Credit Card Rebates

Periodically I see questions or comments about how we use operations research in our personal lives.  The truth, of course, is that for the most part we don't.  We may use the systematic analysis and critical thinking inherent in OR, but generally we neither need nor bother with the mathematical models.  (As an example of the "critical thinking", consider the ads you see on TV for insurance companies, touting that "customers who switched to <insert company name> saved an average of <insert large positive amount> on their premiums".  A typical viewer may think "wow, they're pretty cheap".  An OR person thinks "no kidding -- people with negative savings didn't switch, so the data is censored".)  Recently, however, I actually found an application for an OR model in my personal life.

In the aftermath of the "Financial Debacle of 2008" (or the "Great Recession", or whatever you prefer to call it), banks are scrambling to make money.  Thus, among other things, credit card rebate programs have become more byzantine.  Once upon a time, my Chase credit card earned rebates that were simply posted monthly, automatically and in the full amount I'd earned.  Couldn't have been simpler.  Didn't last.

I now "enjoy" the benefits of the Chase Ultimate Rewards program. Rebates are no longer credited automatically; I have to log in each month and claim them.  There can be delays in how quickly they post. Rebate balances below \$20 cannot be redeemed (they carry over to the following month).  I have options for claiming the rewards, including buying things I don't need through Chase (probably at higher than market prices) or asking them to cut me a check (then waiting for it to arrive, then depositing it somewhere).  The most convenient (or should I say least inconvenient?) way to redeem them may be what Chase calls the "pay yourself back" option, in which you apply the rebate to purchases made within the past 60 days.  The amount redeemed shows up as a credit on your next statement.

Besides the delay in receiving the credit, there are other minor hassles with the "pay yourself back approach".  You cannot pay yourself back for part of a purchase; you must have sufficient rebate credit accumulated to pay back the entire amount.  The web form only allows you to pay back one purchase at a time, and the \$20 minimum limit applies to each individual redemption, not to the combined set of redemptions.  Most of the time, this is a non-issue for me, since it usually takes me more than one billing cycle to accrue a rebate balance above \$20, at which point I immediately repay myself for a recent \$20+ purchase and drop the remaining balance back below \$20, to sit for another cycle or two.

Occasionally, however, some combination of unusual expenditures gets me a larger balance.  The trick then is to find a collection of purchases within the past 60 days, each \$20 or more, whose combined total comes closest to my available rebate balance without exceeding it.  That's probably trial-and-error for most people, but readers of this blog may recognize the problem as a binary knapsack, where the value and "size" of an item are both the amount charged, the constraint limit is the available rebate balance, and only recent purchases of \$20 or more make it into the model.  So I now have a spreadsheet containing just that model, which I'll probably need once or perhaps twice a year.