Photo of Nils

About Me

Hi, I'm Nils Löhndorf. I am an assistant professor at WU Vienna. As researcher and entrepreneur, I help decision-makers to make better in decisions in the face of uncertainty.
My research interest are in stochastic optimization, in particular approximate dynamic programming, and its application to decision problems that involve uncertainty as they often occur in asset valuation and operations management.

Hydro Storage Optimization

In June (2017), WU featured my research on optimal operations and valuation of pumped-hydro storage power plants as part of their Researcher of the Month series. Check out the video, where I explain, why I believe that storing the energy of water is important and why optimizing it is worthwhile (in German):

QUASAR Optimizer

Based on my research on stochastic optimization, I have developed a general-purpose solver for stochastic-dynamic optimization called QUASAR. The solver is intended for analysts, decision-makers, and researchers who want to solve difficult sequential decision problems that involve uncertainty. You can use QUASAR to solve linear multistage stochastic programs, continuous Markov decision processes, or stochastic-dynamic programs. QUASAR features

  • an algebraic modeling language for expressing continuous-state, finite-horizon, stochastic-dynamic decision problems.
  • a solution engine that combines scenario tree generation, approximate dynamic programming, and risk measures.
  • various functions and data structures to store, analyze, and visualize the optimal stochastic solution.

QUASAR is written in Java but provides native interfaces for Matlab and Python. If you want to try QUASAR go to and sign up for a free trial. QUASAR is entirely free for academic usage.


  • Löhndorf N, Shapiro A. 2017. Modeling time-dependent randomness in stochastic dual dynamic programming. Available on Optimization Online. Download
  • Löhndorf N, Wozabal D. 2017. Indifference pricing of natural gas storage contracts. Available on Optimization Online. Download
  • Löhndorf N. 2016. An empirical analysis of scenario generation methods for stochastic optimization. European Journal of Operational Research 255(1), 121-132. Download
  • Löhndorf N, Riel M, Minner S. 2014. Simulation optimization for the stochastic economic lot scheduling problem with sequence-dependent setup times. International Journal of Production Economics 157, 170-176. Download
  • Löhndorf N, Wozabal D, Minner S. 2013. Optimizing trading decisions for hydro storage systems using approximate dual dynamic programming. Operations Research 61, 810-823. Download
  • Löhndorf N, Minner S. 2013. Simulation optimization for the stochastic economic lot scheduling problem. IIE Transactions 45, 796-810. Download
  • Transchel S, Minner S, Kallrath J, Löhndorf N, Eberhard U. 2011. A hybrid general lot-sizing and scheduling formulation for a production process with a two-stage product structure. International Journal of Production Research 49(9), 2463-2480. Download
  • Francas D, Löhndorf N, Minner S. 2011. Machine and labor flexibility in manufacturing networks. International Journal of Production Economics 131(1), 165-174. Download
  • Löhndorf N, Minner S. 2010. Optimal day-ahead bidding with renewable energies and storage. Energy Systems 1(1), 61-77. Download

Online Scenario Generator

Generate scenarios from a multivariate distribution (normal, log-normal, uniform) for Monte Carlo simulation, numerical integration or stochastic programming. The generator is based on experiments with different scenario generation methods which are described in this article. The code is available on GitHub.

© Nils Löhndorf, 2017. Base theme/CSS by Skeleton.