Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. We also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size. Summary of Contribution: Chance-constrained programs are in general NP-hard but widely used in practice for lowering the risk of undesirable outcomes during decision making under uncertainty. Assuming finite scenarios of uncertain parameter, chance-constrained programs can be reformulated as mixed-integer linear programs with binary variables representing whether or not the constraints are satisfied in corresponding scenarios. A useful quantile bound for solving chance-constrained programs can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. In this paper, we develop algorithms for optimally and heuristically grouping scenarios to tighten the quantile bounds. We aim to improve both the computation and solution quality of a variety of chance-constrained programs formulated for different Operations Research problems.

Hybrid cluster analysis of customer segmentation of sea transportation users

Purpose The purpose of this study is to apply hybrid cluster analysis in classifying PT Pelindo I customers based on the level of customer satisfaction with passenger services of PT Pelindo I. Design/methodology/approach Hybrid cluster analysis is a combination of hierarchical and non-hierarchical cluster analysis. This hybrid cluster analysis appears to optimize the advantages of hierarchical and non-hierarchical methods simultaneously to obtain optimal grouping. Hybrid cluster analysis itself has high flexibility because it can combine all hierarchical and non-hierarchical methods without any limits in the order of analysis used. Findings The results showed that 72% of PT Pelindo I customers felt PT Pelindo I service was special, while the remaining 28% felt PT Pelindo I service was good. Originality/value In total, 117 customers of PT Pelindo I were involved in a study using the non-probability sampling method.

Mathematical justification of the use of control tools to improve traffic safety

The question of the dependence of the number of accidents on systematic and random factors is considered. The article provides a mathematical justification for predicting road safety and creating conditions for optimal grouping of controls in the system, from the point of view of traffic safety. The problem of optimizing the management indicator is solved. Keywords technical controls, systematic and random factors of accidents, the task of optimizing the management indicator, monitoring sites by the size of violations