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Operations research and mathematical methods to illustrate decision-making process based on uncertain human psychology

Takashi Hasuike
Associate Professor, Waseda University Faculty of Science and Engineering

Operations research (OR) is a science that is useful to society

I specialize in a field of engineering known as "OR," which pursues problem-solving and decision-making processes using optimization models and mathematical analysis. Mentioning OR may cause some people to imagine an unapproachable discipline dominated by difficult numerical formulas. It is true that many models are described mathematically, but it covers all aspects of society. OR originally started as research to support military decision-making process during World War II; but since then, it has expanded the target of its research to include business, finance, policy-making, and industrial engineering.

To begin with, OR is based on practical researches, and I believe that OR is meaningless unless it helps make better choices in the real world. Of course, many OR researchers pursue advanced mathematical theory in order to assist better decision-making. The results of theoretical research are valuable, but on the other hand, there are also many researchers who strive to practically apply theory and whose research is driven by interest in society. In particular, I believe that the real thrill of OR is to use mathematical models to describe the real world, which is complicated, human-like, rationally unexplainable by the logic of 0 or 1, and provide methods that allow users to derive highly reasonable decisions close to decision maker’s feelings.

When I was preparing to go on to university, I wanted to study something related to mathematical science and took examinations for a university that offered such courses of study. I specialized in asset allocation in financial engineering during my undergraduate years, a study of the so-called portfolio selection that I have continued to the present day. Specifically, this study involves analyzing the movements of security prices and investors' forecasts for market trends by linking the two, building models of market trends and profitability, and providing asset allocation plans that satisfy investors. The movements of security prices can be predicted to a certain extent by statistically analyzing huge volumes of historical data for simulations; but in fact, each investor's forecasts for market trends involved, or decisions based on personal views and intuition which cannot be obtained through data alone, make data-based predictions difficult.

As I grapple with this issue, I assume that there are investors with different forecasts for market trends, including those who predict the future positively and those who do so negatively, and build a model of when they make a profit or suffer a loss. Thus, this brings research results that allow investors to make decisions on portfolio selection (asset allocation) with more realistic developments in the stock market in mind. Formerly, financial engineering did not treat ambiguous notions like forecasts for market trends scientifically, but tackling them head-on, I am attempting to express them using mathematical models while expanding OR methods to the maximum extent.

With a focus on phenomena which is greatly affected by subjective views of people, OR has continued to develop areas that have been left untapped. One major characteristic and strength of my studies is that it does not only numerically express uncertainty deriving from probabilistic events. OR also works to mathematically treat uncertain, ambiguous phenomena such as human psychology, which is generally difficult to express in numerical terms.

Developing untapped areas

The intuitive rationality of humans such as "without knowing why," "feeling like this," and "considerably cheap" often makes decisions that surpass mathematical rationality. Problems can be solved swiftly if they are all explained using probability theory, but there are many cases in which the subjective elements of people's language-based decision-making process do not follow probabilistic axioms such as complete additivity required for objective events. Language-derived uncertainty cannot be turned into models using probability theory alone.

The fuzzy theory is one of the theories that attempts to turn such uncertainty into models using the notion of ambiguity or fuzziness. It enables researchers to express variables such as gradation that change ambiguously in numerical or functional terms using membership functions (Figures 1 and 2). Discussions about precision and universality are continuing even today, but my approach is to not stick to the logic of 0 or 1 alone. I employ the fuzzy theory and other methods as required and in the end examine various uncertainties in the world as closely as possible using mathematical models.

Figure 1: Example of membership functions.

Figure 2: Expressing the subjectivity of people in numerical and functional terms using membership functions and forming the optimal consensus.

In addition, I am developing methods to decide optimal sightseeing routes using appropriate optimization methods to help determine sightseeing routes to maximize tourist satisfaction. Some factors to consider are tourists' preferences, the allocation of tour buses and their crew, and road congestion and crowds at tourist destinations. Tourists differ in terms of where they want to go, what they want to do, how much time and money they have, and how satisfied they feel, which make optimizing sightseeing routes difficult.

Lately, I have also worked to study an agricultural supply chain management. Unlike industrial products, the quantity and quality of agricultural products affected by weather and soil conditions, causing varied crop sizes and heavy losses. Moreover, building an efficient supply chain with consideration for environmental needs has been a challenge since agricultural products are disposed in large quantities where there is excessive production. System design is required to maintain the situation that is optimal for all three parties: farmers, retailers, and consumers (Figure 3). I use approaches in OR such as matching and game theory, but agricultural product markets involve high levels of uncertainty. This forces researchers to take complex, interwoven factors into account which further complicates the issue.

Figure 3: Modeling of an agricultural supply chain management to ensure optimal relationships among farmers, retailers, and consumers.

Right now, I am testing various models focusing on how to match farmers and retailers. For example, what if retailers can specify crop area in exchange of an agreement to purchase all crops farmers grow? I am working to build mathematical models while examining what is actually happening in the field.

Exchange with different fields is vital to research

In a seminar at the laboratory

Financial services, tourism, and agriculture are all quite different from one another, but it is essential to go to worksites in these industries and listen to people engaged therein. I try to participate actively in workshops and exchange events to foster connection with key people so that I can find out what those working in the field are truly feeling. Modeling divergent from the real world is meaningless. I believe that modeling by understanding how indefinite, uncertain, and complicated worksites are and absorbing the subsequently acquired knowledge contribute to practical applications in the end.

In general, OR cuts itself off from the real world briefly to turn its phenomena into theory or models. However, the more in depth it does so, the more mathematical and formal it becomes, deviating itself from reality. In order to ensure that the research results of OR are used at the site of policy-making and strategy planning effectively, OR researchers must make efforts or act as intermediaries to explain OR's recondite theory in simple terms to give back to society. It is important to obtain models from the real world and refine them for society's benefit by securing points of contact with society in terms of both inputs and outputs.

I often tell young researchers and students in my laboratory that communicating with people from different fields is vital. It is necessary to acquire skills to identify problems through technical stories told by experts of various fields and ask appropriate questions, not to mention the mathematical skill required for OR research. To that end, researchers must constantly pursue their studies while being alert and refining their sensibilities.

Artificial intelligence (AI) has enjoyed a boom in recent years, but I often discuss with my research colleagues about whether AI can really make the most genuine, ultimate judgements in human society. Use of AI technology enables us to find knowledge that could not be acquired by humans simply by looking at the results of its outputs. For example, the development of technology for driverless cars is under way, and it may be true that AI exceeds humans in safety. Suppose, on the other hand, that a person suddenly appears when you are riding in a driverless car. If the car proceeds, the person in its front would be seriously injured, but if the car tries to avoid the person, you would seriously get injured in the car. If you encounter a moment of such an ultimate choice, can you leave the decisions to AI? It would be quite difficult to do so.

I believe that the advantage of using OR and mathematical models is the processing leading up to the decision-making is not a "black box," but they can express the process explicitly to a certain extent. More research in the field of OR is needed on how explicit expressions play a significant role in ultimate choices humans have to make. I imagine a breakthrough in decision-making processes would be achieved if the strengths of AI could be combined with those of OR.

Takashi Hasuike
Associate Professor, Waseda University Faculty of Science and Engineering

Takashi Hasuike holds a Ph.D. in information science from Osaka University Graduate School of Information Science and Technology. After working as a research associate at Osaka University and teaching the system mathematics course, he became an associate professor in the Department of Industrial and Management Systems Engineering, School of Creative Science and Engineering, Waseda University in 2015. Awards received in the past include: the Osaka University Graduate School of Information Science and Technology award (2007), the 9th Funai Foundation for Information Technology research encouragement award (2010), the Young Researcher Award, IEEE Computational Intelligence Society, Japan Chapter (2012 and 2013), the FY2013 Japan Industrial Management Association thesis encouragement award, the FY2013 Operations Research Society of Japan research award/encouragement award, and the FY2015 Waseda University research award (ability to communicate international research) along with many other recognitions for his papers.

Website of the Hasuike laboratory