3.0 Forecasting Demand
Demand for LPG is an important factor that influences Liquigas Ltdís 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 Singletonís 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 Crostonís 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 Proís 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 Proís 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:
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.