# Mathematical models and operations research in biosciences

## Subject description

The subject is regarding the content methodological, since the emphasis is on generating the mathematical models for supporting the decisions in biosciences.

1. General approach to mathematical modeling and defining problems/models
• procedures of mathematical modeling and review of approaches that most often appear in biosciences
•  decision process as an ecological-economic-social-technical process in natural systems – biosciences
• structure of a system and integration of individual quantitative and qualitative methods in the overall model (system) of system management (decision support systems – DSS)
• selected chapters from linear algebra, probability calculation, differential equations, theory of graphs, sequences and series (Taylor’s and Fourier’s sequences), functions of two variables (gradient)
• the role and review of post-optimal testing and analysis, and adaptiveness in evaluating solution of an overall model
• the role, overview and use of suitable software (Excel, Expert Choice, MS project, Web-HIPRE, etc.)
1. Linear and nonlinear models
• phases of decision-making, discrete and continuous systems, linear models, data envelopment analysis (DEA) , decision-making regarding several criteria, multi-criteria linear programming, goal programming, Kuhn-Tucker solution
• preferential relations, decision-making in complete uncertainty and with risks, different competition models, strategic situation, non-cooperative games, Nash equilibrium, dynamic games, games with incomplete information
• general linear models, duality and sensitivity, integer linear programming
• nonlinear models (Lagrange multipliers, quadratic and separable programming)
1. Multiphase processes
• network – basic definitions, maximum flow (Bellman principle of optimality)
• discrete deterministic and stochastic dynamic models
• homogeneous Markov chain
• combinatorial optimization
• location problems
• supply chain management
1. Multiple parameters decision-making
• methods ELECTRE and PROMETHEE
• hierarchical models (AHP, ANP, DEXi)
• conjoint analysis (CA),
• utility functions (MAUT)
1. Fuzzy logic methodology, qualitative methods for non-market valuation
• introduction to fuzzy sets, linguistic variables, relations between fuzzy sets
• fuzzy linear programming
• methods for assessing benefits and costs of the environmental (direct methods – CVM, WTP, WTAC and indirect methods – TCM
•  group decision-making and social choice, methods for assessing alternatives regarding several decision makers
• econometric modeling and assessing the parameters
• methods for measuring the biodiversity (indices and parameters)

## Objectives and competences

Educational objectives: The basic aim is to acquaint students with more demanding mathematical concepts and decision-making models. The purpose is also that the students deepen and obtain additional knowledge in the field of linear and non-linear models, multi-criteria and multi-phase models, and methods for evaluating and classifying decisions in environmental management.

The acquired knowledge will assure the understanding of linkages between professional categories and methodological means. The students will understand the ability of particular methods for proper solving professional problems and sensitivity of these methods to changes of input data.

Competences: Students will master the fundamental terminology from the field of mathematical modeling and will be acquainted with the newest research methodology used for solving the problems in the fields of biosciences. They will possess the specific knowledge for self-governmental gaining of further information and the use of mathematical models/methods in biosciences.

## Teaching and learning methods

Teaching of the subject is organized with lectures (10 hours), project/seminar work (15 hours), laboratory exercises in computer classroom using specific computer programs (15 hours), consultations (5 hours) and student’s individual work (80 hours).

## Expected study results

Knowledge, understanding and usage:

Students’ learning outcome is to qualify the candidate for independent research work in the field of modeling and monitoring the optimal decisions in bioscience, taking into account economic, ecological and social factors. The results of such research will make an important contribution to students’ basic and applicative research in the field of managing natural resources and other systems in Slovenia and in the world.

Reflections and transferable skills:

This methodological subject qualifies the students for understanding the theory and some abstract issues, like methods of optimization, and their application in praxis. Student is taught to be critical when developing the results and conclusions.

Student is able to produce logical conclusions, to perform precise diction, to be critical to written sources, to understand sophisticated models and processes, to identify, formulate and solve some quantitative models and to report the results in written form.

## Basic sources and literature

• Powell S.G. in Baker K.R. 2010. Management science. The art of modeling with spreadsheets, ISBN 978-0-470-53067-2.
• Ragsadale C.T. 2010 Spreadsheet Modeling & decision analysis. Edition 6. ISBN-13:978-0-538-74632-8
• Winston W. L. 2004. Operations research, application and algorithms. Belmont, Thomson Learning
• Jones D. in Tamiz M., 2010. Practical goal programming. International Series in Operations Research and Management Science. New York, Springer
• Bronson, R. in Naadimuthu, G., 1997. Schaum's Outline of Operations Research. McGrawHill, ISBN-13-978-0070080201
• Hillier, F.S. in Liebermann, G.J., 2020, Introduction to Operations Research, McGraw-Hill, ISBN-13- 978-1259872990
• Saaty, T.L:, 2006. Fundamentals of Decision Making with the Analytic Hieararchy Process. RWS Publications, ISBN-13978-0-962031762.
• Bouyssou, D., Marchant, T., Pirlot, M., Tsoukias, A., Vincke, P., 2006. Evaluation and Decision Models with Multiple Criteria; Stepping Stone for the Analyst. Springer, New York, 445 str., ISBN: 0-387-31098-3
• Curwin, J., Slater, R., 2008. Quantitative methods for business decisions. Thomson Learning, London.
• Ishizaka, A., Nemery, P., 2013. Multi-CriteriaDecision Analysis, John Wiley.
• Weintraub, A., Romero, C., Bjorndal, T., Epstein, R., 2007. Handbook of Operations Research in natural resources, Springer
• Boucherie, R.J. in van Dijk, N.M., 2017. Markov Decision Processes in Practice, Springer,. ISBN 978-3-319-47764-0
• Članki iz tekoče znanstvene periodike s področja modeliranja in upravljanja v naravnih sistemih (Forest Science, Forest Ecology and Management, Ecological Modeling, European Journal of Operations Research, Central European Journal of Operations Research,….…) posredovani na predavanjih in vajah.

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana