Approximation in enumeration techniques for large scale zero-one programming for corporate average fuel economy planning

Mathematical programming was used to achieve corporate average fuel economy standards at minimum cost. Computational difficulties were experienced on the large-scale zero-one linear integer programming problems that arose. To alleviate these difficulties, a method based on adaptive estimates of the optimal objective function value was implemented in a computer code using implicit enumeration. With this approach the computational problems encountered in determining minimum-cost allocation of mass and/or fuel-efficient components among car lines are reduced substantially. Results are presented showing that problems with 100 to 350 variables are handled easily and solved within a minute. These enhanced capabilities permit extensive sensitivity analyses, and thus provide numerous practical alternatives to the decision-maker