A Clustering Approach to Solving Large Stochastic Matching Problems
This work addresses a computational bottleneck in business and investment applications, offering an incremental improvement for handling large-scale stochastic matching problems.
The paper tackles the stochastic planning problem of maximizing expected profit by selecting buy and sell contracts, which is computationally infeasible for large scales due to exponential complexity. It proposes a clustering-based heuristic to approximate solutions efficiently, demonstrating its quality and feasibility through experimental data.
In this work we focus on efficient heuristics for solving a class of stochastic planning problems that arise in a variety of business, investment, and industrial applications. The problem is best described in terms of future buy and sell contracts. By buying less reliable, but less expensive, buy (supply) contracts, a company or a trader can cover a position of more reliable and more expensive sell contracts. The goal is to maximize the expected net gain (profit) by constructing a dose to optimum portfolio out of the available buy and sell contracts. This stochastic planning problem can be formulated as a two-stage stochastic linear programming problem with recourse. However, this formalization leads to solutions that are exponential in the number of possible failure combinations. Thus, this approach is not feasible for large scale problems. In this work we investigate heuristic approximation techniques alleviating the efficiency problem. We primarily focus on the clustering approach and devise heuristics for finding clusterings leading to good approximations. We illustrate the quality and feasibility of the approach through experimental data.