In yesterday’s post, I described a simple multiple-criterion decision problem (binary decisions, no constraints), and suggested a possible way to identify a portion of the Pareto frontier using what amounts to guesswork: randomly generate weights; use them to combine the multiple criteria into a single objective function; optimize that (trivial); repeat ad nauseam. I ran …
One of the challenges of multiple-criteria decision-making (MCDM) is that, in the absence of a definitive weighting or prioritization of criteria, you cannot talk meaningfully about a “best” solution. (Optimization geeks such as myself tend to find that a major turn-off.) Instead, it is common to focus on Pareto efficient solutions. We can say that …
Okay, this is the last post on the subject. I promise! If you’re coming into this movie on the last reel, you may need to skim the last few posts to see what it’s about. I’m trying not to repeat myself too much. To summarize where we are at: Hardmath123 posted a solution (generated by …
I’m continuing the recent theme of solving a quadratic assignment problem that lays out the 26 letters of the English alphabet on a one-dimensional “keyboard” for an 18th century typewriter. I thought this would be the last post, but something new turned up, so there will likely be one more. In the blog post that …
This continues the discussion (okay, monologue) from the two previous posts about the problem of laying out a one-dimensional typewriter keyboard. This is not the last post in the series, but I can at least guarantee that the series is converging. In the previous post, I gave a MIP model (named MIP1) that used binary …
This continues my previous post about the problem of optimally laying out a one-dimensional typewriter keyboard, where “optimally” is taken to mean minimizing the expected amount of lateral movement to type a few selected books. As I noted there, Nate Brixius correctly characterized the problem as a quadratic assignment problem (QAP). I’ll in fact try …
This is going to be the first of a few posts on the same problem. My efforts are based on a blog post by Nate Brixius (@natebrix) titled “Optimizing 19th Century Typewriters“, which in turn is based on a post titled “Tuning a Typewriter” by “Hardmath123”. As the image in Hardmath123’s post shows, an old …
In a recent blog post titled “Excessive Precision“, John D. Cook points out the foolishness of articulating results to an arbitrarily high degree of precision when the inputs are themselves not that precise. To quote him: Excessive precision is not the mark of the expert. Nor is it the mark of the layman. It’s the …
I seem to bring up “big M” models a lot, so apologies if I end up repeating myself in places here. Not long ago, someone passed along highlights of a “big M” type model to me and asked if he could somehow reformulate to get rid of \(M\). I did not see any good way …
A question posed on OR-Exchange in 2017 asked the following: Given a tour of nodes, how does one best add two new nodes while respecting the ordering of the original tour. Specifically, the author began with a tour 0 – 1 – 2 – 4 – 6 – 0 (where node 0 is a depot) …
I just finished reading a somewhat provocative article on the CIO website, titled “10 reasons to ignore computer science degrees” (when hiring programmers). While I’m not in the business of hiring coders (although I recent was hired as a “student programmer” on a grant — the Universe has a sense of humor), I find myself …
Someone posted an interesting question about box sizes on Mathematics Stack Exchange. He (well, his girlfriend to be precise) has a set of historical documents that need to be preserved in boxes (apparently using a separate box for each document). He wants to find a solution that minimizes the total surface area of the boxes …
I thought I would follow up on my June 29 post, “Does Computer Science Help with OR?“, by giving a quick example of how exposure to fundamentals of computer science recently helped me. A current research project involves optimization models containing large numbers of what are basically set covering constraints, constraints of the form \(\displaystyle …
Fair warning: tl/dr. After reading a blog post yesterday by John D. Cook, “Does computer science help you program?“, I decided to throw in my two cents (convert to euros at your own risk) on a related topic: does computer science (which I will extend to including programming) help you as an OR/IE/management science/analytics professional? …
A change I made to an answer I posted on OR-Exchange, based on a comment from a well-informed user of OR-X, might be worth repeating here on the blog. It has to do with issues that can occur when using “big M” type integer programming models, a topic I’ve covered here before. As I mentioned …
As I grow older, I’m starting to forget things (such as all the math I ever learned) … but that’s not the reason for the title of this post. A somewhat interesting question popped up on Mathematics StackExchange. It combines a basic sequencing problem (ordering the processing of computational tasks) with a single resource constraint …
[T]he report of my death was an exaggeration. (Mark Twain, 1897) In a recent blog post, “Data Science Is Not Dead“, Jean-Francois Puget discussed and dissented with a post by Jeroen ter Heerdt titled “Data Science is dead.” Barring the possibility that Schroedinger shoved data science into a box and sealed it, both assertions cannot …
Pro Bono Analytics is a program by INFORMS (the Institute for Operations Research and the Management Sciences, for the acronym-averse), “the largest society in the world for professionals in the field of operations research (O.R.), management science, and analytics”. PBA “connects our members and other analytics professionals with nonprofit organizations working in underserved and developing communities”. …
I thought I might use a few graphs to help explain an answer I posted on Quora recently. First, I’ll repeat the question here: In parametric optimization with unknown parameters, does a better estimator of the parameter always lead to better solutions to the actual problem? Here we’re trying to minimize f(x,θ) with respect to …
In some circumstances, you might want to build an optimization model containing two sets of variables, say and , and constrain them so that the sort order of each matches. That condition is easily expressed in logical terms: if and only if for all pairs with . Translating that into a mathematical programming model that …
Two years ago (two years and one day if you’re being picky), I posted a pointer to a Spanish language web site hosted by Francisco Yuraszeck (professor at the Universidad Técnica Federico Santa María in Viña del Mar, Chile). The site, Gestión de Operaciones, is listed in the resources box on the right. Recently, Francisco …
ORiginals is a YouTube channel co-hosted by Dr. Banafsheh Behzad (@banafsheh_b) of CSU Long Beach and my colleague Dr. David Morrison (@drmorr0). They present short (five or six minute) videos featuring researchers describing their research to a general (non-expert) audience. Their tag line is “Outstanding research in everyday language”, and I think the first two installments …
Someone asked an interesting question on a support forum recently. The gist was: “How do I confirm that my model is correct?” On the occasions that I taught simulation modeling, this was a standard topic. Looking back, I don’t recall spending nearly as much time on it when teaching optimization, which was a mistake on …
A tweet by Nate Brixius (@natebrix) led me to read the article “The Natural Order and Divine Order of Optimization” published by the Wisconsin Institute for Discovery, a rebuttal/counterpoint to a New York Times Magazine article titled “A Sucker is Optimized Every Minute“. The former sings the praises of optimization (somewhat) and the latter vilifies …
Armed with the contents of my last two posts (“The Geometry of a Linear Program“, “Branching Partitions the Feasible Region“), I think I’m ready to get to the question that motivated all this. Let me quickly enumerate a few key take-aways from those posts: The branch and bound method for solving an integer linear program …
Yesterday’s post got me started on the subject of the geometry of a linear program (LP). Today I want to review another well-known geometric aspect, this time of integer linear programs (ILPs) and mixed integer linear programs (MILPs), that perhaps slips some people’s minds when they are wrestling with their models. Most solvers use some …
I frequently see questions on forums, in blog comments, or in my in-box that suggest the person asking the question is either unfamiliar with the geometry of a linear program, unsure of the significance of it, or just not connecting their question to the geometry. This post is just the starting point for addressing some …
Not infrequently, I am asked about my academic specialty. When I reply “operations research”, as I usually do, I’m often met with a polite but blank stare. This happened to me a couple of times at a recent party. If the questioner inquires further, I’ll try to give an example or two of what OR …
Fellow OR blogger Laura McLay recently wrote a post “in defense of model simplicity“, which is definitely worth the read. It contains a slew of links to related material. As I read it, though, my contrarian nature had me thinking “yes … as long as the model is not too simple”. A recent piece in …
A question I saw online not too long ago caused me a flashback to my days teaching linear programming (LP) to masters students. The poster had developed an optimization model — I can’t recall if it was an LP, a quadratic program (QP) or a mixed-integer program (MIP) — and had no problem solving it. …
My phone (a Samsung Galaxy S3) updated itself to Android 4.3 this morning. I’m sure it has all sorts of wizardous new features (most of which I’ll never use). One feature that is somewhat handy is that you now have some control over which “quick setting buttons” you have in the notifications panel (top of …
I’ve come to like R quite a bit for statistical computing, even though as a language it can be rather quirky. (Case in point: The anova() function compares two or more models using analysis of variance; if you want to fit an ANOVA model, you need to use the aov() function.) I don’t use it …
I just noticed that I managed to go the entire month of October without a post. This was a combination of several factors: it’s conference season for me (INFORMS in October, Decision Sciences Institute coming up soon); I was a guest blogger at the INFORMS conference (sample here); deciduous trees + autumn + Michigan = …