现货价格波动下原材料最优采购决策研究
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摘要
随着经济全球化的快速发展,我国经济与世界经济关系不断密切,每个企业的经营活动都受到外部国际市场的影响。世界经济环境瞬息万变,因而企业面临越来越多的不确定性。由于受到各种因素的影响,如国际政治形势、自然灾害、货币汇率等,原材料供需关系经常变化,市场价格经常剧烈波动。原材料市场的波动给企业的采购过程带来了风险,让很多制造企业陷入了两难的困境。制造业中原材料的采购成本往往占销售额的60-80%,原材料价格的波动很大程度上影响企业利润的稳定性,因而许多企业非常注重采用适当策略控制采购成本以提高企业的竞争力。本文研究不确定环境下风险规避制造商的最优采购决策。
在总结现有采购风险管理相关研究的基础上,根据待采购原材料是否存在采购合约以及相应的金融工具,建立一个含四种采购情景的框架,并研究了各情景下采购者的最优采购策略。先讨论了单周期的最优采购策略,研究中运用均值——方差效用与期望效用理论来刻画决策者的风险规避行为,用风险管理理论分析风险环境下决策者的混合采购策略与套期保值策略。接着从离散时间与连续时间两个方面讨论了多周期下的最优采购策略,用随机动态规划方法研究离散时间的采购情形,而用最优控制方法研究连续时间的采购情形。
本文的主要研究结论如下：
(1)制造商利用长期合约或期权合约从供应商订购原材料,同时也从现货市场购买原材料。通过建立采购模型得到了制造商的最优混合采购策略。组合利用长期合约与现货方式采购时,最优长期合约订购数量与决策者风险规避度或现货价格波动的关系受到现货价格期望值与长期合约价格两者大小关系的影响；并且最优合约订购量随着现货价格期望值的变大而增加。
当组合期权合约与现货方式采购时,最优期权购买量与决策者风险规避度的关系受到期权定价的影响。采用混合策略后,制造商的均值——方差效用水平得以提高。
(2)原材料相应的金融市场工具存在时,制造商能利用期货或期权金融工具来应对原材料的采购风险。期货合约存在时,制造商的最优购买量(期货合约或长期合约)与风险规避度或现货价格波动的关系也会受到现货价格期望值与合约价格两者大小的影响。当期权合约存在时,制造商的最优期权合约与长期合约购买量受到决策者风险规避或现货价格波动影响的方向不同,若期权合约(长期合约)购买量增加,长期合约(期权合约)购买量则减少。用实证方法分析金属铜现货价格与期货价格间存在的均衡关系,以及得到了不完美套期保值时金属铜的最优套期保值比率。
(3)制造商利用长期合约与现货市场进行多周期采购时,分析了多周期的最优采购策略。在两周期的简化情形下,研究结果表明长期合约价出现不同的走势时,决策者的采购策略是不同的：原材料长期合约市场上价格有下跌风险时,决策者第一期的采购量仅用于满足第一期末的生产需求；原材料长期合约市场上价格有上涨风险时,决策者在第一期的采购量大于两期的生产需求之和；原材料长期合约市场价格平稳时,决策者会采用短视的采购策略。
(4)采购合约与金融工具都不存在时,获得了制造商仅利用现货市场的最优采购策略。制造商面临单个需求时,获得了最优库存控制策略。然后考查了离散时间采购的近似最优策略,结果表明风险规避的决策者采用分散采购策略,而风险中性的决策者会采用bang-bang采购策略。多个需求下决策者的最优采购策略取决于购买单位原材料效用的减小量与使用单位库存效用减少量的相对大小。最后,比较了风险规避与风险中性时总采购成本的差别,风险规避时制造商的采购成本并不会都低于风险中性下的采购成本,但是通过分散采购的方式能使总采购成本平均化。
Our economy is getting increasingly close to the world economy with the rapid development of economic globalization, and every enterprise's operations in our country are affected by the international market. The global economy is changing rapidly, so every enterprise is facing more and more uncertainties. The supply and demand balance of raw materials changes frequently as it is influenced by different factors, such as the international political situation, natural disasters, and currency exchange rates. Therefore, raw material price fluctuates a lot, which brings a great risk to procurement activities, and many manufacturers fall into trouble. The procurement cost of raw materials generally accounts for60-80%of total revenue in the manufacturing industry. The fluctuation of raw material price influences the stability of profits, so many enterprises put a lot of emphasis on adopting strategies to control procurement cost in order to increase their competitiveness. In this thesis optimal procurement strategies for a risk-averse manufacturer under uncertainty are investigated.
After making a summary of current researches on procurement risk management, a framework consisted of four purchasing scenarios is built, depending on whether the purchasing contracts and the corresponding financial tools of raw materials exist. First the optimal procurement strategy in one period is discussed. Mean-variance utility and expected utility theories are used to characterize a decision maker's (DM's) risk-averse behavior, and the risk management theory is used to analyze a DM's mixed procurement strategy and hedging strategy. Then the optimal procurement strategy in multiple period is discussed from both discrete-time and continuous-time perspectives. Stochastic dynamic programming is used to study the discrete-time situation, and the optimal control method is used to study the continuous-time situation.
The main conclusions of this thesis are as follows:
(1) A manufacturer utilizes a long-term contract or an option contract to order raw materials from a supplier, and he also buys materials from a spot market. An optimal mixed strategy is obtained for the manufacturer by building a purchasing model. When combining a long-term contract and a spot market for purchase, the relationship between the optimal ordering quantity via a long-term contract and the risk aversion degree of a DM or the volatility of spot price depends on whether the expected spot price or the price of a long-term contract is bigger. And the optimal ordering quantity via a long-term contract increases as the expected spot price becomes higher.
When combining an option contract and a spot market for purchase, the relationship between the optimal ordering quantity via an option contract and the risk aversion degree of a DM is affected by the option premium. The mean-variance utility of a manufacturer is improved after adopting a mixed strategy.
(2) If the corresponding financial tools of a raw material exist, a manufacturer can utilize futures or option contracts to hedge the procurement risk. When futures contracts exist, the relationship between the optimal purchasing quantity (via a futures contract or a long-term contract) and the risk aversion degree of a DM or the volatility of spot price also depends on whether the expected spot price or the price of a contract is bigger. When option contracts exist, the optimal purchasing quantities via an option contract and a long-term contract are influenced differently by the risk aversion degree of a DM or the volatility of spot price. If the purchasing quantity via an option contract increases, the purchasing quantity via a long-term contract decreases. An empirical method is used to analyze the equilibrium relationship between the spot price and futures price of copper. And the optimal hedge ratio of copper is obtained in the situation of imperfect hedge.
(3) When a manufacturer utilizes a long-term contract and a spot market for a multi-period purchase, the optimal procurement strategy in multiple periods is analyzed. In a two-period reduced model, it is demonstrated that a DM's procurement strategies are different when the price of a long-term contract exhibits different trends. If the contract price has a downward trend, the purchasing quantity in the first period only satisfies the demand at the end of the first period. If the contract price has an upward trend, the purchasing quantity in the first period is greater than the sum of the demands of both periods. If the contract price is stable, a myopic procurement strategy will be used.
(4) When both purchasing contracts and financial tools don't exist, only the spot market is used for purchase. If a manufacturer faces a single demand, an optimal inventory control policy is obtained. Then the approximate optimal strategy of discrete-time procurement is investigated. A risk-averse DM uses a decentralized procurement strategy, while a risk-neutral DM uses a bang-bang procurement strategy. The optimal strategy in multiple periods depends on whether the utility reduction of buying a raw material or the utility reduction of using inventory is bigger. Finally, the difference of total purchasing costs between a risk-averse DM and a risk-neutral DM is compared. The purchasing cost of a risk-averse DM is not always lower than that of a risk-neutral DM; however, the total purchasing cost can be averaged by a decentralized procurement strategy.
在总结现有采购风险管理相关研究的基础上,根据待采购原材料是否存在采购合约以及相应的金融工具,建立一个含四种采购情景的框架,并研究了各情景下采购者的最优采购策略。先讨论了单周期的最优采购策略,研究中运用均值——方差效用与期望效用理论来刻画决策者的风险规避行为,用风险管理理论分析风险环境下决策者的混合采购策略与套期保值策略。接着从离散时间与连续时间两个方面讨论了多周期下的最优采购策略,用随机动态规划方法研究离散时间的采购情形,而用最优控制方法研究连续时间的采购情形。
本文的主要研究结论如下：
(1)制造商利用长期合约或期权合约从供应商订购原材料,同时也从现货市场购买原材料。通过建立采购模型得到了制造商的最优混合采购策略。组合利用长期合约与现货方式采购时,最优长期合约订购数量与决策者风险规避度或现货价格波动的关系受到现货价格期望值与长期合约价格两者大小关系的影响；并且最优合约订购量随着现货价格期望值的变大而增加。
当组合期权合约与现货方式采购时,最优期权购买量与决策者风险规避度的关系受到期权定价的影响。采用混合策略后,制造商的均值——方差效用水平得以提高。
(2)原材料相应的金融市场工具存在时,制造商能利用期货或期权金融工具来应对原材料的采购风险。期货合约存在时,制造商的最优购买量(期货合约或长期合约)与风险规避度或现货价格波动的关系也会受到现货价格期望值与合约价格两者大小的影响。当期权合约存在时,制造商的最优期权合约与长期合约购买量受到决策者风险规避或现货价格波动影响的方向不同,若期权合约(长期合约)购买量增加,长期合约(期权合约)购买量则减少。用实证方法分析金属铜现货价格与期货价格间存在的均衡关系,以及得到了不完美套期保值时金属铜的最优套期保值比率。
(3)制造商利用长期合约与现货市场进行多周期采购时,分析了多周期的最优采购策略。在两周期的简化情形下,研究结果表明长期合约价出现不同的走势时,决策者的采购策略是不同的：原材料长期合约市场上价格有下跌风险时,决策者第一期的采购量仅用于满足第一期末的生产需求；原材料长期合约市场上价格有上涨风险时,决策者在第一期的采购量大于两期的生产需求之和；原材料长期合约市场价格平稳时,决策者会采用短视的采购策略。
(4)采购合约与金融工具都不存在时,获得了制造商仅利用现货市场的最优采购策略。制造商面临单个需求时,获得了最优库存控制策略。然后考查了离散时间采购的近似最优策略,结果表明风险规避的决策者采用分散采购策略,而风险中性的决策者会采用bang-bang采购策略。多个需求下决策者的最优采购策略取决于购买单位原材料效用的减小量与使用单位库存效用减少量的相对大小。最后,比较了风险规避与风险中性时总采购成本的差别,风险规避时制造商的采购成本并不会都低于风险中性下的采购成本,但是通过分散采购的方式能使总采购成本平均化。
Our economy is getting increasingly close to the world economy with the rapid development of economic globalization, and every enterprise's operations in our country are affected by the international market. The global economy is changing rapidly, so every enterprise is facing more and more uncertainties. The supply and demand balance of raw materials changes frequently as it is influenced by different factors, such as the international political situation, natural disasters, and currency exchange rates. Therefore, raw material price fluctuates a lot, which brings a great risk to procurement activities, and many manufacturers fall into trouble. The procurement cost of raw materials generally accounts for60-80%of total revenue in the manufacturing industry. The fluctuation of raw material price influences the stability of profits, so many enterprises put a lot of emphasis on adopting strategies to control procurement cost in order to increase their competitiveness. In this thesis optimal procurement strategies for a risk-averse manufacturer under uncertainty are investigated.
After making a summary of current researches on procurement risk management, a framework consisted of four purchasing scenarios is built, depending on whether the purchasing contracts and the corresponding financial tools of raw materials exist. First the optimal procurement strategy in one period is discussed. Mean-variance utility and expected utility theories are used to characterize a decision maker's (DM's) risk-averse behavior, and the risk management theory is used to analyze a DM's mixed procurement strategy and hedging strategy. Then the optimal procurement strategy in multiple period is discussed from both discrete-time and continuous-time perspectives. Stochastic dynamic programming is used to study the discrete-time situation, and the optimal control method is used to study the continuous-time situation.
The main conclusions of this thesis are as follows:
(1) A manufacturer utilizes a long-term contract or an option contract to order raw materials from a supplier, and he also buys materials from a spot market. An optimal mixed strategy is obtained for the manufacturer by building a purchasing model. When combining a long-term contract and a spot market for purchase, the relationship between the optimal ordering quantity via a long-term contract and the risk aversion degree of a DM or the volatility of spot price depends on whether the expected spot price or the price of a long-term contract is bigger. And the optimal ordering quantity via a long-term contract increases as the expected spot price becomes higher.
When combining an option contract and a spot market for purchase, the relationship between the optimal ordering quantity via an option contract and the risk aversion degree of a DM is affected by the option premium. The mean-variance utility of a manufacturer is improved after adopting a mixed strategy.
(2) If the corresponding financial tools of a raw material exist, a manufacturer can utilize futures or option contracts to hedge the procurement risk. When futures contracts exist, the relationship between the optimal purchasing quantity (via a futures contract or a long-term contract) and the risk aversion degree of a DM or the volatility of spot price also depends on whether the expected spot price or the price of a contract is bigger. When option contracts exist, the optimal purchasing quantities via an option contract and a long-term contract are influenced differently by the risk aversion degree of a DM or the volatility of spot price. If the purchasing quantity via an option contract increases, the purchasing quantity via a long-term contract decreases. An empirical method is used to analyze the equilibrium relationship between the spot price and futures price of copper. And the optimal hedge ratio of copper is obtained in the situation of imperfect hedge.
(3) When a manufacturer utilizes a long-term contract and a spot market for a multi-period purchase, the optimal procurement strategy in multiple periods is analyzed. In a two-period reduced model, it is demonstrated that a DM's procurement strategies are different when the price of a long-term contract exhibits different trends. If the contract price has a downward trend, the purchasing quantity in the first period only satisfies the demand at the end of the first period. If the contract price has an upward trend, the purchasing quantity in the first period is greater than the sum of the demands of both periods. If the contract price is stable, a myopic procurement strategy will be used.
(4) When both purchasing contracts and financial tools don't exist, only the spot market is used for purchase. If a manufacturer faces a single demand, an optimal inventory control policy is obtained. Then the approximate optimal strategy of discrete-time procurement is investigated. A risk-averse DM uses a decentralized procurement strategy, while a risk-neutral DM uses a bang-bang procurement strategy. The optimal strategy in multiple periods depends on whether the utility reduction of buying a raw material or the utility reduction of using inventory is bigger. Finally, the difference of total purchasing costs between a risk-averse DM and a risk-neutral DM is compared. The purchasing cost of a risk-averse DM is not always lower than that of a risk-neutral DM; however, the total purchasing cost can be averaged by a decentralized procurement strategy.
引文
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