Lars Relund NielsenLars Relund Nielsen
Department of Economics and Business Economics
Fuglesangs Allé 4
DK-8210 Aarhus V
Office M330
Phone: +45 871 65145/+45 61 300 299 (mobile)

Cand.scient.oecon. (M.Sc.), Ph.D. 2004 in Mathematics and Economics at the University of Aarhus. Professor at Department of Economics and Business Economics, Business and Social Sciences, Aarhus University.

Using LocalSolver to solve VRP problems

R, Teaching 17. May 2017

The last days I have been playing a bit with LocalSolver and tried to model various vehicle routing problems (VRP). LocalSolver is a heuristic solver based on a heuristic search approach combining different optimization techniques. It includes a math modeling language (LSP) and there is a package so that it can be used from R. You need to download and install LocalSolver (I used v7.0) and get an academic license from their webpage. Læs mere »

Plotting IP and MO-IP models in R

LaTeX, R, Teaching 20. February 2017

I recent released a small package gMOIP which can make 2D plots of linear and integer programming models (LP/IP). With the package you can make plots of the feasible region (or solution space) of an LP, visualize the integer points inside the region and the iso profit curve. Moreover, can also make a plot of a bi-objective criterion space and the non-dominated (Pareto) set. Figures are prepared for LaTeX and can automatically be transformed to TikZ using tikzDevice. Læs mere »

Markov decision theory

Teaching 28. March 2014

During the this semester I am teaching the course “Markov decision theory” at the Department of Mathematics. The course presents the algorithmic aspects of Markov decision theory and illustrates the wide applicability of this theory to a variety of realistic problems. First, the course consider the Poisson process followed by Renewal/Reward Processes. Next we study the theory of Markov chains. Then follows a thorough presentation of the theory of Markov Decision Processes, including some applications. Finally, further applications are discussed based on reports made by the students. A course plan is given here.

Course on supervision

Administration, Teaching 13. May 2013

During the past months I have been participating in a course about supervision. The course, which runs over several days, covers master, PhD and fellow supervision and use results from research, practice and experiences from the participants. It aims at strengthen the participants’ overall supervisory skills in the form of

  • clear and specific criteria-based guidance
  • better feedback when commenting on text from the student
  • establishment and maintenance of a mutually binding supervision agreement
  • initial, ongoing and final project evaluation and feedback
  • using meta-communication of supervision content and processes

The course included video-filming ourselves in doing supervision which was a good way of seeing how one actually perform. The course can be recommended to all university staff doing supervision.

Sets, sums and constraints – A suvival guide for Business School students

Teaching 30. August 2012

Often when I teach students at our Business School they have a hard time understanding compact linear programming (LP) formulations. So here it is,  a short introduction to some of the concepts you need to know for understanding compact LP formulations.


A set is a group of elements, e.g. $\{1,2,4\}$ is a set with 3 elements, namely, $1,2$ and $4$ and $A=\{(2,3),(4,5),(6,8),(5,6)\}$ is a set called $A$ with 4 elements (pairs), namely,  $(2,3),(4,5),(6,8)$ and $(5,6)$. Note that in the last case each element is a pair $(i,j)$. Sets containing pairs are often used when we formulate LPs based on network problems where the pair $(i,j)$ denote the arc/edge from node $i$ to node $j$. Læs mere »

Using when introducing students to VRP

Teaching 22. December 2011

In my recent course on transportation and distribution systems for undergraduate business students I used a week talking about vehicle routing problems (VRP). Since their math skills aren’t that high the focus was not on algorithms instead I tried to talk about the general structure of the problem. Here the site is very good and provide a way of making a realistic problem case.

Logvrp is a web based vehicle route planner software cable of minimize transportation costs and to minimize fleet mileages. It uses Google maps to display routes and trips. Moreover, it supports many different VRP problems. Current two heuristics are implemented and can be run simultaneously on a problem instance. This is a good thing since the students can see that the heuristics behave differently on the same instance and that there is no general winner.

I created an exercise about a small-sized company located in Aarhus which sell organic fruits and vegetables to companies and private persons. The procedure to create the data to be used at logvrp was as follows: first I created sets of customers using the logvrp site. Each customer group was saved as csv files and modified using R. Next, a sets of orders was generated randomly using R and saved as csv files. The students was now able to answer the different questions using the csv files provided.

A typical solution visualized using crow fly distances.


The solution shown using shortest paths.

Transportation and distribution systems

Teaching 3. December 2011

During the fall 2011 I have been teaching the course “Transportation and distribution systems” an optional course for undergraduate students. We have considered various topics within transportation such as its role in the global economy, modal choice, 3PL, VRP problems, flow problems, airline management, ITS, green logistics etc.

Each week the students was given an exercise where they in most cases had to formulate and solve an mathematical programming model. I also have tried to introduce CPLEX OPL studio to them with minor success. Mostly they like to formulate their models in Excel and with OpenSolver it is possible even for quite large models.

Teaching large classes

Teaching 23. February 2011

Wordle: UntitledYesterday I participated in a short course about how to teach large classes. Focus was on how to align teaching for constructive learning, collaborative learning techniques and other active learning tricks. The main point can be summarized in this statement

“If students are to learn desired outcomes in a reasonably effective manner, then the teacher’s fundamental task is to get students to engage in learning activities that are likely to result in their achieving those outcomes… It is helpful to remember that what the student does is actually more important in determining what is learned than what the teacher does.” (Shuell, 1986: 429)

Teaching Management Science

Teaching 15. December 2010

Just finished my last Management Science lecture for this semester. This is the first time I theach this introductory course to Business Students. Topics are linear and integer programming, goal programming, simulation and network models. Læs mere »

Seminar in Business Studies – First Experience

Teaching 4. May 2010

The from February to May this year I have been teaching in “Seminar in Business Studies” a bachelor course (HA – 4. semester).

The course represents a teaching and form of learning where a group of 12 students with one or more teachers discusses selected issues and problems in management science. First the student should write a 10 page report on a specific subject. The report should provide the possibility of in-depth studies of theories, models and methods in management science. While writing the report he can use the assigned advisor for at most 1.5 hours. Second the student, 2 weeks after delivering the report, should give a 10 minutes presentation about their report. Afterwards there is time for 30 minutes of discussion and last 5 minutes for giving a grade.

I was assigned 59 students in 6 groups. In 4 of the groups I was the only teacher. In the last 2 groups we were 3 teachers.

Below you will find some experiences collected during the course. Please post a comment if you have suggestions for improvements. Læs mere »

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