Stocks and flows—inventories in petroleum refining

• Author: Robert Tischer
• Published date: 01 June 2020
• DOI: http://doi.org/10.1111/opec.12178
• Date: 01 June 2020

Stocks and flows—inventories in petroleum

refining

Robert Tischer

Shadow-K Research Fellowship. Email: robert.tischer@colorado.edu

Abstract

This paper addresses the question of whether an (S,s) inventory management model, combined

with a stockout-avoidance mechanism, is appropriate for explaining the inventory process for oil

refining. The analysis uses a fixed-proportion production function to model dynamic profit

maximisation in crude oil refining. The model distinguishes the use of production crude oil from

crude oil inventories as inputs into oil refining. The result is a relationship between oil production,

oil inventory and the difference between the prices of crude oil and refined petroleum products.

Estimation results indicate that the (S,s) model is consistent with data measuring crude oil

inventory management and results also imply a modest stockout-avoidance mechanism.

1. Introduction

This paper examines whether the (S,s) inventory model with a stockout-avoidance

motivation is an appropriate theory for analysing observed inventory management by oil

refineries. Different models have been proposed to describe how and why firms hold

inventories. Among these are production smoothing,

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stock adjustment,

2

stockout-

avoidance,

3

quasi-fixed factor

4

and the (S,s) model.

Arrow et al. (1951) provided an early influential study of optimal inventory policies

for finished goods. This placed an early focus of the literature examining inventories on

output inventories. Additionally, researchers began to observe that changes in aggregate

inventories tracked changes in GNP Blinder et al. (1981). This caused much of the focus

on inventories in the 1950s and 1960s to explore inventory impacts on macroeconomic

output Blinder et al. (1981). Overall, research concerned with output inventories is often

concerned with trying to explain the relative variances of output and sales. Blinder and

Maccini (1991a) noted that from a microeconomic perspective, production was more

variable than sales, while similarly for the macroeconomy, GNP was more variable than

final sales.

Some research has addressed input inventories, but input inventory research is most

often concerned with explaining output price movements. For example, Antoniou et al.

(2017) used input inventories to examine the asymmetric responses of output prices to an

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increase versus a decrease in input prices. Diaz-Rainey et al. (2017) looked at possible

speculative effects over time from crude oil inventory holdings on crude oil prices. More

relevant here, Blinder and Maccini (1991b) noted that the (S,s) inventory model may be

most appropriate for examining input inventories and Scarf (1959) showed that the (S,s)

inventory model is optimal if inventory holding costs plus stockout costs are convex.

More recent research involving (S,s) inventory models has focused on identifying

optimal (S,s) inventory strategies under different conditions (see for example Wen

(2011), Kams

¸hk et al. (2019), Perera et al. (2018), and Basheer et al. (2018)). Thus far,

no research has tried to connect crude oil inventories held by refineries to the (S,s)

model, although some research has examined crude oil inventories.

Looking more specifically at crude oil inventory research, Considine (1997)

examined refinery input and output inventories using quasi-fixed factors of production,

which is a means of arriving at a production smoothing mechanism. Another oil

inventory paper, Considine and Larson (2001), employed a stochastic control model of

profit maximisation with price uncertainty to generate a model that compared the

marginal benefits with marginal costs of storage. In that paper, the marginal costs of

storage included a convenience yield

5

term and a risk premium. More recently, Byun

(2017) looked at gasoline production and also examined crude oil inventories. The Byun

(2017) model included inventories as a separate production input and also included a

storage convenience yield.

In a similar fashion, the theoretical model employed in this paper assumes that a

refinery seeks to maximise the discounted stream of profits and that they operate in

competitive input and output markets. The model examines inventory adjustments using

a two-input fixed-proportion production function with crude oil and a composite input.

Use of this function relies on the close connection between the amounts of refined

petroleum products produced from one barrel (42 gallons) of crude oil. This functional

form seems natural given the nature of crude oil and crude oil refining.

Unlike prior research

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into oil refining, this paper defines inventories of crude oil to

include only those crude oil stocks held by refineries. This more narrow definition is

better suited to develop a refinery-specific model of inventory storage that is necessary to

address the implications of an (S,s) inventory model. The empirical analysis directly

estimates contemporaneous parameters suggested by the structural theoretical model.

The format of the empirical model is derived from the solution of the theoretical model.

Results show that the data are consistent with expectations associated with an (S,s)

inventory model. Contemporaneous relationships show the existence of endogeneity

with respect to the change in inventories, output prices, input prices and the difference

between output and input prices. Although the theoretical model shows the existence of a

relationship involving the difference in output and input prices and the change in overall

storage costs, estimation suggests modelling the individual variables separately may also

©2020 Organization of the Petroleum Exporting Countries OPEC Energy Review June 2020

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