随机产出环境下联产品的产量及价格策略研究
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摘要
基于制造商生产主产品的过程中会随机产出两类存在替代关系的副产品的联产品系统,采用清仓定价模型,研究了不同需求函数(线性需求和指数需求)下,制造商对于主产品和副产品的最优产量与定价策略。通过两阶段优化模型的建立和求解,确定了主产品的最优产量和价格。借助数值分析,归纳出产品替代度和产出波动性对最优产量和利润的影响。研究结果表明,随着产品替代度的增加,制造商的产量上升;随着波动性的增加,制造商的产量下降。最后,将模型扩展到市场非出清的情况,并得出制造商的最优生产决策。
This article investigates the manufacturer's optimal pricing and quantity strategies in a co-product system assuming a clearance pricing policy in the by-product markets. This system includes one prime product and two by-products. By a two-stage optimization model,we obtain the optimal pricing and quantities under different demand functions( i. e.,linear demand and exponential demand). Through numerical examinations,we explore the effects of different parameters( substitutability,standard deviation) on the manufacturer's quantity and profit. The results show that the substitutability has a positive effect on the quantity of the prime product.But standard deviation has negative effects on this quantity. The reason is that the manufacturer will produce more products to satisfy the demand of by-product market when the substitutability of by-products becomes larger which means the products become similar. But standard deviation and coefficient of correlation have negative effects on this quantity. The intuition of this result is that the manufacturer will decrease the production of primary product to reduce risk when the risk of obtain profits from by-product increases owing to the increasing of the volatility of random yield. Finally,we extend our basic model by considering that the byproduct market is not clear and derive the manufacturer's optimal production decision.
This article investigates the manufacturer's optimal pricing and quantity strategies in a co-product system assuming a clearance pricing policy in the by-product markets. This system includes one prime product and two by-products. By a two-stage optimization model,we obtain the optimal pricing and quantities under different demand functions( i. e.,linear demand and exponential demand). Through numerical examinations,we explore the effects of different parameters( substitutability,standard deviation) on the manufacturer's quantity and profit. The results show that the substitutability has a positive effect on the quantity of the prime product.But standard deviation has negative effects on this quantity. The reason is that the manufacturer will produce more products to satisfy the demand of by-product market when the substitutability of by-products becomes larger which means the products become similar. But standard deviation and coefficient of correlation have negative effects on this quantity. The intuition of this result is that the manufacturer will decrease the production of primary product to reduce risk when the risk of obtain profits from by-product increases owing to the increasing of the volatility of random yield. Finally,we extend our basic model by considering that the byproduct market is not clear and derive the manufacturer's optimal production decision.
引文
[1]张勇.中国循环经济年鉴[M].北京:冶金工业出版社,2015. 145-152.
[2] Hsu A,Bassok Y. Random yield and random demand in a production system with downward substitution[J].Operations Research,1999,47(2):277-290.
[3] Bassok Y,Anupindi R,Akella R. Single-period multiproduct inventory models with substitution[J].Operations Research,1999,47(4):632-642.
[4] Netessine S,Rudi N. Centralized and competitive inventory models with demand substitution[J]. Operations Research,2003,51(2):329-335.
[5] Stavrulaki E,Fong D K H,Lin D K J. Two-resource stochastic capacity planning employing a bayesian methodology[J]. Journal of the Operational Research Society,2003,54(11):1198-1208.
[6] Rao U S,Swaminathan J M,Zhang J. Multi-product inventory planning with downward substitution,stochastic demand and setup costs[J]. IIE Transactions,2004,36(1):59-71.
[7] Shumsky R A,Zhang F. Dynamic capacity management with substitution[J]. Operations research,2009,57(3):671-684.
[8] Xu H,Yao D D,Zheng S. Optimal control of replenishment and substitution in an inventory system with nonstationary batch demand[J]. Production and Operations Management,2011,20(5):727-736.
[9]牟博佼,肖勇波,陈剑.基于MNL选择模型的替代产品定价和库存决策研究[J].中国管理科学,2010,18(3):25-32.
[10]官振中,任建标.价格和库存驱动替代的两产品动态定价策略[J].系统管理学报,2012,22(2):177-184.
[11]孟丽君,黄祖庆.基于退货的单周期替代性两产品的联合库存模型[J].系统管理学报2013,22(5):631-639.
[12]慕银平.随机需求下单向替代的两产品订货与定价联合决策研究[J].管理学报,2011,8(5):752-757.
[13]慕银平.需求替代的两产品动态批量最优预测时阈研究[J].管理科学学报,2011,14(3):10-23.
[14] Drezner Z,Gurnani H,Pasternack B A. An EOQ model with substitutions between products[J]. Journal of the Operational Research Society,1995:887-891.
[15] Tang C S,Yin R. Joint ordering and pricing strategies for managing substitutable products[J]. Production and Operations Management,2007,16(1):138-153.
[16] Parlar M. Game theoretic analysis of the substitutable product inventory problem with random demands[J].Naval Research Logistics(NRL), 1988, 35(3):397-409.
[17] Wang Q,Parlar M. A three-person game theory model arising in stochastic inventory control theory[J]. European Journal of Operational Research,1994,76(1):83-97.
[18] Zhu K,Thonemann U W. Coordination of pricing and inventory control across products[J]. Naval Research Logistics(NRL),2009,56(2):175-190.
[19] Li Q,Zheng S. Joint inventory replenishment and pricing control for systems with uncertain yield and demand[J]. Operations Research,2006,54(4):696-705.
[20] Tang C S,Yin R. Responsive pricing under supply uncertainty[J]. European Journal of Operational Research,2007,182(1):239-255.
[21] Ciarallo F W,Akella R,Morton T E. A periodic review,production planning model with uncertain capacity and uncertain demand—optimality of extended myopic policies[J]. Management Science,1994,40(3):320-332.
[22] Chao X,Chen H,Zheng S. Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity[J]. European Journal of Operational Research,2008,191(1):142-155.
[23] Feng Q. Integrating dynamic pricing and replenishment decisions under supply capacity uncertainty[J].Management Science,2010,56(12):2154-2172.
[24] Xu M,Lu Y. The effect of supply uncertainty in pricesetting newsvendor models[J]. European Journal of Operational Research,2013,227(3):423-433.
[25] Kazaz B. Production planning under yield and demand uncertainty with yield-dependent cost and price[J].Manufacturing&Service Operations Management,2004,6(3):209-224.
[26] Kazaz B,Webster S. The impact of yield-dependent trading costs on pricing and production planning under supply uncertainty[J]. Manufacturing&Service Operations Management,2011,13(3):404-417.
[27] Xu H,Zuo X,Liu Z. Configuration of flexibility strategies under supply uncertainty[J]. Omega,2015,51:71-82.
[28]程晋石,李帮义,龚本刚.考虑副产品生产的再制造市场结构演化分析[J].计算机集成制造系统,2013,19(9):2271-2279.
[29] Sunar N,Plambeck E. Allocating emissions among coproducts:implications for procurement and climate policy[R]. Working paper, UNC Kenan-Flagler,2015.
[30] Chen Y J,Tomlin B,Wang Y. Coproduct technologies:product line design and process innovation[J]. Management Science,2013,59(12):2772-2789.
[31] Tomlin B,Wang Y. Pricing and operational recourse in coproduction systems[J]. Management Science,2008,54(3):522-537.
[32] Boyabath O. Supply management in multiproduct firms with fixed proportions technology[J]. Management Science,2015,61(12):3013-3031.
[33] Boyabath O,Dang N. Capacity management for oilseeds processors[R]. Working Paper,2011.
[34] Boyabatli O,Kleindorfer P R,Koontz S R. Integrating long-term and short-term contracting in beef supply chains[J]. Management Science,2011,57(10):1771-1787.
[35] Lee D. Turning waste into by-product[J]. Manufacturing&Service Operations Management,2012,14(1):115-127.
[2] Hsu A,Bassok Y. Random yield and random demand in a production system with downward substitution[J].Operations Research,1999,47(2):277-290.
[3] Bassok Y,Anupindi R,Akella R. Single-period multiproduct inventory models with substitution[J].Operations Research,1999,47(4):632-642.
[4] Netessine S,Rudi N. Centralized and competitive inventory models with demand substitution[J]. Operations Research,2003,51(2):329-335.
[5] Stavrulaki E,Fong D K H,Lin D K J. Two-resource stochastic capacity planning employing a bayesian methodology[J]. Journal of the Operational Research Society,2003,54(11):1198-1208.
[6] Rao U S,Swaminathan J M,Zhang J. Multi-product inventory planning with downward substitution,stochastic demand and setup costs[J]. IIE Transactions,2004,36(1):59-71.
[7] Shumsky R A,Zhang F. Dynamic capacity management with substitution[J]. Operations research,2009,57(3):671-684.
[8] Xu H,Yao D D,Zheng S. Optimal control of replenishment and substitution in an inventory system with nonstationary batch demand[J]. Production and Operations Management,2011,20(5):727-736.
[9]牟博佼,肖勇波,陈剑.基于MNL选择模型的替代产品定价和库存决策研究[J].中国管理科学,2010,18(3):25-32.
[10]官振中,任建标.价格和库存驱动替代的两产品动态定价策略[J].系统管理学报,2012,22(2):177-184.
[11]孟丽君,黄祖庆.基于退货的单周期替代性两产品的联合库存模型[J].系统管理学报2013,22(5):631-639.
[12]慕银平.随机需求下单向替代的两产品订货与定价联合决策研究[J].管理学报,2011,8(5):752-757.
[13]慕银平.需求替代的两产品动态批量最优预测时阈研究[J].管理科学学报,2011,14(3):10-23.
[14] Drezner Z,Gurnani H,Pasternack B A. An EOQ model with substitutions between products[J]. Journal of the Operational Research Society,1995:887-891.
[15] Tang C S,Yin R. Joint ordering and pricing strategies for managing substitutable products[J]. Production and Operations Management,2007,16(1):138-153.
[16] Parlar M. Game theoretic analysis of the substitutable product inventory problem with random demands[J].Naval Research Logistics(NRL), 1988, 35(3):397-409.
[17] Wang Q,Parlar M. A three-person game theory model arising in stochastic inventory control theory[J]. European Journal of Operational Research,1994,76(1):83-97.
[18] Zhu K,Thonemann U W. Coordination of pricing and inventory control across products[J]. Naval Research Logistics(NRL),2009,56(2):175-190.
[19] Li Q,Zheng S. Joint inventory replenishment and pricing control for systems with uncertain yield and demand[J]. Operations Research,2006,54(4):696-705.
[20] Tang C S,Yin R. Responsive pricing under supply uncertainty[J]. European Journal of Operational Research,2007,182(1):239-255.
[21] Ciarallo F W,Akella R,Morton T E. A periodic review,production planning model with uncertain capacity and uncertain demand—optimality of extended myopic policies[J]. Management Science,1994,40(3):320-332.
[22] Chao X,Chen H,Zheng S. Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity[J]. European Journal of Operational Research,2008,191(1):142-155.
[23] Feng Q. Integrating dynamic pricing and replenishment decisions under supply capacity uncertainty[J].Management Science,2010,56(12):2154-2172.
[24] Xu M,Lu Y. The effect of supply uncertainty in pricesetting newsvendor models[J]. European Journal of Operational Research,2013,227(3):423-433.
[25] Kazaz B. Production planning under yield and demand uncertainty with yield-dependent cost and price[J].Manufacturing&Service Operations Management,2004,6(3):209-224.
[26] Kazaz B,Webster S. The impact of yield-dependent trading costs on pricing and production planning under supply uncertainty[J]. Manufacturing&Service Operations Management,2011,13(3):404-417.
[27] Xu H,Zuo X,Liu Z. Configuration of flexibility strategies under supply uncertainty[J]. Omega,2015,51:71-82.
[28]程晋石,李帮义,龚本刚.考虑副产品生产的再制造市场结构演化分析[J].计算机集成制造系统,2013,19(9):2271-2279.
[29] Sunar N,Plambeck E. Allocating emissions among coproducts:implications for procurement and climate policy[R]. Working paper, UNC Kenan-Flagler,2015.
[30] Chen Y J,Tomlin B,Wang Y. Coproduct technologies:product line design and process innovation[J]. Management Science,2013,59(12):2772-2789.
[31] Tomlin B,Wang Y. Pricing and operational recourse in coproduction systems[J]. Management Science,2008,54(3):522-537.
[32] Boyabath O. Supply management in multiproduct firms with fixed proportions technology[J]. Management Science,2015,61(12):3013-3031.
[33] Boyabath O,Dang N. Capacity management for oilseeds processors[R]. Working Paper,2011.
[34] Boyabatli O,Kleindorfer P R,Koontz S R. Integrating long-term and short-term contracting in beef supply chains[J]. Management Science,2011,57(10):1771-1787.
[35] Lee D. Turning waste into by-product[J]. Manufacturing&Service Operations Management,2012,14(1):115-127.