Advances in Production Engineering & Management Volume 11 | Number 3 | September 2016 | pp 216-226 http://dx.doi.Org/10.14743/apem2016.3.222 ISSN 1854-6250 Journal home: apem-journal.org Original scientific paper A green production strategies for carbon-sensitive products with a carbon cap policy Ma, C.a, Liu, X.b*, Zhang, H.b, Wu, Y.b aTian Fu College of SouthWestern University of Finance and Economics, Chengdu, China international Business School, Sichuan Technology and Business University, Chengdu, China A B S T R A C T A R T I C L E I N F O This paper discusses the production strategies used by manufacturers of carbon-sensitive products that have a carbon cap Policy under both deterministic demand and stochastic demand. In this study, we examine green manufacturing strategies for carbon-sensitive products under carbon cap policy regulations. We primarily consider the two scenarios of deterministic demand and stochastic demand. When the carbon cap Policy regulation has no restriction to the production of the manufacturers, the higher the carbon sensitivity coefficient of the product, the lower the profit of the manufacturing enterprise. When carbon cap Policy regulation of manufacturing enterprise production is a constraint, for the deterministic demand, with the higher carbon sensitive coefficient, manufacturing enterprise profit is higher; for stochastic demand, With the increasingly high carbon sensitive coefficient, manufacturing enterprise profit is low. Through the above research, the conclusion of this paper has reference value and guiding role to carbon-sensitive products' green production strategies with a carbon cap policy. © 2016 PEI, University of Maribor. All rights reserved. Keywords: Production strategy Carbon sensitive Carbon cap policy *Corresponding author: uestc-vip@163.com (Liu, X. ) Article history: Received 12 June 2016 Revised 5 July 2016 Accepted 18 July 2016 1. Introduction Productivity has greatly improved since the Industrial Revolution. However, that production consumes a significant amount of energy and produces large quantities of carbon dioxide, which has triggered changes in the global climate. The International Energy Agency (IEA) estimates a world gross domestic product (GDP) of 70 trillion in 2011 and 3.4 percent average annual growth from 2008 to 2035. With economic development, energy consumption has greatly increased, and our country will soon be confronted by the serious issue of energy-resource shortages. If each 1 percent GDP increase results in a 0.47 percent energy-consumption increase, world economic development will primarily rely on fossil fuels. More importantly, a non-profit government consulting institute, the LMI Research Institute, has stated that commercial activity in all manufacturing sectors count for much in carbon emissions. The carbon emissions produced by the manufacturing industry are caused by the use of raw materials (the transportation of semiconductors, steel, energy resources), manufacturing processes (heating treatments, welding, pressing) and waste-disposal process (carbon emission from waste-disposal plants). To mitigate global warming and reduce environmental pollution, governments worldwide are actively responding by publishing policies intended to solve this problem. The primary issue is how to transform human production and lifestyles to achieve a low-carbon economy and lifestyle. The Kyoto protocol provided a standard and direction for solving the global-warming 216 A green production strategies for carbon-sensitive products with a carbon cap policy problem. The implementation of a carbon quota has been derived from the Kyoto Protocol, which aims to achieve effective emissions reduction through a binding, legal requirement that greenhouse-gas emissions be maintained within a certain range. Furthermore, with an increase in environmental protection consciousness, consumers hope decrease carbon emissions as well as lower the prices, and enhance environmental protections. However, industrially manufactured products are carbon-sensitive products. With the establishment of a carbon quota mechanism, enterprises must consider the issue of carbon emissions. Simultaneously, because consumers are more likely to buy products with low carbon and environmental protections, a product's carbon sensitivity also has an impact on product demand. In this context, production enterprises can both improve market demand and increase corporate profits by emphasizing the low-carbon , environmentally protective characteristics of carbon-sensitive products. Therefore, when an enterprise is required to adopt a carbon quota policy, the question of how it can realize sustainable development and social responsibility while growing its profits becomes a key aspect of both enterprise operation and enterprise development. Simultaneously, this issue has become the subject of major research both at home and abroad. Therefore, research on the production strategy of carbon-sensitive products under a carbon cap policy can provide the basis of and reference for an enterprise's production activities. There have been relevant studies both at home and abroad on the production strategy associated with carbon quota policies. Hong et al. [1] considers retailer ordering and pricing decisions under carbon cap policies and discusses the impact of carbon emissions trading on retailer ordering, pricing and maximizing expected profit. Bouchery et al. [2] add carbon cap-and-trade to the inventory model, analyzing the effect of carbon quotas on the inventory model. Chaabane et al. [3] find that regarding carbon emissions trading, with the establishment of a relevant supply chain model, carbon limits can effectively reduce carbon emissions. Benjaafar et al. [4] study the impact of carbon limitation and transaction policies on enterprises' behavior associated with investment, production, inventory and ordering decisions. Enterprises can maximize profits by modifying order quantity. Zhang and Xu [5] investigate the multi-item production-planning issue associated with carbon cap-and-trade mechanisms where an enterprise produces vary products that fulfil independent stochastic demands with a common capacity and carbon emission quota; those authors use numerical analyses both to illustrate their findings and to identify managerial insights and policy implications. Using an economic order quantity (EOQ) model, Chen et al. [6] provide a situation where it is possible to lower emissions by altering the number of orders. They also provide the situations where the emissions reduction is comparatively greater than the cost increase. Moreover, they study the elements that influences differences in the magnitude of decrease in emission and rise in cost Ma et al. [7] demonstrates the effectiveness of the use of cap-and-trade policy as a mechanism to encourage manufacturers to reduce carbon emissions while obtaining expected profits through their use of green technology inputs. Qi et al. [8] stress the value of centralized management of value chain decisions and sharing of knowledge for Mass customization capability. Regarding to economic benefit and emission reduction, a multi-goal optimization model has been set by Qu et al. to show their relationship; they show that when it compared with the original policy, the collection of diverse emission-reduction policies make greater-efficiency emission reduction and less economic loss. Mutingi [10] plays an important role in both academics and professionals in the field of green supply-chain management. First, Mutingi's study provides a great deal of information to construct a practical tool or framework for managers in the development of green supply-chain tactics given the certain industrial situations where those tactics are used. Second, Mutingi's taxonomic framework provides managerial view about the effects of the selection of certain strategies for a supply chain's operations policies. Using a duopoly model, Wang and Wang [11] quantitatively explore the impact of a carbon offsetting scheme on both emission-trading participants' profits and industry output by drawing on the advanced experience of carbon-offsetting schemes in developed countries. A negative relationship between firms' carbon intensity and their equilibrium output in the product market is revealed from the outcomes. Furthermore, that study presents a commencement for the com- Advances in Production Engineering & Management 11(3) 2016 217 Ma, Liu, Zhang, Wu pared importance of duopoly enterprises' carbon intensity where their absolute output will differ dramatically. Sengupta [12] considers that when consumers are aware of a product's green and environmental protections, they assume that green technology can both improve the production of green products and offer environmental protection; an appropriate increase in prices will generate additional profits. Koren et al. [13] analyses the effect of technical and organizational views on the product complexity and to identify where most incentives for innovation initiate, and the influence on the product complexity. Buchmeister et al. [14] think the implication of weak demand discrepancy and level constraints within the supply chain on the bullwhip effect was evident. Liu et al. [15] use a Stackelberg model to study the problem of competition in the two stages of the supply chain, discussing not only product competition among suppliers but also competition among retailers. Those authors consider how suppliers and retailers can both obtain more benefits and improve their level of competitiveness. Xu and Zhao [16] show that supply chain cooperation can raise the emissions reduction level and increase the expected total profit. Finally, the effects of different parameters on the coordination of supply chain's performance are discussed. Li et al. [17] through the establishment of the Stackelberg game model, it is concluded that the optimal emission reduction level and the optimal proportion of the retail and supply, and the optimal profit value of the two in different contract forms. Huang and Zhao [18] study bargaining between manufacturers and retailers in the case of consumers' low carbon preferences, analysing both the influence of a manufacturer's pricing on the retailer and the function of the two parties. Because of the relevant environmental protection policy and consumer awareness of both environmental protection and low carbon emissions, research on carbon-sensitive product manufacturers' production strategies under a Cap policy can provide manufacturers with valuable information. 2. Problem statements and basic assumptions This paper studies a manufacturer in a monopoly market. The manufacturer produces only one product (for example, a smart phone); the remaining inventory is produced in accordance with residual value processing at the end of a sales period. The product's decision-making value is its production; the manufacturer's decision-making goal is profit maximization. The government has specified the largest carbon emissions E, under its carbon cap policy. To achieve carbon-emissions reduction targets, the carbon emissions of manufacturers' production activities cannot exceed the maximum level set by the government. At the same time, consumers demand low-carbon and environmental-protection features in their products; those features are associated with the products' carbon-sensitive coefficient k. Therefore, consumer demand influences production. This paper primarily studies the following two issues: Under the deterministic demand condition, demand is equal to the economic order quantity (EOQ) and thus, to both a manufacturer's production strategy with a carbon cap policy and the influence of a carbon-sensitive coefficient on profits; and Under the stochastic demand condition, requirements are related to price and a product's degree of carbon sensitivity and thus, to both a manufacturers' production strategy with a carbon cap policy and the influence of a carbon-sensitive coefficient on profits. For convenience, the model's main variables are listed below: k - Carbon-sensitive coefficient e - Product's per-unit carbon emissions E - Government limit on carbon emissions a - Unit of time of potential market demand D - Deterministic demand per unit of time Q - Production v - Residual value per unit product 218 A - Deterministic costs of each order at a particular time h - Annual inventory holding cost per unit product c - Cost of production per unit product p - Unit price of the product g - Shortage cost of one unit of the product 60 Advances in Production Engineering & Management 11(3) 2016 A green production strategies for carbon-sensitive products with a carbon cap policy 3. Deterministic demand model establishment and analysis Under the deterministic demand condition, demand is equal to EOQ and the relationship between demand and the carbon-sensitive coefficient k is D = a — ke(D,a,k,e > 0). 3.1. Basic model In the case of no carbon constraints, take the related parameters into the EOQ formulae: D Q TC = cD + -A + 2h (1) TC of Q derivative: dTC (a — ke)A h ~dQ= QÏ +2 Make ^^ = 0, and obtain the optimal production: Q* = M 2(a — ke)A ,„, — (2J h The optimal profit of the manufacturer is: n*(Q) = (p — c)Q*, that is, M by Eq. 3 2{a — ke)A (3) h Proposition 1: In the absence of a carbon quota restriction, if other conditions remain unchanged, the optimal profit n*(Q) is a decreasing function of the carbon-sensitive coefficient k. Proof: n*(Q) of k derivative: d n*(Q) = dk M 2e2A <0 h{a — ke) The profit is a decreasing function n*(Q) of the carbon-sensitive coefficient k; with an increase in k, n*(Q) decreases, while with a decrease in k, n*(Q) increases. End of proof. 3.2. Manufacturers' production strategy under a carbon cap policy Under the carbon-limitation condition, the EOQ can be obtained: TC = cD +-A+-h (4) Q 2 s.t.eQ 0, the constraint conditions can be: eQ-E <0 (6) Advances in Production Engineering & Management 11(3) 2016 219 Ma, Liu, Zhang, Wu e = 0 (8) dTC When

0, by Eq. 8, ^ = (a~*2e)A + ^ = q)e>0; therefore Qa E, then Qa < Q*, so we obtain n(Qa) E, the profit function of a manufacturer of carbon-sensitive products na is an increasing function of the carbon-sensitive coefficient k, and with a decrease in k, na decreases, while with an increase in k, na increases. Proof: 1. Because eQ* < E, equivalent to a non-carbon cap, with a proof of theorem 1. 2. When eQ* >E, na(Qa) of k derivative: eQ*E (9) Theorem 2: (10) 220 Advances in Production Engineering & Management 11(3) 2016 A green production strategies for carbon-sensitive products with a carbon cap policy Because g—— > 0, the profit function na is an increasing function of the carbonsensitive coefficient k; with a decrease in k, na decreases, while with an increase in k, na increases. End of proof. In summary, the demand is determined, there is a carbon quota policy regulation, and the optimal production quantity of manufacturing enterprises for Q* = if carbon emissions from manufacturing enterprises are far less than the carbon limits and will not exceed the carbon limits. With an increased carbon-sensitive coefficient k, manufacturing enterprises might consider it appropriate to reduce production and increase profits. With a decrease in the carbonsensitive coefficient k, manufacturing enterprises might consider it appropriate to reduce production and increase profits. With a decrease in the carbon-sensitive coefficient, manufacturing enterprises can appropriately increase production and profits. If production increases, a manufacturing enterprise's carbon emissions will exceed the carbon quota and the enterprise needs to control production activities. With an increase in the carbon-sensitive coefficient k, manufacturing enterprises can appropriately increase production and then improve profits. With a decrease in the carbon-sensitive coefficient k, manufacturing enterprises can consider appropriately reducing production and increasing profits. 3.3. Numerical analysis From the model solution, in a carbon-sensitive demand situation, the carbon-sensitive coefficient will affect the manufacturer's optimal production and maximum profit. To understand the influence of the carbon-sensitive coefficient and the carbon cap policy on the manufacturers' optimal production and the maximum profit, the following numerical analysis method was used to analyze the sensitivity of the parameters. For the convenience of numerical analysis, let a = 100 , e = 10 , ^ = 10 , h = 20, p = 100 , c = 50, g = 30, E = 80, e = 10. Making k e (1 , 10), we can obtain Fig. 1 and Fig. 2. From Fig. 1 and Fig. 2, we can see that with the decrease in both the carbon-sensitive coefficient and production, manufacturer's profits first decrease and then increase, which means that when a carbon cap policy does not work, with the increase in the carbon-sensitive coefficient, profits decrease. When the carbon cap policy works, with the increase in the carbon-sensitive coefficient, profits increase. The optimal production at this time is Q* = J2(a~*e)A = 9.75. 10 ° - 9.7 9.4 8- 9.2 ———a a 6 8.6 ...........................................................................^.................................................................................. ~ O - * \ 8.3 8.0 —a— n*a(Q*a) —a— n'a(Q'a) 7.7 —k 2 —x— Q* 7.0 x x Fig. 1 Carbon-sensitive coefficient impact on profits Fig. 2 Production impact on profits Advances in Production Engineering & Management 11(3) 2016 221 Ma, Liu, Zhang, Wu 4. The stochastic demand model establishment and analysis With the stochastic demand, make x as a stochastic demand and obey follow the probability density function of the demand for /(•) distribution. According to the demand function and supply function, the price function for the relationship with the carbon-sensitive coefficient k is: p= j — keQ, (, k, e, Q > 0, k as the carbon-sensitive coefficient) 4.1. Basic model In the case of no carbon constraints, we construct the model according to the relationship of price and the carbon-sensitive coefficient function, combined with the newsboy structure of profit model for production Q: n(Q) = U ~keQ rQ — v) I xf(x)dx Jo -(c-v)f Qf(x)dx + (j-keQ + g (11) Jo „ CD „ CD ~c) I Qf(x)dx — g I xf(x)dx Jn Jn If we make dn (Q) rQ dQ = (j + g — c) — 2keQ + ke I F(x)dx = 0 we then obtain J j + g — c = — j F(x)dx^ke For ease of calculation, make G(Q) = 2Q — j® F(x)dx. The optimal production is as follows: n(Q) of k derivative allows us to obtain dn(Q) rQ dk = -eQ[\ xf(x)dx+\ Qf(x)dx]<0 (13) Jo Jq Proposition 2: When demand is stochastic, there is no carbon quota policy constraint and the profit of a manufacturer of carbon-sensitive products n(Q) is a decreasing function of the carbon-sensitive coefficient k; with an increase in k, n(Q) decreases, while with a decrease in k, n(Q) increases. Proof: From (12), optimal production Q* is a decreasing function of the carbon-sensitive coefficient k, The general model of the profit function is: n = (p — c — v) Q*. Profit n is proportional to the carbon-sensitive coefficient Q*, and profit n has an inverse relationship with the carbonsensitive coefficientk; with an increase in k, n decreases, while with a decrease in k, n increases. In conclusion, the results are the same as for (13), and the proof is complete. End of proof. 4.2. Manufacturers' production strategy under carbon cap policy Under the carbon cap policy, carbon emissions in manufacturers' production activities must not exceed the government's largest carbon emissions. The largest production for manufacturers is -. Through a discussion of the optimal production strategy in this case, the following theorems are obtained: 222 Advances in Production Engineering & Management 11(3) 2016 A green production strategies for carbon-sensitive products with a carbon cap policy Theorem 3: Under conditions of stochastic demand, a manufacturer of carbon-sensitive products has a carbon cap policy of its optimal production Qa 0, can be obtained by constraint conditions: eQ-E <0 (14) q>(e Q-E) = 0 (15) rQ (j + g-c)-2(ke)Q + ke \ F(x)dx- 0, using Eq. 16 we can obtain dn^^ = (j + g — c) — 2(ke)Q + ke f® F(x)dx = 0, therefore, we can obtain Qa E, then Qa