Solving the problem of equipment distribution using the method of recurrent relations

Abstract

The method of recurrent relations was used to solve the problem of distribution of equipment between prepress sections of the printing company. The recurrent method made finding the required minimum costs easier by using a smaller number of variables. This task was considered to be a dynamic process despite the lack of temporal data. Therefore, dynamic programming based on the Bellman functional equation was used to solve it. The problem of optimal distribution of equipment between sections was solved using a forward dynamic programming algorithm, dividing a complex task into simple tasks (steps). The number of steps was equal to the number of divisions to which the equipment was distributed, so conditional and unconditional optimizations were multi-step. As a result, the optimal number of equipment units for each division was determined, ensuring the minimum total costs for its transportation and maintenance during the technical re-equipment of divisions.