The Optimal Round Placing of the Equipment for the Products Random Routes

Abstract

In many publications the equipment placing task was studied under very stringent assumption of no loops in the products manufacturing routs and for this particular case only the approximate, heuristic solution methods were off ered. In this article, the mentioned routes are arbitrary. For this general a new, generalized definition of the item-streams matrix case is proposed for the first time. It has proved being fruitful because allowed to keep most of the results previously obtained by the author for the above mentioned special case.
First of all, it takes the explicit form of the objective function which does not require time-consuming counting the number of turns of subjects. Besides that we still have the opportunity for application of a very effective method of exact solutions based on the use of necessary conditions found by the author for the optimality of the desired displacement of numbers of machines. This condition is sufficiently rigid, i.e. close to the necessary and sufficient condition, resulting in a set of “suspicious for optimality” displacements is very narrow, and oft en consisted of a single (and thus the optimal) displacement.
All of received allegations and properties are illustrated by numerical examples.

Keywords:

line production, equipment placing, technological routes, turnover on the line, optimal displacement