Operations research

What’s new?

In the 12 June issue of Defence Connect reports the former chief of the Royal Australian Navy, Tim Barrett, is quoted as saying that the regeneration of the Australian fleet over the next decade “is an ideal opportunity for Australia to make significant changes to structure and strategy – not just in terms of the fleet itself, that is, but how deployments are analysed. To that end, he calls for a `thinking navy’, arguing the OR [Operations Research] is a crucial piece of this puzzle.”

What does it mean?

Operations research is, of course, research on operations. INFORMS (the Institute for Operations Research and the Management Sciences) states “Operations research (O.R.) is defined as the scientific process of transforming data into insights to making better decisions.” INFORMS pairs OR with Analytics, adding, “Analytics is the application of scientific & mathematical methods to the study & analysis of problems involving complex systems.”

Operations research began with military applications.  The above picture shows my copy of the first textbook on OR, Methods of Operations Research, by Philip M. Morse (my academic grandfather, that is, he was the PhD advisor of my PhD advisor) and George E. Kimball (1950, MIT Press and John Wiley & Sons). The two authors were members of the Operations Research Group of the U.S. Navy and the first version of the book was published as a classified document just after World War II.

The first sentence of the book defines OR: “Operations research is a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control.” Morse was a professor of physics and Kimball of chemistry, so they were familiar with the scientific method; they and others contributed to the war effort by applying the scientific method to improve operations. Presciently, they remarked “experience since the war has shown [that] the techniques and approach of operations research can be of help in arriving at executive decisions concerning operations in any field, industrial and governmental as well as military.” Indeed, many parts of engineering started with military engineering and only later became civil engineering, as seen in the legacy of that term.

This book is a nice introduction to OR. On page 3, the authors give their first simple example still often cited by OR researchers and practitioners:

The first example, simple to the point of triviality, involves the line-up of soldiers washing their mess kits after eating at a field mess station. An operations research worker during his first day of assignment to a new field command noticed that there was considerable delay caused by the soldiers having to wait in line to wash and rinse their mess kits after eating. There were four tubs, two for washing and two for rinsing. The operations research worker noticed that on the average it took three times as long for the soldier to wash his kit as it did for him to rinse it. He suggested that, instead of there being two tubs for washing and two for rinsing, there should be three tubs for washing and one for rinsing. This change was made, and the line of waiting soldiers did not merely diminish in size; on most days no waiting line every formed.

They point out several features of this story. “[T]he solution, when seen, was absurdly simple …” The improvement required no additional equipment. The solution was conveyed to someone who could make the needed change – and did. Finally, the waiting was reduce to almost zero when the flow should have increased by 50 percent; waiting lines have the property that “the longer they get, the longer they tend to get,” a “self-aggravating property” present in many system. This story and the analysis still make me smile, almost 50 years after I first read them.

They describe other examples of OR that require more analysis and more technical background, including optimizing the depth setting of antisubmarine depth charges to improve the sinking of U-boats and setting the size of convoys to reduce average ship losses. They discuss the problem of finding the problem, sensitivity analysis, and more.

Since that book, OR has expanded greatly. INFORMS lists, among others, the following techniques and subfields: algorithms, databases, decision analysis, dynamic program/optimal control, facilities planning, forecasting, game theory, inventory management / production planning, optimization / mathematical programming, probability and stochastic models, quality and reliability, queueing models, scheduling, search and surveillance, simulation, systems thinking, time series methods, and utility and value theory. These techniques of OR have wide application.

Linear programming, a technique for optimization, involves choosing values for specified decision quantities to maximize or minimize a function of those quantities; the chosen values must also satisfy certain constraints (equations or inequalities).  All functions in the mathematical formulation are linear in form concerning the decision variables.

For example, in 1945 George Stigler described the diet problem in which the amounts of foods in a diet are chosen to minimize the cost of the diet while meeting the minimum daily requirements of different nutrients. When I was a faculty member at Ohio State in the 1980s I worked with some agricultural engineering faculty; Ohio State produced a program to help dairy farmers optimize the feed for cattle using the linear programming formulation of the diet problem. In 2012, Ohio State professor Dr Luis Morales published a paper updating the diet problem for cattle to include consideration of methane emissions from cattle.

OR problems are often formulated in mathematics and the solution methods are often sophisticated. George Dantzig, later a professor of operations research at Stanford, formulated the military planning problems he worked on during the war as a linear programming model. He eventually developed a method for the solution of such problems, called the simplex method.

The linear programming model and the simplex method are just one example of an OR problem and associated solution method with wide applicability. Successful application of linear programming models (and generalizations) include assigning jobs to machines, scheduling of crews for airlines, routing products from production facilities to warehouses to retail locations, selecting the highest value way to cut a log into lumber, scheduling jobs through a production process, minimizing the distance travelled to deliver meals in a Meals-on-Wheels program, and so forth. The use of linear programming is often taught in business programs, especially MBA programs.

Other methods of OR incorporate uncertainty by modeling using the mathematics of probability. All OR methods require data about the real world system. The Defence Connect article I started this article with quotes the Head of US Naval Air Forces Vice Admiral DeWolfe Miller as saying “I love data,” one of my favorite sayings.

What does it mean for you?

This week I attended the online national conference of the American Society for Engineering Education (ASEE), the international organization where engineering faculty present research, discuss, and learn how to improve engineering education. A nice paper presented there (“Creating a Community of Practice for Operations Research by Co-creating a High Impact Executive Education Program in India,” by Venugopalan Kovaichelvan and Patrick A Brunese,) described a program at a company in India, in which senior managers from the Indian company worked with faculty from a US university to create three modules delivered to students over a 10 month period using online, on site, synchronous and asynchronous modes of delivery, combining learning with immediate application to supply chain problems. The topics focused on sensing and framing problems, developing a model for study, selecting appropriate modeling methods and data, applying the methods, interpreting results, implementing and validating the solution, and developing a comprehensive framework for decision support. Students worked on projects they identified (for example, reorganizing a distribution network for a particular product) and their work was rigorously assessed. Graduates are supported in a community of practice and 32 senior managers are now qualified as advanced OR practitioners. Savings from the 14 initial projects provided “one-time monetary benefits equivalent to the investment for the entire development and delivery of the advanced OR program.”

The first delivery of the program was done by US faculty and the second iteration is being delivered by participants from the first program. A social learning program is supporting the 60 members of the community of practice.

I started this article with a quote from Tim Barrett former chief of the Royal Australian Navy, including his call for a “thinking navy.” Seventy years ago, in the final chapter of Methods of Operations Research, Morse and Kimball wrote:

“Referring again to the first sentence of Chapter 1 [the definition of operations research], we may emphasize at this point that operations research is not a pure research activity separated from all else; it is an integral part of an operating organization. It is a part of the thinking process of the operating organization, so to speak, the summing up of the facts bearing on the problem before a decision is made. Separate existence, by itself, would be as anomalous as the separate existence of the front lobe of a brain without the rest of the brain and body.” [emphasis added]

Thinking doesn’t just occur with OR methods, but the habits of OR certainly do promote thinking – logical thinking based on data. Is your organization a thinking organization? How do you promote the rigorous identification and solution of problems? OR may be a part of the strategy you use to answer those questions.

Where can you learn more?

The papers from the 2020 conference of the American Society for Engineering Education will soon be available here.

INFORMS has excellent information about Operations Research.

The Library of Congress listing for Methods of Operations Research is here.

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