Supplier Selection Problems with Considering E-business via Particle ...

Supplier Selection Problems with Considering E-business via Particle Swarm Optimization Supplier Selection Problems with Considering E-business Y.N. Wang

H.S. Wang

Z.H. Che

Department of Industrial Engineering and Management National Taipei University of Technology Taipei City, Taiwan R.O.C. e-mail: [email protected]

Department of Industrial Engineering and Management National Taipei University of Technology Taipei City, Taiwan R.O.C. e-mail: [email protected]

Department of Industrial Engineering and Management National Taipei University of Technology Taipei City, Taiwan R.O.C. e-mail: [email protected]

Abstract—In this paper, an optimal mathematical model was constructed to solve the supplier selection problems. The cost factors along with quantity discount policies are considered in the proposed problem. In addition, Ebusiness is taken as an important factor in the supplier appraisal. A Particle Swarm Optimization (PSO) approach is proposed for solving the mathematical model to figure out the suitable suppliers and appropriate quantity allocation of selected suppliers efficiently. Finally, a realistic case is proposed and analysis result shows that the quality solution can be obtained by applying the PSO approach.

Chain Management (SCM) plays an interfacing role in these activities. But, many research papers on ebusiness of supply chain focus on modal analysis and utilization [2, 3,4]. In an effort to improve the performance and competitive advantages of the entire supply chain, it is worthy to discuss the supplier selection model with the introduction of e-business. The research of Fukuyama [5] show that Particle Swarm Optimization(PSO) could address efficiently nonlinear continuous optimization and hybrid integer nonlinear optimization problems.

Keywords- supplier selection; quantity discount; Ebusiness; Particle Swarm Optimization

II. DEVELOPMENT OF ELECTRONIC EVALUATION MODEL

I.

INTRODUCTION

Cost factors were previously considered by enterprises as a major influential factor to the selection of suppliers. With the growing requirements on the quality, rapid response and service level, the purchasers place higher demands on the midstream and downstream suppliers, who have to supply top-quality materials on time at a reasonable price; so many factors have to be taken into account for the selection of suppliers. The applications of Information Technology (IT) contribute to save the cost and improve the productivity of the enterprises, as well as create absolute competitive advantages [1]. With the rapid development of the Internet and IT, e-business has become a key element to the competitive advantages, which involves logistics, cash flow and information flow, integration of electronic tools and technologies in the trading process. So, this paper also discusses ebusiness evaluation criterion in addition to cost considerations. In recent years, R&D, design, production, warehousing and marketing, etc., are prevailing across the world with the development of world-wide sales & marketing models. Thus, Supply

Step 1. Set up an electronic evaluation sheet in TABLE I, P j represents the suppliers, S represents k,s

the scores of degree[1,2,3,4,5], of which the secondary criterion j of electronic evaluation criterion has four items: k=A,B,C,D. Step 2. Classify the degree into 1~5 scores as listed in Table 2, a higher score means a higher degree. Step 3. Calculate the mean degree of evaluation items, I sj represents the mean degree of secondary evaluation criterion j of suppliers. B

A

I s1

=

∑ Pkj, s ，

k =1

A

s = 1,2,3" S

I s2

=

C

j

∑ Pk ,s ，

k =1

B

I s3

=

D

j

∑ Pk , s ， k =1 C

I s4

=

j

∑ Pk ,s

k =1

D

(1)

TABLE I. Criteria

ELECTRONIC EVALUATION SHEET Item

…

1. network bandwidth and speed 1. e2. system safety infrastructure construction ( P1 ) A. file recording AS

Supplier(S) 2 …. S 1 P1 P12 …. P1S1 1

11

1 1 …. 1 P21 P2S P22

…. 1 PA11 PA1 2 …. PAS

O sp, w

1. R&D of products

PC sp

…

TC sp

P113 P123 …. P1S3 3 3 …. 3 2. computer-aided design P21 P22 P2S 3. production …. ( P3 ) cS C. production process programming P 3 P 3 …. P 3 C1 C 2 CS 1. product demand planning

P114 P124 …. P1S4 4 P214 P224 …. P2S

…

4. marketing and 2. Sales order and processing transportation …. (P4 ) D. account checking (with clients) P 4 P 4 …. P 4 DS D2 D2 DS and payment mode TABLE II.

DEGREE OF E-COMMERCE

Scale Connotation Electronic system, with structural data form, automatic data 1 transfer among systems. Electronic system, with structural database form, transfer via 2 Internet or system. Electronic system, with structural database form, traditional 3 data transfer form. Computerized, without structural data form, such as: Word, 4 Excel files. 5 Not computerized, communication via telephone, fax or mails.

III. OPTIMIZED MATHEMATICAL MODEL Under the framework of a single product, multiple spare parts and multi-suppliers, this paper analyzes the supplier evaluation criterion covering the cost and degree of e-business. Given the quantity discount and capacity constraints, this author tried to optimize the allocation of the suppliers’ quantity to minimize the total cost. The mathematical model of this research is established below: Decision variables: Quantity of spare parts p purchased from QC sp the supplier s ⎧1 Y = 1,if supplier s employed Ys = ⎨ ⎩0 y sp

⎧1 =⎨ ⎩0

s

…

1. how to make an inquiry from 2 2 P11 P12 …. P1S2 suppliers 2. data transfer of suppliers’ raw P 2 P 2 …. P 2 21 22 2S 2. raw materials Materials purchase ( P 2 ) BS …. 2 B. account checking (with suppliers) P 2 PB22 …. PBS B1 and payment mode

Description of other symbols: S Index of suppliers, s = 1,2,3" S Index of parts, p = 1,2,3" P P Np Total number of required part p p Unit cost of part p of s − th supplier PRs Fs Fixed cost for employment of supplier s Fixed cost of feedstock generated when E sp delivering part p by supplier s Discount rate of part p of s − th supplier Dp

S

else 0 y sp = 1,if part p is provided by supplier s else 0

I si I 1s I s2

Ordering quantity required for the discount of part p of s − th supplier at phase w Unit purchase cost of part p of s − th supplier Unit transportation cost of part p of s − th supplier Degree of e-business evaluation index I of supplier s Mean degree of e-infrastructure construction of supplier s

ITs

Mean degree of e-purchase of supplier s Mean degree of e-manufacturing of supplier s Mean degree of e-transportation& marketing of supplier s Mean degree of e-business of supplier s

OH sp

Min. capacity of product p of supplier s

OLsp

Max. capacity of product p of supplier

IT Z

Mean degree of e-business of supplier Production cost after T

t

E-business after T

I s3 I s4

t

I ⎧1 ⎩0

μw ⎨

s

u w = 1 ,quantity is at w discount stage

else 0 Due to different units of evaluation criterion in this model, T-score technology was used for conversion [6] to obtain a minimized multi-target mathematical mode, with the target function (2) shown below (2) minimize t Z + t I (1) Cost The fixed cost, purchase cost and transportation cost are considered: S

S P

S P

s =1

s =1 p =1

s =1 p =1

Z = ∑ Fs × Ys + ∑ ∑ y sp × E sp + ∑ ∑ (QCsp × PC sp + QCsp × TC sp )

(3) The price of spare parts is expressed in Eq. (4):

S

(4)

P

PC sp = ∑ ∑ PR sp × Dsp s =1 p =1

⎧D p ⎪ sp,0 ⎪ Ds ,1 ⎪ p ⎪ Ds ,2 p Ds = ⎨ ⎪ ⎪ ⎪ ⎪D p ⎩ s, w

，

O sp,0 ≤ QC sp < Osp,1

，

Osp,1 ≤ QC sp < O sp, 2

(5)

， Osp,2 ≤ QC sp < Osp,3 ‧ ‧ ‧ ‧ ‧ ‧ ， Osp,w ≤ QC sp

p = 1,2,3" P

s = 1,2,3" S

0 < Dsp,w < Dsp,w−1 < Dsp,w−2 < ..... < Dsp,0 < 1 Where,

DSP,0

represents original price of part

p

(6)

from supplier s

(2) E-Business Degree E-business degree was divided into four secondary criterion: e-infrastructure construction, e-purchase, emanufacturing and e-marketing /transportation. S 4 (7) I = ∑ ∑ IWsi × I si s =1i =1

S.T. ordering quantity must meet the capacity constraints of the suppliers p = 1,2,3" P s = 1,2,3" S OLPs ≤ QC sp ≤ OH sp (8) Meeting the demand constraints of individual stocks S (9) ∑ QC sp ≥ N p s =1

The suppliers’ e-business degree must be higher than the mean level, otherwise, they will be removed from the list of candidate suppliers. (10) IT S ≥ IT s = 1,2,3" S S

∑ ITs

IT =

(11)

s =1

S

Check if suppliers have purchased any spare part, if yes, 1, otherwise, 0 Ys ∈ {0,1} s = 1,2,3" S If part p is supplied by supplier s, 1, otherwise, 0 (12) (13) y sp ∈ {0,1} p = 1,2,3" P s = 1,2,3" S (14) p = 1,2,3" P s = 1,2,3" S QC p ≥ 0 s

IV. PSO-SOLVING APPROACH Particle Swarm Optimization (PSO), initiated by Eberhart and Kemmedy [7], is an optimization method based on the flying of birds. During particle swarm optimization, every particle will exchange previous experience, and enable the others to fly to fetch food along a shorter path, this is referred to as wisdom of groups. PSO is an algorithm for multi-dimensional searching in the space, and used to solve many optimization tasks. Thanks to rapid convergence

capability, it is well suited for resolving multiple target programming issues [8]. The iterative searching process of PSO is to decide the shift direction of every particle according to Pbest (Particle best value) and Gbest (Global best value). As such, the particle swarm could gradually approach to their target positions in the space, with the steps below: Step 1: Generate initial solution randomly in ndimension space, which contains the position and speed of every particle. The range needs to fit the constraint equations (8) - (10), which are substituted into target function Eq. (2) to obtain optimal function value. Step 2: The particle memorizes best position of individuals according to the fitness value and best value (Pbest) obtained from target function Eq. (2), so as to amend the particle speed in next searching. Step 3: If Pbest is superior to Gbest, gbest is memorized as current pbest; meanwhile, every particle amends the particle speed in next searching according to gbest. Step 4: Apply the Inertia Weight Method developed by Eberhart and Shi [9] to update the current position of every particle. vid = w ∗ vid + C1 ∗ rand () ∗ ( p id − xid ) + C 2 ∗ rand () ∗ ( p gd − xid )

(15) (16)

xid = xid + vid

Where Eqs. (15) and (16) represent the updated speed and position of Inertia Weight Method, Eq. (15) updates the speed according to previous optimal position of various particles (Pbest) and the current optimal position (Gbest). Eq. (16) calculates the updated position by adding the current position and updated speed, w represents inertia weight. Step 5: Stop, if the stop condition is met, otherwise, return to Step2. Step 6: Stop Condition: Find out Global Optimal or reach maximum number of generations. V. CASE STUDY To verify the research methods in this paper, the display of a notebook computer was used to describe a single product and multi-part framework, with the BOM sheet shown in Figure 1. It is hypothesized that various suppliers consider the quantity discount, and every spare part of this framework is supplied by a group of suppliers with different purchase quantities. The purchase policy could be implemented successfully through a combination of suppliers and allocation of different quantities.

3 0 0 4 0 0 5 0 0 6 1250 0 7 250 250 Optimal fitness=26.55122

0 0 0 0 0

0 0 0 1250 250

0 0 0 0 0

0 0 0 250 1250

Figure 1. BOM of production

It is hypothesized that the required quantity is 1500, so the total demand of spare parts is 1500 according to BOM. The evaluation criterion is based on the cost and e-business degree. In addition, optimal combinations of parameters are found out experimentally. Thirty experiments were conducted separately based on the research results of Shi and Eberhart [9], i.e.: learning factors C1 = C 2 = 2 , number of particles (20, 30, 40), Vmax (1.0, 1.5, 2.0) and number of generations (500, 1000, 2000), with the mean optimal fitness value listed in TABLE III. The experimental results indicate that, the optimal particle combination is: number of particles 40, Vmax 1.5, number of generations 1000. So, this case is solved by this optimal parameter combination PSO, with the final combination of suppliers and allocation of quantities listed in TABLE IV, and convergence of target functions shown in Figure 2. TABLE III. Particle number 20

30

40

TEST DATA

Generation Vmax 1 1.5 2 1 1.5 2 1 1.5 2

500

1000

2000

72.54 61.84 66.85 75.86 63.87 76.86 51.45 66.85 50.86

66.48 60.13 60.14 65.15 66.48 66.16 60.8 48.16 53.84

72.16 65.16 73.41 60.84 55.94 54.15 68.68 68.91 56.56

GenerationObject value

Convergence graph of objective function 110 90 70 50 30 10 1

119 237 355 473 591 709 827 945 Generation

Figure 2. Convergence chart of target functions

VI. CONCLUSION The enterprises often share information, methods and plans with their partners through e-business integration. So, the e-business degree is considered as an important indicator for selection of suppliers, and more specifically, electronic factors are taken into account to reduce information and data transfer problems among organizations, cut down the cost and improve the performance efficiently. Meanwhile, the capacity constraints of suppliers are considered to allocate the demands, minimize uncertain factors and improve the stability of sources of goods. Finally, PSO is used to quickly obtain the combination of suppliers and allocation of quantities in line with purchase policies, thus assisting the decision-makers in developing purchase packages. REFERENCES [1] R. Palmer, “There’s no business like e-business”, Qualitative Market Research, vol. 5, no. 4, 2002, pp. 261–267. [2] J. Dilworth and A.K. Kochhar, “Creation of an e-business requirements specification model”, Journal of Manufacturing Technology Management, vol. 18, no. 6, 2007, pp. 659-677. [3] M. Webster, R. Beach, and I. Fouweather, “E-business strategy development: An FMCG sector case study”, Supply Chain Management., vol. 11, no. 4, 2006, pp. 353-362.

TABLE IV.

Supplier 1 2

COMBINATION OF SUPPLIERS AND ALLOCATION OF QUANTITIES A 1500 0 0

B 1500 0 1250

C 1500 500 1000

D 1500 0 0

E 1500 500 1000

F 1500 0 0

[4] C. Dubelaar, A. Sohal, and V. Savic, “Benefits, impediments and critical success factors in B2C”, E-business adoption Technovation, vol. 25, no. 11, 2005, pp. 1251-1262.

[5] Y. Fukuyama and H. Yoshida, “A particle swarm optimization for reactive power and voltage control in electric power systems”, in Congress Evolutionary Computation, vol. 1, 2001, pp. 87-93. [6] H.S. Wang and Z.H.Che, “An integrated model for supplier selection decisions in configuration changes”, Expert System. Application., vol. 32, 2007, pp. 1132-1140. [7] R.C. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory”, in Proc. Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, pp. 39-43.

[8] K.E. Parsopoulos. and M.N Vrahatis, “Particle swarm optimization method in multi objective problems”, ACM symposium on applied computing, 2002, pp. 603–607. [9] R.C. Eberhart and Y. Shi, “Comparison between genetic algorithms and particle swarm optimization”, in Proc. Seventh Annual Conference on Evolutionary Programming, San Diego, 1998, pp. 611-616.