Optimization of Manufacturing Processes and of Systems Under the Conditions of Uncertainty

Abstract

This study is dedicated to optimization of manufacturing processes and manufacturing systems wherein interrelated activities are conducted in order to achieve the united common goal of converting the input flows of material, informational and financial resources into output ones valuable for the consumer. The process outcomes are a priori unknown and are determined by uncertain factors such as the future demand, risks and opportunities, the future states of the economy and finances, the market conjuncture, the prices of energy carriers and many others. In order to design the processes and process systems adequately, their mathematical optimization models must take into account the uncertainty of all the factors that exert influence on the course and outcomes of the processes in future. For this purpose, the study has devised a mathematical probabilistic optimization model of a process and process system with taking into account the uncertainty of the future values of the factors and the states of the (competitive, political, economic, financial, conjunctural, etc.) environment. A model in the form of an intervally stochastic random value with the arbitrary unimodal distribution of its values within their change interval has been accepted as the mathematical model of the factor uncertainty. The intervally stochastic model of the uncertainty is adequate for the real uncertainty and conforms to the agent's psychology when making the decision and quantitatively estimating the uncertainties. The mathematical model devised by this study describes the processes conducted both in the separate manufacturing, ensuring, servicing links and in the process system in whole. To ensure the possibility of numerically determining the optimal parameter values for a process and process system, the probabilistic mathematical optimization model is reduced to a determinate mathematical optimization model, the solution of which can be effortlessly obtained by means of existing software intended for the solution of mathematical programming problems. The application of the devised mathematical models has been exemplified by optimization of a particular production process that includes ensuring and logistic processes, too. This study considers influence of the uncertain factors, such as investments into the process, future prices of the production factors and energy carriers, consumer's demand, price of the end product, as well as future actualization of the possible opportunities and risks. It has been shown that the results of modelling and optimizing the processes under the uncertainty conditions are intervally stochastic and must be represented in the form of the intervals of their values depending on the probabilities of actualization of the risks and opportunities.