价格随机变化的企业原材料库存决策研究
|
摘要
采购价格随机变化有着广泛的实际应用环境,复杂多变的世界经济环境决定了原材料价格固定不变成为历史,随着时间变化而改变的原材料随机价格问题引起愈来愈多的关注和研究。研究价格随机变化的最优库存控制对有效提高企业库存管理水平及增强企业综合竞争力有积极的作用。现有文献对随机库存控制模型的研究主要集中在需求随机和提前期随机的库存控制模型,并取得较为成熟的理论成果,对价格随机变化的库存控制模型的研究并不多见。因此,本文以价格随机变化为出发点,研究在价格随机变化的前提下最优库存的特点,从而丰富和发展库存理论并为实践应用提供参考。
本文以原材料采购价格随机变化的企业为研究对象,分析在不同企业治理模式及不同市场结构下,以企业利润最大化为目标函数,运用随机控制理论方法对企业原材料库存进行优化,并对不同企业治理结构下和不同竞争环境下的企业最优库存进行对比分析,最后对所做的数理模型进行模拟分析。
通过对各模型进行分析,本文不仅获得了一些定量的结论,同时也获得了一些定性的结论。在原材料价格随机波动条件下,企业治理模式将对企业最优库存决策产生影响。对于委托-代理企业,代理期限的长短对企业的最优库存决策产生影响。当原材料价格波动的趋势是下降的趋势时,代理人的任期越长,则其最优的库存就会越多。当原材料价格波动的趋势是上升的趋势时,代理人的任期越长,则其最优的库存就会越少。原材料价格的趋势与波动与企业的最优库存成反向相关关系；产品价格的波动与企业的最优库存的波动成正向关系。通过对委托代理企业和家族经营企业的最优库存比较分析可知,当原材料价格变化的趋势是下降时,家族经营企业的最优库存大于委托-代理企业的库存；而当原材料价格变化的趋势是上升时,家族经营企业的最优库存大于委托-代理企业的最优库存；而当原材料价格变化的趋势为零时,家族经营企业的最优库存与委托-代理企业的最优库存相同。
本文的创新主要在以下两个方面：
研究视角的创新：本文以利润最大化为目标函数,打破了现有文献绝大多数从成本最小化为切入点进行分析。在理论与逻辑分析上具有创新意义和持续拓展作用。无论对企业还是对个人而言,利润最大化比成本最小化更为直观和可实用性。因此,以利润最大化为新的研究视角可以提升理论的实效性和可持续性。另外,本文从不同企业治理结构的企业角度出发,重点分析他们各自在经营活动中为实现企业利益最大化而采取的库存策略有何不同。
理论框架的创新：本文构建“价格随机波动—利润最大化分析—最优控制”分析框架,以价格随机波动情况下的最优控制理论为框架支点,以委托—代理模型和家族经营两种企业性质为枝干,重点分析在该框架下的不同最优库存模型。另外,现有的模型主要是假设在完全竞争市场中,企业采取的最优库存,本文尝试从不完全竞争市场条件下,即企业的行为可以影响成品市场的价格,企业将采取何种采购决策使自身利益最大化。最后文章运用数值模拟对理论上出现的四种模型进行分析对比。
Stochastic purchasing price often takes place in business practice. Because of the complex and changing world economy, the deterministic price becomes less and less practical. As a result, research on the stochastic price models, which because it changes over time, it is more adaptable, and gains more and more attention. It is a useful alternative for enterprises who wish to improve their management levels and enhance their competitiveness. Current research on stochastic inventory model is mostly focused on stochastic demand and stochastic lead time, which creates a more mature theoretical achievement. However, study on stochastic price is still in the initial stage. Therefore, with this paper, stochastic price is examined as a viable supplement to stochastic models, and thereby enriching inventory theory.
This paper mainly talks about the raw material inventory decision of a firm with a stochastic price. The raw material inventory is optimized in order to maximize the profit of the firm under different corporate government modes and different market structures, by using the stochastic control theory. The comparative analysis of the firms is carried out under different corperate government modes and different competitive environment. The numerical simulation analysis is given to the mathematical models established at last.
Through establishing and solving of the model with the assumptions, this paper obtains not only the quantitative optimal inventory, but also some qualitative propositions.
With the stochastic raw material price, the government mode of the firm has a certain influence on the optimal decision. Under the principle-agent mode, the term of the agent has also influence on the optimal decision. It is negative correlation between the optimal decision and the trend and the volatility of the raw material price. It is positive correlation between the optimal decision and the trend and the volatility of the product price. It is negative correlation between the optimal decision and the trend and the volatility of the raw material price. It is positive correlation between the optimal decision and the trend and the volatility of the product price.
Comparing the optimal inventory of the agent-principle based firm with that of the family business, we get the results as follows:when facing the same stochastic price and during the same period, if the trend of the raw material price is declining, the optimal inventory of the family enterprise is larger than it of the principal-agent based enterprise; and if the trend of the raw material price is increasing, the optimal inventory of the family enterprise is smaller than it of the principal-agent based enterprise; and the optimal inventory of the family enterprise is equal to it of the principal-agent based enterprise when the trend of the raw material price is zero which means the price is deterministic.
The innovation suggested by this paper addresses two aspects:
Firstly, innovation in the perspective of the study:Taking the maximum profit as the objective function, breaking the existing literature most from the total cost as the starting point for analysis, which has innovative in theory and logic analysis. Whether for enterprises or for individuals, profit maximization is more intuitive and practical than the cost minimization. Therefore, profit maximization as a new perspective can improve the effectiveness and sustainability of the theory. In addition, this paper starts from different company governance structures, focuses on analyzing their optimal inventories in order to maximize the profit of the enterprise.
Innovation in theoretical framework:this paper establishes the analytical framework "stochastic price-profit maximization-optimal control", based on the optimal control theory, and the principal-agent model and family enterprise, and analyses the different models under this framework. In addition, the existing models are assumed in a perfectly competitive market, this paper tries to modify the models in an imperfect competition market, in which the behavior of the enterprise can affect the price in the product market. Finally, numerical simulation is studied for the models and the comparison between them.
本文以原材料采购价格随机变化的企业为研究对象,分析在不同企业治理模式及不同市场结构下,以企业利润最大化为目标函数,运用随机控制理论方法对企业原材料库存进行优化,并对不同企业治理结构下和不同竞争环境下的企业最优库存进行对比分析,最后对所做的数理模型进行模拟分析。
通过对各模型进行分析,本文不仅获得了一些定量的结论,同时也获得了一些定性的结论。在原材料价格随机波动条件下,企业治理模式将对企业最优库存决策产生影响。对于委托-代理企业,代理期限的长短对企业的最优库存决策产生影响。当原材料价格波动的趋势是下降的趋势时,代理人的任期越长,则其最优的库存就会越多。当原材料价格波动的趋势是上升的趋势时,代理人的任期越长,则其最优的库存就会越少。原材料价格的趋势与波动与企业的最优库存成反向相关关系；产品价格的波动与企业的最优库存的波动成正向关系。通过对委托代理企业和家族经营企业的最优库存比较分析可知,当原材料价格变化的趋势是下降时,家族经营企业的最优库存大于委托-代理企业的库存；而当原材料价格变化的趋势是上升时,家族经营企业的最优库存大于委托-代理企业的最优库存；而当原材料价格变化的趋势为零时,家族经营企业的最优库存与委托-代理企业的最优库存相同。
本文的创新主要在以下两个方面：
研究视角的创新：本文以利润最大化为目标函数,打破了现有文献绝大多数从成本最小化为切入点进行分析。在理论与逻辑分析上具有创新意义和持续拓展作用。无论对企业还是对个人而言,利润最大化比成本最小化更为直观和可实用性。因此,以利润最大化为新的研究视角可以提升理论的实效性和可持续性。另外,本文从不同企业治理结构的企业角度出发,重点分析他们各自在经营活动中为实现企业利益最大化而采取的库存策略有何不同。
理论框架的创新：本文构建“价格随机波动—利润最大化分析—最优控制”分析框架,以价格随机波动情况下的最优控制理论为框架支点,以委托—代理模型和家族经营两种企业性质为枝干,重点分析在该框架下的不同最优库存模型。另外,现有的模型主要是假设在完全竞争市场中,企业采取的最优库存,本文尝试从不完全竞争市场条件下,即企业的行为可以影响成品市场的价格,企业将采取何种采购决策使自身利益最大化。最后文章运用数值模拟对理论上出现的四种模型进行分析对比。
Stochastic purchasing price often takes place in business practice. Because of the complex and changing world economy, the deterministic price becomes less and less practical. As a result, research on the stochastic price models, which because it changes over time, it is more adaptable, and gains more and more attention. It is a useful alternative for enterprises who wish to improve their management levels and enhance their competitiveness. Current research on stochastic inventory model is mostly focused on stochastic demand and stochastic lead time, which creates a more mature theoretical achievement. However, study on stochastic price is still in the initial stage. Therefore, with this paper, stochastic price is examined as a viable supplement to stochastic models, and thereby enriching inventory theory.
This paper mainly talks about the raw material inventory decision of a firm with a stochastic price. The raw material inventory is optimized in order to maximize the profit of the firm under different corporate government modes and different market structures, by using the stochastic control theory. The comparative analysis of the firms is carried out under different corperate government modes and different competitive environment. The numerical simulation analysis is given to the mathematical models established at last.
Through establishing and solving of the model with the assumptions, this paper obtains not only the quantitative optimal inventory, but also some qualitative propositions.
With the stochastic raw material price, the government mode of the firm has a certain influence on the optimal decision. Under the principle-agent mode, the term of the agent has also influence on the optimal decision. It is negative correlation between the optimal decision and the trend and the volatility of the raw material price. It is positive correlation between the optimal decision and the trend and the volatility of the product price. It is negative correlation between the optimal decision and the trend and the volatility of the raw material price. It is positive correlation between the optimal decision and the trend and the volatility of the product price.
Comparing the optimal inventory of the agent-principle based firm with that of the family business, we get the results as follows:when facing the same stochastic price and during the same period, if the trend of the raw material price is declining, the optimal inventory of the family enterprise is larger than it of the principal-agent based enterprise; and if the trend of the raw material price is increasing, the optimal inventory of the family enterprise is smaller than it of the principal-agent based enterprise; and the optimal inventory of the family enterprise is equal to it of the principal-agent based enterprise when the trend of the raw material price is zero which means the price is deterministic.
The innovation suggested by this paper addresses two aspects:
Firstly, innovation in the perspective of the study:Taking the maximum profit as the objective function, breaking the existing literature most from the total cost as the starting point for analysis, which has innovative in theory and logic analysis. Whether for enterprises or for individuals, profit maximization is more intuitive and practical than the cost minimization. Therefore, profit maximization as a new perspective can improve the effectiveness and sustainability of the theory. In addition, this paper starts from different company governance structures, focuses on analyzing their optimal inventories in order to maximize the profit of the enterprise.
Innovation in theoretical framework:this paper establishes the analytical framework "stochastic price-profit maximization-optimal control", based on the optimal control theory, and the principal-agent model and family enterprise, and analyses the different models under this framework. In addition, the existing models are assumed in a perfectly competitive market, this paper tries to modify the models in an imperfect competition market, in which the behavior of the enterprise can affect the price in the product market. Finally, numerical simulation is studied for the models and the comparison between them.
引文
[1]Abad, P. Optimal policy for a retailer when the supplier offers a temporary reduction in price. Decision sciences,1997(28),637-649.
[2]Abad, P. Optimal price and lot size when the supplier offers a temporary price reduction over an interval. Computers & operations research,2003(30),63-74.
[3]Abad, P. Quantity restrictions and the reseller's response to a temporary price reduction or an announced price increase. Asia-Pacific journal of operational research,2006(23),1-23.
[4]Abad, P. Buyer's response to a temporary price reduction incorporating freight costs. European journal of operational research,2007(182),1073-1083.
[5]Aggarwal, S.C. Purchase-inventory models for inflationary conditions. Interfaces, 1981,11(4),18-23.
[6]Arcelus, F., & Srinivasan, G. Generalizing the announced price increase problem. Decision science,1993(24),847-866.
[7]Arcelus, F. J., & Srinivasan, G. Discount strategies for one-time-only sales. HE transactions,1995,27(5),618-624.
[8]Arcelus, F.J., & Srinivasan, G Ordering policies under one time only discount and price sensitive demand. HE transactions,1998,30(11),1057-1064.
[9]Arcelus, F., & Srinivasan, G. Costing partial order cycles in the temporary sale price problem. International journal of production economics,1998,21-27.
[10]Arcelus, F., Pakkala, T., & Srinivasan, G. The temporary sale problem with unknown termination date. INFOR,2001(39),71-88.
[11]Arcelus, F., Pakkala, T., & Srinivasan, G. Special sales with guaranteed minimum duration but uncertain termination date. Applied mathematical modeling, 2003(27),677-699.
[12]Arcelus, F., Pakkala, T.P.M., & Srinivasan, G. Retailer's inventory policies for a one time only manufacturer trade deal of uncertain duration. Annals of operations research,2008(164),3-15.
[13]Arcelus, F.J., & Srinivasan, G. Marketing/inventory interactions in the characterization of retailer response to manufacturer trade deals. Managerial and decision economics,2006(27),537-547.
[14]Arcelus, F.J., Srinivasan, G., & Shah, N. H. Forward buying policies for deteriorating items under price sensitive demand and temporary price discounts. International journal of operations and quantitative management,2003,9(2), 87-101.
[15]Arcelus, F.J., Shah, N.H., & Srinivasan, G. Retailer's response to special sales: price discount vs trade credit. Omega,2001,29(5),417-428.
[16]Ardalan, A. Combined optimal prices and optimal inventory replenishment policies when a sale results in increase in demand. Computers and operations research,1991(18),721-730.
[17]Ardalan, A. Optimal prices and order quantities when temporary price discounts result in increase demand. European journal of operational research 1994,72(1), 52-61.
[18]Ardalan, A. Optimal ordering policies in response to a sale. IIE transactions, 1988(20),267-279.
[19]Arnold, J., Minner, S., & Eidam, B. Raw material procurement with fluctuating prices. International journal of production economics,2009,121(2),353-364.
[20]Arrow, K.J., Harris, T., & Marschak, J. Optimal Inventory Policy. Econometrica, 1951(19),250-273.
[21]Aucamp, D., & Kuzdrall, P. Lot sizes for one-time-only sales. Journal of the operational research society,1986(37),79-86.
[22]Aucamp, D., & Kuzdrall, P. Order quantities with temporary price reductions. Journal of the operational research society,1989(40),937-940.
[23]Aull-Hyde, R. Evaluation of supplier-restricted purchasing options under temporary price discounts. IIE transactions,1992(24),184-186.
[24]Axaster, S. Inventory control. Norwell, MA:Kluwer,2000.
[25]Baker, R. Inventory policy for items on sale during regular replenishment. Production and inventory management,1976(4),55-64.
[26]Banerjee, S., & Meitei, N.S. Effect of declining selling price:profit analysis for a single period inventory model with stochastic demand and lead time. Journal of the operational research society,2010,61(4),696-704.
[27]Berling, P. On determination of inventry cost parameters, Ph.D. Thesis, Lund University,2005.
[28]Berling, P. The capital cost of holding inventory with stochastically mean-reverting purchase price. European journal of operational research, 2008(186),620-636.
[29]Berling, P., & Rosling, K. The effect of financial risks on inventory policy. Management science,2005,51(12),1804-1815.
[30]Berling, P., & Martinez-de-Albeniz, V. Optimal inventory policies when purchase price and demand are stochastic. Operations research,2011,59(1),109-124.
[31]Bierman, H., & Thomas, J. Inventory decisions under inflationary conditions. Decisions sciences,1977(8),151-155.
[32]Buzacott, J.A. Economic order quantities with inflation. Operational research quarterly,1975,26(3, i),553-558.
[33]Chan, L.M.A., Shen, Z.J.M., Simchi-Levi, D., & Swann, J.L. Coordination of pricing and inventory decisions:a survey and classification. International series in operations research and management science,2004(74),335-392.
[34]Chambers, M. J., & Bailey, R. E. A theory of commodity price fluctuations. The review of economic studies,.1996,104(5),429-441.
[35]Chandra, J., & Bahner, M. The effect of inflation and the value of money on some inventory systems. International journal of production research,1985(23), 723-730.
[36]Chen, F.94%-effective policies for a two-stage serial inventory system with stochastic demand. Management science,1999,45(12),1679-1696.
[37]Chen, F., & Song, J-S. Optimal policies for multiechelon inventory problems with Markov-modulated demand. Operations research,2001,49(2),226-234.
[38]Chu, P., Chen, P., & Niu, T. Note on supplier-restricted order quantity under temporary price discounts. Mathematical methods of operations research, 2003(58),141-147.
[39]Deaton, A., & Laroque, G. On the behaviour of commodity prices. The review of economic studies,1992,59(1),1-23.
[40]Deaton, A., & Laroque, G. Competitive storage and commodity price dynamics. Journal of political economy,1996,104(5),896-923.
[41]Donaldson, W.A. Inventory replenishment policy for a linear demand:an analytical solution. Journal of the operational research society,1977,32(1), 37-42.
[42]Dye, C. Joint pricing and ordering policy for a deteriorating inventory with partial backlogging. Omega,2007,35(2),184-189.
[43]Edgeworth, F. The mathematical theory of banking. Journal of statistic society, 1888(51),113-127.
[44]Elmaghraby, W., & Keskinocak, P. Dynamic pricing in the presence of inventory considerations:research overview, current practices, and future directions. Management science,2003,49(10),1287-1309.
[45]Fabien, T., Fisher, J., Sasieni, W., & Yardeni, A. Purchasing raw material on a fluctuating market. Operations research,1959(7),107-122.
[46]Federgruen, A., Groenevelt, H., & Tijms, H. C. Coordinated replenishments in a multi-Item inventory system with compound Poisson demands. Management science,1984.30(3),344-357.
[47]Federgruen, A., & Zipkin, P. An inventory model with limited production capacity and uncertain demands I. The average-cost criterion. Mathematics of operations research,1986,11(2),193-207.
[48]Gao, J.S., Liu, Y.K., & Lan, Y.F. Optimizing material procurement planning problem by two-stage fuzzy programming. Computers & industrial engineering, 2010,58(1),97-107.
[49]Gascon, A. On the finite horizon EOQ model with cost changes. Operations research,1995,43(4),716-717.
[50]Geman, H. Commodities and commodity derivatives:modeling and pricing for agriculture, metals and energy. Wiley, Chichester,2005.
[51]Goel, A., & Gutierrez, G.J.2006. Integrating commodity markets in the optimal procurement policies of a stochastic inventory system. Working paper, Department of Information Risk and Operations Management, University of Texas-Austin.
[52]Golabi, K. Optimal inventory policies when ordering prices are random. Operations research,1985,33(3),575-588.
[53]Goyal, S.K. A note on the paper:an inventory model with finite horizon and price changes. The journal of the operational research society,1979,30(9),839-840.
[54]Goyal, S.K. Reply to comment on an improved procedure for the finite horizon and price changes inventory model. The journal of the operational research society,1980,31(1),81-82.
[55]Goyal, S.K. Economic ordering policy during special discount periods for dynamic inventory problems under certainty. Engineering costs and production economics,1990(20),101-104.
[56]Goyal, S.K. A note on "inventory models with cost changes". Operations research,1992,40(2),414-415.
[57]Goyal, S.K. An inventory model for a product for which purchase price fluctuates. New Zealand operational research,1975(3),112-117.
[58]Goyal, S.K. A comment on Martin's:note on an EOQ model with a temporary sale price. International journal of production economics,1996(43),283-284.
[59]Goyal, S.K. A comment on lot sizes for one-time-only sales. Journal of the operational research society,1986(37),817-818.
[60]Goyal, S.K., Srinivasan, G., & Arcelus, F. One time only incentives and inventory policies. European journal of operational research,1991(54),1-6.
[61]Goyal, S.K., & Jaber, M.Y. A note on optimal ordering policies in response to a discount offer. International journal of production economics,2008(112), 1000-1001.
[62]Goyal, S.K., & Bhatt, S.K. A generalized lot size policy for price increases. OPSEARCH,1988(25),272-278.
[63]Grubbstrom, R.W., & Kingsman, B.G. Ordering and inventory policies for step changes in the unit item cost:a discounted cash flow approach. Management science,2004,50(2),253-267.
[64]Grubbstrom, R.W., & Kigsman, B.G. Economic order quantity under price variations.11th meeting European working group financial model, Italy, and working paper WP-178, department of production economics, Linkoping institute of technology, SE-581,83 Linkoping, Sweden.
[65]Harris, F.W. How many parts to make at once. Factory, the magazine of management,1913(10),135-136,152.
[66]Harris, F.W. Economic order quantity model. Management science,1915,35(3), 898-900.
[67]Hall, R. Price changes and order quantities:impacts of discount rate and storage costs. HE transactions,1992(24),104-110.
[68]Hannan, E.L., & Smith, L.A. Economic order quantity for a finite demand horizon with a single price change-a note. New Zealand operations research, 1981(9),1.
[69]Hariga, M. The inventory replenishment problem with a linear trend in demand. Computer engineering,1993,24(2),143-150.
[70]Hariga, M.A. Optimal EOQ for deteriorating items with time-varying demand. Journal of operational research society,1996(47),1228-1246.
[71]Hariga, M.A., & Benkherouf, L. Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand. European journal of operational research,1994(79),123-137.
[72]Hartman, R. The effect of price and cost uncertainty on investment. Journal of economic theory,1972(5),258-266.
[73]Hite, G.L. On the theory of the firm in a capital asset pricing model world. In handbook of financial economics (edited by Bicksier J.L.), Amsterdam North-Holland,1979,163-188.
[74]Huang, W., Kulkarni, V.G., & Swaminathan, J.M. Optimal EOQ for announced price increases in infinite horizon. Operations Research,2003,51(2),336-339.
[75]Hsiao, Y-C. A note on integrated single vendor single buyer model with stochastic demand and variable lead time. International Journal of Production Economics.2008(114),294-297.
[76]Hsu, W.K., & Yu, H. EOQ model for imperfective items under a one-time only discount. Omega,2009,37(5),1018-1026.
[77]Jia, S. A note on the economic management of inventory or resource under stochastic prices. Journal of statistical planning and inference,2006,136(3), 1020-1038.
[78]Joglekar, P., & Lee, P. Comments on:a comparative analysis for determining optimal price and order quantity when a sale increases demand. European journal of operational research,1998,109(1),228-241.
[79]Joglekar, P., & Lee, P. Responding to a one-time-only sale of a product subject to sudden obsolescence. Academy of information and management sciences journal, 2003, January-July.
[80]Joglekar, P. A heuristic to determine price and lot size in face of a supplier's temporary price reduction over an interval. Academy of information and management science journal,2005,8(1),11/103.
[81]Joglekar, P., Lee, P., & Farahani, A.M. Continuously increasing price in an inventory cycle:an optimal strategy for E-tailers. Journal of applied mathematics and decision sciences,2008,14.
[82]Kalymon, B.A. Stochastic prices in a single-item inventory purchasing model. Operations research,1971,19(6),1434-1458.
[83]Kalymon, B.A. Stochastic costs in multi-period decision models. Ph.D. dissertation, Yale University, New Haven, Connecticut,1970.
[84]Kaplan, R.S. A dynamic inventory model with stochastic lead times. Management science,1970,16(7),491-507.
[85]Khouja, M., & Park, S. Optimal lot sizing under continuous price decrease. Omega,2003(31),539-545.
[86]Kingsman, B. Raw material purchasing:an operational research approach. Pergamon press, Oxford, UK,1985.
[87]Kingsman, B., & Boussofiane, A. Ordering and stock holding under price inflation when prices increase in successive discrete jumps. Production economics,1989(17),395-407.
[88]Lev, B., & Soyster, A.L. An inventory model with finite horizon and price changes. The journal of the operational research society,1979,30(1),43-53.
[89]Lev, B., Soyster, A.L., & Weiss, H.J. Comment on an improved procedure for the finite horizon and price changes inventory model. The journal of the operational research society,1979,30(9),840-842.
[90]Lev, B., & Weiss, H.J. Inventory models with cost changes. Operations research, 1990,38(1),53-63.
[91]Lev, B., Weiss H.J. & Soyster, A.L. A optimal ordering policies when anticipating parameter changes in EOQ systems. Naval research logistics quarterly,1981(28),267-279.
[92]Lev, B., & Soyster, A.L. An inventory model with finite horizon and price changes. The journal of the operational research society,1979,30(1),43-53.
[93]Li, C.L., & Kouvelis, P. Flexible and risk-sharing supply contract under price uncertainty. Management science,1999(45),1378-1398.
[94]Liberatore, M.J. Planning horizons for a stochastic lead-time inventory model. Operations research,1977,25(6),977-988.
[95]Liberatore, M.J. The EOQ model under stochastic lead time. Operations research, 1979,27(2),391-396.
[96]Lim, A., & Rodrigues, B. A note on the optimal EOQ for announced price increases in the infinite horizon. Operations research,2005(53),731-732.
[97]Maiti, A.K., Maiti M.K., & Maiti M. Inventory model with stochastic lead-time and price dependent demand incorporating advance payment. Applied mathematical modeling,2009,33(5),2433-2443.
[98]Martel, A., & Gascon, A. dynamic lot-sizing with price changes and price-dependent holding costs. European journal of operational research, 1998(111),114-128.
[99]Martin, G. Note on an EOQ model with a temporary sale price. International journal of production economics,1994(37),241-243.
[100]Markowski, E. Criteria for evaluating purchase quantity decisions in response to future price increases. European journal of operational research,1990(47), 364-370.
[101]Moinzadeh, K. Replenishment and stocking policies for inventory systems with random deal offerings. Management science,1997(14),90-114.
[102]Porteus, E.L. Foundations of stochastic inventory theory. Stanford, CA: Stanford University Press,2002.
[103]Presman, E., & Sethi, S.P. Inventory models with continuous and Poisson demands and discounted and average costs. Production and operations management,2006,15(2),279-293.
[104]Ramasesh, R.V. Lot-sizing decisions under limited-time price incentives:a review. Omega,2010(38),118-135.
[105]Ramasesh, R., & Rachamadugu, R. Lot-sizing decisions under limited-time price reduction. Decision science,2001(32),125-143.
[106]Rau, H., & Ouyang, B-C. A general and optimal approach for three inventory models with a linear trend in demand. Computer & industrial engineering,2007, 52(4),521-532.
[107]Rau, H., & Ouyang, B-C. Modelling of the inventory replenishment problem with a two-segment piecewise linear demand. International journal of systems science,2011,42(10),1613-1624.
[108]Samuelson, P.A. Rational theory of warrant pricing. Industrial management review,1965(6),13-31.
[109]Sana, S.S. The stochastic EOQ model with random sales price. Applied mathematics and computation,2011,218(2),239-248.
[110]Sarker, B.R., & Kindi, M.A. Optimal ordering policies in response to a discount offer. International journal of production economics,2006(100),195-211.
[111]Schmitt, A.J., Snyder, L.V., & Shen, Z.M. Inventory systems with stochastic demand and supply:properties and approximations. European Journal of operational research,2010,206(2),313-328.
[112]Schwartz, E., & Smith, J.E. Short-term variations and long-term dynamics in commodity prices. Management science,2000(46),893-911.
[113]Schwartz, E. S. The stochastic behaviour of commodity prices:implications for valuation and hedging. The journal of finance,1997,52(3),923-973.
[114]Schwarz, L.B. Economic ordering quantities for products with finite demand horizons. AIIE transactions,1972(4),234-237.
[115]Secomandi, N. Optimal inventory-trading policy for commodity storage assets. Working paper, Tepper school of business, Carnegie Mellon University, Pittsburgh, Pennsylvania,2007.
[116]Sethi, S.P., & Cheng, F. Optimality of (s, S) policies in inventory models with Markovian demand. Operations research,1997,45(6),931-939.
[117]Silver, E. Supplier planning a price increase? Industrial distribution,1980, 91-94.
[118]Silver, E., Edward, A., Pyke, D.F., & Rein, P. Inventory management and production planning and scheduling,3rd ed. Hoboken, NJ:Wiley,1998.
[119]Silver, E.A., Robb, D.J., & Rahnama, M.R. Random opportunities for reduced cost replenishments. HE transactions,1993(25),111-120.
[120]Song, J-S, Xu, S.H, & Liu, B. Order-fulfillment performance measures in an assemble-to-order system with stochastic lead times. Operations research,1999, 47(1),131-149.
[121]Song, J-S. The effect of leadtime uncertainty in a simple stochastic inventory model. Management science,1994,40(5),603-613.
[122]Taylor, S.G., & Bradley, C.E. Optimal ordering strategies for announced price increases. Operations research,1985,33(2),312-325.
[123]Tersine, R.J. Economic replenishment strategies for announced price increases. European journal of operational research,1996(92),266-280.
[124]Tersine, R.J., & Grasso, E.T. Forward buying in response to announced price increases. Journal of purchasing and materials management,1978(14),20-22.
[125]Tersine, R., & Schwarzkopf, A. Optimal stock replenishment strategies in response to temporary price reductions. Journal of business logistics,1989(10), 123-45.
[126]Tersine, R.J., & Price, R.L. Temporary price discounts and EOQ. Journal of purchasing and materials management,1981(17),23-27.
[127]Tersine, R.J., & Barman, S. Economic purchasing strategies for temporary price discounts. European journal of operational research,1995(80),328-343.
[128]Tersine, R.J. Economic replenishment strategies for announce price increases. European journal of operational research,1996(92),266-280.
[129]Teunter, R. A note on "Khouja and Park, optimal lot sizing under continuous price decrease". Omega,2005(31),467-471.
[130]Thorstenson, A., & Hultman, P. Price uncertainty and the effect of capital costs in a poin in-point out inventory investments. Managerial and decision ecomonics,1992,13(5),389-397.
[131]Tyagi, R.K. A characterization of retail response to manufacturing trade deals. Journal of marketing research,1999(36),510-516.
[132]Wilson, R.H. A scientific routine for stock control. Harvard business review, 1934(13),116-134.
[133]Wagner, H.M., & Whitin, T.M. Dynamic version of the economic lot size model. Management science,1958(5),89-96.
[134]Wang, Y. The optimality of myopic stocking policies for systems with decreasing purchasing prices. European journal of operational research,2001, 133(1),153-159.
[135]Whitin, T.M. Inventory control and price theory. Management science,1955(2), 61-68.
[136]Yanasse, H.H. EOQ systems:the case of an increase in purchase cost. The journal of the operational research society,1990,41(7),633-637.
[137]Yang, J., & Xia, Y.S. Acquisition management under fluctuating raw material prices. Working paper, Department of industrial and manufacturing engineering, New Jersey Institute of Technology, Newark, NJ,2008.
[138]Yano, C.A.,& Gilbert, S.M. Coordinated pricing and production/procurement decisions:a review. In:Chakravarty A., Eliashberg J., editors. Management business interfaces:marketing, engineering and manufacturing perspectives. Bostons, M.A.:Kluwer academic publishers,2002.
[139]Zalkind, D. Order-level inventory systems with independent stochastic leadtimes. Management science,1978,24(13),1384-1392.
[140]Zheng, Y.S. On properties of stochastic inventory systems. Management science, 1992(38),87-103.
[141]Zheng, Y. S. Optimal control policy for stochastic inventory system with Markovian discount opportunities. Operations research,1994,42(4),721-738.
[142]Zipkin, P.H. Foundations of inventory management, McGraw-Hill, Singapore, 2000.
[143]陈晖.几类库存控制模型研究.博士学位论文,重庆大学,2007.
[144]陈利华,赵庆祯.供应链不确定条件下制造商库存模型研究.物流科技,2009(05),65-68.
[145]白少布.面向供应链管理的库存控制理论与方法研究.博士学位论文,南京理工大学,2007.
[146]白少布,薛恒新.随机提前期多产品供应链库存控制策略研究.经济师,2006(12),26-27.
[147]曹晓刚.原材料价格波动下的生产—库存管理研究.博士学位论文,武汉大学,2009.
[148]曹晓刚,闻卉,夏火松.价格波动下的生产-库存控制研究.控制与决策,2010,25(5),730-734.
[149]戴更新,侯云章,于庆东.基于随机提前期的二级库存系统的优化方法. 数学的实践与认识,2006,36(3),52-57.
[150]方定宝,童晓萍.系列化生产企业的原料采购模型研究.数量经济技术经济研究,2003(4),117-121.
[151]高振,唐立新,王梦光.钢铁企业原燃料多目标采购模型.东北大学学报(自然科学版),2001(12),619-622.
[152]高振,唐立新,陶炜,肖新华.大型钢铁企业原料采购计划模型.系统工程学报,2003(12),566-570.
[153]龚光鲁,钱敏平.应用随机过程教程.北京：清华大学出版社,2004.
[154]耿修林.管理科学原理.北京：科学出版社,2006.
[155]黄欣.随机提前期与供给水平联和约束的库存问题.合肥学院学报(自然科学版),2005,15(1),42-45.
[156]李海清,图海宁,刘建胜.基于随机提前期的多品种备件库存成本控制研究.机械设计与制造,2006(11),153-154.
[157]林勇,蒋莲,乐晓娟.基于随机提前期的(Q,s)库存模型.物流技术,2007,26(7),32-34.
[158]林勇,马士华.基于随机提前期的通用件安全库存管理.工业工程与管理,2003(3),6-9.
[159]刘静,刘荣,郭小霞.基于随机提前期两种物品库存决策的优化仿真.高等函授学报(自然科学版),2010,23(2),60-62.
[160]刘培德.泛函分析基础.武汉：武汉大学出版社,1992.
[161]马士华,林勇.基于随机提前期的(Q,r)库存模型.计算机集成制造系统,2002,8(5),396-398.
[162]彼得.贝利等.采购原理与管理(第8版).王增东,杨磊译.北京：电子工业出版社,2003.
[163]向晋乾,李杰,黄培清.工业企业原材料采购与库存策略.上海管理科学,2004(2),39-42.
[164]杨杰.非平稳需求库存控制策略研究.博士学位论文,中国科学技术大学,2007.
[165]张春晓,谢金星.随机提前期随机需求条件下的二级库存模型.数学的实践与认识,2004,34(7),1-8.
[166]周永务.物流系统的库存控制模型与方法研究.博士学位论文,合肥工业大学,2002.
[167]周永务,王圣东.库存控制理论与方法.北京：科学出版社,2009.
[2]Abad, P. Optimal price and lot size when the supplier offers a temporary price reduction over an interval. Computers & operations research,2003(30),63-74.
[3]Abad, P. Quantity restrictions and the reseller's response to a temporary price reduction or an announced price increase. Asia-Pacific journal of operational research,2006(23),1-23.
[4]Abad, P. Buyer's response to a temporary price reduction incorporating freight costs. European journal of operational research,2007(182),1073-1083.
[5]Aggarwal, S.C. Purchase-inventory models for inflationary conditions. Interfaces, 1981,11(4),18-23.
[6]Arcelus, F., & Srinivasan, G. Generalizing the announced price increase problem. Decision science,1993(24),847-866.
[7]Arcelus, F. J., & Srinivasan, G. Discount strategies for one-time-only sales. HE transactions,1995,27(5),618-624.
[8]Arcelus, F.J., & Srinivasan, G Ordering policies under one time only discount and price sensitive demand. HE transactions,1998,30(11),1057-1064.
[9]Arcelus, F., & Srinivasan, G. Costing partial order cycles in the temporary sale price problem. International journal of production economics,1998,21-27.
[10]Arcelus, F., Pakkala, T., & Srinivasan, G. The temporary sale problem with unknown termination date. INFOR,2001(39),71-88.
[11]Arcelus, F., Pakkala, T., & Srinivasan, G. Special sales with guaranteed minimum duration but uncertain termination date. Applied mathematical modeling, 2003(27),677-699.
[12]Arcelus, F., Pakkala, T.P.M., & Srinivasan, G. Retailer's inventory policies for a one time only manufacturer trade deal of uncertain duration. Annals of operations research,2008(164),3-15.
[13]Arcelus, F.J., & Srinivasan, G. Marketing/inventory interactions in the characterization of retailer response to manufacturer trade deals. Managerial and decision economics,2006(27),537-547.
[14]Arcelus, F.J., Srinivasan, G., & Shah, N. H. Forward buying policies for deteriorating items under price sensitive demand and temporary price discounts. International journal of operations and quantitative management,2003,9(2), 87-101.
[15]Arcelus, F.J., Shah, N.H., & Srinivasan, G. Retailer's response to special sales: price discount vs trade credit. Omega,2001,29(5),417-428.
[16]Ardalan, A. Combined optimal prices and optimal inventory replenishment policies when a sale results in increase in demand. Computers and operations research,1991(18),721-730.
[17]Ardalan, A. Optimal prices and order quantities when temporary price discounts result in increase demand. European journal of operational research 1994,72(1), 52-61.
[18]Ardalan, A. Optimal ordering policies in response to a sale. IIE transactions, 1988(20),267-279.
[19]Arnold, J., Minner, S., & Eidam, B. Raw material procurement with fluctuating prices. International journal of production economics,2009,121(2),353-364.
[20]Arrow, K.J., Harris, T., & Marschak, J. Optimal Inventory Policy. Econometrica, 1951(19),250-273.
[21]Aucamp, D., & Kuzdrall, P. Lot sizes for one-time-only sales. Journal of the operational research society,1986(37),79-86.
[22]Aucamp, D., & Kuzdrall, P. Order quantities with temporary price reductions. Journal of the operational research society,1989(40),937-940.
[23]Aull-Hyde, R. Evaluation of supplier-restricted purchasing options under temporary price discounts. IIE transactions,1992(24),184-186.
[24]Axaster, S. Inventory control. Norwell, MA:Kluwer,2000.
[25]Baker, R. Inventory policy for items on sale during regular replenishment. Production and inventory management,1976(4),55-64.
[26]Banerjee, S., & Meitei, N.S. Effect of declining selling price:profit analysis for a single period inventory model with stochastic demand and lead time. Journal of the operational research society,2010,61(4),696-704.
[27]Berling, P. On determination of inventry cost parameters, Ph.D. Thesis, Lund University,2005.
[28]Berling, P. The capital cost of holding inventory with stochastically mean-reverting purchase price. European journal of operational research, 2008(186),620-636.
[29]Berling, P., & Rosling, K. The effect of financial risks on inventory policy. Management science,2005,51(12),1804-1815.
[30]Berling, P., & Martinez-de-Albeniz, V. Optimal inventory policies when purchase price and demand are stochastic. Operations research,2011,59(1),109-124.
[31]Bierman, H., & Thomas, J. Inventory decisions under inflationary conditions. Decisions sciences,1977(8),151-155.
[32]Buzacott, J.A. Economic order quantities with inflation. Operational research quarterly,1975,26(3, i),553-558.
[33]Chan, L.M.A., Shen, Z.J.M., Simchi-Levi, D., & Swann, J.L. Coordination of pricing and inventory decisions:a survey and classification. International series in operations research and management science,2004(74),335-392.
[34]Chambers, M. J., & Bailey, R. E. A theory of commodity price fluctuations. The review of economic studies,.1996,104(5),429-441.
[35]Chandra, J., & Bahner, M. The effect of inflation and the value of money on some inventory systems. International journal of production research,1985(23), 723-730.
[36]Chen, F.94%-effective policies for a two-stage serial inventory system with stochastic demand. Management science,1999,45(12),1679-1696.
[37]Chen, F., & Song, J-S. Optimal policies for multiechelon inventory problems with Markov-modulated demand. Operations research,2001,49(2),226-234.
[38]Chu, P., Chen, P., & Niu, T. Note on supplier-restricted order quantity under temporary price discounts. Mathematical methods of operations research, 2003(58),141-147.
[39]Deaton, A., & Laroque, G. On the behaviour of commodity prices. The review of economic studies,1992,59(1),1-23.
[40]Deaton, A., & Laroque, G. Competitive storage and commodity price dynamics. Journal of political economy,1996,104(5),896-923.
[41]Donaldson, W.A. Inventory replenishment policy for a linear demand:an analytical solution. Journal of the operational research society,1977,32(1), 37-42.
[42]Dye, C. Joint pricing and ordering policy for a deteriorating inventory with partial backlogging. Omega,2007,35(2),184-189.
[43]Edgeworth, F. The mathematical theory of banking. Journal of statistic society, 1888(51),113-127.
[44]Elmaghraby, W., & Keskinocak, P. Dynamic pricing in the presence of inventory considerations:research overview, current practices, and future directions. Management science,2003,49(10),1287-1309.
[45]Fabien, T., Fisher, J., Sasieni, W., & Yardeni, A. Purchasing raw material on a fluctuating market. Operations research,1959(7),107-122.
[46]Federgruen, A., Groenevelt, H., & Tijms, H. C. Coordinated replenishments in a multi-Item inventory system with compound Poisson demands. Management science,1984.30(3),344-357.
[47]Federgruen, A., & Zipkin, P. An inventory model with limited production capacity and uncertain demands I. The average-cost criterion. Mathematics of operations research,1986,11(2),193-207.
[48]Gao, J.S., Liu, Y.K., & Lan, Y.F. Optimizing material procurement planning problem by two-stage fuzzy programming. Computers & industrial engineering, 2010,58(1),97-107.
[49]Gascon, A. On the finite horizon EOQ model with cost changes. Operations research,1995,43(4),716-717.
[50]Geman, H. Commodities and commodity derivatives:modeling and pricing for agriculture, metals and energy. Wiley, Chichester,2005.
[51]Goel, A., & Gutierrez, G.J.2006. Integrating commodity markets in the optimal procurement policies of a stochastic inventory system. Working paper, Department of Information Risk and Operations Management, University of Texas-Austin.
[52]Golabi, K. Optimal inventory policies when ordering prices are random. Operations research,1985,33(3),575-588.
[53]Goyal, S.K. A note on the paper:an inventory model with finite horizon and price changes. The journal of the operational research society,1979,30(9),839-840.
[54]Goyal, S.K. Reply to comment on an improved procedure for the finite horizon and price changes inventory model. The journal of the operational research society,1980,31(1),81-82.
[55]Goyal, S.K. Economic ordering policy during special discount periods for dynamic inventory problems under certainty. Engineering costs and production economics,1990(20),101-104.
[56]Goyal, S.K. A note on "inventory models with cost changes". Operations research,1992,40(2),414-415.
[57]Goyal, S.K. An inventory model for a product for which purchase price fluctuates. New Zealand operational research,1975(3),112-117.
[58]Goyal, S.K. A comment on Martin's:note on an EOQ model with a temporary sale price. International journal of production economics,1996(43),283-284.
[59]Goyal, S.K. A comment on lot sizes for one-time-only sales. Journal of the operational research society,1986(37),817-818.
[60]Goyal, S.K., Srinivasan, G., & Arcelus, F. One time only incentives and inventory policies. European journal of operational research,1991(54),1-6.
[61]Goyal, S.K., & Jaber, M.Y. A note on optimal ordering policies in response to a discount offer. International journal of production economics,2008(112), 1000-1001.
[62]Goyal, S.K., & Bhatt, S.K. A generalized lot size policy for price increases. OPSEARCH,1988(25),272-278.
[63]Grubbstrom, R.W., & Kingsman, B.G. Ordering and inventory policies for step changes in the unit item cost:a discounted cash flow approach. Management science,2004,50(2),253-267.
[64]Grubbstrom, R.W., & Kigsman, B.G. Economic order quantity under price variations.11th meeting European working group financial model, Italy, and working paper WP-178, department of production economics, Linkoping institute of technology, SE-581,83 Linkoping, Sweden.
[65]Harris, F.W. How many parts to make at once. Factory, the magazine of management,1913(10),135-136,152.
[66]Harris, F.W. Economic order quantity model. Management science,1915,35(3), 898-900.
[67]Hall, R. Price changes and order quantities:impacts of discount rate and storage costs. HE transactions,1992(24),104-110.
[68]Hannan, E.L., & Smith, L.A. Economic order quantity for a finite demand horizon with a single price change-a note. New Zealand operations research, 1981(9),1.
[69]Hariga, M. The inventory replenishment problem with a linear trend in demand. Computer engineering,1993,24(2),143-150.
[70]Hariga, M.A. Optimal EOQ for deteriorating items with time-varying demand. Journal of operational research society,1996(47),1228-1246.
[71]Hariga, M.A., & Benkherouf, L. Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand. European journal of operational research,1994(79),123-137.
[72]Hartman, R. The effect of price and cost uncertainty on investment. Journal of economic theory,1972(5),258-266.
[73]Hite, G.L. On the theory of the firm in a capital asset pricing model world. In handbook of financial economics (edited by Bicksier J.L.), Amsterdam North-Holland,1979,163-188.
[74]Huang, W., Kulkarni, V.G., & Swaminathan, J.M. Optimal EOQ for announced price increases in infinite horizon. Operations Research,2003,51(2),336-339.
[75]Hsiao, Y-C. A note on integrated single vendor single buyer model with stochastic demand and variable lead time. International Journal of Production Economics.2008(114),294-297.
[76]Hsu, W.K., & Yu, H. EOQ model for imperfective items under a one-time only discount. Omega,2009,37(5),1018-1026.
[77]Jia, S. A note on the economic management of inventory or resource under stochastic prices. Journal of statistical planning and inference,2006,136(3), 1020-1038.
[78]Joglekar, P., & Lee, P. Comments on:a comparative analysis for determining optimal price and order quantity when a sale increases demand. European journal of operational research,1998,109(1),228-241.
[79]Joglekar, P., & Lee, P. Responding to a one-time-only sale of a product subject to sudden obsolescence. Academy of information and management sciences journal, 2003, January-July.
[80]Joglekar, P. A heuristic to determine price and lot size in face of a supplier's temporary price reduction over an interval. Academy of information and management science journal,2005,8(1),11/103.
[81]Joglekar, P., Lee, P., & Farahani, A.M. Continuously increasing price in an inventory cycle:an optimal strategy for E-tailers. Journal of applied mathematics and decision sciences,2008,14.
[82]Kalymon, B.A. Stochastic prices in a single-item inventory purchasing model. Operations research,1971,19(6),1434-1458.
[83]Kalymon, B.A. Stochastic costs in multi-period decision models. Ph.D. dissertation, Yale University, New Haven, Connecticut,1970.
[84]Kaplan, R.S. A dynamic inventory model with stochastic lead times. Management science,1970,16(7),491-507.
[85]Khouja, M., & Park, S. Optimal lot sizing under continuous price decrease. Omega,2003(31),539-545.
[86]Kingsman, B. Raw material purchasing:an operational research approach. Pergamon press, Oxford, UK,1985.
[87]Kingsman, B., & Boussofiane, A. Ordering and stock holding under price inflation when prices increase in successive discrete jumps. Production economics,1989(17),395-407.
[88]Lev, B., & Soyster, A.L. An inventory model with finite horizon and price changes. The journal of the operational research society,1979,30(1),43-53.
[89]Lev, B., Soyster, A.L., & Weiss, H.J. Comment on an improved procedure for the finite horizon and price changes inventory model. The journal of the operational research society,1979,30(9),840-842.
[90]Lev, B., & Weiss, H.J. Inventory models with cost changes. Operations research, 1990,38(1),53-63.
[91]Lev, B., Weiss H.J. & Soyster, A.L. A optimal ordering policies when anticipating parameter changes in EOQ systems. Naval research logistics quarterly,1981(28),267-279.
[92]Lev, B., & Soyster, A.L. An inventory model with finite horizon and price changes. The journal of the operational research society,1979,30(1),43-53.
[93]Li, C.L., & Kouvelis, P. Flexible and risk-sharing supply contract under price uncertainty. Management science,1999(45),1378-1398.
[94]Liberatore, M.J. Planning horizons for a stochastic lead-time inventory model. Operations research,1977,25(6),977-988.
[95]Liberatore, M.J. The EOQ model under stochastic lead time. Operations research, 1979,27(2),391-396.
[96]Lim, A., & Rodrigues, B. A note on the optimal EOQ for announced price increases in the infinite horizon. Operations research,2005(53),731-732.
[97]Maiti, A.K., Maiti M.K., & Maiti M. Inventory model with stochastic lead-time and price dependent demand incorporating advance payment. Applied mathematical modeling,2009,33(5),2433-2443.
[98]Martel, A., & Gascon, A. dynamic lot-sizing with price changes and price-dependent holding costs. European journal of operational research, 1998(111),114-128.
[99]Martin, G. Note on an EOQ model with a temporary sale price. International journal of production economics,1994(37),241-243.
[100]Markowski, E. Criteria for evaluating purchase quantity decisions in response to future price increases. European journal of operational research,1990(47), 364-370.
[101]Moinzadeh, K. Replenishment and stocking policies for inventory systems with random deal offerings. Management science,1997(14),90-114.
[102]Porteus, E.L. Foundations of stochastic inventory theory. Stanford, CA: Stanford University Press,2002.
[103]Presman, E., & Sethi, S.P. Inventory models with continuous and Poisson demands and discounted and average costs. Production and operations management,2006,15(2),279-293.
[104]Ramasesh, R.V. Lot-sizing decisions under limited-time price incentives:a review. Omega,2010(38),118-135.
[105]Ramasesh, R., & Rachamadugu, R. Lot-sizing decisions under limited-time price reduction. Decision science,2001(32),125-143.
[106]Rau, H., & Ouyang, B-C. A general and optimal approach for three inventory models with a linear trend in demand. Computer & industrial engineering,2007, 52(4),521-532.
[107]Rau, H., & Ouyang, B-C. Modelling of the inventory replenishment problem with a two-segment piecewise linear demand. International journal of systems science,2011,42(10),1613-1624.
[108]Samuelson, P.A. Rational theory of warrant pricing. Industrial management review,1965(6),13-31.
[109]Sana, S.S. The stochastic EOQ model with random sales price. Applied mathematics and computation,2011,218(2),239-248.
[110]Sarker, B.R., & Kindi, M.A. Optimal ordering policies in response to a discount offer. International journal of production economics,2006(100),195-211.
[111]Schmitt, A.J., Snyder, L.V., & Shen, Z.M. Inventory systems with stochastic demand and supply:properties and approximations. European Journal of operational research,2010,206(2),313-328.
[112]Schwartz, E., & Smith, J.E. Short-term variations and long-term dynamics in commodity prices. Management science,2000(46),893-911.
[113]Schwartz, E. S. The stochastic behaviour of commodity prices:implications for valuation and hedging. The journal of finance,1997,52(3),923-973.
[114]Schwarz, L.B. Economic ordering quantities for products with finite demand horizons. AIIE transactions,1972(4),234-237.
[115]Secomandi, N. Optimal inventory-trading policy for commodity storage assets. Working paper, Tepper school of business, Carnegie Mellon University, Pittsburgh, Pennsylvania,2007.
[116]Sethi, S.P., & Cheng, F. Optimality of (s, S) policies in inventory models with Markovian demand. Operations research,1997,45(6),931-939.
[117]Silver, E. Supplier planning a price increase? Industrial distribution,1980, 91-94.
[118]Silver, E., Edward, A., Pyke, D.F., & Rein, P. Inventory management and production planning and scheduling,3rd ed. Hoboken, NJ:Wiley,1998.
[119]Silver, E.A., Robb, D.J., & Rahnama, M.R. Random opportunities for reduced cost replenishments. HE transactions,1993(25),111-120.
[120]Song, J-S, Xu, S.H, & Liu, B. Order-fulfillment performance measures in an assemble-to-order system with stochastic lead times. Operations research,1999, 47(1),131-149.
[121]Song, J-S. The effect of leadtime uncertainty in a simple stochastic inventory model. Management science,1994,40(5),603-613.
[122]Taylor, S.G., & Bradley, C.E. Optimal ordering strategies for announced price increases. Operations research,1985,33(2),312-325.
[123]Tersine, R.J. Economic replenishment strategies for announced price increases. European journal of operational research,1996(92),266-280.
[124]Tersine, R.J., & Grasso, E.T. Forward buying in response to announced price increases. Journal of purchasing and materials management,1978(14),20-22.
[125]Tersine, R., & Schwarzkopf, A. Optimal stock replenishment strategies in response to temporary price reductions. Journal of business logistics,1989(10), 123-45.
[126]Tersine, R.J., & Price, R.L. Temporary price discounts and EOQ. Journal of purchasing and materials management,1981(17),23-27.
[127]Tersine, R.J., & Barman, S. Economic purchasing strategies for temporary price discounts. European journal of operational research,1995(80),328-343.
[128]Tersine, R.J. Economic replenishment strategies for announce price increases. European journal of operational research,1996(92),266-280.
[129]Teunter, R. A note on "Khouja and Park, optimal lot sizing under continuous price decrease". Omega,2005(31),467-471.
[130]Thorstenson, A., & Hultman, P. Price uncertainty and the effect of capital costs in a poin in-point out inventory investments. Managerial and decision ecomonics,1992,13(5),389-397.
[131]Tyagi, R.K. A characterization of retail response to manufacturing trade deals. Journal of marketing research,1999(36),510-516.
[132]Wilson, R.H. A scientific routine for stock control. Harvard business review, 1934(13),116-134.
[133]Wagner, H.M., & Whitin, T.M. Dynamic version of the economic lot size model. Management science,1958(5),89-96.
[134]Wang, Y. The optimality of myopic stocking policies for systems with decreasing purchasing prices. European journal of operational research,2001, 133(1),153-159.
[135]Whitin, T.M. Inventory control and price theory. Management science,1955(2), 61-68.
[136]Yanasse, H.H. EOQ systems:the case of an increase in purchase cost. The journal of the operational research society,1990,41(7),633-637.
[137]Yang, J., & Xia, Y.S. Acquisition management under fluctuating raw material prices. Working paper, Department of industrial and manufacturing engineering, New Jersey Institute of Technology, Newark, NJ,2008.
[138]Yano, C.A.,& Gilbert, S.M. Coordinated pricing and production/procurement decisions:a review. In:Chakravarty A., Eliashberg J., editors. Management business interfaces:marketing, engineering and manufacturing perspectives. Bostons, M.A.:Kluwer academic publishers,2002.
[139]Zalkind, D. Order-level inventory systems with independent stochastic leadtimes. Management science,1978,24(13),1384-1392.
[140]Zheng, Y.S. On properties of stochastic inventory systems. Management science, 1992(38),87-103.
[141]Zheng, Y. S. Optimal control policy for stochastic inventory system with Markovian discount opportunities. Operations research,1994,42(4),721-738.
[142]Zipkin, P.H. Foundations of inventory management, McGraw-Hill, Singapore, 2000.
[143]陈晖.几类库存控制模型研究.博士学位论文,重庆大学,2007.
[144]陈利华,赵庆祯.供应链不确定条件下制造商库存模型研究.物流科技,2009(05),65-68.
[145]白少布.面向供应链管理的库存控制理论与方法研究.博士学位论文,南京理工大学,2007.
[146]白少布,薛恒新.随机提前期多产品供应链库存控制策略研究.经济师,2006(12),26-27.
[147]曹晓刚.原材料价格波动下的生产—库存管理研究.博士学位论文,武汉大学,2009.
[148]曹晓刚,闻卉,夏火松.价格波动下的生产-库存控制研究.控制与决策,2010,25(5),730-734.
[149]戴更新,侯云章,于庆东.基于随机提前期的二级库存系统的优化方法. 数学的实践与认识,2006,36(3),52-57.
[150]方定宝,童晓萍.系列化生产企业的原料采购模型研究.数量经济技术经济研究,2003(4),117-121.
[151]高振,唐立新,王梦光.钢铁企业原燃料多目标采购模型.东北大学学报(自然科学版),2001(12),619-622.
[152]高振,唐立新,陶炜,肖新华.大型钢铁企业原料采购计划模型.系统工程学报,2003(12),566-570.
[153]龚光鲁,钱敏平.应用随机过程教程.北京：清华大学出版社,2004.
[154]耿修林.管理科学原理.北京：科学出版社,2006.
[155]黄欣.随机提前期与供给水平联和约束的库存问题.合肥学院学报(自然科学版),2005,15(1),42-45.
[156]李海清,图海宁,刘建胜.基于随机提前期的多品种备件库存成本控制研究.机械设计与制造,2006(11),153-154.
[157]林勇,蒋莲,乐晓娟.基于随机提前期的(Q,s)库存模型.物流技术,2007,26(7),32-34.
[158]林勇,马士华.基于随机提前期的通用件安全库存管理.工业工程与管理,2003(3),6-9.
[159]刘静,刘荣,郭小霞.基于随机提前期两种物品库存决策的优化仿真.高等函授学报(自然科学版),2010,23(2),60-62.
[160]刘培德.泛函分析基础.武汉：武汉大学出版社,1992.
[161]马士华,林勇.基于随机提前期的(Q,r)库存模型.计算机集成制造系统,2002,8(5),396-398.
[162]彼得.贝利等.采购原理与管理(第8版).王增东,杨磊译.北京：电子工业出版社,2003.
[163]向晋乾,李杰,黄培清.工业企业原材料采购与库存策略.上海管理科学,2004(2),39-42.
[164]杨杰.非平稳需求库存控制策略研究.博士学位论文,中国科学技术大学,2007.
[165]张春晓,谢金星.随机提前期随机需求条件下的二级库存模型.数学的实践与认识,2004,34(7),1-8.
[166]周永务.物流系统的库存控制模型与方法研究.博士学位论文,合肥工业大学,2002.
[167]周永务,王圣东.库存控制理论与方法.北京：科学出版社,2009.