Imperfect Classifications

As I think has become increasingly obvious by my topic choice, I believe one of the biggest flaws many OR models have when dealing with emergencies is a lack of clear information.  Some models treat the problem stochastically, which adds to the complexity of the model, but hopefully improves the resulting decisions.  Others, like Rath and Gutjahr [1], which I detailed in my previous post, seeks to look at the problem through the lens of trade-offs.  Argon and Ziya [2] tackle the problem of imperfect information head on by considering how well priority assignment systems work with imperfect information, how to prioritize with imperfect ‘signals’ of severity, and what systems best handle this problem.

Argon and Ziya look at a queuing system with different priorities of patients.  The specific instance that we will consider is that of an EMS dispatch system.  Patients arriving to the system are either type 1 patients who need immediate treatment or type 2 patients who should wait until all type 1 patients are served.  The dispatcher, however, only receives a signal that details how likely a patient is to be type 1.  More specifically, this is not necessarily strictly a probability, since as long as the signals can be ordered such that signals from type 1 patients are larger than from type 2 in likelihood ratio ordering.  The dispatcher must use these signals to assign patients to priority levels, where higher priority levels must all be served before a lower priority level receives any service.

It is worth noting that Argon and Ziya assume penalties are linearly related to waiting time for most of paper.  In the instance where linearity holds, increasing the number of priority levels that dispatchers can assign the patients to will never result in worse outcomes, and may in fact result in better outcomes.  Following this thought to its logical conclusion, the authors argue for a Highest-Signal-First (HSF) policy which serves patients in order from most likely to be type 1 to least likely.

A more important take-away to me is that a two-priority policy achieves a majority of the improvement HSF sees of First-Come First-Serve (FCFS) while being far more practical to implement.  Better yet, when the authors investigate nonlinear wait time penalties, the two-priority policy consistently outperforms HSF and at worst performs on par with FCFS.  Unfortunately, they only look at a single nonlinear function that increases the penalty quadratically with wait time.  This is not very representative of cardiac arrest patients who suffer most of their penalty in the first minutes after their call [3].

A worthwhile extension of this research would be to consider the case where patient penalties are exponentially decaying (similar to what we expect for cardiac arrest victims) and compare two-priority and three-priority policies to FCFS.  These policies are easier to implement and are used in practice.

Further, this can be combined with historic data on the accuracy of the ‘signal’ the dispatchers receive to determine best practices for when to assign a patient to high priority based on system load.  Argon and Ziya argue that as the system load increases, we should become less discriminate in and accept more patients as high priority, but this does not seem to necessarily hold in the exponentially decaying case.  Instead, it may move toward more discrimination in labeling patients as high priority since there is only a major benefit to serving a type 1 patient if it is done so quickly.

I believe that by looking at the possibility that our information is not quite accurate, we can develop better policies that work under a variety of conditions.  Whether this means using a deterministic policy only as a guide or better yet, determining a policy that best mitigates the effects of imperfect information as above, it is better than simply ignoring the problem.

 

[1] Rath, Stefan, and Walter J. Gutjahr. “A math-heuristic for the warehouse location–routing problem in disaster relief.” Computers & Operations Research 42 (2014): 25-39.

[2] Argon, Nilay Tanik, and Serhan Ziya. “Priority assignment under imperfect information on customer type identities.” Manufacturing & Service Operations Management 11.4 (2009): 674-693.

[3] Valenzuela, Terence D., et al. “Estimating effectiveness of cardiac arrest interventions a logistic regression survival model.” Circulation 96.10 (1997): 3308-3313.

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