Research on selecting the sale channel model of the information goods

28 203 2 JOURNAL OF SYSTEMS ENGINEERING Vol.28 No. Feb. 203,2,, (., 300072; 2., 30034) :,,., Fixed-fee Per-copy.,.,,., Fixed-fee,, Per-copy.,,. : Stackelberg : F49 : A : 000 578(203)0 009 0 Research on selecting the sale channel model of the information goods Liu Zhiyong,2, Li Minqiang, Kou Jisong (. College of Management and Economics, Tianjin University, Tianjin 300072, China; 2. Business School, Tianjin University of Commerce, Tianjin 30034, China ) Abstract: The information goods manufacturer can distribute their products through many kinds of channels, e.g. online direct sale and traditional retail marketing. The retailer pays a manufacturer based on two common payment schemes, the Fixed-fee policy and the Per-copy policy. Which channel and sell model is preferable for the manufacture? The product quality, the price, and the customer acceptance for direct channel are the decisive factors. Through analyzing the decision behaviors of the manufacture, retailer and consumer, the model of maximizing the manufacture s profit is presented in the presence of both direct and retail channel. Based on the comparison among different channels, the paper shows that when the valuation for the information goods has a uniform distribution, the manufacture prefers the Fixed-fee policy through the direct sale channel, whereas the Per-copy policy is preferable through dual-channel. The best sale channel strategy is to distribute the highquality version through the direct sale channel and the low-quality version through the retailing channel for the manufacturer. Key words: information goods; supply chain; Stackelberg game; dual-channel., : 20 08 3; : 202 03 29. : (70925005).

0 28, [].,..,., Kindle. 2009 2 3.5.. itunes 50,.3, 40.,,..,. [2 4].,,.,,,..,. :,. 2.,,. Chiang.,,,. [5]. Cai, 4, (R) (D) && (RD) 2(RR). [6]., Dumrongsiri,,.,,, [7].,,., Khouja.,,, [8]. Hua,.,.,, [9].,..,,..,, ( ),

:.. 3,.,,. x, x X. p r x... Stackelberg, Stackelberg.,,.,,,.,,,..., (Brick & Mortor),.,,. (Click & Mortor) [0].,...,, x, p r.,,, c(x).. u(v)., u(v) = vx, u(v) = vx p, v,, x, p ( p r, p d ).,, f( ), F ( ). F ( ) = F ( ).,.,, q Pr{v p r x }, F { p r x }.,,. 4, Fixed-fee, R,,. Per-copy, x, rx. Chellappa,., Per-copy, Fixed-fee [].,, Per-copy Fixed-fee,. 4. Fixed-fee, Π m = Rx C, C,. : Π r = q r p r b r x 2 /2 Rx, q, b r x 2 /2, [7], b r,,.,,..

2 28 Per-copy, x 2, rx 2, Π m = q r2 rx 2 C. Π r = q r2 p r2 b r x 2 2/2 q r2 rx 2. Stackelberg,, Π r = 0, p r Π r = 0, Fixed-fee ( ()) Per-copy ( (2)) x. t t = F (t ) f(t ). 5 F (t 2 ) + f (t 2 ) t 2 t 2 = 3f(t 2 ) + f (t 2 ) 4.2 [ ] 2 F (t2) f(t 2) [ F (t2) f(t 2) Π m = t4 f 2 (t ) 4b r Π r = t4 f 2 (t ) 8b r R = t2 f(t ) 2 x = t2 f(t ) 2b r, Π m = F ( 3 (t 2 ) t 2 F ) (t 2 ) b r f(t 2 ) f(t 2 ) Π r = F 4 (t 2 ) 2b r f 2 (t 2 ) r = t 2 F (t 2 ) f(t 2 ) x 2 = F 2 (t 2 ) b r f(t 2 ), ].. θv, θ [2]. θ =,.,,,,. θ., u d = θvx p d, p d. b 2 dx d 2, b d. q d. q d =Pr{θvx p d 0}. (3). t 3 t 3 = F (t 3 ) f(t 3 ). 4.3 Π d m = θ2 t 4 3f 2 (t3) 2b d x 2 = θt2 3f(t 3 ) b d,, v [0, ]., () (2) (3)

: 3,. Table Direct sale vs. retail marketing Fixed-fee Per-copy θ 2 8b d r = 4 R = 8 45 52b 6b θ 9 4b d 64b 8b 3 2 8 2 θ 2 27 32b d 2048b 64b 8 892b 28b,.,., Fixed-fee,., Per-copy., Fixed-fee,,, Per-copy,, 3/8., Fixed-fee., 2. 2, : ) =, x d >, p r = p d, Πm r = Πm d., ; 2) = x d, p r p d, Πm r Πm d,, ; 3), θ θ. 2bd b r. b d 5.,,., u d = θvx d p d, u r = v p r, v = p r p d,, v > v,, v < v, =, p r = p d ( v p r v p d, =, p r p d,, ).,. α, β, α + β =., >, p r > p d ( p r p d, (v p r ) (v p d ), ),, p r p d p d, p r > p d q d = 0,, q r = p r p d, p r > p d p r,.

4 28, <, p r < p d ( p r p d, (v p r ) (v p d ), ),, p r p d, p r < p d p r p d x q d = r θx p r, p r < p d d p q r = d,. 0,. θ,. (v 2 v ) ; (v v ) ; (v v v 2 ).. 5. Fixed-fee Fig. Segmentation of consumer Fixed-fee.,.. w, w, w. Fixed-fee, 2.. Table 2 2 Fixed-fee Solution of the dual-channel model based on Fixed-fee policy < > = (wθ) 2 (wθ ) 2 2(4wθ 3) 2 (b d w 2 +2b r) (w θ) 2 w 4 2(2w θ) 4 (b d w 2 +2b r) θ 2 32(b d +2b rθ 2 ) b r(wθ) 2 (wθ ) 2 n rw 6 (w θ) 2 b rθ 4 2(4wθ 3) 2 (b d w 2 +2b r) 2 2(2w θ) 4 (b d +2b rw 2 ) 2 32(b d +2b rθ 2 ) 2 wθ(wθ ) w(w θ)(4w+θ) θ 2 (4wθ 3)(2b r+b d w 2 ) 4(4w 3θ)(b d +2b rw 2 ) 4(b d +2b r) 2wθ 2 α 0 4wθ 3 2 wθ w β 4wθ 3 2w θ 2,,. b d = b r = b, 2, 3 4. 3,,,.,..,. ( = ),,,. 4,, <,,,.. 3/4. [ ]. 2wθ a) v 4wθ 3, ; 2 b d = b r, θ 2,. θ..

78 6789 89 22 227889 622 522 3 : 5 [ wθ b) v 4wθ 3, 2wθ ] ; [ 4wθ 3 c) v 0, wθ ]. 4wθ 3, Fixed-fee. 5,. θ,.,., θ =, 2, 3,,,,.,.0 2 Fixed-fee Fig. 2 The supplier s profit under the dual-channel model based on Fixed-fee policy0 3 Fixed-fee Fig. 3 The retailer s profit under the dual-channel model based on Fixed-fee 53 63 43 04 5.2 Per-copy Per-copy 3. 2. Table 3 3 Per-copy Solution of the dual-channel model based on Per-copy policy < > = (θw) 2 32(4b r+b d w 2 ) b r(θw) 2 32(4b r+b d w 2 ) 2 wθ(wθ ) (4wθ 3)(2b r+b d w 2 ) 4b r(wθ )+b d (wθ )w 2 (8b r+2b d w 2 )(wθ ) br(wθ )(4br+b d w 2 ) (8b r+2b d w 2 )(wθ ) b rwθ 2 b r(wθ )(4b r+b d w 2 ) ( 28w 2 (b d +4b rw 2 ) 3 ) 2b d θw + 5b rθw 3 + 3b rw 4 + brw 4 (w θ)(4b d θ + b rw 2 (7θ + 9w)) ( 2b d θw b rθw 3 + 9b rw 4 + 3 b rw 4 (w θ)(4b d θ + b rw 2 (7θ + 9w)) 4 3br(w θ)w+ br(w θ)(4b d θ + b rw 2 w 2 (7θ + 9w)) 52b r(w θ) 2 (b d +4b rw 2 ) 4 2b dθw b rθw 3 + 9b rw 4 + 3 b rw 4 (w θ)(4b d θ + b rw 2 (7θ + 9w)) 6 27( α)b rθ ) 32(b 2 d ( α)+2b r(2 α)θ 2 ) 3 8( α) 2 3 b r θ 8 32(b d ( α)+2b r(2 α)θ 2 ) 4 9( α)b rθ 4 8(b d +4b rw 2 ) 2 4(b d ( α)+2b r(2 α)θ 2 ) 2 2b d(w θ)w + 5b r(w θ)w 3 br(w θ)w 4 (4b d θ + b rw 2 (7θ + 9w)) 4(w θ)w(b d +4b rw 2 ) 3br(w θ)w3 + br(w θ)w 4 (4b d θ + b rw 2 (7θ + 9w)) 4(w θ)w(b d +4b rw 2 ) 3αb rθ 2 2(b d ( α)+2b r(2 α)θ 2 ) 3βb rθ 2 2(b d ( α)+2b r(2 α)θ 2 )

89 8 789 722 22 4769 023 04536 0 7889 622 5422 3 0 30 6 28 Per-copy, b d = b r = b, ( 4 5), w.8,,.. 4 Fig. 4 The supplier s profit based on Per-copy policy0 5 Fig. 5 The retailer s profit based on Per-copy, Fixed-fee Per-copy,,,. 5.3 Fixed-fee Per-copy,,,,.,, Fixed-fee Per-copy, θ =. ( 6 7), < θx 3 d,, Per-copy Fixed-fee, Per-copy,. 4 6 w 4 + 6, Fixed-fee, Per-copy. 6 < x d Fig. 6 The supplier s profit (Fixed-fee vs. Per-copy)0 0435 223 0 7 < x d Fig. 7 The retailer s profit (Fixed-fee vs. Per-copy) 65,, Per-copy,,,,. 3,,.

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8 28 2 3 Fixed-fee Fixed-fee,. ) < :Π m = q p d b d x 2 d /2 + R C :Π r = q 2 p r b rx 2 r /2 R q = pr p d p d x d pr < p d p d p r θx, q 2 = d 0 pr pr < p d. w = x d, w θ. t = p d, t 2 = p r., Π r / = 0, Π r / t 2 = x d 0, t 2 = t /(2θ), = 4Rθ + t 2 w 4Rθ 2 w. t 2,, t = 2θ(wθ ) 4wθ 3 2) > q = 4b r θ(wθ ), R = wθ(wθ )(b dw 2 + b r (5 4wθ)) (4wθ 3) 2, = (2b r + b d w 2 ) { pr p d p d 0 pr > p d, q 2 = { pr p d pr wθ(wθ ) (4wθ 3)(2b r + b d w 2 ). pr > p d = wx d, w θ. t = p d, t 2 = p r., Π r / = 0, Π r / t 2 = 0, x d t 2 = t θ + w, = t 2 + 2t (w θ) + (w θ)(θ + ( 4R)w) wθ θ2. q 0, t 2w 4b r θ(w θ) 2w θ. wθ θ2 t = k, 0 k., 2w θ R = (w θ)(b d((k )θ + 2w) 2 b r w 2 (( k 2 )θ 2 4( k 2 )wθ + 4w 2 )) 4(2w θ) 2. w(b d + 2b r w 2 ), k =. (w θ) 2 w 4 Π m = 2(2w θ) 4 (b d + 2b r w 2 ), Π b r w 6 (w θ) 2 r = 2(2w θ) 4 (b d + 2b r w 2 ) 2. 3) =,. p r = p d, t = p r. α, β, α + β =. Π m = b r θ 4 Π r = 32(b d + 2b r θ 2 ) 2. Fixed-fee. 2 Per-copy. θ 2 32(b d + 2b r θ 2 ), Per-copy., Stackelberg,,,,..