…,N; α=1,2,…,

to deliver per ton material in one

Sic

kilometer, for i=1,2,…,N; j=1,2,…, M i ; β=1,2,…, S ij

m

Tikpγ

The transport price for supplier γ to deliver

Dαc

The distance to supplier α

per ton component i in one kilometer, for i=1,2,…,N; k=1,2,…, Pi ;γ=1,2,…, Sikp Dβm

The distance to supplier β

Dγp

The distance to supplier γ

PC

The total procurement cost of CoPS

Cim

The material cost of component i, for i=1,2,…,N

Cip

The production cost of component i, for 10

Cit

The

transportation

cost

of

i=1,2,…,N Ricα

component i, for i=1,2,…,N

The reliability of component i provided by

Rikpγ

component i provided by supplier γ

supplier α Y

The reliability of process k for

The life cycle of CoPS

R

l

The reliability of CoPS between moment l and l+1, for l=0,1, …, L

Ri

The initial reliability of component i

L

The number of maintenance

ϕ (i)

State effect function

h0 (i)

Baseline hazard function

λl

The Failure rate of CoPS

cd

The stop loss per unit time

cf

The

cp

The average cost in a preventive

average

cost

in

a

broken-down

maintenance f1

maintenance

The average maintenance time for a

f2

breakdown Ci'

The average maintenance time for a prevention

The procurement cost for component i

R

' i

The

required

reliability

of

component i

3.4. Bi-objective optimization mathematical model In this section, a bi-objective LSS&CoPS model is established to reconstruct the procurement activity considering the operating phase cost in CoPS’s life cycle. A mathematical formulation is developed for procurement cost and operating cost. Other factors such as component reliability are considered as constrains in the model.

3.4.1. Procurement cost There are many components included in CoPS, and each component has plenty of materials and manufacturing processes. Some components are purchased directly, and the others manufactured with purchasing material or outsourced for a specific process. Hence, the procurement cost to complete CoPS is mainly composed with material cost, production cost and transportation cost as follows. The material cost of component i is given by

⎧U icα N ic , Xi =1 ⎪ m Cim = ⎨ Sij m m ⎪∑U ijβ N ij , X i = 0 ⎩ j =1

(1)

After the purchase of material, the production cost of component i is given by

Xi = 1 ⎧0, ⎪ Pi Ci = ⎨ p p ⎪ ∑Wikγ U ikγ Qi , X i = 0 ⎩ k =1 p

The transportation cost of component i is given by 11

(2)

⎧Tiαc Qi Dαc , Xi =1 ⎪ Mi t Pi Ci = ⎨ m m m p p T N D + ⎪∑ ijβ ij β ∑ Tikγ Qi Dγ , X i = 0 k =1 ⎩ j =1

(3)

In sum, the procurement cost of CoPS has the following form. N

N

N

i =1

i =1

i =1

PC = ∑ Cim + ∑ Cip + ∑ Cit

(4)

3.4.2. Operating cost The operating cost will be occurred during CoPS’s operating stage and it has a close relationship with reliability. Drawing upon the above assumption, the CoPS reliability at initial moment (0) is formulated by N

R 0 = ∏ Ri

(5)

i =1

The reliability of component i can be classified into two categories, these are reliability for purchasing finished product and purchasing material to manufacture. It is calculated as

⎧ Ricα , Xi =1 ⎪ Pi Ri = ⎨ p ⎪∏ Rikγ , X i = 0 ⎩ k =1

(6)

Because of the variability of CoPS reliability in the life cycle, many researchers have proposed different reliability models to calculate an adjusted hazard function. In this paper, authors consider one of these models, the Proportional Hazards Model (PH model) used by (Ghasemi et al. 2010; Guerra et al. 2014) which has been widely used to measure the reliability of CoPS, and adapted it to the case when the life cycle of CoPS has been divided into L intervals. According to PH model, the conditional reliability at moment l depends on reliability at moment l-1, for l=1, 2,…, L, is given as

R l = P{(l + 1)T > t > lT , R l -1},0
(

= exp −ϕ ( R l −1 ) ∫

( l -1)T +t

( l -1)T

)

(7)

h0 (t )dt ,0
The choice of T depends on the nature of the CoPS, and the historical knowledge of its performance. In this paper, T is preventive maintenance interval of equipment. The operating cost is composed with preventive maintenance cost, fault maintenance cost and break-down cost, which is formulated by L

L

l =1

l =1

MC = c p L + c f ∑ N l + cd ( f1 ∑ N l + f 2 L) 12

(8)

In formula (8), the Nl represents the shutdown times between moment l-1 and moment l which caused by the equipment fault λl, is formulated by

Nl = ∫

lT

( l −1)T

λ l dt

(9)

By using the relationship between the reliability Rl and the equipment fault λl, the function is given as

(

R l = exp − ∫

lT

( l −1)T

)

λ l dt , l = 1, 2,…, L

(10)

3.4.3. Constrains To enhance the practical ability of the model, some factors such as procurement cost and reliability of component i are considered as constrains of the model.

Cim +Cip +Cit ≤ Ci' Ri ≥ Ri'

(11) (12)

Eq. (11) is the procurement cost constrain for component i. Eq. (12) ensures that the reliability of component i is no less than required reliability of component i.

4. Solution approach This paper proposed a modified PGA with MSC strategy (MSCGA) to approximate the Pareto optimal solutions of the bi-objective combinatorial optimization problem for the LSS&CoPS model. There are three ways (self-made, purchasing the finished component and outsourcing) to complete a component of CoPS, which lead to the variable-length of encoding chromosome, so the encoding method should be adapted to this change. The superior individuals have some common genes and the hybridization of different heuristics provides more efficient search for exploration and exploitation of the space (Moslehi and Mahnam 2011). Comprehensive above factors, the flowchart of the MSCGA is shown in Fig. 3 and the details are illustrated as follows.

13

Fig. 3. The flowchart of MSCGA algorithm

4.1. Dual-chromosome encoding The encoded chromosome is a formal description of genetic solution which suitable for the application of genetic operators. In this paper, a single chromosome cannot translate the genetic solution for the various length of chromosome as the changing of decision variable Xi, a dual-chromosome method is proposed. The dual-chromosome has two parts, one is decision chromosome (DC) represents Xi for component i, and the other is value chromosome (VC) represents the component and supplier code as shown in Fig. 4. Therefore, the DC is coded with the 0-1 integer and the VC is coded with integer of supplier code. For example, consider the individual 1 and individual 2 in Fig. 4. The VC of individual has a fixed length for a certain portfolio of components, but it can be changed in length with DC of individual.

14

Fig. 4. Example of Dual-chromosomes

4.2. Heuristic generation of initial population The initial population’s quality can largely affect the evolutionary process of a genetic algorithm. As a result, a carefully crafted heuristic method is required to generate random chromosomes with all constraints satisfied. The steps can be summarized as follows: (i) Identify VC with group sizes PopSize, where VC is a group of component, material and process supplier for each component. In this way, the length of VC is fixed. The gene in VC is generated randomly from family members of suppliers. (ii) Identify the bi-objective values of vci based on dci for 0-1 permutation with repetition length of N. The algorithm for computing the procurement cost and operating cost of each individual is shown in the Algorithm 1. After step (ii), two matrixes DM (decision chromosome matrix) and OM (bi-objective values matrix) will be formed for individual x as shown in formula (13) and (14).

0  0⎤ 0  0⎥ ⎥   ⎥ ⎥ 1 1 1⎦ 2N ×N

DM i = ( dmi ) m×n

⎡0 ⎢1 =⎢ ⎢ ⎢ ⎣1

OM i = (omi ) m×n

⎡ PC1 ⎢ PC 2 =⎢ ⎢  ⎢ ⎣ PC2 N

MC1 ⎤ MC2 ⎥ ⎥  ⎥ ⎥ MC2 N ⎦

(13)

(14) 2 N ×2

(iii) Identify the gene of dci for individual x. For each component Pi in individual x, change the corresponding gene of Pi in dci with 0-1 and remain other genes unchanged, then DMi resolved into DM0,i and

DM1,i by DMi(:,n)=0 and DMi(:,n)=1, while corresponding with OMi resolved into OM0,i and OM1,i, and calculate the variance of bi-objective values by formula (15) and (16), in which, D0,i is the variance for purchase material of component i, D1,i is the variance for purchase finished component i, Sum signifies the Sum function and Std signifies the std function. If D0,i > D1,i, it shows purchase materials to manufacture has greater effect on bi-objective values for individual x, so the dci gene of position i will be chosen 0 to reduce such influence, otherwise chosen 1. 15

⎛ Std (OM 0 ,i ) ⎞ D0 ,i = Sum ⎜ ⎟ 2 ⎝ ⎠

(15)

⎛ Std (OM 1,i ) ⎞ D1,i = Sum ⎜ ⎟ 2 ⎝ ⎠

(16)

(iv) Repeat step (ii) and (iii) until dci for initial population is satisfied.

4.3. Fitness evaluation To calculate fitness value, the first step is to obtain each separate objective function value, PC and MC. The algorithm for computing PC and MC is shown in the Algorithm 1. And then, the population is sorted in terms of the objective function value of each chromosome into different fronts based on the non-domination method from (Deb et al. 2002). The non-dominated solution individuals are selected from the population and defined as rank 1 and those individuals are removed from the population. Next set of non-dominated individuals is searched and rank 2 is assigned to them. The procedure is repeated for the subsequent fronts until the entire population is sorted and non-dominantly divided to different fronts. The individual assigned the smaller rank value, represents it is the better one. Furthermore, map the rank value to fitness value with the following formula for normalization modified from (Che and Chiang 2010; Wang et al. 2013).

f ( xi ) = 1 −

∑ rr =( 1xi ) ( r × nr ) ∑mr=1 ( r × nr )

(17)

Where f ( xi ) represents the fitness function value for individual xi , m signifies the maximum rank,

r ( xi ) denotes the grade for individual xi , and nr denotes the number of individuals for rank r . Algorithm 1: Algorithmic flow for calculating procurement cost and operating cost 1. initialize parameter in Table 1 2. for each component i in the individual x from current population curpop do 3. switch manufacture type of component i then 4. case: purchase finished product 5. calculating the value of Cim by Eq. (1) where X i = 1 6. calculating the value of Cit by Eq. (3) where X i = 1 7. 8. 9.

calculating the value of R 0 by Eq. (5) case: purchase material calculating the value of Cim by Eq. (1) where X i = 0

10.

calculating the value of Cip by Eq. (2) where X i = 0

11.

calculating the value of Cit by Eq. (3) where X i = 0

12. 13.

calculating the value of R 0 by Eq. (5) and (6) Loop to update Cim , Cip , Cit , R 0 for each material and process of component i

14. 15. 16. 17. 18. 19.

end switch end for calculating the total procurement cost PC by Eq. (4) for each maintenance phase l in the life cycle of Y calculating the value of R l by Eq. (7) calculating the value of λ l by Eq. (10) 16

20. 21. 22. 23.

calculating the value of N l by Eq. (9) end for calculating the value of MC by Eq. (8) Return PC and MC of individual x

4.4. Selection operator The stochastic tournament strategy (Lei 2011) and elite preservation strategy (Wang et al. 2013) are applied in this study to selection operator. The stochastic tournament strategy is implemented on the whole individuals and randomly chosen a series of individuals and retained the highest fitness individual to next generation, while elite preservation strategy is implemented on the global optimal individuals to replace the worst individuals in next generation.

4.5. Crossover operator The main purpose of crossover operator is to generate better offspring by combining the genetic alleles of two selected parents from the population with probability Pc. A multi-intersection and similarity crossover (MSC) strategy is employed here and crossover position is generated randomly. The procedure is randomly chosen a series of individuals and then determined two selected individuals with the highest similarity as Eq. (18), in which, LenDC and NDC(xi,xj) respectively represents the length of DC and the number of same gene in individual xi and xj, as well as LenVC and NVC(xi,xj) for VC. The crossover process is illustrated in Fig. 5.

s( xi , x j ) =

N DC ( xi , x j ) + NVC ( xi , x j ) LenDC + LenVC

(18)

Fig. 5. Crossover operator

4.6. Mutation operator In addition, each offspring is assigned a small probability of mutation to improve the local search ability and diversity of the population with the probability Pm. With probability, randomly generate the mutation genes 17

sequence and then select new genes from the related gene domain.

4.7. New population After the above operations, the individuals in the previous step become a new population.

4.8. Pareto optimal solution When the stopping criterion is satisfied, output the Pareto optimal solution which provides the optimal strategy for selecting suppliers with considering the life cycle cost of CoPS.

5. Illustrative example and performance analysis To demonstrate the application of the proposed model and algorithm, the authors investigate the manufacturing

process

in

a

cement

equipment

company

located

in

Tianjin

of

China

(http://www.sinoma-tec.com.cn/en/default.aspx). The product in case company is large complex cement equipment for cement production line, such as preheater system, rotary kiln, stacker reclaimer, which is composed by dozens of key components with hundreds of manufacturing resources. As a service guarantee of equipment quality for customer, it is necessary to consider total cost cover phases of cement equipment manufacturing and operating. The component, material and process suppliers’ selection of complex cement equipment system of side reclaimer with 5 key components is simulated in this paper. Table 6 shows the components, materials and processes of the complex cement equipment. Table 7, Table 8 and Table 9 shows the suppliers of component, material and process in details. The life cycle parameters of cement equipment are shown in Table 10. The change of cement equipment reliability is adopted from (Ghasemi et al. 2007). The hazard function h0(t), representing the aging process, follows a Weibull distribution, and the equipment condition is given in an exponential form, which is given by Eq. (19) and (20).

h0 (t ) = λ t λ −1 / μ λ , t ≥ 0, λ = 2, μ = 1

(19)

ϕ ( R l ) = e0.5( R −1)

(20)

l

Table 6 The components, materials and processes of the cement equipment. Material composition Material code and numbers composition code 1 Tension rod 1 25 (3,5)(5,8) 1,3,5 2 Travelling mechanism 2 20 (1,3)(4,4)(5,6) 1,2,3,4,5 3 Beam 1 30 (2,5)(3,2)(4,7)(6,6) 1,2,5 4 Locomotive power 2 15 (1,2)(2,2)(3,5)(5,4) 1,2,4,5 5 Chain and scraper 3 30 (2,6)(4,6)(5,3)(6,8) 1,2,5 Table 7 The component suppliers’ information of unit price, reliability, transport price, distance for providing No.

Component Name

Number

Quantity

component. No. 1

Provided component 1,3,4,5

Unit price

Reliability

2528,3298,2622,3900

0.95,0.98,0.96,0.94 18

Transport price/(km/T) 15

Distance/Km 25

2 1,4,5 3200,2902,4200 0.98, 0.94,0.96 15 24 3 1,2,3,5 2492,2708,3190,5300 0.94,0.93,0.93,0.93 15 27 4 2 3200 0.92 15 26 5 2,4,5 4500,3100,3400 0.98,0.95,0.96 15 23 6 3,5 2900,3820 0.98,0.93 15 24 7 1,2,3,4 2300,2598,3192,2700 0.96,0.92,0.93,0.96 15 20 8 4,5 3040,3620 0.93,0.98 15 30 Table 8 The material suppliers’ information of unit price, transport price, distance for providing material. Provided Transport Unit price Distance/Km material price/(km/T) 1 1,2,4,6 160,130,160,138 15 24 2 1,5 155,179 15 29 3 1,2,3 145,131,120 15 20 4 1,4,6 145,165,136 15 21 5 3,5 169,182 15 21 6 2,5,6 140,167,140 15 24 7 3,4,5,6 162,139,195,142 15 29 8 3,6 158,120 15 28 9 1,2,4 168,150,146 15 20 10 2,4,5 164,132,129 15 24 Table 9 The process suppliers’ information of unit price, reliability, transport price, distance for providing process. No.

Provided Unit price Reliability process 1 2,3,4,5 125,176,180,137 0.94,0.96,0.94,0.93 2 1,3,4,5 145,169,165,120 0.95,0.92,0.97,0.97, 3 2,3,4,5 169,140,158,128 0.96,0.96,0.95,0.93 4 1,3 172,135 0.98,0.94 5 5 152 0.93 6 1,2,4,5 175,173,172,158 0.98,0.93,0.97,0.97 7 2,3,5 148,154,149 0.96,0.95,0.93 8 1,5 170,143 0.98,0.94 9 1,2,4,5 136,128,162,143 0.93,0.94,0.94,0.92 10 1,2 150,153 0.96,0.97 Table 10 The life cycle parameters of cement equipment. No.

Y/year 5

L/day 20

Cd 100

Cf 150

Cp 80

f1/hour 36

Transport price/(km/T) 15 15 15 15 15 15 15 15 15 15

Distance/Km 24 22 25 23 30 30 20 28 22 24

f2/hour 24

5.1. Computational outcomes The parameters of proposed MSCGA algorithm are population size, generation number, league size, crossover ratio and mutation ratio, which shown in Table 11 after running some pilot tests. The MSCGA algorithm has been coded in Matlab R2009b and run on a 2.6GHz Intel(R) Core(TM) i5-3230M CPU with 4G RAM in Windows 8 platform. After executing the MATLAB codes with input parameters, a Pareto optimal solution set is obtained. The Pareto optimal solution set includes 3 Pareto optimal solutions, and its distribution is as shown in Fig. 6. One of the Pareto optimal solutions is compared with the original solution of buying the finished component with lowest-price-based strategy shown in Table 12. It is evident that this solution is optimal to the original solution with reduction of the procurement cost drops from 86294 to 77083 (10.68% reduction) and operating cost drops from 3901 to 3825 (1.95% reduction). Table 11 The MSCGA algorithm parameters. 19

Population size 40

Generation number 100

League size 2

Crossover ratio 0.85

Mutation ratio 0.05

Fig. 6. The distribution of Pareto optimal solutions Table 12 Comparison between original and optimal solution. Original solution Pareto solution

Supplier scheme 7,3,6,7,5 7,7,1,5,1

Reduction

Procurement cost 86294 77083

Operating cost 3901 3825

10.68%↓

1.95%↓

5.2. Comparison experiment To demonstrate the effectiveness of MSCGA, the comparison experiment has been carried out with comparing the obtained results with that of Non-dominated Sorting Genetic Algorithm (NSGA-II) (Deb et al. 2002). NSGA-II is an effective multi-objective genetic algorithm in many continuous nonlinear optimization problems which is characterized by the elitism and the crowding distance to maintain the diversity of the population so that it can find as many Pareto optimal solutions as possible. The average values of the objective functions are employed as metric to illustrate the evolution process shown in Fig. 7.

Fig. 7. Evolution process of MSCGA and NSGA-II

Although the quality of the final solution obtained for both approaches is approximately equivalent for 20

engineering application, there is a slight difference among the optimal value returned by them. In a more precise way, the proposed MSCGA can find a better Pareto solutions (see Table 13) compared to NSGA-II. Table 13 Result comparison. Approach NSGA-II MSCGA

Average procurement cost 73000 70100

Average operating cost 4000 3910

Reduction

3.97%↓

2.25%↓

5.3. Managerial insights Among various supplier selection models, this paper proposed a LSS&CoPS model, which pays attention to minimize the life cycle cost of CoPS with the viewpoint of trade-off procurement cost and operating cost. The proposed mathematical model can be categorized as a straight rebuy strategy according to the supplier selection framework presented in De Boer, Labro, and Morlacchi (2001). As a result, various groups of supplier should be identified to support different processes, materials or components for a CoPS. In practice, medium-/long-term contracts should be made with the selected groups of suppliers for stable cooperation and quality assurance. According to the results of LSS&CoPS model, the Pareto optimal solutions might be varied to decrease the life cycle cost of CoPS and the decision-makers can select a supplier schema from Pareto optimal solutions by changing preferences in practice situation. Furthermore, if the required data is gathered as described in the previous section, the proposed model could be easily coded and applied by industrial/computer engineer who is familiar with operations research and optimization software like Matlab. Also, an expert system with user-friendly interface could be also designed to facilitate the proposed model by the non-expert personnel of the company’s purchasing department.

6. Conclusion and future work Procurement cost and operating cost are the major parts in CoPS’s lifecycle cost. It is highly desired to obtain the optimal supplier schema for minimum procurement cost and operating cost. To enhance the performance and efficiency of supplier selection with considering the life cycle cost, this paper proposed a bi-objective LSS&CoPS model to capture the procurement cost and operating cost risks for CoPS. In terms of the fact that minimization of procurement cost is not synonymous with minimization of operating cost, Pareto approach is applied to obtain the optimal solution set. So a novel MSCGA method is proposed to approximate the Pareto optimal solutions of the bi-objective supplier selection optimization problem. In this MSCGA method the dual-chromosome (DC and VC) is used to adjust the variable-length of individuals. Also, the MSC strategy is used to determine two selected individuals for crossover in a stochastic group with the highest similarity. The method is demonstrated with an example from a supplier selection for complex cement equipment in a cement equipment enterprise. Simulation results indicate that the results generated by the proposed MSCGA approach are better than those obtained by NSGA-II without MSC strategy. Moreover, if the manufacturing enterprises implement the method proposed in this paper, it will be able to consider operating cost of CoPS for customer in Pareto optimal solutions set. With this information, the company will 21

be able to make-decision and decrease CoPS’s lifecycle cost. Also as a direct result, supplier schema will improve the CoPS’s reliability level, the costumers’ satisfaction will increase and as well as the company’s revenues. In the aspect concerning the limitations of this research, it is important to notice that the Pareto supplier selection of CoPS is undertaken in the viewpoint of a manufacturer, whereas the CoPS’s life cycle involves costumer, designer, manufacturer, supplier and logistics provider. Mover, the reliability of providing components and processes are constant evaluation results for a selected supplier, while the reliability risk exists under a practical production system. Other points that can be cited here are the implementation of a single heuristic algorithm, and also the fact that an implementation of performance evaluation for CoPS’s supplier schema has not been done. Concerning the limitations of this research proposed in previous section, the suggestions for further research are listed as below: (1) Making decisions for supplier selection with multiple participants but not just manufacturing enterprise itself and tradeoff cost with multiple participants in CoPS’s lifecycle. (2) Combining the fuzzy approach into the proposed method to effectively determine the reliability of process, component, and CoPS. (3) Optimizing the supplier schema with variance of cost as an objective, the integrating optimization and simulation algorithm into a decision support system. (4) Evaluating the performance of CoPS’s supplier schema with fuzzy TOPSIS, fuzzy AHP, etc. from a systematic viewpoint. Acknowledgments: The authors are grateful for the valuable comments and suggestions by the respected reviewers, which have enhanced the strength and significance of this work. This research is financially supported by the National Nature Science Fund Project of China (71171154) and the Fundamental Research Funds for the Central Universities (2013-YB-021, 2014-IV-104, 2014-IV-016).

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Highlights • Consider supplier selection for minimum the life cycle cost of complex product system. • Develop Pareto solution approach for bi-objective optimization. • Conduct a case study to test the performances of the approaches. • Results show proposed approach outperforms for Pareto optimal solution searching.

26