Mister

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 customers 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 “degree days”, A degree day is 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. (If the degree day calculation results in a negative number, the degree days number is recorded as 0.) By keeping track of the number of degree days since the customer’s last oil fill, by knowing the size of the customer’s oil tank, and by 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,...