Course content

This course covers use of mathematical models as decision support for planning in technological organizations. The planning problem will often consist of maximizing or minimizing an economical objective under scarce resources and technological requirements. The planning is done by 1) formulating a simplified model of the problem, 2) calculate an optimal solution for the model and 3) interpret and implement the calculated solution. This course covers both deterministic and stochastic problems. The following list indicates which subjects that will be covered: Different optimization models (linear, non-linear, simple integer and network models), decision trees, simple inventory-, queuing theory and simulation. The course will cover the use of commercial spread sheet software on models both for optimization and simulation.

Learning outcome

Position and function within the study program: The course is compulsory in the third year of the MTIØT study program. The course requires knowledge from basic courses in mathematics, statistics, computer science and the course TIØ4118 Industrial economic Analysis. The course shall contribute to fulfill learning objective 2.4 in the detailed list of learning objectives for MTIØT, where broad and sound basic knowledge in administrative and economic areas are demanded. By the end of the course, the students should be able to: - define what is meant by operations research, and account for which phases are normally part of a study applying operations research - describe the assumptions on which linear programming (LP) is built - formulate LP models on the basis of verbal problem descriptions - solve LP problems graphically (for two variables), by using spreadsheets , and by hand using the simplex method, both algebraic and in tabular form - perform sensitivity analysis on the basis of optimal simplex tableaus, and describe the economic information that can be drawn from the analysis - formulate integer programming models, describe some principles that can be used to solve problems formulated using such models, and solve them using spreadsheets - formulate non-linear programming models and identify classes of non-linear programming models based on properties of the objective function and the constraint set - solve some types of non-linear problems using the method of Lagrangean multipliers, KKT conditions, or spreadsheets - indicate which additional challenges arise for problems where the parameters are not known with certainty - formulate and solve some problems with uncertainty using decision trees - calculate the expected value of experimentation and the expected value of perfect information - formulate different types of network models and solve these - create queueing models based on verbal problem descriptions - derive formulas for queueing models based on exponential distributions - derive formulas for simple inventory models, including models with uncertainty - describe discrete event simulation and differentiate this from other types of simulation - implement simple simulation models in spreadsheets - discuss the pros and cons of the different types of models and the associated solution methods in view of specific problems.

Learning methods and activities

Lectures, cases and exercises with and without computers.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course requires knowledge from basic courses in mathematics (corresponding to the courses TMA4100 Matematikk 1 and TMA4115 Matematikk 3 at NTNU), statistics, computer science and the course TIØ4118 Industrial Economic analysis.

Course materials

Given at the start of the course.

Credit reductions