**2.0 Forecasting Supply**

**2.1 Overview**

In order to have more control over the security of supply, information
is the key. The more information one has regarding supply and demand, the
better one is able to plan one’s operations to avoid being unable to meet
customer orders, or extra costs associated with excess inventory on hand. Three
models were developed using Dynamic Regression:

I.
A model to forecast daily
supply for a forecasting horizon of up to about one week

II.
A model to forecast daily
supply for a forecasting horizon of up to one year

III.
A model to forecast
monthly supply for a forecasting horizon of up to 6 months

**2.2 Model I and II - Dynamic
Regression **

A Dynamic Regression model states how an output
variable is linearly related to current and past values of one or more input
variables. It also takes into account the possible autocorrelation pattern of
the disturbance series - Pankratz
A. *Forecasting with Dynamic Regression
Models*, John Wiley & Sons, Canada (1991)

In normal regression model where there is a
dependant variable *Y* and a set of independent variables* X _{i}*.
Dynamic Regression takes this one step further by modeling the errors of the
model as an ARIMA model. The form of the model is:

μ is the constant, ω_{i} are the coefficients for
explanatory variables X_{i,t-j, } θ and Ф are coefficients to model
the error, a_{t}, where B is the backshift operator. The first part of
the model is basically a simple linear regression model, and the second term is
the ARIMA error term.

Through
research, investigation and meetings with the clients, a pool of potential
explanatory variables were established that may help in forecasting daily LPG
supply from *forward selection* when building simple linear
regression models. After an initial model is selected by Forecast Pro, the
model is fine-tuned by adding in other significant variables, one at a time as
suggested by Forecast Pro (these tend to be lags of the explanatory variables
in the model so far, or perhaps a variable which is taken out, later to be put
back in). Any non-significant variables identified after each insertion of a
significant variable, is taken out one at a time (in order of most
non-significance), and the model updated (the coefficients and significance
statistics for each variable) after each time. This is because taking all the
non-significant variables all together can produce a different model, from when
one is taken out at a time.

In
order for these models to be of use, the explanatory variables need to be forecasted
for the period of interest. Some of the variable in Model I and II were
deterministic and did not need to be forecasted. For short term forecasting of
daily LPG supply, temperature data, one of the variables in Model I, may be
obtained easily from external sources such as the New Zealand Meteorological
Service. Model II also uses temperature data, and would need daily temperature
forecasts for a longer period into the future. For this, we developed several
temperature forecasting models using ARIMA modelling. While on a day to day
basis, our models would give inaccurate forecasts, over a period of time, the
models were able to capture the behaviour of temperature, with their regular
seasonal cycles and variation from day to day. Using these forecasts in Model
II would give an idea of the future outlook of daily LPG supply.

The
reason that Model I is limited to only short term forecasting is due to the
inability to develop a good forecasting model for one of the explanatory
variables in the model – MAUIMA, which is the average of the last seven days
daily supply of LPG from

**2.3 Model III – Forecasting Monthly Supply of LPG **

LPG is the by-product of the natural gas
production. Model III aims to predict the future LPG supply from

Figure 1 - Model III

**2.4 Conclusions, Limitations and Recommendations**

Model I is the better of Models I and II for forecasting daily supply,
if the forecasting horizon is less than about one week. While this model is
useful for short-term planning, if one wanted to forecast a long enough period
into the future, then this model is unsuitable. This is because in order to use
Dynamic Regression, one also needs the forecasted values of the explanatory
variables that are in the model for the period that we want to forecast the
dependant variable. Due to the inability at this stage to develop a good model
to forecast one of the explanatory variables in this model, this model is best
used for short-term forecasting.

Model II attempts to rectify the problem of Model I, and was developed
for the purpose of forecasting a long period into the future. These daily
forecasts would be useful if one wanted to carry out analysis for long-term
planning purposes. Orbit Systems Ltd[1] has
developed a Simulation Model for the purposes of evaluating such things as the
effect on storage levels under different configurations of shipping rules and
different demand situations. A required input is daily supply data of LPG.
Model II was developed as a complement to this Simulation Model.

Model III, a monthly supply model, was developed as a complement to a
monthly demand model for LPG that had previously been developed by another
party hired by Liquigas Ltd. This would be useful for Liquigas Ltd to plan its
medium-term operations such as when to import LPG from overseas. While monthly
supply may be estimated by summing up the relevant daily forecasts from Model
II, Model III incorporates information regarding natural gas production, and
uses a different forecasting approach from Model II. It was hoped this approach
would give more accurate monthly forecasts.

Whist several
attempts had been made to produce accurate and precise forecasting methods for
forecasting supply of LPG, several limitations hindered our capability to
achieve this.

Firstly, the
conversion rate between natural gas and LPG is only a rough average, given by
our clients. Since Model III depends heavily on this to produce accurate
forecasts, our efforts can only go so far when this piece of information is not
precise. Even if we could develop models that proved precise and accurate when
compared to the actual figures available for 2006, ‘unpredictable’ events in
the future would cause our models to become obsolete. Currently, it is clear
that

Finally, assuming that new wells will not be built, the depletion
of

*“Gas depletes
differently from oil. … There were no market signals of the approach of the cliff
at the end of the plateau. It accordingly came without warning, causing prices
to surge through the roof, and bringing power blackouts to *Colin Campbell,
2001.

Due to the nature of natural gas, production is normally capped at far below capacity, leaving an in-built and unseen ‘balloon’ or spare capacity. Not knowing how much is left in the wells makes it difficult to predict when it could suddenly run out.

With the
depletion of

**4.0
Evaluating Storage Facilities**

[1] A consulting company that
was contracted by Liquigas Ltd to do some consulting work for them including
building a simulation model to mimic the rules and operations of the business.