Dupree Fuels Company is facing a difficult problem. Dupree sells heating oil to residential customers. Given the amount of competition in the industry, both from other home heating oil suppliers and from electric and natural gas utilities, the price of the oil supplied and the level of service are critical in determining a company’s success. Unlike electric and natural gas customers, oil customers are exposed to the risk of running out of fuel. Home heating oil suppliers therefore have to guarantee that the customer’s oil tank will not be allowed to run dry. In fact, Dupree’s service pledge is,“50 free gallons on us if we let you run dry.” Beyond the cost of the oil, however, Dupree is concerned about the perceived reliability of his service if a customer is allowed to run out of oil.
To estimate customer oil use, the home heating oil industry uses the concept of a degree-day, equal to the difference between the average daily temperature and 68 degrees Fahrenheit. So if the average temperature on a given day is 50, the degree-days for that day will be 18. By keeping track of the number of degree-days since the customer’s last oil fill, knowing the size of the customer’s oil tank, and estimating the customer’s oil consumption as a function of the number of degree-days, the oil supplier can estimate when the customer is getting low on fuel and then resupply the customer.
Dupree has used this scheme in the past but is disappointed with the results and the computational burdens it places on the company. First, the system requires that a consumption-per-degree-day figure be estimated for each customer to reflect that customer’s consumption habits, size of home, quality of home insulation, and family size. Because Dupree has more than 1500 customers, the computational burden of keeping track of all of these customers is enormous. Second, the system is crude and unreliable.
The consumption per degree-day for each customer is computed by dividing the oil consumption during the preceding year by the degree-days during the preceding year. Customers have tended to use less fuel than estimated during the colder months and more fuel than estimated during the warmer months. This means that Dupree is making more deliveries than necessary during the colder months and customers are running out of oil during the warmer months.
Dupree wants to develop a consumption estimation model that is practical and more reliable. The following data are available in the file Dupree Fuels.xlsx:
The number of degree-days since the last oil fill and the consumption amounts for 40 customers.
The number of people residing in the homes of each of the 40 customers. Dupree thinks that this might be important in predicting the oil consumption of customers using oil-fired water heaters because it provides an estimate of the hot-water requirements of each customer. Each of the customers in this sample uses an oil-fired water heater.
An assessment, provided by Dupree sales staff, of the home type of each of these 40 customers. The home type classification, which is a number between 1 and 5, is a composite index of the home size, age, exposure to wind, level of insulation, and furnace type.A low index implies a lower oil consumption per degree-day, and a high index implies a higher consumption of oil per degree-day. Dupree thinks that the use of such an index will allow them to estimate a consumption model based on a sample data set and then to apply the same model to predict the oil demand of each of his customers. Use regression to see whether a statistically reliable oil consumption model can be estimated from the data.