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190 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

MANAGEMENT SCIENCE IN ACTION

Pupil transportation in North Carolina
nsuring value for money for the taxpayer is a these different factors. There was then a pro-
E key expectation placed on every public sector gramme over four years of phasing in the funding
organization. At the time of this project, North Car- allocations to match the adjusted efficiency scores,
olina was spending around US$150 million every with considerable effort going into convincing the
year on pupil transportation to and from school decision makers that the new system was both fair
with around 13 000 school buses transporting and provided an incentive for the less efficient
almost 700 000 every day to 100 school districts. school districts to improve their performance over
The Department of Public Instruction was tasked time and hence increase funding. The modelling
with reviewing the situation, specifically to ensure project has resulted in school districts, including
that school districts that operated efficiently were those with high efficiency scores, reviewing their
reimbursed in full for pupil transportation costs transportation arrangements and seeking perform-
whilst those less efficient were reimbursed only as ance improvements. Among the improvements
much as was seen to be fair and equitable. It was realized were:
recognized that DEA had considerable potential to
• reduction in the number of buses needed;
inform these decisions. The DEA model that was
developed used two inputs: the number of buses • reduction in distance travelled;
used to transport pupils and total operating expen- • reduced operating costs;
diture; and one output, the average number of
• improved safety.
pupils transported per day. However, the problem
was complicated by the fact that school districts With total projected savings of around $130 million
were very diverse in terms of their population base, over a six-year period.
demographic mix and school locations. As a result
Based on T. R. Sexton, S. Sleeper and R. E. Taggart Jr, ‘Improving
the initial efficiency scores resulting from the DEA pupil transportation in North Carolina’, Interfaces 24 1 (1994):
solution were then adjusted to compensate for 87–103.

Summary

l This chapter has introduced a number of common areas of application of linear programming in
business and management.
l The formulation stage of LP is typically one of the most difficult in the real world and one where
practise, experience and awareness of other LP applications does make things much easier.
l LP applications in the same area often have similar characteristics and this can be helpful when
formulating a new problem in the same area.
l Specialist software has been developed for a number of these application problem types, dedicated
websites have been established to bring users together and in some cases academic journals and
member societies created.

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