Maximizing benefits in project selection: a hybrid approach

ABSTRACT

Charitable foundations and government programmes should endeavour to allocate their limited resources to best serve their constituents. Yet, mathematical programming techniques are rarely used despite overwhelming evidence of their superiority in selecting projects that yield higher levels of total benefits. We present a novel ‘hybrid selection model’ that combines binary linear programming and heuristic rank-based models applied to two case studies. The first case focuses on providing services to women and shows a hybrid model would have selected the top three ‘signature’ projects and maintained an above-average overall project benefit while securing a 180% improvement in the number of projects funded, a 66% improvement in the number of women served and a 132% improvement in the total benefit achieved. In the second case, we apply the hybrid approach to data from the US government’s largest forest preservation programme and demonstrate that the hybrid approach could allow the programme to select up to 11 top-scoring projects while still achieving a 97% gain in the total overall benefit compared to their traditional method. These case studies show that the hybrid approach has the potential to be applied in a variety of settings and improve how foundations and programmes achieve their goals.

KEYWORDS:

• Binary linear programming
• charitable donation allocation
• goal programming
• hybrid selection model

JEL CLASSIFICATION:

• C44
• C61
• L31

Acknowledgements

This work was supported by the National Science Foundation EPSCoR under Grant number 1301765.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The budget of $136,219 represented the initial budget of $130,000 and $6219 by which the fund exceeded its budget in fully funding all of the projects selected using the rank-based approach. Including the overage actually spent allowed us to compare the two methods of project selection accurately.

² Some projects served two or more counties.

³ All of the selected projects are fully funded based on the initial project requests.

⁴ We also tested GP models with a different set of goals – maximizing the aggregate score and minimizing differences in the number of projects selected from each county. The results of those models were similar and are available from the authors upon request.

⁵ Given the limitations of the data set, the goals we set are not necessarily independent, but it is still interesting to see how the organization could balance different objectives.

⁶ Note that the hybrid-10 model is the same as using the rank-based method since those 10 parcels exhaust the budget and that the hybrid-0 model is the same as using BLP.

⁷ The analysis was conducted using the Risk Solver Platform for Microsoft Excel (v11.0).

⁸ A detailed project scoring guidance can be found on the Forest Legacy Program official website.

⁹ All optimization was conducted using the Risk Solver Platform V11.0.1.0.

Additional information

Funding

This work was supported by the National Science Foundation EPSCoR under Grant number 1301765.