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

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In the rapid development of information technology, modern publishing and prin­ting companies must constantly be advancing. Some forms of such advances include technical re-equipment or reconstruction, which increases the volume and accelerates the production, improves the quality and working conditions. One of the most challenging tasks of technological advancement is the distribution of equipment between printing divisions. Each division of the enterprise is interested in obtaining new equipment units and increasing the volume of work. However, it is necessary to take into account the underlying costs because the technical characteristics of the equipment are the same, and so is the performance.

This paper investigates the dependence of transportation and maintenance costs on the amount of equipment provided to different divisions of the printing enterprise.

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.

Keywords: printing, equipment distribution, Bellman principle of optimality, re­cur­rent relations.

doi: 10.32403/1998-6912-2021-1-62-87-94

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