Automation of optimization of discrete technological processes

Evgeniy Kudryavtsev,V. Andreev,T. Matseevich,A. Adamtsevich,A. Ter-Martirosyan

doi:10.1051/matecconf/201819604067

Evgeniy Kudryavtsev, V. Andreev + Show 3 more

Open Access

https://doi.org/10.1051/matecconf/201819604067

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Abstract

The article describes the procedure automation of optimization discrete technological processes with using of Bellman’s functional (recurrent) equation and system Mathcad. As rule the technological processes includes n of operations and each operation can be executed by various types of equipment. Expenses (cost, time, …) on execution of i operation by k equipment after execution by j equipment (i-1) operation are known - c (i, j, k). Expenses for execution by k equipment i operation can depend on the equipment - j, which executed previous (i-1) operation. It is necessary to execute automation of optimization technological process with the minimum expenses. The algorithm of the decision of a problem by Bellman’s method includes two phases. The first phase is calculations of the minimum expenses for execution of all partial technological processes, from last operation of process to the first. The second phase is definition of the required optimum set of equipment which is carrying out all technological process with the minimum expenses. The proposed procedure of automation of optimization technological process using Bellman’s method and system Mathcad significantly decreases time and labour costs on execution of such calculations and efficiently to execute investigations related with change of equipment parameters.

Highlights

IntroductionFor execution automation of optimization of technological processes it’s possible to use various decision methods and tools [1-20]
For execution automation of optimization of technological processes it’s possible to use various decision methods and tools [1-20].The technological process includes n of operations
Expenses on execution of i operation by k equipment after execution by j equipment (i - 1) operation are known - c (i, j, k)

Summary

Introduction

For execution automation of optimization of technological processes it’s possible to use various decision methods and tools [1-20]. The technological process includes n of operations. Each operation can be executed various types of equipment. Expenses (cost, time, ...) on execution of i operation by k equipment after execution by j equipment (i - 1) operation are known - c (i, j, k). The size of expenses for execution by k equipment of i operation can depend on the equipment j, execution previous (i-1) operation. It is necessary to execute structurally-parametrical optimization of technological process with the minimum expenses. The initial information is presented in the Table 1. The equipment k executes flowing i operation k=1 k=2 k=3 k=1 k=2 k=3 k=1 k=2 k=3

Description of technological process

Mathematical model

Algorithm of the decision

Calculation of the minimum expenses for execution of all operations:

Conclusion