Thursday, July 23, 2009

Optimizing the Health-Care Reform Package of Obama using Operations Research

In his press conference yesterday, President Obama used the word "unconstrained" while talking about the escalating costs within health care system. He later used the term "constrained system" (or was it "constrained model") when talking about financial regulation. Is one of his advisors an OR guy??

Another interesting aspect that he mentioned was that some democrats wanted some additional provisions in the healthcare package that would address their regional interests, which would then cost additional money, so some chopping and changing has to be done and the August deadline is flexible as well. To an Operations Research person, it seems a sin not to optimize and automate the fine-tuning of the package, which would lead to savings in time and money. So after adding all the fundamental (must-have) provisions, the remaining 10-20% of the contentious provisions (bids) can be optimized to save taxpayer money.

If a new health-care provision i brings in v(i) net votes and net cost c(i) and removing a pre-existing provision j results in v(j) net votes at a net cost of c(j), and defining binary decision variables:
xi = 1 if new provision i is added, 0 otherwise
yj = 1 if existing provision j is removed, 0 otherwise

index set i runs over the set of new provisions, while j corresponds to existing provisions that are candidates for removal.

the bill optimization problem becomes:

Minimize sum(i) ci. xi - sum (j) cj. yj
subject to:
sum(i) v(i). xi - sum(j) v(j). yj >= MINIMUM_VOTES_NEEDED_FOR_CONSENSUS
x, y binary

The aim of this optimization model is to minimize the total cost of fine tuning the package, subject to meeting the minimum approval needed to get the package approved. Obviously, this is a simple linear integer knapsack problem and in practice, there may be more constraints and objectives in the world of politics and governance. Furthermore, we assume linearity and a simple model to start off with. To improve acceptance, one can also add constraints based on other provision attributes. e.g, to satisfy budgets by area of Health-care. Alternatively, one can maximize the number of votes in favor of the package and add a constraint on the total incremental cost of fine-tuning.

Conceptually, the model is quite interesting. While it will generally aim to keep the best bang-for-buck provisions, it also recognizes that these provisions cannot be split into 'half-measures' to meet constraints and therefore a greedy selection based on bang-for-buck may be suboptimal.

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