Decisions for a three-echelon supply chain with logistics outsourcing under a dominant retailer

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31 2 2016 4 JOURNAL OF SYSTEMS ENGINEERING Vol.31 No.2 Apr. 2016 1,2, 1,2, 1,2, 1,2, 1,2 (1., 400044; 2., 400044) :,.,,., 3, ;, ;. : ; 3 ; ; : F224 : A : 1000 5781(2016)02 0254 14 doi: 10.13383/j.cnki.jse.2016.02.011 Decisions for a three-echelon supply chain with logistics outsourcing under a dominant retailer Chen Xiaoxu 1,2, Wang Yong 1,2, Sun Hailei 1,2, Chen Zhangyue 1,2, Wang Yili 1,2 (1. School of Economics and Business Administration, Chongqing University, Chongqing 400044, China; 2. Chongqing Key Laboratory of Logistics, Chognqing University, Chognqing 400044, China) Abstract: When the retailer s order quantity is sensitive to the manufacture s wholesale price and the 3PL s service price simultaneously, a supply chain model dominated by retailer with logistics outsourcing is built. The optimal prices and order quantity are acquired by using game theory. Furthermore, the impact of the two sensitivity coefficients, the demand range and the allocation ratio of logistics cost on the decision variables are analyzed. Results show that the retailer can inhibit the manufacturer and 3PL to raise their prices and increase his profit, by controlling the two sensitivity coefficients. As the demand changes, all supply chain members decisions and profits increase or decrease simultaneously. Moreover, the one who bears the ratio of the logistics fee more gets more profit. Key words: retailer dominanting; the third party logistics provider; supply chain; game equilibrium 1, 3 (3PL) [1]., 42% 3PL,, 70% [2]. : 2013 09 05; : 2014 07 21. : (70872123; 71272085); (12YJA630135); (CQKLL12002).

2 : 255 500 80% 3PL [3],, 3PL [4 6]., [7],, 2013 500 4 691.62, 2013-11-11 350.19.,,,, 3PL., ; 3PL,.,. 21,,, 3, 3PL 3.,, 3. Cai [8] 3PL 3,, WMC WDC ; Woo [9] 3, 3PL,,, ; Chen [10] 3PL,, 3PL,, 3PL, 3PL ; [11] 3,, 3 ; [12] 3,,, ; Lei [13], EOQ,, 3.,,. Wang [14], ; Pan [15],,, ; [16], ; [17],,,, Prateo, ; [18] 3 (, 3 ),.,.,.,, 3PL ( ), 3PL, 3PL 3., 3PL.,

256 31. 2 2.1 3PL 3,,, 3PL,. [19], [20, 21], 3PL q = q 0 αw βs, q 0, α > 0,β > 0 w 3PL s., 3PL,. ( 3PL), 3PL,, 3PL. : 1),,, ; 2) 3PL, ; 3) 3PL, 3PL, 3PL ; 4) [I 1,I 2 ](0 < I 1 < I 2 ), µ,σ, I 1 = µ 3σ,I2 = µ + 3σ; 5) 3PL ; 6). : d( ), d > 0 f( ),F( ); v 3PL ; c ; p ; θ 1 (0 θ 1 1) ; θ 2 (0 θ 2 1) ( θ 1 + θ 2 = 1 ); k r ; k m ; k l 3PL ; : q 0 ; q ; w ; s 3PL ;

2 : 257,, pd (w + θ 1 s)(q 0 αw βs) k r, d q π r = (p w θ 1 s)(q 0 αw βs) k r, d > q., d q,,,,, ( ), ;, d > q,,. ( ),. E[π r ] = (p w θ 1 s)(q 0 αw βs) k r p q 0 (q 0 αw βs x)f(x) dx. (1), w,, 3PL., π m = (w c θ 2 s)(q 0 αw βs) k m. (2),, 3PL. s., 3PL, π l = (s v)(q 0 αw βs) k l. (3) q 0 w, 3PL, q 0 w 3PL s, q = q 0 αw βs., (, 3PL ). 1, q 0 ; 2, w ; 3, 3PL s 3PL ;, q = q 0 αw βs., Max E[π r ] = (p w θ 1 s)(q 0 αw βs) k r p q (q q 0 0 αw βs x)f(x) dx 0 s.t. Max π m = (w c θ 2 s)(q 0 αw βs) k m w Max π l = (s v)(q 0 αw βs) k l. s 2.2 3PL 3PL, 3, 3PL (3),, (3) s 1 2 π l s = q 0 αw 2βs + βv, (4)

258 31 2 π l = 2β. (5) s2 β > 0, 2 π l < 0,, (4), 3PL s2 s = q 0 αw + βv. (6) 2β 2.3, (2), (6) (2), w 1 2 π m w = β2 v + (q 0 + αc 2αw)β θ 2 α(αw q 0 ), (7) 2β 2 π m w = 2αβ + θ 2α 2. (8) 2 2β 2 π m w 2 < 0,, (7), w = β(q 0 + αc βv) + θ 2 αq 0. (9) α(2β + θ 2 α) 2.4 (1) A1 0 = 6σ(2c + pθ 2 + 2vθ2 2 )α 2 + (p + 2vθ 2 vθ 1 )βα + 2vβ 2 3pαβ + 12σ((θ1 + 2θ 2 )α + 2β) q + ( 3pcαβ + 3pvαβθ 2 )α + vβ 2 + 4µβ. (10) 3pαβ + 12σ((θ1 + 2θ 2 )α + 2β) 2.5 3, θ 1 = 1 θ 2. (10) q0,, q0 w., 3PL q0 w s., q0, w s. A2 3p((c + w θ2 v)β + 2µθ 2 )α + 2µβ + 6σα(2θ2 2 v + θ 2 p + 2c) = 7 + 3αβp + 12((1 + θ2 )α + 2β)σ 6σβ(2c + 4θ 2 v + p 2v) 3αβp + 12((1 + θ2 )α + 2β)σ, (11) s = 3pα(vβ + µ) + 3σ((p + 2(2θ2 + 1)v 2c)α + 4vβ), (12) 3αβp + 12((1 + θ2 )α + 2β)σ q = αβ( 3pµ 3(2v + 2c p)σ) 3αβp + 12((1 + θ2 )α + 2β)σ. (13) q > 0,, 3pµ 3(2v + 2c p)σ > 0. (14) (14),

2 : 259 p > 2(v + c), (14),,,,,. p < 2(v + c),, (14), µ 3(2v + 2c p) σ >. p,,, ( ),,,,.,,, µ > 3(2v + 2c p)σ/p,., α 3PL β, σ θ 2, 1. 1 α,, 3PL,. α. A3. 1,,,, 3PL,. α,,,,, α,., 3PL,, 3PL, 3PL, 3PL, ;. 3PL,, 3PL. 2 3PL β, 3PL,, σ > pαθ 2 4,, σ < pαθ 2 3θ 1 4, 3θ 1. β 3PL,. A4. 2 3PL,,, 3PL,,,, ;,.,. β, 3PL,,, 3PL, β 3PL, 3PL,.,,,,, ;,,., β. 3 σ,, 3PL. 1 θ 1 = 1 θ 2,, θ 2, θ 2.

260 31 A5. 3,, 3PL. p < 2(v + c), 2,, µ > 0 (µ, ), µ > (p 2v 2c)βα/(4α(1 + θ 2 ) + 8β).,,,,,,, 3PL,,,. p > 2(v + c), 2,,,,. (p 2v 2c)βα µ > 4α(1 + θ 2 ) + 8β,,,,,, 3PL,. (p 2v 2c)βα µ < 4α(1 + θ 2 ) + 8β,,,,,,,,,,,. 3PL,, 3PL,,.,. ( ) ( ), 3PL ; ( ), 3PL. 4 θ 2, 3PL,, p + (2θ 2 2 + 4θ 2 )v 2c > 0,. A6. 4, 3PL,. p + (2θ 2 2 + 4θ 2 )v 2c > 0, p > 2c (2θ 2 2 + 4θ 2 )v,. p > 2c (2θ 2 2 + 4θ 2)v,,,., θ 2,,. 3PL,, θ 2.,,. 3, q = q 0 αw βs, α β,. σ θ 2.

i 2 : 261 α β σ θ 2,. c = 15,v = 5,p = 50,k m = 100,k l = 50,k r = 100, U[100,300], I 1 = 100,I 2 = 300,µ = (I 1 + I 2 )/2 = 200,σ = (I 2 I 1 ) 2 /12 = 100/ 3,θ 1 = 0.5,θ 2 = 0.5,α = 50,β = 50. π. 2, 1,, 1. 3.1, α. 1, α,,,. 1.,. α,,,,,. 1, α,, 3PL. 3PL,, α 50 60, 25.96 25.29 = 0.67, 7.92 7.82 = 0.10,,,.,,., α,. Table 1 1 α The effects of the sensitivity coefficient α to the supply chain members decisions 50.00 1 830.13 7.82 25.96 141.03 60.00 2 059.29 7.92 25.29 146.02 70.00 2 283.95 8.00 24.78 149.81 80.00 2 505.56 8.06 24.38 152.78 90.00 2 725.00 8.10 24.05 155.17 100.00 2 942.86 8.14 23.79 157.14 3 0 0 0 2 5 0 0 2 0 0 0 π 1 5 0 0 1 0 0 0 πl π m π r 5 0 0 0 5 0 6 0 7 0 8 0 9 0 1 0 0 1 α α Fig. 1 The effects of the sensitivity coefficient α to the supply chain members profits 3.2 3PL, β. σ = 100 < pαθ 2 3 4 = 625, 3θ 1 3 2, β,,,. 2. 2

i 262 31,. β,,,. 2, β,, 3PL.,,,, ;,,,, ;, 3PL., β,,, β 3PL. Table 2 2 β The effects of the sensitivity coefficient β to the supply chain members decisions 50.00 1 830.13 7.82 25.96 141.03 60.00 1 874.56 7.41 25.70 144.74 70.00 1 920.40 7.11 25.51 147.51 80.00 1 967.18 6.87 25.36 149.66 90.00 2 014.60 6.68 25.24 151.38 100.00 2 062.50 6.53 25.14 152.78 3 0 0 0 2 5 0 0 2 0 0 0 π 1 5 0 0 1 0 0 0 πl π m π r 5 0 0 0 5 0 6 0 7 0 8 0 9 0 1 0 0 2 β β Fig. 2 The effects of the sensitivity coefficient β to the supply chain members profits 3.3 Table 3 3 σ The effects of the risk parameter σ to the supply chain members decisions 100/ 3 1 830.13 7.82 25.96 141.03 120/ 3 1 794.86 7.68 25.54 133.97 140/ 3 1 764.01 7.56 25.17 127.80 160/ 3 1 736.81 7.45 24.84 122.36 180/ 3 1 712.65 7.35 24.55 117.53 200/ 3 1 691.04 7.26 24.29 113.21, σ. σ,,. 3, σ,. (p 2v 2c)βα 3, p = 50 > 2(v+c) = 40, ( ), µ = 200 > 4α(1 + θ 2 ) + 8β = 250 7,,,. 3PL. 3,, 3PL

i i 0 0 2 : 263.,, 3PL, 3PL,,,. 3 0 0 0 2 5 0 0 2 0 0 0 πl π m π r π 1 5 0 0 1 0 0 0 5 0 0 3 6 0 7 0 8 0 9 0 1 0 0 1 1 0 σ σ Fig. 3 The effects of the risk parameter σ to the supply chain members profits 3.4, θ 2. 4 4. Table 4 4 θ 2 The effects of the ratio of logistics fee he manufacture bears θ 2 to the supply chain members decisions 0.00 1 594.59 7.97 20.95 148.65 0.10 1 642.65 7.94 21.97 147.06 0.20 1 690.21 7.91 22.98 145.50 0.30 1 737.30 7.88 23.99 143.98 0.40 1 783.94 7.85 24.98 142.49 0.50 1 830.13 7.82 25.96 141.03 0.60 1 875.89 7.79 26.93 139.59 0.70 1 921.23 7.76 27.90 138.19 0.80 1 966.17 7.74 28.85 136.82 0.90 2 010.71 7.71 29.80 135.47 1.00 2 054.88 7.68 30.73 134.15 3 0 0 0 2 5 0 0 2 0 0 0 π 1 5 0 0 1 0 0 0 πl π m π r 5 0 0 0 0. 2 0. 4 0. 6 0. 8 1 θ2 4 θ 2 Fig. 4 The effects of the ratio of logistics fee he manufacture bears θ 2 to the supply chain members profits

264 31 4, θ 2,,, θ 2 [0, 1], 2c (2θ 2 2 + 4θ 2)v = 30 5(2θ 2 2 + 4θ 2) 30 < p = 50,, 4. 4, θ 2 3PL,.,.,,,.,,. 3PL,,. 4 3PL, 3PL,,.,, 3PL,, ;,. [12],,, 3PL.,,,,., 3PL. : [1] Basligil H, Kara S S, Alcan P, et al. A distribution network optimization problem for third party logistics service providers. Expert Systems with Applications, 2011, 38(10): 12730 12738. [2] Li F C, Li L, Jin C X, et al. A 3PL supplier selection model based on fuzzy sets. Computers & Operations Research, 2012, 39(8): 1879 1884. [3] Lieb R, Bentz B A. The use of 3PL services by large American manufacturers: The 2004 survey. Transportation Journal, 2005, 44(2): 5 15. [4] Tian Y, Ellinger A E, Chen H Z. Third-party logistics provider customer orientation and customer firm logistics improvement in China. International Journal of Physical Distribution & Logistics Management, 2010, 40(5): 356 376. [5] Rajesh R, Pugazhendhi S, Ganesh K, et al. Influence of 3PL service offerings on client performance in India. Transportation Research: Part E, 2011, 47(2): 149 165. [6] Sohail M S, Sohal A S. The use of third party logistics services: A Malaysian perspective. Technovation, 2003, 23(5): 401 408. [7] Raju J, Zhang Z J. Channel coordination in the presence of a dominant retailer. Marketing Science, 2005, 24(2): 254 262. [8] Cai X Q, Chen J, Xiao Y B, et al. Fresh-product supply chain management with logistics outsourcing. Omega: The International Journal of Management Science, 2013, 4(41): 752 765. [9] Woo H S, Saghiri S. Order assignment considering buyer, third-party logistics provider, and suppliers. International Journal of Production Economics, 2011, 130(2): 144 152. [10] Chen X F, Cai G S. Joint logistics and financial services by a 3PL firm. European Journal of Operational Research, 2011, 214(3): 579 587. [11],.., 2012, 26(3): 42 49. Gong Y D, Li B Y. Analysis of supply chain decisions, stability and efficiency based on dominant mode. Journal of Industrial Engineering and Engineering Management, 2012, 26(3): 42 49. (in Chinese)

2 : 265 [12],,.., 2011, 26(1): 39 49. Gong Y D, Li B Y, Liu T. Model for closed-loop supply chain based on the loading ratio of logistics cost. Journal of Systems Engineering, 2011, 26(1): 39 49. (in Chinese) [13] Lei L, Wang Q, Fan C. Optimal business policies for a supplier-transporter-buyer channel with a price-sensitive demand. Journal of the Operational Research Society, 2006, 57(3): 281 289. [14] Wang J C, Lau A H L, Lau H S. Practical and effective contracts for the dominant retailer of a newsvendor product with price-sensitive demand. International Journal of Production Economics, 2012, 138(1): 46 54. [15] Pan K W, Lai K K, Liang L, et al. Two-period pricing and ordering policy for the dominant retailer in a two-echelon supply chain with demand uncertainty. Omega: The International Journal of Management Science, 2009, 37(4): 919 929. [16],,,.., 2013, 27(1): 171 175. Zhao J S, Duan Y R, Wang S J, et al. Performance comparative study in dual-distribution channel drop shipping supply chain based on different dominant positions. Journal of Industrial Engineering and Engineering Management, 2013, 27(1): 171 175. (in Chinese) [17],,. Downside risk., 2012, 20(1): 117 122. Chen J H, Zhang Y Q, Shi C D. Study on risk sharing contract design of retailer-leading supply chain with downside risk control. Chinese Journal of Management Science, 2012, 20(1): 117 122. (in Chinese) [18],,.., 2011, 19(5): 29 36. Wang W B, Da Q L, Nie R. The study on pricing and coordination of closed loop supply chain considering channel power structure. Chinese Journal of Management Science, 2011, 19(5): 29 36. (in Chinese) [19] Dobson P W, Clarke R, Davies S, et al. Buyer power and its impact on competition in the food retail distribution sector of the European Union. Journal of Industry, Competition and Trade, 2001, 1(3): 247 281. [20] Hunt S, Nevin J. Power in a channel of distribution: sources and consequences. Journal of Marketing Research, 1974, 11(5): 186 193. [21] El-Ansary A I, Stern L W. Power measurement in the distribution channel. Journal of Marketing Research, 1972, 9(2): 47 52. : (1988 ),,,, :, Email: chenxiaoxu cxx@126.com; (1957 ),,,,,, :, Email: wangyongkt@163.com; (1982 ),,,, :, Email: sunhailei007@163.com; (1976 ),,,, :, Email: chzhyue@163.com; (1983 ),,,, :, Email: wangyili1015@163.com. A1 (10) A2 (1), (6) (9) (1), q 0 1 2, E[π r] = ( 3pα(((c + θ2v)β + 2µθ 2)α + 12(vβ q 0 + 4µ)β) + 12σ((θ 2 2 v + (c + p 2 )θ2 + θ1c)α2 ))β q 0 24(2β + θ 2α) 2 + ασ 2 E[π r] q 2 0 2 E[π r] q 2 0 (((p + 2 vθ 2 θ 1v)β q 0 (θ 1 + 2θ 2))α + 2vβ 2 2βq 0 )σβ 2(2β + θ 2α) 2, ασ = ( 3pα β + ((12 θ 1 + 24θ 2)α + 24β)σ)β. 24(2 β + θ 2α) 2 α σ < 0,, E[πr] q 0 = 0, (10).. (11) (13), (10) (9) (11)., (10) (11) (6) 3PL (12)., (10) (12) q = q 0 αw βs (13).. A3 1

266 31 (14), s α = 24( 3pµ 3σ(2v + 2c p))σβ ( 3pα β + 12σ((θ 2 + 1)α + 2 β)) 2 > 0, q α = 24( 3pµ 3σ(2v + 2c p))σβ 2 ( 3pαβ + 12σ((θ 2 + 1)α + 2 β)) 2 > 0, w α = (( 6β p + 12(v + c)β + 24 µ(θ 2 1)) 3pσ 72(2v p + 2c)(θ2 1)σ 2 6 p 2 µβ)β ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2 G = 1 β ( 3pα β + 12 σ(αθ 2 + α + 2 β)) 2. G 1 = ( 6β p + 12(v + c)β + 24 µ(θ 2 1)) 3pσ 72(2v p + 2c)(θ 2 1)σ 2 6 p 2 µβ = 24(θ 2 1)σ( 3pµ 3(2v p + 2c)σ) 2 3βp( 3pµ 3(2v p + 2c)σ) = (24(θ 2 1)σ 2 3βp)( 3pµ 3(2v + 2c p)σ) = (24(1 θ 2 )σ + 2 3βp)( 3pµ 3(2v + 2c p)σ) < 0. w α < 0.. A4 2 (14) 3pµ 3(2v + 2c p)σ > 0, s 3pα + 24σ)( 3pµ 3(2v + 2c p)σ)α β = ( ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2 < 0, q β = 12(1 + θ 2)( 3pµ 3(2v + 2c p)σ)σα 2 ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2 > 0, w β = ((( 6α p + 12(v + c)α)θ 2 24 µ(θ 2 1)) 3pσ + 72(2v + 2c p)(θ2 1)σ 2 6 p 2 µαθ 2 )α ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2 = G 2 α ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2, G 2 = (( 6α p + 12(v + c)α)θ 2 24 µ(θ 2 1)) 3pσ + 72(2v + 2c p)(θ 2 1)σ 2 6 p 2 µαθ 2 = 24(θ 2 1)σ( 3pµ 3(2v p + 2c)σ) 2 3αpθ 2 ( 3pµ 3(2v p + 2c)σ) = ( 24(θ 2 1)σ 2 3αpθ 2 )( 3pµ 3(2v + 2c p)σ) = 2 3(4 3(1 θ 2 )σ αpθ 2 )( 3pµ 3(2v + 2c p)σ). 4 αpθ 3(1 θ 2 )σ αpθ 2 > 0, σ > 2 4 3(1 θ 2 ) = αpθ 2 4, G 2 > 0, w 3θ 1 β > 0; 4 3(1 θ 2 )σ αpθ 2 < 0, σ < αpθ 2 4 3(1 θ 2 ) = αpθ 2 4, G 2 < 0, w 3θ 1 β < 0.. A5 3 G 3 = ((2v p + 2c)β + 4 µ(θ 2 + 1))α + 8 µβ, q0 σ = 6 3(2 β + α θ2 )α pg 3 ( 3pαβ + 12 σ(α θ 2 + α + 2 β)) 2, w σ = 6 3(β + α θ2 ) pg 3 ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2, s σ = 3 3αpG3 ( 3pαβ + 12 σ(αθ 2 + α + 2 β)) 2,

2 : 267 q σ = 3 3αβpG3 ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2. Q σ A6 G 3 > 0, µ > > 0, w σ > 0, s σ 4 (p 2v 2c)βα 4α(1 + θ 2 ) + 8β > 0, q σ > 0., q 0 σ < 0, w σ (14), s = 12( 3pµ 3(2v + 2c p)σ)σα 2 θ 2 ( 3pα β + 12 σ(αθ 2 + α + 2 β)) 2 < 0, < 0, s σ q < 0, σ < 0; G (p 2v 2c)βα 3 < 0, µ < 4α(1 + θ 2 ) + 8β, q = 12( 3pµ 3(2v + 2c p)σ)σβα 2 θ 2 ( 3pα β + 12 σ(α θ 2 + α + 2 β)) 2 < 0, q0 = 6 3pσα 2 ((p + (2 + 4θ 2 )v 2c)αβ + 8vβ 2 + 4µα) + 72σ 2 α(p + (2θ2 2 + 4θ 2 )v 2c) θ 2 ( 3pαβ + 12 σ(αθ 2 + α + 2 β)) 2 + 3p 2 α 3 β(βv + 2µ) + 576σ 2 αβv((1 + θ 2 )α + β) ( 3pαβ + 12 σ(α θ 2 + α + 2 β)) 2, w = 6 3pσα((p + (2 + 4θ2 )v 2c)αβ + 8vβ 2 + 4µ(β + α 2 )) + 72σ 2 α 2 (p + (2θ2 2 + 4θ 2 )v 2c) θ 2 ( 3pαβ + 12 σ(αθ 2 + α + 2 β)) 2 + 72αβσ 2 (p + (6 + 8θ 2 )v 2c) + 3p 2 α 2 β(βv + 2µ) + 576σ 2 β 2 v ( 3pα β + 12 σ(αθ 2 + α + 2 β)) 2., p + (2θ2 2 + 4θ 2)v 2c > 0, p + (2θ2 2 + 4θ 2)v 2c (p + (2 + 4θ 2 )v 2c) = 2(1 θ2 2 )v 0, p + (2 + 4θ 2 )v 2c (p + (6 + 8θ 2 )v 2c) = (4 + 4θ 2 )v < 0, p + (2 + 4θ 2 )v 2c > 0, p + (6 + 8θ 2 )v 2c > 0, q 0 > 0, w > 0.. θ 2 θ 2.