Optimal Maintenance Strategies at
California Gasoline Refiners
Larry Harris
January 8, 2013
Abstract
California permits the sale of only special grades of gasoline. They are produced primarily by 9 California
refiners, five of which have two refineries each that collectively account for 70% of the market. Few
suppliers and low demand elasticities ensure that occasional supply disruptions at individual refineries
cause prices to rise substantially. Gasoline prices spiked in the fall of 2012 when two refineries
experienced production problems.
This paper considers how refiners may behave strategically when budgeting for maintenance. Refiners
with multiple plants may spend less on maintenance, and thus experience greater failure probabilities,
than refiners in more competitive markets. For firms with multiple production lines, increased prices
offset revenue losses when one production line fails.
Introduction
Since the winter of 1992, California law permits the sale of only certain special grades of gasoline in the
state. The state requires that gasoline be specially formulated to reduce pollution. The formulations
differ between the summer and winter months. Twice each year, refiners switch from producing the
summer formulation to the winter formulation. The California formulations are more expensive to
produce than those used in other states.
The regulations governing the sale of gasoline in California effectively isolate the California wholesale
gasoline market from wholesale gasoline markets in other states. During the summer, gasoline
formulated for other states cannot be sold in California, and selling gasoline specially prepared for the
California market in other states is cost prohibitive.
The isolation of the California gasoline markets is widely thought to account for increased gasoline price
volatility in the state. Gasoline prices are volatile because the both demand and supply are quite
inelastic over short intervals and because the semi-annual shift from one formulation to the other
makes storing gasoline very expensive if the gasoline in storage cannot be sold for six months.
Figure 1 illustrates the higher volatility of the California gasoline market. The plot presents annual
standard deviations of weekly price returns for retail West Coast regular-grade gasoline prices. The
standard deviations for reformulated gasoline (produced primarily for the California market) are
uniformly above those for conventional gasoline, which is sold in other markets.
1
Since only nine refiners produce the summer California formulations (See Table 1), supply disruptions
due to production problems at individual refineries occasionally cause prices to rise substantially.
California most recently experienced a substantial spike in gasoline prices in the fall of 2012 when two
refineries experienced production problems. The first disruption occurred on August 6 when a fire at
the Chevron Corp. Richmond refinery stopped production. The second occurred on October 1 when the
ExxonMobil Torrance refinery shut down for four days due to a power problem.
Figure 2 presents margin refiner margins computed as the difference between reported average
wholesale gasoline prices and the price of Alaskan crude oil necessary to produce a gallon of gasoline.
The second panel of the figure clearly shows the 2012 spike in prices. Refiner margins rose from
$0.40/gal for the week ending August 6 to $1.23/gal for the week ending October 8. They then fell to
$0.31/gal for the week ending October 22. During the eleven week period from August 6 to October 22,
the refiners earned produced approximately $800M more than usual from margins that averaged
$0.30/gal higher than their $0.37/gal average over the three years before August 6, 2012.
When a process problem stops a production line at a refinery, that refinery cannot profit from continued
production on that line. However, the resulting increase in wholesale profits may cause the company’s
overall profits to rise if it has other production lines or if it had substantial finished inventory in storage.
Other companies, of course, benefit substantially when prices rise unexpectedly.
These considerations suggest that refineries may behave strategically when budgeting for maintenance.
In particular, California refiners may choose to spend less on maintenance than refiners in other markets
that face more competition from other refiners. Lower maintenance expenditures lead to a greater
probability of failure. For firms that have multiple production lines or that normally hold substantial
inventories, the resulting increase in price offsets the loss of production in the failed line, and may even
more than make up for it.
These considerations also suggest that refineries could benefit substantially if they could collude to
decrease production. Explicit collusion would be illegal and presumably does not occur. However, the
possibility of its occurrence has led to the creation of various state and federal surveillance systems to
enforce anti-trust laws. The operation of these systems hopefully helps deter explicit collusion.
In contrast, even if firms do not explicitly or implicitly collude with each other, each company
undoubtedly considers what other companies might do when setting their maintenance budgets. As a
result, they each may independently and rationally decide to undertake less maintenance than they
would if they competed in more competitive markets. Assuming that no collusion occurs, such behavior
is not illegal, but it would be a matter of concern to public policy makers.
This short note examines a simple model of imperfect competition among a limited number of refiners,
each of whom can set their maintenance budgets to maximize their overall profits. The model employs
a Nash equilibrium in which refiners independently set their maintenance budgets on the assumption
that other refiners are doing the same. The model assumes that no entry or exist occurs in the shortterm, presumably because capital costs and regulatory costs associated with environmental approvals
are extremely high.
2
The results predict that maintenance budgets would indeed be lower when few refiners compete with
each other. These results suggest that California regulators may want to regulate maintenance budgets
to protect the public welfare.
This model does not examine how storage strategies might interact with maintenance strategies. In
particular, it could be optimal to shut a line when storage levels are high to benefit from higher prices.
The shutdown could be intentional, or it could be the result of inadequate maintenance due to
underfunding such as is described by the model.
These results apply to any industry where few competitors compete with each other to supply products
produced by multiple production lines that they sell into markets characterized by inelastic demands
and supplies and expensive storage. These conditions characterize the production of gasoline for the
California markets. They may also characterize production in other markets, such as for specialty
plastics.
The model
Assume that each of 𝑁 refiners has 𝑛𝑖 production lines. A production line is a productive process for
which all output stops if a single element of the process fails. If a company has two refineries, it clearly
has at least two production lines. But a company may have more than one production line in each
refinery. For example, a refinery might employ two crackers or two distillers that do essentially the
same work at a single refinery. If one fails, output for the refinery presumably would drop by half.
For simplicity, assume that each production line is identical within a firm and across firms. Let 𝑞𝑖
represent the total production at firm 𝑖. Assume that each production line produces one unit of
quantity with production probability 𝑝𝑖 , and zero units with probability 1 − 𝑝𝑖 . Finally, assume that the
production probability is independent across lines so that total production 𝑞𝑖 follows a (𝑛𝑖 , 𝑝𝑖 ) binomial
process. The expected production level and the variance of that production thus are given by
E𝑞𝑖 = 𝑛𝑖 𝑝𝑖
and
var(𝑞𝑖 ) = 𝑛𝑖 𝑝𝑖 (1 − 𝑝𝑖 ).
Assume that the production probability 𝑝𝑖 for a given line is an increasing function of maintenance
expenditure 𝑀𝑖 on that line so that
𝑝𝑖 = 𝑓(𝑀𝑖 )
and
𝑝𝑖′ =
𝑑𝑓(𝑀𝑖 )
> 0.
𝑑𝑀𝑖
Assume further that
3
𝑝𝑖′′ =
𝑑2 𝑓(𝑀𝑖 )
<0
𝑑𝑀𝑖2
so that the rate at which additional expenditures on maintenance increase reliability is decreasing.
Finally, assume that each refiner spends the same amount on maintenance for each line that it runs.
Each refiner chooses maintenance per line expenditure 𝑀𝑖 to maximize expected profits:
max E𝜋 = E((𝑃 − 𝐶)𝑞𝑖 − 𝑛𝑖 𝑀𝑖 )
𝑀𝑖
where 𝑃 is the total price of all quantity produced by a functioning production line and 𝐶 is the total
variable cost of the production.
Production under Perfect Competition
Under perfect competition, each refiner takes the price 𝑃 as given and independent of its production
levels. Under these assumptions, the objective function is
max 𝐸𝜋 = E(𝑃 − 𝐶)E𝑞𝑖 − 𝑛𝑖 𝑀𝑖 = E(𝑃 − 𝐶)𝑛𝑖 𝑝𝑖 − 𝑛𝑖 𝑀𝑖
𝑀𝑖
so that the first order condition is
E(𝑃 − 𝐶)𝑛𝑖 𝑝𝑖′ − 𝑛𝑖 = 0
or
E(𝑃 − 𝐶)𝑝𝑖′ = 1
The second order condition is negative as it should be for maximization:
E(𝑃 − 𝐶)𝑛𝑖 𝑝𝑖′′ < 0.
The first order expression indicates that expenditure on maintenance will increase when the expected
price increases because 𝑝𝑖′′ < 0. This result can be seen by examining the total differential of the first
order condition:
𝑝𝑖′ 𝑑(E𝑃) + E(𝑃 − 𝐶)𝑝𝑖′′ 𝑑𝑀𝑖 = 0
Rearranging terms yields:
𝑑𝑀𝑖
𝑝𝑖′
=−
>0
𝑑E𝑃
E(𝑃 − 𝐶)𝑝𝑖′′
The Perfect Competition Equilibrium
To obtain the competitive market equilibrium, assume a linear demand function as a local
approximation to the actual demand function and set it equal to the total market supply:
4
N
𝑄𝐷 = 𝛼 − 𝛽𝑃 = 𝑄𝑆 = ∑ 𝑞𝑖
i=0
where 𝛼 > 0 and 𝛽 > 0.
Inverting this expression gives the price function
N
𝛼 1
𝑃 = − ∑ 𝑞𝑖
𝛽 𝛽
i=0
so that the expected price is given by
N
𝛼 1
E𝑃 = − ∑ 𝑛𝑖 𝑝𝑖
𝛽 𝛽
i=0
For the purpose of illustration, assume that 𝑛𝑖 = 𝑛𝑗 = 𝑛 for all 𝑖, 𝑗 so that 𝑝𝑖 = 𝑝𝑗 = 𝑝. This assumption
allows us to express the optimal production probability 𝑝 in terms of 𝑝′ . Under this assumption
E𝑃 =
𝛼 𝑁𝑛𝑝
−
𝛽
𝛽
so that the first order condition is
𝛼 𝑁𝑛𝑝
( −
− 𝐶) 𝑝′ = 1
𝛽
𝛽
Solving this expression for 𝑝 gives
𝛼 − 𝛽𝐶 −
𝑝𝐶𝑜𝑚𝑝 =
𝛽
′
𝑝𝐶𝑜𝑚𝑝
𝑁𝑛
where the superscript “Comp” refers to the competitive equilibrium.
Production under Imperfect Competition
Now consider the refiners’ optimization problem assuming that the refiner knows that it has market
power. The optimization problem is now given by
max E𝜋 = E((𝑃 − 𝐶)𝑞𝑖 ) − 𝑛𝑖 𝑀𝑖
𝑀𝑖
The expectation can be evaluated by assuming the same linear demand function presented above.
N
𝛼 1
𝐸((𝑃 − 𝐶)𝑞𝑖 ) = E ((( − ∑ 𝑞𝑖 ) − 𝐶) 𝑞𝑖 )
𝛽 𝛽
i=0
5
N
𝛼
1
𝑞𝑖
= 𝐸 (( − 𝐶 − ∑ 𝑞𝑗 − ) 𝑞𝑖 )
𝛽
𝛽
𝛽
j≠i
N
𝛼
1
𝐸𝑞𝑖2
= ( − 𝐶 − ∑ 𝐸𝑞𝑗 ) 𝐸𝑞𝑖 −
𝛽
𝛽
𝛽
j≠i
N
𝛼
1
𝑛𝑖 𝑝𝑖 + 𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖2
= ( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑛𝑖 𝑝𝑖 −
𝛽
𝛽
𝛽
j≠i
Substituting this expression into the objective function and differentiating gives the imperfect
competition first order condition:
N
𝛼
1
𝑛𝑖 𝑝𝑖′ + 2𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖 𝑝𝑖′
′
( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑛𝑖 𝑝𝑖 −
− 𝑛𝑖 = 0
𝛽
𝛽
𝛽
j≠i
The second order condition is
N
𝛼
1
𝑛𝑖 𝑝𝑖′′ 2𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖 𝑝𝑖′′ 2𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖′
′′
( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑛𝑖 𝑝𝑖 −
−
−
𝛽
𝛽
𝛽
𝛽
𝛽
2
j≠i
N
𝛼
1
𝑛𝑖 𝑝𝑖′ 2𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖 𝑝𝑖′ 𝑝𝑖′′ 2𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖′
−
(( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑛𝑖 𝑝𝑖′ −
) ′−
𝛽
𝛽
𝛽
𝛽
𝑝𝑖
𝛽
j≠i
2
𝑛𝑖
𝑝𝑖′′ 2𝑛𝑖 (𝑛𝑖 − 1)𝑝𝑖′
−
<0
𝑝𝑖′
𝛽
as it should be for maximization.
For 𝑛𝑖 = 1 the first order condition reduces to
N
𝛼
1
𝑝𝑖′
( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑝𝑖′ − − 1 = 0
𝛽
𝛽
𝛽
j≠i
or
N
𝛼 1
( − (∑ 𝑛𝑗 𝑝𝑗 + 1) − 𝐶) 𝑝𝑖′ = 1
𝛽 𝛽
j≠i
6
2
When one unit of production is small relative to total expected production, the quantity in the large
parentheses is essentially expected price, so that this problem has essentially the same first order
condition as the competitive solution.
Manipulating the first order condition gives:
N
𝛼
1
𝑝𝑖′ + 2(𝑛𝑖 − 1)𝑝𝑖 𝑝𝑖′
( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑝𝑖′ −
=1
𝛽
𝛽
𝛽
j≠i
N
𝛼
1
−𝑛𝑖 𝑝𝑖 𝑝𝑖′ + 𝑝𝑖′ + 2(𝑛𝑖 − 1)𝑝𝑖 𝑝𝑖′
( − 𝐶 − ∑ 𝑛𝑗 𝑝𝑗 ) 𝑝𝑖′ −
=1
𝛽
𝛽
𝛽
j=1
E(𝑃 − 𝐶)𝑝𝑖′ −
(1 + (𝑛𝑖 − 2)𝑝𝑖 )𝑝𝑖′
=1
𝛽
E(𝑃 − 𝐶)𝑝𝑖′ = 1 +
(1 + (𝑛𝑖 − 2)𝑝𝑖 )𝑝𝑖′
>1
𝛽
Since the expression on the right is greater than one, for given price expectations E𝑃, the maintenance
budget under imperfect competition will be less than the maintenance budget for a price taker.
The Imperfect Competition Nash Equilibrium
If we assume again for illustration that 𝑛𝑖 = 𝑛𝑗 = 𝑛 for all 𝑖, 𝑗 so that 𝑝𝑖 = 𝑝𝑗 = 𝑝, we can obtain an
implicit equation for the Nash equilibrium under the assumption that all refiners expect everyone else to
behave the same as they do. To obtain the equilibrium optimal 𝑝 as a function of 𝑝′ , solve the following
expression derived from the first order condition for 𝑝:
𝛼
𝑁𝑛𝑝 ′ (1 + (𝑛 − 2)𝑝)𝑝′
( −𝐶 −
)𝑝 −
=1
𝛽
𝛽
𝛽
(𝛼 − 𝛽𝐶 − 𝑁𝑛𝑝)𝑝′ − (1 + (𝑛 − 2)𝑝)𝑝′ = 𝛽
(𝛼 − 𝛽𝐶 − 𝑁𝑛𝑝) − (1 + (𝑛 − 2)𝑝) =
(−𝑁𝑛 − 𝑛 + 2)𝑝 + 𝛼 − 𝛽𝐶 − 1 =
𝛼 − 𝛽𝐶 − 1 −
𝑝𝑁𝑎𝑠ℎ =
𝛽
′
𝑝𝑁𝑎𝑠ℎ
(𝑁 + 1)𝑛 − 2
where the superscript “Nash” now refers to the Nash equilibrium.
7
𝛽
𝑝′
𝛽
𝑝′
Comparison of the Two Equilibria
For when 𝑛𝑖 = 𝑛𝑗 = 𝑛 for all 𝑖, 𝑗, showing that the production probability in the Nash equilibrium is
smaller than or at most equal to the probability in the competitive equilibrium is fairly easy:
The competitive equilibrium is described by
𝛼
𝑁𝑛𝑝𝑐 ′
( −𝐶−
) 𝑝𝑐 = 1
𝛽
𝛽
while the Nash equilibrium is described by
𝛼
𝑁𝑛𝑝𝑛 ′ (1 + (𝑛 − 2)𝑝𝑛 )𝑝𝑛′
( −𝐶−
) 𝑝𝑛 −
=1
𝛽
𝛽
𝛽
Note that the second term of this equation is positive for 𝑛 ≥ 2 so that
𝛼
𝑁𝑛𝑝𝑛 ′
( −𝐶−
) 𝑝𝑛 > 1
𝛽
𝛽
Note that also that
𝛼
𝑁𝑛𝑝𝑛
( −𝐶−
)>0
𝛽
𝛽
and
𝛼
𝑁𝑛𝑝𝑐
( −𝐶 −
)>0
𝛽
𝛽
since 𝑝𝑛′ > 0 and 𝑝𝑐′ > 0.
Now suppose 𝑝𝑐 < 𝑝𝑛 . That would imply
𝛼
𝑁𝑛𝑝𝑛
𝛼
𝑁𝑛𝑝𝑐
( −𝐶−
)<( −𝐶−
)
𝛽
𝛽
𝛽
𝛽
It also implies 𝑝𝑐′ > 𝑝𝑛′ so that
𝛼
𝑁𝑛𝑝𝑛 ′
𝛼
𝑁𝑛𝑝𝑐 ′
( −𝐶 −
) 𝑝𝑛 < ( − 𝐶 −
) 𝑝𝑐 = 1
𝛽
𝛽
𝛽
𝛽
But we already established that
𝛼
𝑁𝑛𝑝𝑛 ′
( −𝐶−
) 𝑝𝑛 > 1
𝛽
𝛽
so the assumption that 𝑝𝑐 < 𝑝𝑛 cannot be true. Instead, 𝑝𝑛 ≥ 𝑝𝑐 .
8
The Nash equilibrium production probability can be expressed in terms of the competitive equilibrium
production probability when 𝑛𝑖 = 𝑛𝑗 = 𝑛 for all 𝑖, 𝑗:
𝛼 − 𝛽𝐶 − 1 −
𝑝𝑁𝑎𝑠ℎ =
𝛽
′
𝑝𝑁𝑎𝑠ℎ
(𝑁 + 1)𝑛 − 2
𝛼 − 𝛽𝐶 −
𝑝𝐶𝑜𝑚𝑝 =
𝛽
′
𝑝𝐶𝑜𝑚𝑝
𝑁𝑛
′
𝑝𝐶𝑜𝑚𝑝
𝛽
′ − 1 + 1) 𝐶𝑜𝑚𝑝 ′
𝑝
𝑝𝑁𝑎𝑠ℎ
(𝑁 + 1)𝑛 − 2
𝛼 − 𝛽𝐶 − 1 − (
𝑝𝑁𝑎𝑠ℎ =
𝛼 − 𝛽𝐶 −
=
(𝛼 − 𝛽𝐶 −
=
𝛽
𝑝
′
𝑝𝐶𝑜𝑚𝑝
𝛽
′ − 1) 𝐶𝑜𝑚𝑝 ′
𝑝
𝑝𝑁𝑎𝑠ℎ
(𝑁 + 1)𝑛 − 2
−1−(
𝐶𝑜𝑚𝑝 ′
′
𝑁𝑛
𝑝𝐶𝑜𝑚𝑝
𝛽
−
1
−
)
(
′
′ − 1) 𝐶𝑜𝑚𝑝 ′
𝑝𝐶𝑜𝑚𝑝 𝑁𝑛
𝑝
𝑝𝑁𝑎𝑠ℎ
(𝑁 + 1)𝑛 − 2
𝛽
′
𝑝𝐶𝑜𝑚𝑝
𝛽
′ − 1) 𝐶𝑜𝑚𝑝 ′
𝑝
𝑝𝑁𝑎𝑠ℎ
(𝑁 + 1)𝑛 − 2
𝑝𝐶𝑜𝑚𝑝 𝑁𝑛 − 1 − (
=
′
= 𝑝𝐶𝑜𝑚𝑝
1
−
1
2
1+ −
𝑁 𝑀𝑛
(
𝑝𝐶𝑜𝑚𝑝
𝛽
′ − 1) 𝐶𝑜𝑚𝑝 ′
1
𝑝
𝑝𝑁𝑎𝑠ℎ
−
(𝑁 + 1)𝑛 − 2
(𝑁 + 1)𝑛 − 2
Note that the two production probabilities converge as 𝑁 gets large.
If four refiners are in the market (𝑁 = 4) and each has two processes (𝑛 = 2) then
𝑝𝑁𝑎𝑠ℎ > 𝑝𝐶𝑜𝑚𝑝 (
1
1
1
)−
= 𝑝𝐶𝑜𝑚𝑝 −
1
2
(4 + 1)2 − 2
8
1+4−4×2
The inequality arises because the second of the three terms above is negative.
Calibration
Suppose that 𝑁 refiners each have 𝑛 lines. When all lines are running, total production is 𝑄 = 𝑁𝑛.
Suppose that occurs where price is 𝑃𝑎𝑙𝑙 . Suppose further that the absolute value of the demand curve
elasticity is 𝜀. Finally, assume constant elasticity demand
9
𝑄𝐷 = 𝑎𝑃−𝜀
These conditions imply
𝑎=
𝑁𝑛
−𝜀
𝑃𝑎𝑙𝑙
Linearization of the demand curve at 𝑃 = 𝑃𝑎𝑙𝑙 yields:
𝑄𝐷 =
𝑁𝑛 −𝜀 𝑁𝑛 −𝜀
−𝜀 𝑃𝑎𝑙𝑙 − −𝜀 𝜀𝑃𝑎𝑙𝑙 (𝑃 − 𝑃𝑎𝑙𝑙 )
𝑃𝑎𝑙𝑙
𝑃𝑎𝑙𝑙
= 𝑁𝑛 − 𝑁𝑛𝜀(𝑃 − 𝑃𝑎𝑙𝑙 )
= 𝛼 − 𝛽𝑃
where
𝛼 = 𝑁𝑛(1 + 𝜀𝑃𝑎𝑙𝑙 )
𝛽 = 𝑁𝑛𝜀
Now assume that 𝑝 = 1 − exp(−𝛿𝑀)
Assume that if all lines are running, price will be $3.50. Assume further that the variable costs are also
$3.50 so that nobody is profiting. Finally, assume that demand elasticity is 0.2.
𝑃𝑎𝑙𝑙 = $3.50
𝐶 = $3.50
𝜀 = 0.2
For 𝑁 = 4 and 𝑛 = 3 a value of 𝛿 = 20 (the calibration variable) produces the following results:
Variable
P
M
Expected price
Expected
profit
Competitive
Equilibrium
0.9
0.115129
Nash
Equilibrium
0.8
0.080472
$4.00
$1.2375
$4.50
2.20
10
The expected profit under the Nash equilibrium has price at $4.50, which is about the average price of
gasoline including occasional spikes due to shutdowns. As expected, less maintenance is done than if
the refiners were operating in perfectly competitive markets.
Conclusion
The simple model developed in this paper shows that refiners who have multiple production lines may
spend less on maintenance when they have market power than when they compete in competitive
markets. This result was developed under the Nash assumption that the refiners do not actively collude
with each other, but rather simply assume that each refiner will take the other refiners’ behavior as
given.
These results suggest that California energy regulators may want to mandate maintenance expenditures
through a regulatory process to ensure that refiners do not exploit their market positions to the
disadvantage of gasoline consumers.
Game theorists recognize that strategic behavior among firms engaged in imperfect competition can
take many forms. The Nash equilibrium examined here represents only one possible equilibrium in
which each refiner takes as given the behavior of all other refiners, and each refiner assumes that all
other refiners will do the same. Other equilibrium concepts such as tick-for-tat can lead to more
profitable implicit collusions. The possibility of even more harmful equilibria further suggests that
regulators should pay close attention to these markets.
This model does not examine the incentives to shut down or defer maintenance when a refiner has
substantial finished product inventory in stock. Regulators also should be sensitive to these issues.
Finally, this model does not consider the startup costs that a refinery incurs following a shutdown or
whether continual preventative maintenance is substantially cheaper than the cost of remedial
maintenance following a shutdown. Both issues favor continuous plant maintenance, but neither issue
eliminates the benefits that multi-plant refiners obtain from their other plants when one plant is shut
down. However, if shutdown costs or remedial maintenance costs are sufficiently high, efforts to avoid
them may completely dominate these benefits so that maintenance decisions by all refiners will be the
same regardless of how many plants they run.
11
Possible further extensions:
Calibrate the model using the actual numbers of refiners and the number and sizes of their production
lines and information about demand. Show how the results depend on demand elasticity.
Show that California prices have been more volatile than other prices.
Show that maintenance expenditures for gasoline production lines are lower and reliability is lower at
California refineries as compared at refiners in other states. <<Getting data will be hard or
impossible.>>
Extend the model to include storage.
Show the shutdowns occur more often when finished product in shortage at that refinery is high.
<<Getting data will be hard or impossible.>>
12
Table 1: California Refineries that Produce CARB Gasoline
Barrels per Day
(1,000)
Refinery
ALON USA, Bakersfield Refinery
ALON USA (Paramount Petroleum Corporation),
Paramount Refinery
BP West Coast Products LLC, Carson Refinery
Chevron U.S.A. Inc., El Segundo Refinery
Chevron U.S.A. Inc., Richmond Refinery
ConocoPhillips, Rodeo San Francisco Refinery
ConocoPhillips, Wilmington Refinery
ExxonMobil Refining & Supply Company, Torrance
Refinery
Kern Oil & Refining Company, Bakersfield Refinery
Shell Oil Products US, Martinez Refinery
Tesoro Refining & Marketing Company, Golden Eagle
(Avon/Rodeo)
Tesoro Refining & Marketing Company, Wilmington
Refinery
Valero Benicia Refinery
Valero Wilmington Refinery
Totals
Multi-refinery
Producers
66
66
50
50
240
276
245
78
139
276
245
78
139
150
26
156
166
166
104
104
132
78
132
78
1,906
1,334
70%
Source: California Energy Commission Almanac at energyalmanac.ca.gov/petroleum/refineries.html
13
16%
14%
12%
10%
8%
Conventional
6%
Reformulated
4%
2%
0%
1990
1995
2000
2005
2010
2015
Figure 1: Yearly West Coast Weekly Retail Regular-Grade Gasoline Price Return Standard Deviations.
Reformulated gasoline is produced primarily for the California market while conventional gasoline is sold
in other markets.
Source: U.S. Energy Information Administration at
www.eia.gov/oil_gas/petroleum/data_publications/wrgp/mogas_history.html.
14
$1.40
$1.20
$1.00
$0.80
$0.60
$0.40
$0.20
$0.00
1997
($0.20)
1999
2001
2003
2005
2007
2009
2011
2013
2012
$1.40
$1.20
$1.00
$0.80
$0.60
$0.40
$0.20
$0.00
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Figure 2: California Refiner Margins (for unbranded refiners). The margin is the difference between
reported average wholesale gasoline prices and the price per gallon of Alaskan crude oil (no adjustments
is made for other refined products).
Source: California Energy Commission Almanac at energyalmanac.ca.gov/gasoline/margins/index.php.
15