Friday, August 19, 2011

On some decision optimization models for micro-credit planning and operations

Thanks to modern-day micro-credit pioneer Muhammad Yunus and e-commerce, it's become much easier to invest in and provide loans to entrepreneurs who do not have access to formal credit channels. Encouraged by Mr. Yunus' success story, India witnessed a bunch of new micro-credit banking start ups around 2006. Today, most of them have failed or barely survive, but is a different story. It operates like a non-profit organization that attracts 'social investors' and if success is measured in terms of the number of people helped, their track record has been amazing so far. There are lots of mischievous as well as helpful NGOs (non-governmental organizations) in India. RangDe is one of the good guys! Kiva is another well known, really good, global micro-credit organization.

Repayment rate
RangDe's payback statistics are pretty good. For example, if the rate of repayment R = 100%, and your (one-time) loan amount (support-level) is A, then the average number of people helped at this support-level after N-1 additional investments without injecting additional funds, is of course N and you still have your principal amount (plus any interest). If R is less than 1, then the upper bound on the eventual number of 'persons helped' at this support level before the money disappears would be = 1/(1-R). For example, if the average repayment rate is 90%, then you can expect to cover no more than 10 'A'-sized loans over the lifetime of this the initial amount. After 2 years, my experimental small initial sum of 55$ via paypal has funded rural Indian entrepreneurs five times and counting. Overall, RangDe's repayment rate cited on their website is 98.5% (Kiva's is 98.84%).

Pooled Disbursement Models
Loan payments have to be rounded to the nearest 100 ₹ (roughly 2$ increments). The investor has the option of selecting their loan recipient. If they did not avail of that option, then RangDe could best match the total pool of funds (S) accountable at the start of each day (say) to the uncovered demands for that day. They have to decide the integer amount X(i) in 100 ₹ increments that will be allocated to entrepreneur i. A simple knapsack version of this task would be to maximize total value of these decisions
Max Σ V(X(i))
Σ X(i) ≤ S

V(X) could be a metric that depends on, say, the time-critical need for the loan, whether the incremental X added fully completes the loan requirement and gets the recipient off the 'waiting list', 'credit score' of the recipient, etc. Additional constraints can be added to capture other business rules and governmental/accounting regulations governing the disbursement of funds, perhaps leading to a Mixed-Integer Programming (MIP) formulation that can be solved using CPLEX.

However, RangDe can still use such fund pooling optimization models as long as the investor is not allowed to specify an arbitrarily tight time-frame for the funds to be allocated; This appears to be the case, so some flexibility in the pooling of funds to cover more time-prioritized demands is possible. But can we strictly say that similar replacement monies will be available to cover original, intended recipients on time?

Risk-Managed Coverage Models
My 55$ can be used to safely satisfy today's general needs if it can be guaranteed that this amount will be unconditionally available toward covering my target loan D(i) in time. RangDe probably cannot guarantee this, but what if a service-level tolerance, say, 99% was allowable (i suspect this level may be bounded by the repayment rate)? RangDe could provide this option to the investor upfront who can then check a box to allow their money to be used to satisfy more time-critical needs with a small probability that it may not be possible to fund their chosen target on time.

The supply available to meet critical needs can be augmented toward additional at-risk allocations (Y) that can be made at some cost functional C(Y). For sufficiently large positive values of C, Y=0 is optimal and the model reduces to the risk-free disbursement formulation.

Max Σ V(X(i)) - Σ C(Y(j))
Σ D(X(i)) ≤ S + Σ Y(j)

The formulation should satisfy these requirements:
1. No funds at risk will be touched unnecessarily.
2. A fund at-risk will be allocated only if the value from using it exceeds the risk-cost.
3. RangDe has to calibrate this cost function to ensure that the desired service level is maintained over time, and could transparently display the service level profile over time to maintain investor confidence.

The focus of this post is not on building the perfect OR model; rather, one hopes this motivates research in the exciting area of micro-credit optimization and analytics. I'm sure there are many more aspects to micro-credit planning and operations that can be improved using OR approaches. Here is an opportunity to tangibly contribute to the community and maybe even make modest profits to go with it :)

Historical note
"Rang De" literally means "to color". Historically, it is popular as the words in the patriotic song immortalized by India's revered freedom fighter Bhagat Singh as he walked to the gallows in 1931.

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