Kia recommends that I get the oil in my 2009 Rio changed every 7,500 miles. But, anecdotally, it seemed that I always got better gas mileage right after an oil change than I did right before I was due for another one. So, I got to wondering - if an oil change costs $20, but saves me a few MPGs, is it cheaper overall to change my oil sooner than 7,500 miles? If so, where's the optimal point?
So, I got all ready to do some fancy math, and began tracking my gas mileage between two oil changes... And this is what I found:
This is why anecdotal evidence is unreliable.
At least based on this one oil change cycle, my gas mileage theory was 100% imagination. I should stick to oil changes at 7,500 mile intervals.
Of course, this is really a sample of only a single oil change cycle. It started in summer and went into winter, so winter fuel blends came out (which generally have slightly higher MPGs), and I presumably used the A/C less (though my defrost requires my A/C to be on, and I use the defrost a lot). There may be other complicating factors as well. So, I plan to track this all over again and re-visit after my next oil change cycle... because gut feelings die hard.
Over the last several weeks, I’ve blogged about two different methods for solving the small cell suppression problem using SAS Macro code. In the first, we used a heuristic approach to find a solution that was workable but not necessarily optimal. In the second, we solved the problem to proven optimality with SAS PROC OPTMODEL. But all of this leaves a few open questions…
For example, how much better is the optimal approach than the heuristic? Is there ever a reason not to prefer the optimal approach? And what are some other improvements and techniques that a researcher using these macros might want to know about? I’ll spend this post reflecting on our two solutions and covering a few of these bases.
In last week’s post, we constructed a set of constraints to bound a binary integer program for solving the small cell suppression problem. These constraints allow us to ensure that every group of data points which could be aggregated across in a tabular report contains either 0 or 2+ suppressed cells.
At some point before age five, every kid masters the art of satisfying constraints with solutions that are hilariously non-optimal.
Obviously, there’s plenty of ways we could satisfy our constraints – suppressing everything, for example. But we want choose the optimal pattern of secondarily suppressed cells to minimize data loss. So, we’re going to tackle the problem using binary integer programming in PROC OPTMODEL. Strap yourself in, folks – it’s going to be an exciting ride.
In last week’s post we built a SAS macro that found acceptable solutions to the small cell suppression problem using a simple heuristic approach. But what if acceptable isn’t good enough? What if you want perfection? Well, then, you’re in luck!
Benjamin Franklin once attempted to become morally perfect. Too bad he didn’t have PROC OPTMODEL…
I’ve blogged previously about optimization with linear programming in SAS PROC OPTMODEL, and it turns out that the cell suppression problem is another class of problems that can be tackled using this approach. (If you’re unfamiliar with linear programming, check out the linear programming Wikipedia article to get up to speed.) Over the next two posts, we’ll be setting up a SAS Macro that builds the constraints necessary to bound our optimization problem, then implementing the actual optimization code in PROC OPTMODEL.
Last weekend, I decided to build a bed. I looked up some plans online, made some modifications, drew up a list of the lengths and sizes of lumber I needed, and went to the store to buy lumber. That’s when the trouble started. The Lowe’s near me sells most of the wood I needed in 6ft, 8ft, 10ft, and 12ft lengths, with different prices. And I needed a weird mix of cuts – ranging from only 10 or 11 inches up to 5 feet. How was I supposed to know which lengths to buy, or how many boards I needed?
Of course, I could have just planned out my cuts on a sheet of paper, gotten close to something that looked reasonable, and called it a day. But I figured there had to be a better way. Turns out, there is, and there’s a huge body of academic literature on the subject. The problem I was facing was simply an expanded version of the classic “cutting stock problem.” It’s a basic integer linear programming problem that can be solved pretty easily by commercial optimization software. So, I decided to try out some optimizations!