I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math Model be it Integer Programming or Linear Programming which are being used in especially in Transportation domain or Resource Planning. The idea is to look at large number of Math Models so that I could be able to formulate the optimization model on my own. Currently I am not very good at writing the problem into a math model be it the objective function or the constraints.
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2$\begingroup$ I think you should start with the bible, it has many practical examples: web.stanford.edu/~boyd/cvxbook Whatever application or problem type you want to do, you should start with the bible $\endgroup$– independentvariableCommented Jun 1, 2019 at 14:38
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$\begingroup$ Related question on the meta forum: or.meta.stackexchange.com/q/44/71 $\endgroup$– Michiel uit het BroekCommented Jun 4, 2019 at 8:24
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17 Answers
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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 (rigorous) maths behind them.
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2$\begingroup$ Williams is good, but especially his (limited) part on implementation is fairly dated IMO. $\endgroup$– RichardCommented Jun 5, 2019 at 14:17
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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.
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Since the OP asked for Transportation domain, I recommend the following:
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Joe Geunes's book Operations Planning does a nice job of teaching MIP modeling in an operations context (production, distribution, facility location, etc.).
answered Jun 2, 2019 at 1:34
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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.
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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 cornucopia of applied optimization models that have been successfully deployed across industries. Highly recommended, if you're not aware of it already. Basically every article is a successful case study.
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Production Planning by Mixed Integer Programming by Yves Pochet and Laurence A. Wolsey might fit the bill. Panos Padalos says on MathSciNet: "... Practitioners who are interested in using MIP solvers to solve different production planning problems, can use the book to identify the most efficient way to formulate the problems and to choose the most efficient solution method.... Since the book summarizes the state of the art in the area of formulations and solution methods of production planning problems, it also can serve as a good reference for students and researchers."
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Also in the Transportation domain, a good case-by-case analysis book is Operational Research in Industry by Tito Ciriani. It covers problems from airline-fleet scheduling to designs for flexible transit.
In the Resource Planning domain, Equitable Resource Allocation: Models, Algorithms and Applications by Hanan Luss provides many examples of resource allocation using mathematical modelling.
answered Jun 1, 2019 at 15:30
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We wrote a book on Supply Chain Network Design. It is meant to be a practical guide to that problem. It starts with a simple network design formulation and then adds more to it throughout the book. It both presents the mathematical formulation as well as a description of the problem, assumptions baked in, and reasons for those assumptions.
We also recently released the models from the book in Python. Here is a short blog explaining that. You might find that useful for working through the problems.
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This is not really to learn how to model, but could be inspirational: I recently discovered this podcast from INFORMS, that I found very interesting as it is showcasing examples of OR in practice and the people behind them. You can find it on Spotify as well (https://pubsonline.informs.org/magazine/orms-today/podcasts). They also have videos from the Edelman competition that show applications of OR in practice.
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This may be out of print but shouldn't be too hard to find. One of the best in my opinion on the Practical Aspects... Patrick Rivett's 'The Craft of Decision Modelling'
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$\begingroup$ Judging from this review this book seems to be a lot of fun. $\endgroup$ Commented Jun 11, 2019 at 10:30
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Another good reference in my opinion : Network Flows by Ahuja et al.
It focuses on ... networks as hinted by the title, but it is incredible all the problems that can be tackled with such structures. Solutions of odd numbered exercises are also available, which is helpful when learning on your own.
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Introduction to Operations Research (10th ed.) by Hiller and Liebermann is also a great book for concrete and complete examples of applications.
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2$\begingroup$ Welcome to Operations Research! Please have a look at or.meta.stackexchange.com/questions/192/… for tips on presenting references. $\endgroup$ Commented Jul 15, 2019 at 11:20
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For Operations Research in the power industry, I recommend the following five introductory books, covering short-term trading, stochastic programming, decomposition algorithms, complementarity and long-term investment. These OR models are data hungry, thus summarized as data-driven decision making under uncertainty. These videos DTU CEE Summer School 2019: Data-Driven Analytics and Optimization for Energy Systems provide an overview.
- Morales, J. M., Conejo, A. J., Madsen, H., Pinson, P., & Zugno, M. (2013). Integrating renewables in electricity markets: operational problems (Vol. 205). Springer Science & Business Media.
- Conejo, A. J., Carrión, M., & Morales, J. M. (2010). Decision making under uncertainty in electricity markets (Vol. 1). New York: Springer.
- Conejo, A. J., Castillo, E., Minguez, R., & Garcia-Bertrand, R. (2006). Decomposition techniques in mathematical programming: engineering and science applications. Springer Science & Business Media.
- Gabriel, S. A., Conejo, A. J., Fuller, J. D., Hobbs, B. F., & Ruiz, C. (2012). Complementarity modeling in energy markets (Vol. 180). Springer Science & Business Media.
- Conejo, A. J., Baringo, L., Kazempour, S. J., & Siddiqui, A. S. (2016). Investment in electricity generation and transmission. Cham Zug, Switzerland: Springer International Publishing, 106.
- Kovacevic, R. M., Pflug, G. C., & Vespucci, M. T. (2013). Handbook of risk management in energy production and trading (Vol. 199). New York: Springer.
Besides, OR for networks is essential in energy industries. Following books are used in the graph theory course by Carsten Thomassen at Technical University of Denmark. They are both theoretical and practical.
- Bondy, J. A., & Murty, U. S. R. (1976). Graph theory with applications (Vol. 290). London: Macmillan.
- Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1988). Network flows.
It's easier to grasp them in some real-world context, and apply them to other industries, especially when they share many common features. For example, the power system is a special kind of supply chains, with more strict requirements. So techniques from the optimal flows, newsvendor's problem, unit commitments, capacity/network investments, market design, etc have been widely applied in the power industry.
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For specific applications in industry, refer to this website:
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I am surprised that no one has mentioned the classic
Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977).
This book was one of the reference books in a few courses when I was an undergrad. It includes many examples and quite a few real world cases solved by mathematical programming. I read a few chapters of the book back then and found them easy to follow, yet with great relevant details. It might be considered old, but its content are still very relevant and informative. It is freely available for download from MIT website.
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In addition to all of the above, the applications of operations research techniques in the airline industry could be found in:
- Barnhart, C., Belobaba, P., & Odoni, A. R. (2003). Applications of operations research in the air transport industry. Transportation science, 37(4), 368-391.[pdf]
- Yu, G. (Ed.). (2012). Operations research in the airline industry (Vol. 9). Springer Science & Business Media. [pdf]
For airline disruption management, read:
- Wu, C. L. (2016). Airline operations and delay management: insights from airline economics, networks and strategic schedule planning. Routledge.
- Clausen, J., Larsen, A., Larsen, J., & Rezanova, N. J. (2010). Disruption management in the airline industry—Concepts, models and methods. Computers & Operations Research, 37(5), 809-821.
- Kohl, N., Larsen, A., Larsen, J., Ross, A., & Tiourine, S. (2007). Airline disruption management—perspectives, experiences and outlook. Journal of Air Transport Management, 13(3), 149-162.
