Solving a Two-stage Continuous-discrete Problem of Optimal Partitioning-Allocation with Subsets Centers Placement

Abstract

A two-stage continuous-discrete optimal partitioning-allocation problem is studied, and a method and an algorithm for its solving are proposed. This problem is a generalization of a classical transportation problem to the case when coordinates of the production points (collection, storage, processing) of homogeneous products are continuously allocated in the given domain and the production volumes at these points are unknown. These coordinates are found as a solution of the corresponding continuous optimal set-partitioning problem in a finite-dimensional Euclidean space with the placement (finding coordinates) of these subsets’ centers. Also, this problem generalizes discrete two-stage production-transportation problems to the case of continuously allocated consumers. The method and algorithm are illustrated by solving two model problems.

Keywords

• infinite-dimensional mathematical programming
• the theory of optimal set-partitioning
• transportation problem
• non-differentiable optimization
• shor’s r-algorithm
• 49m29
• 49j52
• 49k35