On a New Collection of Stochastic Linear Programming Test Problems

Abstract

T he purpose of this paper is to introduce a new test-problem collection for stochastic linear programming that the authors have recently begun to assemble. While there are existing stochastic programming test-problem collections, our new collection has three features that distinguish it from existing collections. First, our collection is web-based with free public access, and we intend to enrich it as new test problems become available. Indeed, we encourage submissions of new test problems. Second, along with the collection we provide documentation of the problems, so that researchers can quickly find information about each family without reading through the original source. Third, all of the data in our collection are provided in SMPS (Birge et al. 1987, Gassmann andSchweitzer 2001) format. In this paper, we provide an introduction to the stochastic linear program, give a brief description of each problem family currently in the test-problem collection, and describe the documentation that accompanies the collection.

Importance Sampling in Stochastic Programming: A Markov Chain Monte Carlo Approach

“…In order to verify that our findings from Section 4.8 generalize to stochastic programming models, we have based the numerical experiments in this section on a collection of 9 benchmark stochastic programming models from Ariyawansa and Felt (2004). We have specifically chosen these models due to the fact that they represented a diverse collection of stochastic optimization problems.…”

“…In addition, the models also pertain to decision-making problems across a wide range of application areas such as energy, finance, and telecommunications. Ariyawansa and Felt (2004) It is worth noting that many of the problems in Ariyawansa and Felt (2004) had to be modified in order to be solved with a sampling-based approach. This was due to the fact that many problems were originally formulated using discrete distributions and scenario trees (sometimes with 3 scenarios).…”

“…In this section, we explain the modifications we made to the set of test problems from Ariyawansa and Felt (2004).…”

“…The coefficient 0.5 and 0.2 are chosen such that the generated exchange rate are as close as possible to the original source. Finally, the target exchange rate is set to 0.463, which is the average of target exchange rates across all scenarios shown in Table 5 in Ariyawansa and Felt (2004). In our experiments, we vary the amount of uncertainty in our model by setting σ i = i.…”

“…The number of time periods is two and the number of funds we used is five. Since the data are not given precisely either in the original source or in Ariyawansa and Felt (2004), the data are created such that they are as close as possible to some of the examples found in the original paper. The data are generated as follows:…”