# Tag Info

27

Not solely dedicated to transportation, but Model Building in Mathematical Programming by Williams is a very good start for every beginner in modeling as it contains the theories on mathematical programming modeling as well as numerous examples. AFAIK, this is one of the best books on modeling as it does not concern itself with solution methodologies and the ...

21

A nice comprehensive collection on applications can be found in the book by Desaulniers, Desrosiers and Solomon: Column Generation. It features articles about Shortest Path Problems with Resource Constraints Vehicle Routing Problem with Time Windows Cutting Stock Problems Large-Scale Models in the Airline Industry Robust Inventory Ship Routing by Column ...

20

Generating routes heuristically, or heuristic pricing, is very common in the vehicle routing literature. Even when the pricing problem can be solved exactly, heuristic pricing is often tried first. Only when no more routes can be generated by heuristics, the exact pricing algorithm is run. When heuristic pricing is used in this way, the overall method is ...

19

In addition to the excellent answers that are already posted, I want to add that for the pragmatic optimizer, quadratic may already be sufficient. For example, the cubic constraint $x^3 \le x$ may be replaced by $xy \le x$ and $y=x^2$, which are both quadratic constraints. Note that these constraints are non-convex, which may not be desirable.* Sometimes non-...

19

"General purpose optimization" is quite broad, so I'll take a step back first, to better identifying the motivation of using ML in optimization settings. To keep things simple, I'll consider a single-objective minimization problem with decision vector $x$, objective function $f$ and some constraints $x \in X$, i.e., \begin{align} (P) \ \ \ \min_{x} ...

17

Surprised that no one has yet mentioned "Applications of optimization with Xpress-mp". Of course it is focused on their Mosel language, but it contains many good applications. Also, a free PDF is available.

17

In the following paper Grothendieck inequalities are applied to OR (Grothendieck was one (if not THE) pioneer of algebraic geometry.) Briët, Jop, and Frank Vallentin. "Grothendieck inequalities for semidefinite programs with rank constraint." arXiv preprint arXiv:1011.1754 (2010). Another example where it is the other way around, i.e. where OR is used to ...

17

Your examples of "technical skills" are centered on optimization. An understanding of at least some aspects of probability models (especially Markov chains and queues) may be important, depending on the work you do. So might a better-than-minimal understanding of statistical modeling and analysis. Again depending on your work, you might need to be able to ...

17

A great cause would be supply chain in countries/regions with poor infrastructure and/or uncertain supply and high price fluctuations. This is particularly important in many developing countries, because getting supplies to their destination and being able to do so on time is not straightforward. Another amazing cause is to formulate & solve travelling ...

16

Reference "Convex Optimization" by Boyd and Vandenberghe https://web.stanford.edu/~boyd/cvxbook/, section 3.2.1, p. 79. These properties extend to infinite sums and integrals. For example if $f(x, y)$ is convex in $x$ for each $y\in A$, and $w(y) \ge 0$ for each $y\in A$, then the function $g$ defined as $$g(x) = \int_A w(y)f(x, y)\, dy$$ is convex ...

16

Here is a nice, succinct,and easy to understand reference for how to do all this and more. Answers to many future questions can be handled by referencing the appropriate section number in this document and then addressing any particular difficulties or concerns the questioner may have. FICO MIP formulations and linearizations Quick reference at https://www....

16

You may be interest in the blog by @prubin, which has many interesting CPLEX posts: OR in an OB World. I think the best way to become better at using solvers, is by actually using them in your own projects. An interesting project could be to solve a problem with Benders decomposition, or with multithreaded callbacks. This blog post from the above-mentioned ...

16

QSopt-Exact by Applegate, Cook, Dash, and Espinoza

15

Joe Geunes's book Operations Planning does a nice job of teaching MIP modeling in an operations context (production, distribution, facility location, etc.).

15

I am not sure whether you are looking for polynomial optimization like Introduction to concepts and advances in polynomial optimization by Martin Mevissen, or polynomial optimization by Hoang Tuy?

14

Since the OP asked for Transportation domain, I recommend the following: Vehicle Routing: Problems, Methods, and Applications by Toth & Vigo: here In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William Cook here

14

A few suggestions. First, the series by Charles R. Shrader from the US Army Center of Military History. [1] History of Operations Research in the United States Army, Volume 1: 1942–1962. (full text or also here or here) [2] History of Operations Research in the United States Army, Volume 2: 1961–1973. (full text) [3] History of Operations ...

14

There's a pretty active research area on incorporating group theory into integer programming (since symmetry can cause a lot of headaches during branch-and-bound). See The Group-Theoretic Approach in Mixed Integer Programming by Richard and Dey, for example.

14

I believe there are long answers to this question, but a very short one is: yes. Here is an example that originated not from the use case you describe, but I believe that they can directly apply their local search to a MIP: LocalSolver.

14

There are multiple levels to operations research. (Before continuing, I want to apologize to anyone about to be scandalized by my omission of their favorite journals.) For some (many?) people working in industry or government, it may be sufficient to be able to "think in systems terms", identify and classify problems ("this is a queuing problem, this other ...

13

Every four years (year mod 4 = 0) there is an international Column Generation conference, alternated with a school on column generation, also every four years (year mod 4 = 2), (e.g. school in 2018, workshop in 2016, etc.), You can find plenty of applications there.

13

I love this historic piece by Alexander Schrijver about max flow and min cut (DOI link).

13

Just about every article in Interfaces—now called INFORMS Journal on Applied Analytics—answers at least some of the questions you laid out. I have found these articles to be very valuable as a way to study how OR gets implemented in practice. If you're asking for a sort of meta-study that looks at those questions in the aggregate, rather than for specific ...

13

This is an answer to the original question before it was edited (Can a problem move from NP to P). No, if a problem is NP-complete then it is not solvable in polynomial time unless P=NP, which has not been proven yet. Furthermore, if there were any NP-hard problem which would be solvable in polynomial time then (by reduction) it could be used to solve any ...

13

I think domain knowledge is essential if you want to be a good OR practitioner. If you don't know how a supply chain works, designing an optimization model for planning and coordinating a complex supply chain could be difficult and time-consuming. The same goes for healthcare, energy, finance, manufacturing, and other industries. Also, domain knowledge could ...

13

The implementation gap may not be a function of the "quality of the model" (or the algorithm used to solve it, which is a separate dimension). I had an experience with a logistics problem where the model was a simple shortest-path network model and the solution method was Dijkstra's shortest path algorithm. Both are time tested and thoroughly accepted. The ...

13

First of all, I would say that "fast solvable in practice" is possible also when your remaining problem still is NP-hard. But since you ask specifically for polytime solvability, there are some cases. Most well-known is probably "TU-ness" of your matrix. When you solve a MIP $$\min\{c^tx \mid Ax\geq b, x\in Z^n\times Q^q\}$$ then you will obtain an integer ...

12

Just to add a different flavor, there's a very good case study section in "The Theory and Practice of Revenue Management" by Talluri and Van Ryzin. Among other things, you will find some interesting optimization models. The other obvious choice, is not a book, but rather a journal. INFORMS Journal on Applied Analytics (formerly known as Interfaces) is a ...

12

The AIMMS Optimization Modeling book is freely available and very accessible. There are lots of worked examples going from problem description to example data and model formulation.

12

Axel Parmentier's thesis discuss about application in some airline operations problems. You didn't really ask for it, but for reference about VRP related problem, see Feillet (2010) and Pessoa et al. (2019) Reference: Parmentier, Axel. “Algorithms for shortest path and airline problems.” Université Paris-Est, 2016. Feillet, Dominique. “A Tutorial on ...

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