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An empirical analysis of the dynamic programming model of stockpile acquisition strategies for China's strategic petroleum reserve
ARTICLE IN PRESS
Energy Policy 36 (2008) 1470–1478 www.elsevier.com/locate/enpol
An empirical analysis of the dynamic programming model of stockpile acquisition strategies for China’s strategic petroleum reserve Gang Wua, Ying Fana, Lan-Cui Liua,b, Yi-Ming Weia, a
Center for Energy and Environmental Policy Research, Institute of Policy and Management (IPM), Chinese Academy of Sciences (CAS), P.O. Box 8712, Beijing 100080, China b Center for Forecasting Science, Chinese Academy of Sciences, Beijing 100080, China Received 25 August 2007; accepted 3 January 2008 Available online 11 February 2008
Abstract The world’s future oil price is affected by many factors. The challenge, therefore, is how to select optimal stockpile acquisition strategies to minimize the cost of maintaining a reserve. This paper provides a new method for analyzing this problem using an uncertain dynamic programming model to analyze stockpile acquisition strategies for strategic petroleum reserve. Using this model, we quantify the impact of uncertain world oil price on optimal stockpile acquisition strategies of China’s strategic petroleum reserve for the period 2007–2010 and 2011–2020. Our results show that the future stockpile acquisition is related to oil prices and their probability and, if not considering the occurrence of oil supply shortage, China should at least purchase 25 million barrels when world oil price is at an optimal level. The optimal price of stockpile acquisition of every year has a stronger relationship with the probability of high price; and the optimal expected price and size of stockpile acquisition is different in each year. r 2008 Elsevier Ltd. All rights reserved. Keywords: Strategic petroleum reserve; Uncertain dynamic programming model; Stockpile acquisition strategies
1. Introduction Energy is one of the most significant factors driving China’s economic growth. With continuous development of China’s economy, there is a need for increasing quantities of oil to meet increasing demand. However, international oil price has fluctuated at the higher levels since 2004. China’s oil import dependence has increased rapidly since 1996 when it became a net oil importer. China’s crude oil import is 145 million tons and import dependence is 43.9 per cent (General Administration of Customs of China, 2007). Most of the oil import came from the unstable Middle East; 80 per cent of the imported oil has to get across the perilous Malacca Strait. Consequently, security of China’s oil supply becomes one of the most serious challenges for economic development. In reality, strategic petroleum reserve (SPR) is one of Corresponding author. Tel./fax: +86 10 62650861.
E-mail addresses: [email protected], [email protected] (Y.-M. Wei). 0301-4215/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2008.01.007
the most effective measures to ensure national oil supply security. It was anticipated that the creation of a significant operational reserve of crude oil would discourage the use of oil as a ‘weapon’. In the event of any interruption, introduction into the market of oil from the reserve was expected to help calm markets, mitigate sharp price spikes, and reduce the economic dislocation. After the OPEC oil embargo, the US established SPR in 1975. The SPR was originally intended to hold at least 750 million barrels of crude oil as an insurance policy against future supply cutoffs. In United States, the US government can fill the SPR by either purchasing oil on the open market, or by collecting royalties from oil producers in the form of ‘in kind’ payments (i.e., oil). Most of the oil added to the reserve in the late 1970s and early 1980s was purchased on the open market when prices were relatively high. This is the main reason why the average price of oil in the SPR is greater than $27 per barrel. Recently, the SPR has been filled by collecting royalty oil from companies who operate leases on the federally owned Outer Continental Shelf. By law, these companies must pay royalties on these leases in
ARTICLE IN PRESS G. Wu et al. / Energy Policy 36 (2008) 1470–1478
the range of 12.5–16.7 per cent of the oil produced. This percentage can be paid in oil dollars equivalent or by actually delivering the oil ‘in kind’. In order to enhance oil supply security, China’s government established its own SPR in 2004. The Zhenhai base was finished in August, 2006. Subsequently, the most important question for China’s decision-makers is how to fill the reserve. The establishment of SPR requires spending large amount of capital, including the cost to buy oil and the cost of maintenance. Hence, the challenge is to determine how much oil to purchase to fill the reserve in an uncertain world oil market. Since the 1980s, several researchers have established models to quantify the optimal SPR, stockpile acquisition, and release strategies. Wei et al. (2008) quantifies China’s optimal SPR for the period 2005–2020, using a decision tree model based on a cost function. Murphy et al. (1989) presented and analyzed a Nash dynamic game model for investigating public and private sector oil inventory policies in unstable world oil markets. Samouilidis and Berahas (1982) established a cost function which includes the inventory procurement and maintenance cost and the shortage cost inflicted by a petroleum shortfall, and evaluated each scenario based on the cost function and decision tree model. Samouilidis and Magirou (1985) presented a simple analysis for the optimal selection of the level of petroleum reserve for a small country, based on the study of Samouilidis and Berahas (1982). Zweifel and Bonomo (1995) developed an optimal reserve model that takes into account multiple risks for oil and gas, and identified that one-dimensional rules such as ‘oil reserve for 90 days’, result in not only suboptimally, but also require adjustments that exacerbate suboptimality. Teisberg (1981) developed a stochastic dynamic programming model that allows explicit consideration of such uncertainty. The model has been used to determine the size of the US SPR and the optimal fill-up and draw-down rate contingent upon the supply conditions, time, and available inventory. Hogan (1983) extends the Teisberg’s model of US stockpiling to a Stackelberg model, examining the interactions between two consuming countries, where one follows the other’s lead. Oren and Wan (1986) explored a simple model to determine the optimal size, stockpile acquisition, and draw-down rates for an SPR under a variety of supply and demand conditions. Murphy et al. (1987) present a Nash dynamic game model of interactions among oil inventory and tariff policies for oil importing countries. They presented empirical results of the size of the stockpiles as a function of disruption probabilities, tariff policies, and cooperation versus non-cooperation between nations. Chao and Manne (1983) developed a multi-period dynamic programming model for determining optimal stockpiles and petroleum usage rates, based on their analysis of US petroleum supply policies. Similar interactions between public and private stocks in the US are considered by Wright and Williams (1982), though their focus is primarily on the implications of oil price controls and on game-
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theoretic ‘dynamic consistency’ questions that arise in comparing Nash and Stackelberg outcomes. Balas (1981) studied a short-run game between importing nations and a politically motivated cartel that takes advantage of disruptions to inflict economic losses on importing nations. In this context, he examines the ‘deterrence effect’ of strategic stocks where the deterrence effect is the value of a strategic reserve when the stockpile not only reduces the economic losses from a disruption, but also reduces the likelihood of a disruption. Greene et al. (1998) demonstrated the potential for future price shocks and economic losses based on a simulation model of the world market and price impacts on the US economy. His results indicated that the use of strategic reserve is relatively ineffective in reducing the damage to the US economy from such a prolonged price shock. There are relatively few studies on China’s stockpile acquisition strategies. Chen and Zheng (2006) analyzed qualitatively the imminence and necessity of SPR for China. They consider that China should not purchase oil to fill the reserve when world oil price is high, in addition to consideration of the experience of SPR in US. For decision-makers, this kind of descriptive analysis may not provide scientific information for the optimal decisions, due to uncertain world oil prices and economic risks of stockpile acquisition for SPR. Moreover, it is difficult to make scientific decisions using only judgments based on intuition. Therefore, it is necessary to quantify the optimal stockpile acquisition strategies for SPR in different years, based on an uncertain dynamic programming model. This article is organized as follows. Section 2 describes the methods and assumption of uncertain dynamic programming modeling. Section 3 presents and discusses the empirical results of optimal stockpile acquisition strategies. The final section presents conclusions and policy implications. 2. An uncertain dynamic programming model of China’s SPR Based on the US SPR models developed by Teisberg (1981), Samouilidis and Berahas (1982), Samouilidis and Magirou (1985), Oren and Wan (1986), and Murphy et al. (1987), we also develop an uncertain dynamic programming model of the china’s SPR. The establishment of SPR means that China must purchase sufficient oil to fill the reserve. Yet, it is impossible to buy this from the open market in a single purchase. In order to reduce the reserve cost, China needs to make varying decisions at different times because of the uncertainty of international oil prices. Moreover, such decisions will directly influence future decisions for filling the reserve. When decisions at different times are made, it will form the decisions series. Therefore, the optimal stockpile acquisition is a problem of multi-period decisions. Hence, this paper presents an uncertain dynamic programming model of China’s SPR. We also explore the
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problem of stockpile acquisition and if it affects world oil prices. Here the world oil price is an uncertain variable, with a probability distribution. This paper uses a dynamic programming with each year as a stock stage and yearly oil price as the state of its stage. So the uncertainty dynamic programming model of China’s SPR can be expressed as M 0 ðEðtÞ; tÞ ¼ minfC 0 ðEðtÞ; A; tÞg. A
(1)
The stockpile cost function of SPR: C 0 fEðtÞ; A; tg ¼ A f t ðpt Þ þ v ½EðtÞ þ A.
(2)
The optimal decision of the stockpile opportunity of SPR: ( 1 when f t ðpt Þ ¼ pt ; xt ¼ (3) 0 when f t ðpt Þ ¼ ptE ; f t ðpt Þ ¼ minfpt ; ptE g
pt 2 st .
(4)
From the definition of ptE and f t ðpt Þ we know that X ptE ¼ Eff tþ1 ðptþ1 Þg ¼ ri f tþ1 ðptþ1 Þ, (5) where ri is the probability of different oil price in the oil market. The definition of variables in the model can be found in Table 1. 3. Assumptions and data for empirical analysis 3.1. Assumptions of the model (1) We assume that China’s stockpile acquisition does not affect world oil price. The first project of China’s SPR will be finished at the end of 2008, its inventory is about 12 million tons (about 87.6 million barrels), and Table 1 The definition of variables in the model Variables
Definition of variables
pt st xt
State variables, the normal oil price in year t State set, the range of oil prices in the future xt is decision variable, ‘xt ¼ 1’ indicates decision to increase stockpiles in year t; ‘xt ¼ 0’ indicates decision to keep stockpiles in year t unchanged It refers to the expected price when adopting optimal decisions after year t The minimal expected price adopting the optimal decision from year t to year t1, when the world oil price in year t is pt It refers to the probability of different world oil prices The stockpile acquisition cost of SPR The stockpile size of the period t The stockpile acquisition The annualized unit stockpile holding cost. Here it is set at $0.32 per barrel The minimized cost of stockpile acquisition of SPR
ptE ft (pt)
ri C 0 fEðtÞ; A; tg E(t) A V 0
M ðEðtÞ; tÞ
average 21.9 million barrels per year during the period of 2007–2010. If all is from the international oil market, it is equal to an increase of 60 thousand barrels per day, and is about 15.1 per cent of daily crude oil import in 2006. In addition, the office of Energy Information Administration (EIA) of the US Department of Energy shows that the oil price should be slightly affected by the rate of stockpiling. Moreover, Teisberg (1981) also considers various scenarios and concludes that stockpile acquisition does not affect world oil price. Therefore, we assume that China’s stockpile acquisition, likewise, does not affect world oil price. (2) We assume that the low, middle, and high world oil price will be $55.0/bbl, $65.0/bbl, $100/bbl, respectively, in 2007–2010. Based on the current world oil price and the future world price forecast (Fig. 1; EIA/AEO2007), we consider two scenarios; in the first scenario, we assume the probabilities of low, middle, and high oil price are 0.3, 0.3, and 0.4, respectively. In the second scenario, we assume the probabilities of low, middle, and high oil price are 0.1, 0.1, and 0.8, respectively. According to the results of AEO2007, we assume that the low, middle, high, and higher world oil price will be $45.0/bbl, $55.0/bbl, $65.0/bbl, and $100/bbl, respectively, in 2011–2020. We consider two scenarios: in the first scenario, we assume the probabilities of low, middle, high, and higher oil price are 0.25, 0.25, 0.25, and 0.25, respectively; in the second scenario, we assume the probabilities of low, middle, high, and higher oil price are 0.1, 0.1, 0.4, and 0.4, respectively. 3.2. Data sources China’s optimal SPR for 2010 and 2020 are based on Wei et al. (2006). Because China’s SPR is at an early stage and there is no unit cost for reserve, we assume that the annual unit holding cost is equal to that of United States,
Fig. 1. 1990–2030 world oil prices in three AEO2007 cases (2005 dollars per barrel). Note: Energy Information Administration/Annual Energy Outlook 2007.
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should it buy to fill the reserve in order to minimize the holding cost in 2007–2010? Based on application of the uncertain dynamic programming model [1], we get the optimal stockpile acquisition strategies of China’s SPR. Results are shown in Fig. 2 and Table 2:
i.e., $0.32/barrel. The capacity of the first SPR bases can reach approximately 87.60 million barrels in 2008. Wei et al. (2008) concludes that the optimal SPR is 100 million barrels in 2010 (equal to the net oil import for 30 days). The Chinese government claims that the reserve capacity of SPR will be 30 days net oil import in 2010, so the yearly rate of stockpile acquisition is 25 million barrels if the optimal decision is to purchase over the period 2007–2010.
(1) When the world oil price is lower than $62.56/bbl in 2007, then China should buy 25 million barrels of crude oil for filling the SPR; otherwise, it should wait and keep the reserve constant until world oil price is lower than $62.56/bbl in 2007. (2) When the world oil price is lower than $66.40/bbl in 2008, then it should at least purchase 25 million barrels of crude oil to raise the SPR to 50 million barrels; otherwise, it should keep the reserve level constant until world oil price is lower than $66.40/bbl in 2008. (3) When the world oil price is lower than $76.00/bbl in 2009, then it should at least buy 25 million barrels of crude oil to increase SPR to 75 million barrels. When the world oil price is higher than $66.40/bbl, and lower
4. Results and discussions 4.1. Scenario 1: the optimal stockpile acquisition for the period 2007–2010, when there is low probability of a high oil price EIA forecasts the world oil price in three cases and, from this, we assume that the oil price will be $55.0/bbl, $65.0/bbl, $100/bbl, respectively, and their probabilities are 0.3, 0.3, and 0.4, respectively. The question then is what oil price level should China purchase oil and how much
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Note: the unit of total expected acquisition cost of SPR is million dollar
Fig. 2. The optimal stockpile acquisition strategies of China’s SPR for the period of 2007–2010 when there is low probability of high oil price.
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Table 2 The optimal stockpile acquisition strategies for China’s SPR in 2007–2010 Year
The low probability of high oil price
The high probability of high oil price
pt ($/bbl)
xt
A (million barrels)
pt ($/bbl)
xt
A (million barrels)
2007
p$62.56/bbl 4$62.56/bbl
1 0
25 0
p$80.48/bbl 4$80.48/bbl
1 0
25 0
2008
p$66.40/bbl 4$66.40/bbl
1 0
25–50 0
p$85.60/bbl 4$85.60/bbl
1 0
25–50 0
2009
p$66.40/bbl $66.40–76.00/bbl 4$76.00/bbl
1 1 0
25–75 25–75 0
p$92.00/bbl
1
25–75
4$92.00/bbl
0
0
The current price
1
25–100
The current price
1
25–100
2010
than $76.00/bbl, it should buy at most 75 million barrels of crude oil; otherwise, it should keep SPR constant until world oil price is lower than $76.00/bbl in 2009. (4) In order to ensure national energy supply security, China should reach the reserve capacity of 100 million barrels in 2010 whatever the world oil price is.
4.2. Scenario 2: the optimal stockpile acquisition for the period of 2007–2010, when there is high probability of high oil price
(4) In order to ensure national energy supply security, it should reach the reserve capacity of 100 million barrels in 2010 whatever world oil price is, and at least buy 25 million barrels whatever world oil price is.
4.3. Scenario 3: the optimal stockpile acquisition for the period of 2011–2020, when there is low probability of high oil price
The unsolved ‘Iran nuclear problem’, new global conflicts, terrorism in some regions, and speculation capital, may induce the world oil price to remain at the higher level. Moreover, future oil prices in 2007–2010 may remain at the higher level. Therefore, we assume that the world oil prices will be $55.0/bbl, $65.0/bbl and $100/bbl, respectively, and their probabilities are 0.1, 0.1, and 0.8, respectively. Then in this scenario, what oil price level should China purchase oil, and how much should it buy to fill the reserve in order to minimize the holding cost in 2007–2010? Based on the uncertain dynamic programming model [1], we get the optimal stockpile acquisition strategies of China’s SPR, which can be found in Fig. 3 and Table 2:
According to the world oil price forecast of EIA (Annual Energy Outlook 2007), we assume that the oil price will be $45.0/bbl, $55.0/bbl, $65.0/bbl and $100/bbl, respectively, and the probabilities of different prices are 0.25. The decision is then what oil price level should China purchase oil, and how much should it buy to fill the reserve in order to minimize the holding cost in 2011–2020? According to the results of Wei et al. (2008), the optimal size of China’s SPR is 60 days of net oil import or 90 days of net oil import in 2020 when oil price is at a high level ($50.0/bbl). In order to meet the greatest volume of SPR, this paper selects 350 million barrels (90 days of net oil import) in this model. Based on the uncertain dynamic programming model [1], we get the optimal stockpile acquisition strategies for 2011–2020, which can be found in Fig. 4 and Table 3.
(1) When the world oil price is lower than $80.48/bbl in 2007, then it should buy 25 million barrels of crude oil for reserve; otherwise, it should keep the reserve constant until world oil price is lower than $80.48/bbl in 2007. (2) When the world oil price is lower than $85.60/bbl in 2008, then it should purchase at least 25 million barrels of crude oil to make the reserve reach 50 million barrels; otherwise, it should keep the reserve constant until world oil price is lower than $85.60/bbl in 2008. (3) When the world oil price is lower than $92.00/bbl in 2009, then it should buy at least 25 million barrels of crude oil to make the reserve reach 75 million barrels; otherwise, it should keep the reserve constant until world oil price is lower than $92.00/bbl in 2009.
(1) When the world oil price is lower than $53.91/bbl in 2011–2017, then it should buy at least 175 million barrels oil to increase the reserve; otherwise, it should keep the reserve constant until world oil price is lower than $53.91/bbl in 2011–2017. (2) When the world oil price is lower than $57.81/bbl in 2018, then it should purchase at least 25 million barrels of crude oil to increase the reserve to 300 million barrels; otherwise, it should keep the reserve level constant until world oil price is lower than $57.81/bbl in 2018. (3) When the world oil price is lower than $57.81/bbl in 2019, then it should purchase at least 25 million barrels of crude oil to increase the reserve to 325 million barrels. When the world oil price is higher than
ARTICLE IN PRESS G. Wu et al. / Energy Policy 36 (2008) 1470–1478
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Fig. 3. The optimal stockpile acquisition strategies of China’s SPR for the period of 2007–2010 when there is high probability of high oil price.
$57.81/bbl, and lower than $66.25/bbl in 2019, it should buy at most 225 million barrels of crude oil; otherwise, it should keep the reserve constant until world oil price is lower than $66.25/bbl in 2019. (4) In order to ensure national energy supply security, China should reach the reserve capacity of 350 million barrels in 2020 whatever the world oil price is.
4.4. Scenario 4: the optimal stockpile acquisition strategies for the period of 2011–2020, when there is high probability of high oil price According to the world oil price forecast of EIA (Annual Energy Outlook 2007), we assume that the oil price will be $45.0/bbl, $55.0/bbl, $65.0/bbl and $100/bbl, respectively, and the probabilities of different prices are 0.1, 0.1, 0.4, and 0.4, respectively. What oil price should China purchase oil, and how much should it buy to fill the reserve in order to minimize the holding cost in 2011–2020? Based on the
uncertain dynamic programming model [1], we get China’s optimal stockpile acquisition strategies results for 2011–2020, which can be found in Fig. 5 and Table 4. (1) When the world oil price is lower than $54.11/bbl in 2011–2012, then it should buy at least 50 million barrels crude oil for the reserve; otherwise, it should keep SPR constant until world oil price is lower than $54.11/bbl in 2011–2012. (2) When the world oil price is lower than $54.11/bbl in 2013–2017, then it should purchase at least 125 million barrels crude oil to make the reserve reach 275 million barrels. When the world oil price is higher than $54.11/bbl, and lower than $62.56/bbl, it should buy at most 175 million barrels of crude oil; otherwise, it should keep the reserve constant until world oil price is lower than $62.56/bbl in 2013–2017. (3) When the world oil price is lower than $76.00/bbl in 2018–2019, then it should buy at least 50 million barrels of crude oil to make the reserve reach 325 million
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Fig. 4. The optimal stockpile acquisition strategies for China’s SPR in the period of 2011–2020 when there is low probability of high oil price.
Table 3 The optimal stockpile acquisition strategies for China’s SPR in 2011–2020, when there is low probability of high oil price Year
pt ($/bbl)
xt
A (million barrels)
2011–2017
p$53.91/bbl 4$53.91/bbl
1 0
X175 0
2018
p$57.81/bbl 4$57.81/bbl
1 0
25–200 0
2019
p$57.81/bbl $57.81–66.25/bbl 4$66.25/bbl
1 1 0
at least 25–225 at most 25–225 0
The current price
1
25–250
2020
barrels. When the world oil price is higher than $54.11/bbl, and lower than $62.56/bbl in 2018–2019, it should purchase 50–225 million barrels crude oil.
When the world oil price is higher than $62.56/bbl, and lower than $76.00/bbl in 2018–2019, it should buy at most 225 million barrels crude oil; otherwise, it should keep the reserve constant until world oil price is lower than $76.00/bbl in 2018–2019. (4) In order to ensure national energy supply security, it should reach the reserve capacity of 350 million barrels in 2020 whatever the world oil price is.
5. Conclusions and policy implications In this paper, the stockpile acquisition problem of SPR is formulated and solved using an uncertainty dynamic programming model. The model takes into consideration the variability of oil price probabilities and its effect on the stockpile acquisition. The future stockpile acquisition is related to the oil prices and their probability, and the optimal world price
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P
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$16353.5
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Fig. 5. The optimal stockpile acquisition strategies of China’s SPR for the period of 2011–2020 when there is high probability of high oil price. Note: P* is $62:56=bblopricep$76:00=bbl, P** is $54:11=bblopricep$62:56=bbl.
Table 4 The optimal stockpile strategies for China’s SPR in 2011–2020, when there is high probability of high oil price Year
pt ($/bbl)
xt
A (million barrels)
2011–2012
p$54.11/bbl 4$54.11/bbl
1 0
X50 0
2013–2017
p$54.11/bbl $54.11–62.56/bbl 4$62.56/bbl
1 1 0
at least 125–175 125–175 0
2018–2019
p$54.11/bbl $54.11–62.56/bbl $62.56–76.00/bbl 4$76.00/bbl
1 1 1 0
at least 50–225 50–225 at most 50–225 0
2020
The current price
1
25–250
level will increase $17.92/bbl from $62.56/bbl to $80.48/bbl when the probability of $100.0/bbl becomes 0.8 from 0.4. Therefore, it is optimal to purchase future oil to fill the reserve. If there is no oil supply shortage, it should purchase at least 25 million barrels when world oil price is at an optimal level. Whatever the oil price is, it should purchase oil to make the SPR 30 days net imports in 2010 and 90 days net imports in 2020. When there is low probability of high oil price in 2007–2010, the minimum expected total acquisition cost of SPR is 6824.0 million dollar; when there is high probability of high oil price in 2007–2010, the minimum expected total acquisition cost of SPR is 8792.0 million dollar; when there is low probability of high oil price in 2011–2020, the minimum expected total acquisition cost of SPR is 14165.0
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million dollar; and when there is high probability of high oil price in 2011–2020, the minimum expected total acquisition cost of SPR is 14146.75 million dollar. This paper further analyzes the stockpile acquisition and release strategies when considering the occurrence of oil supply shortage. Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant nos. 70425001, 70733005, 70701032, and the National Key Projects from the Ministry of Science and Technology of China (Grant 2006-BAB08B01). The authors also thank Professor Nicky France and the anonymous referees for their helpful suggestions and corrections on the earlier draft of this paper according to which the content was improved. References Balas, E., 1981. The strategic petroleum reserve: how large should it be? In: Bayraktar, B.A., et al. (Eds.), Energy Policy Planning. Plenum Press, New York. Chao, H.P., Manne, A.S., 1983. Oil stockpiles and import reductions: a dynamic programming approach. Operations Research 31 (4), 632–651. Chen, S.H., Zheng, S.M., 2006. The time option for China to establish strategic petroleum reserve. Economic Management (21), 22–25 (in Chinese). Energy Information Administration (EIA) of the US Department of Energy, 2007. Annual energy outlook 2007 with projections to 2030 /www.eia.doe.gov/oiaf/aeoS.
General Administration of Customs of China, 2007. The statistical newsletter of customs: the important imports in 2006 /www. customs.gov.cn/ywstaticpageS. Greene, D.L., Jones, D.W., Leiby, P.N., 1998. The outlook for US oil dependence. Energy Policy 26 (1), 55–69. Hogan, W.W., 1983. Oil stockpiling: help they neighbor. The Energy Journal 4 (3), 49–72. Murphy, F.H., Toman, M.A., Weiss, H.J., 1987. A stochastic dynamic Nash game analysis of policies for managing the strategic petroleum reserve of consuming nations. Management Science 33 (4), 484–499. Murphy, F.H., Toman, M.A., Weiss, H.J., 1989. A dynamic Nash game model of oil market disruption and strategic stockpiling. Operation Research 37 (6), 958–971. Oren, S.S., Wan, S.H., 1986. Optimal strategic petroleum reserve policies: a steady state analysis. Management Science 32 (1), 14–29. Samouilidis, J.E., Berahas, S.A., 1982. A methodological approach to strategic petroleum reserves. The International Journal of Management Science 10, 565–574. Samouilidis, J.E., Magirou, V.F., 1985. On the optimal level of a small country’s strategic petroleum reserve. European Journal of Operational Research 20, 190–197. Teisberg, T.J., 1981. A dynamic programming model of the US strategic petroleum reserve. The Bell Journal of Economics 12 (2), 526–546. Wei, Y.M., Fan, Y., Han, Z.Y., Wu, G., 2006. China Energy Report (2006): Strategy and Policy Research. Science Press, Beijing (in Chinese). Wei, Y.M., Wu, G., Fan, Y., Liu, L.C., 2008. Empirical analysis of optimal strategic petroleum reserve in China. Energy Economics 30, 290–302. Wright, B.D., Williams, J.C., 1982. The roles of public and private storage in managing oil import disruptions. The Bell Journal of Economics 13 (2), 341–353. Zweifel, P., Bonomo, S., 1995. Energy security coping with multiple supply risks. Energy Economics 17 (3), 179–183.
Energy Policy 36 (2008) 1470–1478 www.elsevier.com/locate/enpol
An empirical analysis of the dynamic programming model of stockpile acquisition strategies for China’s strategic petroleum reserve Gang Wua, Ying Fana, Lan-Cui Liua,b, Yi-Ming Weia, a
Center for Energy and Environmental Policy Research, Institute of Policy and Management (IPM), Chinese Academy of Sciences (CAS), P.O. Box 8712, Beijing 100080, China b Center for Forecasting Science, Chinese Academy of Sciences, Beijing 100080, China Received 25 August 2007; accepted 3 January 2008 Available online 11 February 2008
Abstract The world’s future oil price is affected by many factors. The challenge, therefore, is how to select optimal stockpile acquisition strategies to minimize the cost of maintaining a reserve. This paper provides a new method for analyzing this problem using an uncertain dynamic programming model to analyze stockpile acquisition strategies for strategic petroleum reserve. Using this model, we quantify the impact of uncertain world oil price on optimal stockpile acquisition strategies of China’s strategic petroleum reserve for the period 2007–2010 and 2011–2020. Our results show that the future stockpile acquisition is related to oil prices and their probability and, if not considering the occurrence of oil supply shortage, China should at least purchase 25 million barrels when world oil price is at an optimal level. The optimal price of stockpile acquisition of every year has a stronger relationship with the probability of high price; and the optimal expected price and size of stockpile acquisition is different in each year. r 2008 Elsevier Ltd. All rights reserved. Keywords: Strategic petroleum reserve; Uncertain dynamic programming model; Stockpile acquisition strategies
1. Introduction Energy is one of the most significant factors driving China’s economic growth. With continuous development of China’s economy, there is a need for increasing quantities of oil to meet increasing demand. However, international oil price has fluctuated at the higher levels since 2004. China’s oil import dependence has increased rapidly since 1996 when it became a net oil importer. China’s crude oil import is 145 million tons and import dependence is 43.9 per cent (General Administration of Customs of China, 2007). Most of the oil import came from the unstable Middle East; 80 per cent of the imported oil has to get across the perilous Malacca Strait. Consequently, security of China’s oil supply becomes one of the most serious challenges for economic development. In reality, strategic petroleum reserve (SPR) is one of Corresponding author. Tel./fax: +86 10 62650861.
E-mail addresses: [email protected], [email protected] (Y.-M. Wei). 0301-4215/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.enpol.2008.01.007
the most effective measures to ensure national oil supply security. It was anticipated that the creation of a significant operational reserve of crude oil would discourage the use of oil as a ‘weapon’. In the event of any interruption, introduction into the market of oil from the reserve was expected to help calm markets, mitigate sharp price spikes, and reduce the economic dislocation. After the OPEC oil embargo, the US established SPR in 1975. The SPR was originally intended to hold at least 750 million barrels of crude oil as an insurance policy against future supply cutoffs. In United States, the US government can fill the SPR by either purchasing oil on the open market, or by collecting royalties from oil producers in the form of ‘in kind’ payments (i.e., oil). Most of the oil added to the reserve in the late 1970s and early 1980s was purchased on the open market when prices were relatively high. This is the main reason why the average price of oil in the SPR is greater than $27 per barrel. Recently, the SPR has been filled by collecting royalty oil from companies who operate leases on the federally owned Outer Continental Shelf. By law, these companies must pay royalties on these leases in
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the range of 12.5–16.7 per cent of the oil produced. This percentage can be paid in oil dollars equivalent or by actually delivering the oil ‘in kind’. In order to enhance oil supply security, China’s government established its own SPR in 2004. The Zhenhai base was finished in August, 2006. Subsequently, the most important question for China’s decision-makers is how to fill the reserve. The establishment of SPR requires spending large amount of capital, including the cost to buy oil and the cost of maintenance. Hence, the challenge is to determine how much oil to purchase to fill the reserve in an uncertain world oil market. Since the 1980s, several researchers have established models to quantify the optimal SPR, stockpile acquisition, and release strategies. Wei et al. (2008) quantifies China’s optimal SPR for the period 2005–2020, using a decision tree model based on a cost function. Murphy et al. (1989) presented and analyzed a Nash dynamic game model for investigating public and private sector oil inventory policies in unstable world oil markets. Samouilidis and Berahas (1982) established a cost function which includes the inventory procurement and maintenance cost and the shortage cost inflicted by a petroleum shortfall, and evaluated each scenario based on the cost function and decision tree model. Samouilidis and Magirou (1985) presented a simple analysis for the optimal selection of the level of petroleum reserve for a small country, based on the study of Samouilidis and Berahas (1982). Zweifel and Bonomo (1995) developed an optimal reserve model that takes into account multiple risks for oil and gas, and identified that one-dimensional rules such as ‘oil reserve for 90 days’, result in not only suboptimally, but also require adjustments that exacerbate suboptimality. Teisberg (1981) developed a stochastic dynamic programming model that allows explicit consideration of such uncertainty. The model has been used to determine the size of the US SPR and the optimal fill-up and draw-down rate contingent upon the supply conditions, time, and available inventory. Hogan (1983) extends the Teisberg’s model of US stockpiling to a Stackelberg model, examining the interactions between two consuming countries, where one follows the other’s lead. Oren and Wan (1986) explored a simple model to determine the optimal size, stockpile acquisition, and draw-down rates for an SPR under a variety of supply and demand conditions. Murphy et al. (1987) present a Nash dynamic game model of interactions among oil inventory and tariff policies for oil importing countries. They presented empirical results of the size of the stockpiles as a function of disruption probabilities, tariff policies, and cooperation versus non-cooperation between nations. Chao and Manne (1983) developed a multi-period dynamic programming model for determining optimal stockpiles and petroleum usage rates, based on their analysis of US petroleum supply policies. Similar interactions between public and private stocks in the US are considered by Wright and Williams (1982), though their focus is primarily on the implications of oil price controls and on game-
1471
theoretic ‘dynamic consistency’ questions that arise in comparing Nash and Stackelberg outcomes. Balas (1981) studied a short-run game between importing nations and a politically motivated cartel that takes advantage of disruptions to inflict economic losses on importing nations. In this context, he examines the ‘deterrence effect’ of strategic stocks where the deterrence effect is the value of a strategic reserve when the stockpile not only reduces the economic losses from a disruption, but also reduces the likelihood of a disruption. Greene et al. (1998) demonstrated the potential for future price shocks and economic losses based on a simulation model of the world market and price impacts on the US economy. His results indicated that the use of strategic reserve is relatively ineffective in reducing the damage to the US economy from such a prolonged price shock. There are relatively few studies on China’s stockpile acquisition strategies. Chen and Zheng (2006) analyzed qualitatively the imminence and necessity of SPR for China. They consider that China should not purchase oil to fill the reserve when world oil price is high, in addition to consideration of the experience of SPR in US. For decision-makers, this kind of descriptive analysis may not provide scientific information for the optimal decisions, due to uncertain world oil prices and economic risks of stockpile acquisition for SPR. Moreover, it is difficult to make scientific decisions using only judgments based on intuition. Therefore, it is necessary to quantify the optimal stockpile acquisition strategies for SPR in different years, based on an uncertain dynamic programming model. This article is organized as follows. Section 2 describes the methods and assumption of uncertain dynamic programming modeling. Section 3 presents and discusses the empirical results of optimal stockpile acquisition strategies. The final section presents conclusions and policy implications. 2. An uncertain dynamic programming model of China’s SPR Based on the US SPR models developed by Teisberg (1981), Samouilidis and Berahas (1982), Samouilidis and Magirou (1985), Oren and Wan (1986), and Murphy et al. (1987), we also develop an uncertain dynamic programming model of the china’s SPR. The establishment of SPR means that China must purchase sufficient oil to fill the reserve. Yet, it is impossible to buy this from the open market in a single purchase. In order to reduce the reserve cost, China needs to make varying decisions at different times because of the uncertainty of international oil prices. Moreover, such decisions will directly influence future decisions for filling the reserve. When decisions at different times are made, it will form the decisions series. Therefore, the optimal stockpile acquisition is a problem of multi-period decisions. Hence, this paper presents an uncertain dynamic programming model of China’s SPR. We also explore the
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problem of stockpile acquisition and if it affects world oil prices. Here the world oil price is an uncertain variable, with a probability distribution. This paper uses a dynamic programming with each year as a stock stage and yearly oil price as the state of its stage. So the uncertainty dynamic programming model of China’s SPR can be expressed as M 0 ðEðtÞ; tÞ ¼ minfC 0 ðEðtÞ; A; tÞg. A
(1)
The stockpile cost function of SPR: C 0 fEðtÞ; A; tg ¼ A f t ðpt Þ þ v ½EðtÞ þ A.
(2)
The optimal decision of the stockpile opportunity of SPR: ( 1 when f t ðpt Þ ¼ pt ; xt ¼ (3) 0 when f t ðpt Þ ¼ ptE ; f t ðpt Þ ¼ minfpt ; ptE g
pt 2 st .
(4)
From the definition of ptE and f t ðpt Þ we know that X ptE ¼ Eff tþ1 ðptþ1 Þg ¼ ri f tþ1 ðptþ1 Þ, (5) where ri is the probability of different oil price in the oil market. The definition of variables in the model can be found in Table 1. 3. Assumptions and data for empirical analysis 3.1. Assumptions of the model (1) We assume that China’s stockpile acquisition does not affect world oil price. The first project of China’s SPR will be finished at the end of 2008, its inventory is about 12 million tons (about 87.6 million barrels), and Table 1 The definition of variables in the model Variables
Definition of variables
pt st xt
State variables, the normal oil price in year t State set, the range of oil prices in the future xt is decision variable, ‘xt ¼ 1’ indicates decision to increase stockpiles in year t; ‘xt ¼ 0’ indicates decision to keep stockpiles in year t unchanged It refers to the expected price when adopting optimal decisions after year t The minimal expected price adopting the optimal decision from year t to year t1, when the world oil price in year t is pt It refers to the probability of different world oil prices The stockpile acquisition cost of SPR The stockpile size of the period t The stockpile acquisition The annualized unit stockpile holding cost. Here it is set at $0.32 per barrel The minimized cost of stockpile acquisition of SPR
ptE ft (pt)
ri C 0 fEðtÞ; A; tg E(t) A V 0
M ðEðtÞ; tÞ
average 21.9 million barrels per year during the period of 2007–2010. If all is from the international oil market, it is equal to an increase of 60 thousand barrels per day, and is about 15.1 per cent of daily crude oil import in 2006. In addition, the office of Energy Information Administration (EIA) of the US Department of Energy shows that the oil price should be slightly affected by the rate of stockpiling. Moreover, Teisberg (1981) also considers various scenarios and concludes that stockpile acquisition does not affect world oil price. Therefore, we assume that China’s stockpile acquisition, likewise, does not affect world oil price. (2) We assume that the low, middle, and high world oil price will be $55.0/bbl, $65.0/bbl, $100/bbl, respectively, in 2007–2010. Based on the current world oil price and the future world price forecast (Fig. 1; EIA/AEO2007), we consider two scenarios; in the first scenario, we assume the probabilities of low, middle, and high oil price are 0.3, 0.3, and 0.4, respectively. In the second scenario, we assume the probabilities of low, middle, and high oil price are 0.1, 0.1, and 0.8, respectively. According to the results of AEO2007, we assume that the low, middle, high, and higher world oil price will be $45.0/bbl, $55.0/bbl, $65.0/bbl, and $100/bbl, respectively, in 2011–2020. We consider two scenarios: in the first scenario, we assume the probabilities of low, middle, high, and higher oil price are 0.25, 0.25, 0.25, and 0.25, respectively; in the second scenario, we assume the probabilities of low, middle, high, and higher oil price are 0.1, 0.1, 0.4, and 0.4, respectively. 3.2. Data sources China’s optimal SPR for 2010 and 2020 are based on Wei et al. (2006). Because China’s SPR is at an early stage and there is no unit cost for reserve, we assume that the annual unit holding cost is equal to that of United States,
Fig. 1. 1990–2030 world oil prices in three AEO2007 cases (2005 dollars per barrel). Note: Energy Information Administration/Annual Energy Outlook 2007.
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should it buy to fill the reserve in order to minimize the holding cost in 2007–2010? Based on application of the uncertain dynamic programming model [1], we get the optimal stockpile acquisition strategies of China’s SPR. Results are shown in Fig. 2 and Table 2:
i.e., $0.32/barrel. The capacity of the first SPR bases can reach approximately 87.60 million barrels in 2008. Wei et al. (2008) concludes that the optimal SPR is 100 million barrels in 2010 (equal to the net oil import for 30 days). The Chinese government claims that the reserve capacity of SPR will be 30 days net oil import in 2010, so the yearly rate of stockpile acquisition is 25 million barrels if the optimal decision is to purchase over the period 2007–2010.
(1) When the world oil price is lower than $62.56/bbl in 2007, then China should buy 25 million barrels of crude oil for filling the SPR; otherwise, it should wait and keep the reserve constant until world oil price is lower than $62.56/bbl in 2007. (2) When the world oil price is lower than $66.40/bbl in 2008, then it should at least purchase 25 million barrels of crude oil to raise the SPR to 50 million barrels; otherwise, it should keep the reserve level constant until world oil price is lower than $66.40/bbl in 2008. (3) When the world oil price is lower than $76.00/bbl in 2009, then it should at least buy 25 million barrels of crude oil to increase SPR to 75 million barrels. When the world oil price is higher than $66.40/bbl, and lower
4. Results and discussions 4.1. Scenario 1: the optimal stockpile acquisition for the period 2007–2010, when there is low probability of a high oil price EIA forecasts the world oil price in three cases and, from this, we assume that the oil price will be $55.0/bbl, $65.0/bbl, $100/bbl, respectively, and their probabilities are 0.3, 0.3, and 0.4, respectively. The question then is what oil price level should China purchase oil and how much
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Fig. 2. The optimal stockpile acquisition strategies of China’s SPR for the period of 2007–2010 when there is low probability of high oil price.
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Table 2 The optimal stockpile acquisition strategies for China’s SPR in 2007–2010 Year
The low probability of high oil price
The high probability of high oil price
pt ($/bbl)
xt
A (million barrels)
pt ($/bbl)
xt
A (million barrels)
2007
p$62.56/bbl 4$62.56/bbl
1 0
25 0
p$80.48/bbl 4$80.48/bbl
1 0
25 0
2008
p$66.40/bbl 4$66.40/bbl
1 0
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p$85.60/bbl 4$85.60/bbl
1 0
25–50 0
2009
p$66.40/bbl $66.40–76.00/bbl 4$76.00/bbl
1 1 0
25–75 25–75 0
p$92.00/bbl
1
25–75
4$92.00/bbl
0
0
The current price
1
25–100
The current price
1
25–100
2010
than $76.00/bbl, it should buy at most 75 million barrels of crude oil; otherwise, it should keep SPR constant until world oil price is lower than $76.00/bbl in 2009. (4) In order to ensure national energy supply security, China should reach the reserve capacity of 100 million barrels in 2010 whatever the world oil price is.
4.2. Scenario 2: the optimal stockpile acquisition for the period of 2007–2010, when there is high probability of high oil price
(4) In order to ensure national energy supply security, it should reach the reserve capacity of 100 million barrels in 2010 whatever world oil price is, and at least buy 25 million barrels whatever world oil price is.
4.3. Scenario 3: the optimal stockpile acquisition for the period of 2011–2020, when there is low probability of high oil price
The unsolved ‘Iran nuclear problem’, new global conflicts, terrorism in some regions, and speculation capital, may induce the world oil price to remain at the higher level. Moreover, future oil prices in 2007–2010 may remain at the higher level. Therefore, we assume that the world oil prices will be $55.0/bbl, $65.0/bbl and $100/bbl, respectively, and their probabilities are 0.1, 0.1, and 0.8, respectively. Then in this scenario, what oil price level should China purchase oil, and how much should it buy to fill the reserve in order to minimize the holding cost in 2007–2010? Based on the uncertain dynamic programming model [1], we get the optimal stockpile acquisition strategies of China’s SPR, which can be found in Fig. 3 and Table 2:
According to the world oil price forecast of EIA (Annual Energy Outlook 2007), we assume that the oil price will be $45.0/bbl, $55.0/bbl, $65.0/bbl and $100/bbl, respectively, and the probabilities of different prices are 0.25. The decision is then what oil price level should China purchase oil, and how much should it buy to fill the reserve in order to minimize the holding cost in 2011–2020? According to the results of Wei et al. (2008), the optimal size of China’s SPR is 60 days of net oil import or 90 days of net oil import in 2020 when oil price is at a high level ($50.0/bbl). In order to meet the greatest volume of SPR, this paper selects 350 million barrels (90 days of net oil import) in this model. Based on the uncertain dynamic programming model [1], we get the optimal stockpile acquisition strategies for 2011–2020, which can be found in Fig. 4 and Table 3.
(1) When the world oil price is lower than $80.48/bbl in 2007, then it should buy 25 million barrels of crude oil for reserve; otherwise, it should keep the reserve constant until world oil price is lower than $80.48/bbl in 2007. (2) When the world oil price is lower than $85.60/bbl in 2008, then it should purchase at least 25 million barrels of crude oil to make the reserve reach 50 million barrels; otherwise, it should keep the reserve constant until world oil price is lower than $85.60/bbl in 2008. (3) When the world oil price is lower than $92.00/bbl in 2009, then it should buy at least 25 million barrels of crude oil to make the reserve reach 75 million barrels; otherwise, it should keep the reserve constant until world oil price is lower than $92.00/bbl in 2009.
(1) When the world oil price is lower than $53.91/bbl in 2011–2017, then it should buy at least 175 million barrels oil to increase the reserve; otherwise, it should keep the reserve constant until world oil price is lower than $53.91/bbl in 2011–2017. (2) When the world oil price is lower than $57.81/bbl in 2018, then it should purchase at least 25 million barrels of crude oil to increase the reserve to 300 million barrels; otherwise, it should keep the reserve level constant until world oil price is lower than $57.81/bbl in 2018. (3) When the world oil price is lower than $57.81/bbl in 2019, then it should purchase at least 25 million barrels of crude oil to increase the reserve to 325 million barrels. When the world oil price is higher than
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Fig. 3. The optimal stockpile acquisition strategies of China’s SPR for the period of 2007–2010 when there is high probability of high oil price.
$57.81/bbl, and lower than $66.25/bbl in 2019, it should buy at most 225 million barrels of crude oil; otherwise, it should keep the reserve constant until world oil price is lower than $66.25/bbl in 2019. (4) In order to ensure national energy supply security, China should reach the reserve capacity of 350 million barrels in 2020 whatever the world oil price is.
4.4. Scenario 4: the optimal stockpile acquisition strategies for the period of 2011–2020, when there is high probability of high oil price According to the world oil price forecast of EIA (Annual Energy Outlook 2007), we assume that the oil price will be $45.0/bbl, $55.0/bbl, $65.0/bbl and $100/bbl, respectively, and the probabilities of different prices are 0.1, 0.1, 0.4, and 0.4, respectively. What oil price should China purchase oil, and how much should it buy to fill the reserve in order to minimize the holding cost in 2011–2020? Based on the
uncertain dynamic programming model [1], we get China’s optimal stockpile acquisition strategies results for 2011–2020, which can be found in Fig. 5 and Table 4. (1) When the world oil price is lower than $54.11/bbl in 2011–2012, then it should buy at least 50 million barrels crude oil for the reserve; otherwise, it should keep SPR constant until world oil price is lower than $54.11/bbl in 2011–2012. (2) When the world oil price is lower than $54.11/bbl in 2013–2017, then it should purchase at least 125 million barrels crude oil to make the reserve reach 275 million barrels. When the world oil price is higher than $54.11/bbl, and lower than $62.56/bbl, it should buy at most 175 million barrels of crude oil; otherwise, it should keep the reserve constant until world oil price is lower than $62.56/bbl in 2013–2017. (3) When the world oil price is lower than $76.00/bbl in 2018–2019, then it should buy at least 50 million barrels of crude oil to make the reserve reach 325 million
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2019
$57.81/bbl
$15002.5 $57.81/bbl
$15010.5
2019
if p > $66.25/bbl if p If 57.81 < p
6.25
$57.81/bbl 66.25
No
More Buy 225Mb
Less Buy 225Mb
No
More Buy 50Mb
Less buy 50Mb
2020
2020
2020
2020
2020
2020
Buy
250Mb
Less Buy 25Mb
More Buy 25Mb
More buy 75Mb
Less buy 25Mb
More Buy 25Mb
$16562.5
$16634.5
$16634.5
$14571.0
$14587.0
$14165.0
Fig. 4. The optimal stockpile acquisition strategies for China’s SPR in the period of 2011–2020 when there is low probability of high oil price.
Table 3 The optimal stockpile acquisition strategies for China’s SPR in 2011–2020, when there is low probability of high oil price Year
pt ($/bbl)
xt
A (million barrels)
2011–2017
p$53.91/bbl 4$53.91/bbl
1 0
X175 0
2018
p$57.81/bbl 4$57.81/bbl
1 0
25–200 0
2019
p$57.81/bbl $57.81–66.25/bbl 4$66.25/bbl
1 1 0
at least 25–225 at most 25–225 0
The current price
1
25–250
2020
barrels. When the world oil price is higher than $54.11/bbl, and lower than $62.56/bbl in 2018–2019, it should purchase 50–225 million barrels crude oil.
When the world oil price is higher than $62.56/bbl, and lower than $76.00/bbl in 2018–2019, it should buy at most 225 million barrels crude oil; otherwise, it should keep the reserve constant until world oil price is lower than $76.00/bbl in 2018–2019. (4) In order to ensure national energy supply security, it should reach the reserve capacity of 350 million barrels in 2020 whatever the world oil price is.
5. Conclusions and policy implications In this paper, the stockpile acquisition problem of SPR is formulated and solved using an uncertainty dynamic programming model. The model takes into consideration the variability of oil price probabilities and its effect on the stockpile acquisition. The future stockpile acquisition is related to the oil prices and their probability, and the optimal world price
ARTICLE IN PRESS G. Wu et al. / Energy Policy 36 (2008) 1470–1478
1477
2011-2012
if p > $54.11/bbl if p
$54.11/bbl
Less buy 50Mb
No 2013-2017 if p > $62.56/bbl if p $54.11/bbl
2013-2017
if p > $62.56/bbl if p
P**
P
Buy 175Mb
No
Less Buy 175Mb
$54.11/bbl
P
Buy
*
P
More Buy 50Mb
50Mb
Less Buy 50Mb
No
More Buy 175Mb
2020
2020
2020
2020
2020
2020
Buy
Less Buy 25Mb
Buy
25Mb
$16768.0 16096.0
$16752.0
P
*
P
$54.11/bbl
More buy Less buy 200Mb 25Mb
$15673.5
$17937.5
if p > $76.00/bbl if p
**
P
Buy
Less buy
175Mb 175Mb 2020
More Buy 25Mb
Buy
25Mb
2020 More Buy 25Mb
$54.11/bbl
P
$54.11/bbl
**
No
More Buy 50Mb
50Mb
Less Buy 50Mb
2020
2020
2020
2020
Buy
Buy
Buy
Buy
75Mb
25Mb
25Mb
2018-2019
if p > $76.00/bbl if p
**
*
More Buy 25Mb
$18009.5 $15657.5 $14178.75 $15297.25 $15313.25 $14641.25 $14218.75
2018-2019
if p > $76.00/bbl if p
2018-2019
if p > $76.00/bbl if p
No
75Mb
125Mb
2018-2019
P**
P*
Less buy 125Mb
Buy
No
2018-2019
if p > $76.00/bbl if p
$54.11/bbl
**
P
*
P
2018-2019
$54.11/bbl
if p > $76.00/bbl if p *
**
P
$54.11/bbl
**
P
No
More Buy 225Mb
225Mb
Less Buy 225Mb
No
More Buy 50Mb
50Mb
Less Buy 50Mb
No
More Buy 50Mb
50Mb
Less buy 50Mb
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
2020
Buy
Less Buy 25Mb
Buy
More Buy 25Mb
Buy
Buy
Buy
Buy
25Mb
75Mb
25Mb
25Mb
More Buy 25Mb
250Mb $19000.0
Buy
$19072.0 $16048.0 $14146.75
Buy
More Buy Less buy Less buy 25Mb 25Mb 75Mb
$15281.25 $15297.25 $14625.25 $14202.75
$16353.5
buy
25Mb
$16369.5 $16369.5 $15275.0
Fig. 5. The optimal stockpile acquisition strategies of China’s SPR for the period of 2011–2020 when there is high probability of high oil price. Note: P* is $62:56=bblopricep$76:00=bbl, P** is $54:11=bblopricep$62:56=bbl.
Table 4 The optimal stockpile strategies for China’s SPR in 2011–2020, when there is high probability of high oil price Year
pt ($/bbl)
xt
A (million barrels)
2011–2012
p$54.11/bbl 4$54.11/bbl
1 0
X50 0
2013–2017
p$54.11/bbl $54.11–62.56/bbl 4$62.56/bbl
1 1 0
at least 125–175 125–175 0
2018–2019
p$54.11/bbl $54.11–62.56/bbl $62.56–76.00/bbl 4$76.00/bbl
1 1 1 0
at least 50–225 50–225 at most 50–225 0
2020
The current price
1
25–250
level will increase $17.92/bbl from $62.56/bbl to $80.48/bbl when the probability of $100.0/bbl becomes 0.8 from 0.4. Therefore, it is optimal to purchase future oil to fill the reserve. If there is no oil supply shortage, it should purchase at least 25 million barrels when world oil price is at an optimal level. Whatever the oil price is, it should purchase oil to make the SPR 30 days net imports in 2010 and 90 days net imports in 2020. When there is low probability of high oil price in 2007–2010, the minimum expected total acquisition cost of SPR is 6824.0 million dollar; when there is high probability of high oil price in 2007–2010, the minimum expected total acquisition cost of SPR is 8792.0 million dollar; when there is low probability of high oil price in 2011–2020, the minimum expected total acquisition cost of SPR is 14165.0
ARTICLE IN PRESS 1478
G. Wu et al. / Energy Policy 36 (2008) 1470–1478
million dollar; and when there is high probability of high oil price in 2011–2020, the minimum expected total acquisition cost of SPR is 14146.75 million dollar. This paper further analyzes the stockpile acquisition and release strategies when considering the occurrence of oil supply shortage. Acknowledgements The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant nos. 70425001, 70733005, 70701032, and the National Key Projects from the Ministry of Science and Technology of China (Grant 2006-BAB08B01). The authors also thank Professor Nicky France and the anonymous referees for their helpful suggestions and corrections on the earlier draft of this paper according to which the content was improved. References Balas, E., 1981. The strategic petroleum reserve: how large should it be? In: Bayraktar, B.A., et al. (Eds.), Energy Policy Planning. Plenum Press, New York. Chao, H.P., Manne, A.S., 1983. Oil stockpiles and import reductions: a dynamic programming approach. Operations Research 31 (4), 632–651. Chen, S.H., Zheng, S.M., 2006. The time option for China to establish strategic petroleum reserve. Economic Management (21), 22–25 (in Chinese). Energy Information Administration (EIA) of the US Department of Energy, 2007. Annual energy outlook 2007 with projections to 2030 /www.eia.doe.gov/oiaf/aeoS.
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