**3.0 Forecasting Demand**

**3.1 Overview**

Demand for LPG is an important
factor that influences Liquigas Ltd’s security of supply. We focused on
developing daily demand forecasting models that would be useful for short-term
planning. These models would act as complements to the daily supply forecasting
model, Model I.

**3.2 Development of Daily Demand Forecasting Models**

In a recent report prepared for Liquigas Ltd - *Sales/Weather Analysis *(2006), Bevan
Singleton details the analysis of four variables that he believed to be
important weather factors that may affect demand for LPG. In order to
select a demand model for each depot, we developed several models, in addition
to the models from Singleton’s* *for comparison.

For each depot,
many of the daily LPG demand values are zero. This is the case because
customers tend to order LPG in bulk quantities to replenish inventory levels.
Since many time series models are not appropriate for unstable data of this
type (reasons for this include difficulty in identifying trends and seasonality
in such circumstances), we considered alternative methods. We firstly
experimented with Croston’s intermittent demand models, however the results
were all poor. To overcome this problem it was necessary to modify the data. We
deleted all zero values, and used Forecast Pro’s interpolation capabilities to
replace them, in order to use other forecasting methods such as ARIMA
modelling. The downside of this is that we are overestimating historical demand
however we believe that this is a better alternative to underestimating it.
Outliers were deleted, and then similarly replaced with interpolated estimates.

The first
model examined in each case was Forecast Pro’s Expert Selection model. We also
developed our own ARIMA models by examining the autocorrelation and partial
autocorrelation functions. Finally, we developed a Dynamic Regression model for
each depot by considering not only maximum temperature as Singleton suggests, but also minimum temperatures for each
depot, maximum/minimum temperatures for the last 3 and last 7 days, and 7-day
moving average maximum/minimum temperatures. As well as temperature variables,
we also considered the following explanatory variables for each demand model:
days of the week, weekend, months of the year, seasons, real price of
electricity and* *the average of the
last seven days demand.

From these models, our selection criteria was based primarily on the
statistical output from the hold-out samples, whilst also taking into account
the simplicity of each model.
The demand forecasting models for each depot are finalised as follows:

**Auckland****:** Dynamic Regression Model involving
temperature and weekend variables.

**Christchurch****:** ARIMA(1,0,1)*(0,1,1)

**Dunedin**

**3.3 Conclusions, Limitations and Recommendations**

These models are most appropriate for
short-term planning of up to about one week. Ships can be redirected at
immediate notice and therefore the daily demand models could provide invaluable
information to avoid stock-outs in the short-term.

**4.0
Evaluating Storage Facilities**