dealuz 0.1.1

a short and simple package implementing Data Envelopment Analysis (DEA)

dealuz

dealuz is a short and simple package that aims to implement Data Envelopment Analysis (DEA) in python language

Why this package, what does it do?

This package is built to deal with the main concerns when applying a DEA model: inputs and outputs, returns to scale, model objective (output and input oriented) and reference sets

The Data Envelopment Analysis is a diagnostic tool that generates efficiency indexes for Decision Making Units based on their Activity. Those indexes are computed primarily based on the ratio of inputs and outputs of each DMU activity, the results, the performance of a DMU in a closed section of time. A practical example is a paper selling company that want to assess their branches performance based on the ratio between office meetings (as input) and sales performed (as output)

If one assumes that to each office meeting the sales grow by a fixed and proportional amount, that one is assuming a Constant Returns to Scale model where each change in the number of meetings turns into a proportional change in the sales amount. On the other hand if a change in the number of meetings does not causes a proportional change in the sales, one may assume a Variable Returns to Scale

Now let's evaluate the company's goal. If the office meetings are the social fuel our sellers crave or the company has not yet conquered the whole market share and is not willing to reduce the number of meetings, one other may use an Output Oriented model that evaluates the branches on their capability of maximising sales. However if the company is facing the scarcity of time or has already conquered the whole market share, thus having no motivation to expand in sales, one other may use the Input Oriented model that focus on the branch capability of minimising their meetings

In the end (if you've done everything right) there may be some inneficient branhces; that's okay, the main purpose of DEA is not evaluate acceptable levels of activity but to evaluate, between similar branches, which one of they exceeds expectations. So, if Scranton branch, is deemed as efficient in despite of Utica, Stamford and Nashua, the Scraton branch sets a new standard for the other branches to follow and the other branches are evaluated in comparison to the effcient branch; this is the reference set for the DEA models

What is included?

This package includes two DEA related functions:

• dealuz.dea which performs the multiplier Data Envelopment Analysis[^2][^3][^4] for an activity table; and
• dealuz.graphical_frontierbased on the work of Bana e Costa et al.[^1] which presents a graphical way to visualize DEA results

For those OOP lovers, the package also has a dealuz.DEAResult object that is returned by dealuz.dea and can be also passed to dealuz.graphical_frontier

References

[^1]: Bana e Costa, C. A.; Soares de Mello, J. C. C. B.; Meza, L. A. "A new approach to the bi-dimensional representation of the DEA efficient frontier with multiple inputs and outputs", European Journal of Operational Research, 2016, https://www.sciencedirect.com/science/article/abs/pii/S0377221716303320 [^2]: Banker, R. D.; Charnes, A.; Cooper, W. W. "Some models for estimating techincal and scale ineficiencies in Data Envelopment Analysis", Management Science, 1984, https://www.jstor.org/stable/2631725?origin=JSTOR-pdf [^3]: Charnes, A.; Cooper, W. W.; Rhodes, E. "Measuring the efficiency of decision-making units", European Journal of Operational Research, 1978, https://www.sciencedirect.com/science/article/abs/pii/0377221778901388 [^4]: Cooper, W. W.; Seiford, L. M.; Tone, K. "Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software", Kluwer Academic Publishers, 2000, https://link.springer.com/book/10.1007/978-0-387-45283-8