ALGORITHMIC APPROACHES TO SOLVING STOCHASTIC-PARAMETRIC TRANSPORTATION PROBLEMS WITH AN OPTIMIZATION COMPONENT - LUKAN, OLEKSANDR (Herald of Khmelnytskyi National University. Technical sciences, 2025)
The article examines stochastic-parametric formulations of the transportation problem as a special class of linear programming problems, in particular cases with a parameter in the objective function and in the constraints, as well as stochastic modifications with an integer constraints. This formulation is driven by the necessity to account for uncertainties of various origins in optimization problems, arising from both random phenomena and deterministic factors characterized by specific control parameters. Approaches to post-optimality analysis and assessment of solution stability are proposed and described. A generalized algorithm for constructing optimal plans based on the sequential narrowing of the selected parameter range using Gomory cuts and the dual simplex method is presented. The relationship between parametric and stochastic transportation models is explored, and practical aspects of their application are outlined.This paper is devoted to constructing the feasible set of solutions when problem parameters have a probabilistic nature and affect the stability of the basis. It is shown that combining stochastic and parametric approaches allows not only improving the reliability of the results but also formalizing the procedure for determining the boundaries of optimality intervals. In the case where the investigated segment of the parameter lies entirely within the working range, it can be considered that the complete set of optimal solutions has been described. The proposed approach provides the ability to localize regions where the optimal plan preserves its structure as the parameter varies and enables smooth transition between adjacent plans via the dual simplex method.The obtained results have applied significance for the optimization of transportation and production-logistics systems under uncertainty. The proposed algorithmic framework allows sensitivity analysis, prediction of optimal plan variations with changing parameters, and the creation of adaptive decision-support models for complex optimization systems.
Keywords: transportation problem; parametric programming; stochastic model; integer linear programming problem; Gomory cuts; stability