NEWPRODUCTDESIGN_省略_HSUBSIDYPOLICIES_.docx

J Syst Sci Syst Eng (Sep 2012)21(3): 356-371 DOI: 10.1007/sll518-0125199-9 ISSN; 1004-3756 (Paper) 1861-9576 (Online) CN11-2983/N NEW PRODUCT DESIGN STRATEGIES WITH SUBSIDY POLICIES Xuemei ZHANG1 Xiaoyan XU2 Ping HE3 School of Management, University of Science 0), where kt and ke are scalar cost coefficients and ke> kt >0 (Garvin 1988). Considering customer differences regarding environmental awareness, the firm has three options of product design strategy: introducing only an ordinary product for the two market segments; introducing a green product and an ordinary product for the green and ordinary market segments, respectively; or introducing only a green product for the green market segment. It should be noted that to simplify our analysis, though comer solutions may exist, we will focus our attention on the interior solutions throughout thispaper (i.e.， kt > max /2 + (1 - y)ve fly and ke > max0,(ve -vt)jl so that all the qualities are nonnegative and not greater than 1). Because of the technological constraint of conflicting attributes, when the firm increases the level of traditional quality, the level of the environmental quality is decreased. The firms objective is to find the products with the quality combinations that maximize its profit. However, the optimal product design strategy may not benefit the environment. In the following, we show how the firm should make its product design decisions and then investigate improvements in total environmental quality through a subsidy policy. 3. Optimal Product Design Strategy Assume that given the information about production costs and customer preferences, a firm must determine optimal product design strategy as well as the corresponding quality levels and retail prices. In this section, we present a firms product design decisions and discuss the optimal product design strategy. Specifically, we are interested in the total environmental quality and whether the optimal product design strategy most benefits the environment. Denote by n profit of the firm from selling products. Adding superscript “1， ” “2， ” “3， ” and to variables represents optimal values of these variables under the three product design strategies. 3.1 Decisions under Each Product Design Strategy 1) One ordinary product for the two market segments max 7t = N(p - ktqf - keq2 e) UP S.t. vtqt p>0, (i) p,qnqe >0. Solving problem (1)， we have 2kevt 2(kt+ke)， qt 2(kke)9 j* 2 :2(k t+ke). And then, the optimal profit under this 362 Zhang et al,: New Product Design Strategies with Subsidy Policies J Syst Sci Syst Eng strategy is i* N(yj +4kevt-4ktke ) n = - 4(ktke) 2) Ordinary and green products for the two market segments max Jt = yN(p0 - k,qf - keqf) + -Y)Npg-ktqf2-keqf) s.t. vtq-po>0, vtqf + v gqf-pg>0, v,qf -pg, (2) vtqf + veqg e pg> vtq° + veq°e - pa, p， q»g， qf， qg e 1 Solving problem (2), we have Pf = v,， P2g = + ve o 2 * _ K +Vt +(1 r)/'v g _ 2(kr+ke) ， ol* = 2 -v, -(1 _， )/， ve e 一 2(k,+ke) , 2* = 2ke+vt-ve ' 2(k t+ke) qf* = Ik, -vf +ve 2(k,+ke) And then, the optimal profit under this strategy is nv _ YNv t+-Y)lr-ve f 4(kt+ke) r(i - r)/r -Kve + k,K - Kvt k， +K ,O-rWjiv, ve)2 +4k evt +4ktve-4ktke Hkl+ke) ' segment max 7T = -y)Np-ktqf -keq) HP * s.t. vtq, + veqg -/?>0, d h Solving problem (3), we have P 3* 2ktve+2kevt +(vtve)2 2(kt+ke ) ， 2ke+v,-ve 3» _ -v,+vg 2(kl+ke) 5 He 2(k,+ke) (3) And then, the optimal profit under this strategy is 疋 3* _ -ve)2 +4k,ve +4kevt-4k,k e 4(冬 + 3.2 Optimal Product Design Strategy Based on the analytical results obtained above, we can investigate the optimal product design strategy. By comparing the firms profits, we obtain the following theorem, which describes the method of deciding optimal product design strategy: Theorem 1 If M > N , then 7t2* > max7T *,7T3* , Le., the strategy of introducing two products for the two market segments is optimal; if M TT2* > f i.e.t the strategy of introducing a green product only for the green market segment is optimal; if M = N， then 7T2* 二 7T3* > W， i.e.， the strategy of introducing two products for the two market segments or introducing the green product only for the green market segment is optimal， 3) One green product only for the green market fVhere, M =(vt+(l /)/ve)2， Zhang et al.: New Product Design Strategies mth Subsidy Policies J Syst Sci Syst Eng 363 N = 4(-y)/yktve+Aktke-4kevt, Theorem 1 indicates that the optimal product design strategy depends on production cost-coefficient parameters, demand parameters, and customers' marginal valuation parameters. From Theorem 1 ? we can determine that the firm will not introduce only the ordinary product for the two market segments. For the product design strategy, the firm will choose between introducing two products for the two market segments and introducing the green product only for the green market segment. That is because the firm must set a lower price when it introduces an ordinary product for the two market segments to ensure nonnegative valuation of purchasing the product among the ordinary customers. 3.3 Can the Optimal Product Design Strategy Benefit the Environment? To investigate whether the optimal product design strategy most benefits the environment, we calculated the total environmental quality defined by Chen (2001). The total environmental quality is defined as the aggregate sum of the environmental quality specified for all products in the market. The index of total environmental quality represents animprovement of environmental quality or reduction in environmental damage as a result of the use of all products sold by the firm. Denote by TEQ1 (? = 1,2,3 ) the total environmental quality. According to the green quality obtained above, we have 卿 1、 H、 ), TEQ = , 2(k t+ke) 2(kt +ke) 卜卿 v,+ve)_ 2(kt+ke) Comparing the total environmental qualities under the three product design strategies obviously gives Proposition 1 TEQ'* = TEQ2* > TEQ?. Proposition 1 indicates that the total environmental quality is not improved as a result of green product development* Because a green product is introduced to the green market segment, the total environmental quality is improved by (l-y)Nve/2(k t +k) compared with that of introducing one ordinary product for the two market segments. To prevent green customers from switching to the ordinary product, the environmental quality of the ordinary product is decreased according to (l-y)/y-ve/2(k t +ke), Thus, the improvement of environmental quality from the green product is negated by the degradation of environmental quality from the ordinary product by the same amount, and the total environmental quality does not increase, i.eM TEQ1* = TEQ2*. In addition, the total environmental quality when introducing one green product for the green market segment is lower than that of introducing two products for the two market segments. The environmental quality of the green product under the second strategy is equal to that of the product under the third strategy, but the ordinary product also includes environmental quality. Theorem 1 and Proposition 1 indicate that the firm chooses the optimal product design strategy by maximizing its profit, and it may introduce only the green product for the two market segments or both the green product and the ordinary product for the two market segments; however, the optimal product design strategy does not always most benefit the 364 Zhang et al.: New Product Design Strategies with Subsidy Policies J Syst Sci Syst Eng environment. In terms of environmental protection, the firm should adopt the strategy of introducing ordinary and green products for the ordinary and green market segments, respectively. These results can provide direction for government policy making, i.e., to protect the environment, governments should introduce appropriate policies to force firms to develop both green products and ordinary products for the two market segments. 4. Impact of a Subsidy Policy Optimal product design strategy does not necessarily benefit the environment; however, this situation can be remedied by environmental policies, such as a subsidy policy (Toshimitsu 2010, Shin & Kim 2010), tax policy (Bansal & Gangopadhyay 2003)， or standards environmental policy (Chen 2001). Chen (2001) found that the standards environmental policy improved the total environmental quality, but that it decreased the firms profits and represented a danger zone. In the present paper, we evaluate the impact of a subsidy policy on product design decisions by simultaneously considering environmental issues and firms benefits. Let s ( > 0) be a subsidy rate for the total environmental quality. Denote by ns profit of the firm and add a superscript “s” to the variables representing this case. 1) One ordinary product for the two market segments mzx 7T = Np-ktqf _keql) + sNqe 'P s.t. vtqt-p>0f Vl0, (6) P 。 之 v l f P g ' + Ve qt+=l Solving problem (6), we have P 2.'、 抓 ， TEQ1*, Tt > nl* y TEQS* = TEQ2s* > TEQis*, i = 1,2,3 . | (l-y)N(v t-ve-s)2 4( +ke) | (1 - y)Nkte + kevt + kts-ktke) kt +ke TEQ is* = N(2k t - v t + s ) 一 2(kt+ke) 3) One green product only for the green market segment max = (1 - y)N(p - k,qf - keq2 e) + s-y)Nqe s.t. vtqt+veqe-pg>0, (7) d1， Proposition 2 indicates that the subsidy policy can improve the total environmental quality and increase the firms optimal profit. We also find that the strategy of introducing ordinary and green products for the two market segments most benefits the environment. This proposition can provide a guide for governments in making effective environmental policies. By comparing the optimal profits, we have the following theorem: Theorem 2 If 5 > max 0,4, the strategy of introducing two products for the two market segments is optimal. Where, Pg， q”qe n Solving this problem, we have 3s* = 2ktve + 2kevt + ( v f - v e )vt -Ve-s) 2(kt+ke) 2ke+vt -ve -s 2kt +ke )， is* = 2kt-vt+ve+s 2(kt+ke ). And then, the firms optimal profit and total environmental quality under this strategy are as follows: -ve sf Mk, +ke) | (1 - y)N(ktve + kevt + k,s -ktke) kt +ke A = 2 k t - v t ) (k +ke )- 2kt +vt + (l -y )v e /y . Theorem 2 indicates that when the subsidy rate 5 satisfies s > max 0,4， with the subsidy policy, the firm always adopts the strategy of introducing two products for the two market segments; it never employs the strategy of introducing the green product only for the green market segment. In this way, the total environmental quality is highest. This also provides a method for governments to make environmental policy according to market demand and production cost-coefficient parameters. Combining Proposition 2 and Theorem 2, we find that under the subsidy policy, the firm 366 Zhang et alt： New Product Design Strategies with Subsidy Policies J Syst Sci Syst Eng heightens the green product quality and can still acquire a higher profit; so the total environmental quality is improved. Then, the firm will have a greater incentive to change its traditional product strategy and adopt a new strategy that most benefits the environment. That is to say, the subsidy policy is effective for environmental protection. Unlike the standards environmental policy proposed by Chen (2001), the subsidy policy outlined in this paper considers not only environmental issues, but also the firms9 profits, which is always valid in environmental protection. 5* Conclusion By considering the interactions among customers preferences, firms product strategies, and government environmental policies, this paper presents a systemic model of a new product design strategy with a subsidy policy. The conditions for developing green products are presented and the impacts of a subsidy policy are analyzed. Without any environmental policy, the firm selects its optimal product design strategy by maximizing its profit, and this determines the corresponding product quality and retail price. Under these circumstances, the firm may introduce both a green product and an ordinary product for the two market segments or only a green product for the green market segment; thus, the maximum total environmental quality cannot always be ensured. Especially, the total environment quality when introducing only the green product for the green market segment is lower than that of introducing both the green product and the ordinary product. In terms of environmental protection, the firm should adopt the strategy of introducing a green product and an ordinary product for, respectively, the green and ordinary market segments. Sometimes, the targets of firms and governments conflict with each other. That is to say, to protect the environment, the firm should develop both a green product and an ordinary product. This result can help provide direction for governments in making policies to protect the environment, i.e., governments should make appropriate environmental policies to force firms to change their traditional product design strategy. By simultaneously considering environmental issues and firms1 benefits, we have designed a subsidy environmental policy, whereby a subsidy is given for environmental quality. With the subsidy policy, the firm changes its primary product design decisions to green product development, and it adopts a new product design strategy to accommodate the environment. The firm raises its green product quality and it can acquire a higher profit, so the total environmental quality is improved. As noted, these results can provide insights for governments in their policy making. When formulating environmental policy, governments should consider not only the environmental problem, but also firms profits. With the above strategy, a win-win situation is created. In addition, governments should also help firms popularize their green products in ways other than making effective policies to protect the environment Because of the complexity of the product design problem, this paper constructs a systemic model only under the assumption of constant market demand. In future more detailed research, we will change some assumptions (e.g., Zhang et al.: New Product Design Strategies with Subsidy Policies J Syst Sci Syst Eng 367 stochastic market demand, repeated-purchase- type products, and competition among companies) to expand this model so as to approach the real situation. In subsequent research, customer purchasing behavior and demand can be investigated by questionnaire to provide market information for green product development. The successful experience of green product development by some companies can be further studied, which can help firms construct a practical theoretical model for green product development. Appendices Proof of Theorem 1. To analyze the optimal product design strategy, we compare the optimal profits under three strategi