I'd recommend getting the 9th or 10th edition of Introduction to Operations Research by Hillier and Lieberman. 9th: https://www.amazon.com/dp/0077298349
You can search for the 10th edition. Both are available used for less than 50 USD in good condition. The book covers a lot more than linear programming. A solution manual for both editions can be found on the internet.
A good "free-pdf" optimization book, to support the above is, Algorithms for Optimization by Kochenderfer & Wheeler ( https://algorithmsbook.com/optimization/ ). It has a chapter on constrained linear optimization with Julia code and is a good secondary resource. Kochenderfer, Wheeler, and colleagues also have two other free optimization books that are a little more advanced. It is exceptionally cool that they make the high quality PDF freely available; more authors in the technical space are making their books freely available as pdf and I applaud them for it.
I'd say to be wary of sharing links to full textbooks unless you are really sure it's posted by the copyright owner. The authors could be best friends with the webmaster and allowed them to post it on their website, but the problem is with the publisher who may not have given consent.
In my work, I use Gurobi and other proprietary/free solvers to optimize some objectives big banks care about. It's not uncommon to use solvers in finance to optimize some metrics of a portfolio. A lot of people I have met in conferences optimize their supply chains (think things like: find the best pattern to draw the various pieces of my table in these planks of wood such that it minimizes wastes, find the best route to deliver my 100 packages...)
Right, the LEAN/TPS application is readily apparent for assembling physical goods.
But do people use it say for large scale software which needs to be tested, certified, translated, deployed, etc? I can imagine such orchestration but I've never seen it professionally. Maybe I just haven't worked at the proper companies
LPs (and MIPs) are used for scheduling, planning, and logistics. These are some of the earliest applications of LPs, dating to the 1930's and 1940's, and these applications are still relevant. The wikipedia page has a good overview of the history and utility of linear programming.
https://en.wikipedia.org/wiki/Linear_programming
That's a clarifying response: I've applied (non)convex programming (LP, QP, MIP, etc) to all the above and a few more, all of which i'd classify as classical applications. Less traditional applications -- I'd like to explore these more --- include data envelopment analysis, which provides a framework for assessing the efficiency of processes based on 1 or more input metrics, and several ideas in papers published at NeurIPS and other conferences that integrate LPs into neural networks in various ways, including AUC maximization. I've also worked on first order methods to solve LPs, and while I'd like to continue in that direction, the area is very crowded with very good existing tools, new and emerging tools that are also often good, and very strong teams building on all of the above. One of the biggest challenges that I see in the OR space is that it requires human expertise to leverage the technology.
In a professional context, I use it to help a client (chemicals company) optimize their deliveries to customers. They have > 100 production sites and thousands of customers, so LP is used to allocate customers to production sites based on the product-cost and availability at supply site and trucking costs. We have evaluated multiple solvers (Gurobi/ Llamasoft/ GAMS/ LocalSolver etc) for optimizing deliveries, as well as evaluating the cost impact of changes to the delivery network.
if you have a license for a good fast solver already for some reason, it can be very effective to reduce some NP-hard problems to integer programming.
also, one interesting application related to data science is to embed a machine learning model (usually regression, maybe decision tree or neural network) inside the integer program, and then maximize over its inputs. this can let you characterize worst-case behavior, or answer questions like "how must a user change their features to flip the prediction?".
solvers are so expensive that MIPs will probably never become part of mainstream data science, but they can be very powerful beyond classic OR problems.
JuMP is comparably good I think. People reasonably don’t want to add a new language to their stack. But if you’re just formulating MPs it’s as nice as anything, free, and you have a well designed modern programming language if you need it.
I really wish I could find solid websites/blogs/resources for operations research, mathematical planning, linear programming, etc aimed at regular software engineers. I feel like a lot of the really crazy parts of codebases often derive from inexperience with these kinds of tools.
I write blog posts about constraint programming from time to time. I always include a step-by-step description of the model, which makes it fairly easy to understand. Hopefully this can be of help for you: https://pedtsr.ca
I've stumbled across it a few times way back when I was looking at MRP stuff for an ERP I worked on. I remember it being a rare gem of a website. I'd throw away 99% of web pages if the ones remaining were all like this one. Thanks for the reminder!
Largest applications may well be in power systems (economic dispatch, unit commitment), material requirements planning, transportation networks, but linear programming can also be used to fit functions, think constrained regression with L1 loss.
The "Model Building in Mathematical Programming" book by Williams is unique in that it talks about how to formulate LP and MILP problems, rather than focusing on the algorithm side of how the simplex algorithm works. That's nice to know, but not really necessary. You really need to get some intuition on thinking about objectives and constraints.
You could just grab or-tools and work through their example problems, then extend it to something in your area of interest. The Python APIs are easy to experiment with.
Isnt this something that could be useful for consulting? I’ve occasionally considered trying to help businesses model MILPs to help solve their problems, but its so specialist that finding good matches is like the actual problem. I wonder how specialists like milp experts find clients.
We needed to get a project based off of ORTools, that some consultants had left us, working and expanded.
After mocking about for a while getting nowhere, we took the optimization course on coursera from Melbourne University and were quite happy with how it helped us move along.
