Addendum to: Dual Sales Channel Management with Service Competition

Size: px

Start display at page:

Download "Addendum to: Dual Sales Channel Management with Service Competition"

Leonard Cain
6 years ago
Views:

1 Addendum to: Dual Sales Channel Management with Service Competition Kay-Yut Chen Murat Kaya Özalp Özer Management Science & Engineering, Stanford University, Stanford, CA. December, Single-Channel Analysis The analysis in Chen, Kaya and Özer (006) (henceforth, the paper ) assumes that the manufacturer already has dual sales channels: a direct online channel, and an independent bricks-and-mortar retail channel. In this section, we study two single channel scenarios, and compare their results with the dual channel scenario results of the paper. First, we consider a manufacturer who sells only through a retail channel. By comparing the results of this scenario with the results of the dual channel scenario, we quantify the benefits of the direct channel to the manufacturer. The manufacturer can compare the benefits with the associated costs in deciding whether to open a direct channel. We also address the retailer s concern about the effects of the direct channel on his profit (See, for example, Tsay and Agrawal 004) by quantifying the impact of the direct channel on the retailer s profit. Some researchers, studying price competition, have found that the direct channel can be used as a tool to influence the retailer s pricing decision (Chiang, Chhhajed and Hess 003). Along the same lines, we address whether the manufacturer can use the direct channel to influence the retailer s service level decision. Second, we consider a manufacturer who sells only through his direct channel. By comparing the results of this scenario with the results of the dual channel scenario, we quantify the benefits of the retail channel to the manufacturer. 1.1 Retail Channel Only Consider a manufacturer who sells only through a bricks-and-mortar retail channel. The retailer s problem is similar to a newsvendor problem with a minimum service level constraint. 1

2 We obtain the retailer s profit function by setting t in Equation 6 in the paper. The retailer s problem is ( max Π r (α) = aα p w p α ), α subject to α [α min, 1]. { } Solving this problem, the retailer sets 1 α p w = max, α p min. Anticipating the retailer s strategy, the manufacturer chooses between two strategies as we present in the following proposition. Proposition 1 In the retail-channel-only scenario, the manufacturer chooses between two strategies depending on whether (p c) ( + )pα min holds, as follows. Condition (p c) ( + )pα min (p c) < ( + )pα min Manufacturer s Strategy Share profit Capture all profit p+c Wholesale price w p(1 α min ) p c Retailer s service level α α p min a(p c) ( Manufacturer s exp. profit Π m (w) aα 4p min p c pα min ) Retailer s exp. profit Π r (α) a(p c) 8p 0 { } p w Proof: The retailer chooses α = max, α p min. The retailer s minimum service level constraint is binding (that is, p w < α p min ) for w > w b p (1 α min ). Thus, the retailer s service level decision is { p w α p (w) =, for w wb Case-U (U for unconstrained), α min, for w > w b Case-C (C for constrained). Anticipating the retailer s strategy, the manufacturer may choose to induce Case-U or Case-C by offering an appropriate wholesale price. The manufacturer s problem is { } max max Π u w w b m, max Π c w>w b m subject to Π r 0. To induce Case-U, the manufacturer s objective function is max w w b Π u m = q(w c) = aα(1 d 1 )(w c) = aα(w c) = a p ( w + w(p + c) cp), because we have d 1 = 0 when there is no direct channel. This function is maximized at w u = p+c, for which the retailer sets α ( p+c ) = p c. The maximizer p wu satisfies the Case-U condition w w b for (p c) 1 Note that the retailer s decision is similar to his reaction in the dual channel scenario, when the manufacturer shuts down the direct channel. See Corollary 1 in the paper.

3 pα min. In that case, we have Π u m = a(p c) and Π u 4p r = aα ( ) p w p α = a(p c) > 0. If 8p w u > w b, then we check the boundary solution w b = p (1 α min ), in which case we have Π b m = aα min (p (1 α min ) c) and Π b r = ap (α min) > 0. To induce Case-C, the manufacturer s objective function is max Π c w>w b m = aα min (w c). The manufacturer chooses the wholesale price for which the constraint Π r 0 binds. From Π r = α min a ( p w p α min ) = 0, we find w c = p ( 1 α min ) which satisfies the Case-C ) ) c and condition w > w b. With this wholesale price, we have Π c m = aα min ( p ( 1 α min Π c r = 0. The manufacturer compares his expected profit under Case-U and Case-C. For (p c) ( pα min, the manufacturer chooses Case-U if (p c) α 4p min p c pα min ) holds (because we have Π u m > Π c m ); otherwise, he chooses Case-C. Conditions (p c) pα min and (p c) 4p ) together are equivalent to (p c) ( + )pαmin. For ( α min p c pα min (p c) < pα min, the manufacturer chooses Case-C because Π b m < Π c m. 1. Direct Channel Only Consider a manufacturer who sells only through his direct online channel. Solving the manufacturer s problem, we find that the manufacturer chooses between two strategies, depending on the relation between the cost of the direct channel (i.e. the direct channel cost parameter m) and the size of the market (i.e. the maximum total demand parameter a). If the ratio m/a is below a threshold, the direct channel cost is low relative to the potential market size. In this case, the manufacturer s optimal strategy is to cover the whole consumer population with the direct channel. The manufacturer sets a relatively short delivery lead time, for which all consumers buy from the direct channel. If the ratio m/a is above a threshold, the direct channel cost is high relative to the potential market size. In this case, the manufacturer covers the consumer population partially, by setting a relatively longer delivery lead time. The impatient consumers (i.e. consumers with high time sensitivity index d) will not buy the product. The following proposition summarizes the solution. Proposition The manufacturer chooses to cover all consumers for a product that has low direct channel cost relative to potential market size (that is, a low ratio m/a); whereas, he chooses to cover the consumer population partially for a relatively costly product. The manufacturer s optimal delivery lead time choice and his expected profit are as follows. Recall that the total demand is distributed uniformly between 0 and a. 3

4 Relative Cost Direct Channel (m/a) Condition Coverage t Π m(t) m Low cost (p c)a Full Coverage v p a 4 m High cost 4m Partial Coverage a 4 (p c)(v p)a m (v p) a (p c) (v p) 16m Proof: The manufacturer s problem is max Π m (t) = (p c)e[dd 1 + t D d ] m. Substituting t E[Dd 1+D d ] from Lemma 3 of the paper, and using α = 0 (because there is no retail channel), we have Π m (t) = (p c) a d m t. Using the d definition in Equation 4 of the paper, the manufacturer s profit function becomes { Π f Π m (t) = m(t) (p c) a m, for t v p (full coverage), t Π p m(t) (p c) a v p m, for t > v p (partial coverage). t t The full coverage profit function Π p m(t) is maximized at t f = v p, which results in profit Π f m (t f ) = (p c)a m (v p). The manufacturer does not set t < v p because t = v p is sufficient to cover all consumers. The partial coverage profit function Π p m(t) is maximized at t p 4m =, which results (p c)(v p)a in profit Π p m (t p ) = (p c) (v p) a. If m (p c)(v p), then t p v p, hence, t p is feasible. 16m a 4 In this case, t = t p because Π p m (t p ) Π f m (t f ). If m < (p c)(v p), then t p < v p, and hence, t p is not feasible. In this case, t = t f a 4 because Π p m(t) is unimodal, and because Π f m(t) = Π f m(t) and Πp m(t) < 0 hold at t = v p. t For t = v p, all consumers derive positive utility from the direct channel, hence consider buying from it. Decreasing the delivery lead time further does not provide any benefit to the manufacturer. 1.3 Comparisons With the Dual Channel Scenario Here, we compare the profit levels and the service levels in the singe-channel scenarios with the dual channel scenario. The comparisons are based on the numerical study that we outline in Section 5 of the paper. We solve the dual channel and the two single channel models with 43 parameter combinations spanning the parameter space. We illustrate the discussion through the results of a representative parameter set as presented in Tables 1 and Profit Comparison First, we compare the dual channel scenario with the retail-channel-only scenario to assess the effects of the manufacturer opening a direct channel. We determine that the retailer s 4

5 concern about the direct channel is valid. The retailer s profit generally 3 decreases with the introduction of the direct channel, whereas the manufacturer s profit increases. The sum of the manufacturer s and the retailer s profits, however, also increases with the dual channel strategy. This finding suggests that the manufacturer can achieve a mutually beneficial outcome by sharing the gains due to the dual channel strategy with the retailer. Table 1 illustrates the profit comparisons for the sample parameter set. Second, we find that the manufacturer s profit in the the dual channel scenario is higher than his profit in the direct-channel-only scenario as well, which signals the strategic importance of the retail channel. Dual Retailer s Profit Manufacturer s Profit Total Profit k Chn. Dual Retailer Dual Retailer Direct Dual Retailer Eql. Channel Only Channel Only Only Channel Only 0.00 ER ER SP SP SP CP CP Table 1: Profit Comparison, where m = 10000, v = 8, p = 4, c = 1, a = Service Level Comparison One may expect the retailer to increase his service level in response to competition from the direct channel. That would make the direct channel a strategic tool; by creating it, the manufacturer can induce the retailer to improve his service level. However, this intuition turns out to be wrong. We find in our numerical study that the retailer sets a lower service level in the dual channel scenario than in the retail-channel-only scenario 4. The primary reason behind the retailer s lower service level is that the manufacturer charges a higher wholesale price in the dual channel scenario 5. Table illustrates the service level and wholesale price comparisons for the sample parameter set. 3 The exceptions are the cases in which the retail-only scenario results in a capture-all-profit type equilibrium whereas the dual channel scenario does not. See the row with k =.5 in Table 1. 4 Again the exceptions are the cases in which the retailer-only scenario results in a capture-all-profit type equilibrium whereas the dual channel scenario does not. See the row with k =.5 in Table. 5 This finding contrasts Chiang, Chhajed and Hess (003), who report that the manufacturer charges a lower wholesale price in the dual channel scenario. Unlike us, however, they study price competition. 5

6 The manufacturer also provides lower service (longer delivery lead time) in the dual channel scenario than in the direct-channel-only scenario. In the dual channel scenario, the manufacturer s marginal return on his direct channel investment is diluted by the retailer s existence; hence, the manufacturer does not have an incentive to provide as high service. In addition, the manufacturer may not prefer to harm his retailer by being a tough competitor. After all, the retailer also sells the manufacturer s product. Dual Wholesale Price w Service Level α Delivery Lead Time t k Channel Dual Retailer Dual Retailer Dual Direct Eql. Channel Only Channel Only Channel Only 0.00 ER ER SP SP SP CP CP Table : Decision Variables Comparison, where m = 10000, v = 8, p = 4, c = 1, a = Conclusion In this section, we study two single channel scenarios, and compare their results with the dual channel scenario results from Chen, Kaya and Özer (006). By studying the retail-channelonly scenario, we find how the introduction of the direct channel affects the manufacturer and the retailer in a traditional manufacturer-retailer supply chain. We show that the retailer s concern regarding the manufacturer s direct channel is valid. The dual channel strategy allows the manufacturer to increase his profit at the expense of the retailer s profit. The direct channel, however, increases the total profits of the manufacturer and the retailer as well, suggesting the possibility of a mutually beneficial outcome. We also determine that competition from the direct channel causes the retailer to decrease his service level to consumers. Hence, the direct channel does not function as a strategic tool to induce the retailer to offer higher service level (i.e., stock more products). By studying the direct-channel-only scenario, we determine that the manufacturer prefers the dual channel setting to the direct-channel-only setting as well. This finding indicates the strategic importance of the retail channel for the manufacturer. We also find that the manufacturer offers longer delivery lead times (lower service) in his direct channel when where is no competing retail channel. 6

7 . The Numerical Analysis and Results In this section, we provide details on our numerical analysis and results. The numerical results are based on an algorithm that we have developed to find the manufacturer s optimal wholesale price and the Nash Equilibrium of the operational decisions game. To cover the parameter space, we choose low, medium and high values for each parameter 6, as illustrated in Table 3. Thus, we solve the model for 3 5 = 43 parameter combinations that correspond to various dual channel environments. Parameter Low Value Medium Value High Value m v p/v k/(v p) c/p Table 3: Parameter Values Table 4 shows the outcome of the manufacturer s optimal solution for sample parameter combinations. As indicated in the rightmost column, we observe three types of equilibria. The full 43 results are presented in Table 6. Table 5 illustrates the optimal strategy we find for different m and k values. Figure 3 in the paper is based on this table. Table 7 presents the numerical study results on which this table is based. 6 We use the relative values p v, k v p and c p because the values of p, k and c are constrained by the conditions p < v, k v p, and c < p. We keep the maximum market size parameter fixed at a = 1000, without loss of generality. 7

8 Parameters Decision Variables Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type ER ER ER CP CP CP SP SP SP d 1 (α ) 1 hence q = 0 Table 4: Sample Results m \ k SP SP SP SP SP SP SP SP SP SP CP CP CP CP SP SP SP SP SP SP SP SP SP SP CP CP CP CP SP SP SP SP SP SP SP SP SP SP CP CP CP CP 1500 SP SP SP SP SP SP SP SP SP SP CP CP CP CP ER ER ER ER SP SP SP SP SP SP CP CP CP CP 7500 ER ER ER ER ER ER ER ER ER SP CP CP CP CP 5000 ER ER ER ER ER ER ER ER ER ER ER ER ER CP 500 ER ER ER ER ER ER ER ER ER ER ER ER ER ER 0 ER ER ER ER ER ER ER ER ER ER ER ER ER ER Table 5: Manufacturer s Optimal Channel Strategy, when v = 8, p = 4, c = 1 Table 6, Part of 6 Parameters Decision Vrbs. Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER

9 Table 6: The Numerical Experiments to Span the Parameter Space Table 6, Part 1 of 6 Parameters Decision Vrbs. Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type ER ER ER ER ER CP CP CP CP ER ER SP ER ER CP CP CP CP SP SP SP SP SP CP CP CP CP ER ER ER ER ER ER ER ER ER ER ER ER ER 9

10 Table 6, Part 3 of 6 Parameters Decision Vrbs. Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type ER SP SP SP SP SP CP CP CP CP SP SP SP SP SP CP CP CP CP SP SP SP SP SP CP CP CP CP ER ER ER ER ER ER ER ER CP ER ER ER 10

11 Table 6, Part 4 of 6 Parameters Decision Vrbs. Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type ER ER ER ER ER CP SP SP SP SP SP CP CP CP CP ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER 11

12 Table 6, Part 5 of 6 Parameters Decision Vrbs. Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type ER ER SP SP SP SP SP CP CP CP CP SP SP SP SP SP CP CP CP CP SP SP SP SP SP CP CP CP CP ER ER SP ER SP CP CP CP CP ER ER 1

13 Table 6, Part 6 of 6 Parameters Decision Vrbs. Profits Sales Eql. m v p k c w t α Π m Π r Direct Retail Lost Type SP SP SP CP CP CP CP SP SP SP SP SP CP CP CP CP ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER SP ER ER CP CP CP CP 13

14 Table 7: Dual Channel Strategy in the m/k Plane Table 7, Part 1 of 4 Parameters Decision Variables Profits Sales Eql. m k w t α Π m Π r Direct Retail Lost Type ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER ER 14

15 Table 7, Part of 4 Parameters Decision Variables Profits Sales Eql. m k w t α Π m Π r Direct Retail Lost Type ER ER ER ER ER ER CP CP CP ER ER ER ER ER ER ER ER ER SP CP CP CP CP CP CP ER ER ER ER SP SP SP SP SP SP CP CP CP CP CP 15

16 Table 7, Part 3 of 4 Parameters Decision Variables Profits Sales Eql. m k w t α Π m Π r Direct Retail Lost Type CP SP SP SP SP SP SP SP SP SP SP CP CP CP CP CP CP SP SP SP SP SP SP SP SP SP SP CP CP CP CP CP CP SP SP SP SP SP SP SP 16

17 Table 7, Part 4 of 4 Parameters Decision Variables Profits Sales Eql. m k w t α Π m Π r Direct Retail Lost Type SP SP SP CP CP CP CP CP CP SP SP SP SP SP SP SP SP SP SP CP CP CP CP CP CP 17

18 References Chiang, W. K., D. Chhajed, J. D. Hess Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design. Management Science 49(1) 1 0. Chen, K., M. Kaya, Ö. Özer Dual sales channel management with service competition. To appear in Manufacturing & Service Operations Management. Tsay, A. A., N. Agrawal Modeling conflict and coordination in multi-channel distribution systems: A review. D. Simchi-Levi, D. Wu, M. Shen, eds. Forthcoming in Supply Chain Analysis in the ebusiness Era. Kluwer Academic Publishers, Norwell, MA. 18

Design Patent Damages under Sequential Innovation

Design Patent Damages under Sequential Innovation Yongmin Chen and David Sappington University of Colorado and University of Florida February 2016 1 / 32 1. Introduction Patent policy: patent protection