1. Introduction

Presently, the information support of production systems management is mainly focused on the control and management of production systems (SCADA), the support of sales and production process (ERP, MRP, Just in Time), organizing production for known customers (CSRP), and product life cycle management (CALS). However, the aspects of tactical and strategical management get information support only on the stage of data preparation for decision making,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

yet on the stage when potential solutions are to be identified based on data we observe lack of information support. The integration of automatization and control systems, the trend towards Industry 4.0 and IIoT leads to an exponential growth of collected data. Hence, on the one hand, it can be expected that the use of big data might help obtain fundamentally new solutions due to their immense nature, but on the other hand, the issues of decision support automation become more acute as we face the trend of an ongoing automation expansion of production systems, and hereafter, can assume a concept of a virtual factory.

models [6] that depend on the current state of market (change in price, sales volumes etc.)) and production risks (the risks related to equipment mortality, failures in the delivery of necessary

The use of probability models is based on the use of risk metrics [7], Bayes' Theorem [8] or

2. Methodology aspect of management task setting in production systems

Production system is regarded as management object that is placed in a state space. The coordinates on this n is the dimensional space are represented by the management parameters that are considered significant for achieving the targets, and their values describe the current

If we mark target goal indexes by the vector Pp, and the current state by the vector Pa, we will

deviates from the goal position that is deemed a sign of progress for project implementation

management, we also need to know the vector of the parameters Y that greatly affect the state of project and consist of the values that describe project, production system and the environments in which project is implemented as well as dynamics of change and prognostic values of all these parameters. It should be noted, that the achievement of the goal values Pp ¼ Pa does

In management tasks values and parameters can be classified in four groups [10]: parameters

(external factors and control action – Y ¼ A ∪ Θ, the A is the set of control actions, Θ is the set of

Therefore, management has to use an automaton where the consecutive state is defined by experts based on the current state and the state that was planned to be achieved on the

<sup>a</sup> ; <sup>T</sup>ð Þ <sup>n</sup> . In order for a new state to come, action <sup>A</sup>ð Þ<sup>i</sup> has to be defined. We can determine such action with help of the production system model that implements innovation projects w<sup>j</sup> ¼ f g U; S , where U is the vector of management parameter, S is the set of project

This approach helps work out hierarchically coordinated managerial decisions by taking into consideration system-interrelated external and internal factors that interact. Management pro-

(the end of implementation, Pp ¼ Pa). However, to know the metrics Pp; Pa

not always mean the achievement of the vector values Y expected for this state.

environment values), values and parameters that describe a goal state Pð Þ<sup>i</sup>

previous stage and the time when it has to be done – Pð Þ<sup>0</sup>

cess is considered then as a holistic undetermined process.

eters that describe the output of system operation by shifting from the state Pð Þ<sup>i</sup>

that shows how the current position

Time Factor in Operation Research Tasks for Smart Manufacturing

http://dx.doi.org/10.5772/intechopen.73085

77

<sup>p</sup> , values and parameters that describe the action

<sup>p</sup> ; Pð Þ<sup>0</sup>

<sup>a</sup> ; <sup>T</sup>ð Þ<sup>0</sup> , Pð Þ<sup>1</sup>

is not enough for

<sup>a</sup> , values and param-

<sup>p</sup> ; Pð Þ<sup>1</sup> <sup>a</sup> ; <sup>T</sup>ð Þ<sup>1</sup> ,

<sup>p</sup> into Pð Þ<sup>i</sup>

<sup>a</sup> - R

materials or parts etc.).

Monte-Carlo Method [9].

state and remoteness from the selected targets.

and values that describe a current state Pð Þ<sup>i</sup>

and time Tð Þ<sup>0</sup> .

…, Pð Þ <sup>n</sup>

<sup>p</sup> ; Pð Þ <sup>n</sup>

resource needs, j is project number.

receive a mathematically measurable metric Pp; Pa

The use of the concepts Industry 4.0 outlines possibilities for the automation of production systems management taking into account the interaction of subsystems and the synchronization of their interaction with external factors. In the age of cutting edge innovation products we cannot talk about the stability of production processes since life cycle of such products is short, the number of modifications and parts is high, and power intensity and resources consumption is much higher. This proves the necessity of collecting reliable information with help of IIoT. The presence of such data helps build predictive models and use preventive control actions as production system is an inertial management object that is not able to adjust the ongoing processes instantaneously. Besides, the change of processes requires additional time resources, financial resources, labor competence, and organization resources.

The implementation of the concepts Industry 4.0 and Industrial Internet of Things [that deals with collecting information about each production unit and provides operation management over production processes in PS] [1] opens new possibilities for developing industrial engineering methods [2].

Taking into account long decades, when production systems were examined only on the basis of general data, data engineers had limited data to develop methods for decision making and took advantage of expert evaluations, i.e. the methods of utility theory (considering customer preferences as maximization of expected utility, probability models (see the works of O. Morgenstern), axiomatic theory of D. Savage that enables measure the utility and subjective probability simultaneously; decision tree approach that partitions the tasks into certain subtasks (look the works of H. Reif); multiple-criteria utility theory (developed in the works of R. Keeney); prospect theory methods, Electre methods (worked out by the French School on MCDA headed by B. Roy), hierarchy analysis method proposed by Saaty [3], heuristic methods (for instance, the method of the weighed sum of its evaluation ratings, compensation methods etc.), the models of bounded rationality by A. Rubinstein, the technic for order of preference by similarity to ideal solution (TOPSIS) [4].

The appearance of a big amount of statistical data encouraged the development of the methods of mathematical formalization used to solve tasks for the management of materials, parts, operations, and choice of suppliers [5] with the consideration of stochastic factors, probability approaches to measure risks taking into account different nature of examined events (joint, correlative, inconsistent and interdependent) used to solve planning tasks taking into account the dynamics of examined processes.

The consideration of random factors and the use of probability approaches help measure risks with help of models. There are planning risks (the risks related to decision making based on models [6] that depend on the current state of market (change in price, sales volumes etc.)) and production risks (the risks related to equipment mortality, failures in the delivery of necessary materials or parts etc.).

yet on the stage when potential solutions are to be identified based on data we observe lack of information support. The integration of automatization and control systems, the trend towards Industry 4.0 and IIoT leads to an exponential growth of collected data. Hence, on the one hand, it can be expected that the use of big data might help obtain fundamentally new solutions due to their immense nature, but on the other hand, the issues of decision support automation become more acute as we face the trend of an ongoing automation expansion of production systems, and

The use of the concepts Industry 4.0 outlines possibilities for the automation of production systems management taking into account the interaction of subsystems and the synchronization of their interaction with external factors. In the age of cutting edge innovation products we cannot talk about the stability of production processes since life cycle of such products is short, the number of modifications and parts is high, and power intensity and resources consumption is much higher. This proves the necessity of collecting reliable information with help of IIoT. The presence of such data helps build predictive models and use preventive control actions as production system is an inertial management object that is not able to adjust the ongoing processes instantaneously. Besides, the change of processes requires additional time

The implementation of the concepts Industry 4.0 and Industrial Internet of Things [that deals with collecting information about each production unit and provides operation management over production processes in PS] [1] opens new possibilities for developing industrial engi-

Taking into account long decades, when production systems were examined only on the basis of general data, data engineers had limited data to develop methods for decision making and took advantage of expert evaluations, i.e. the methods of utility theory (considering customer preferences as maximization of expected utility, probability models (see the works of O. Morgenstern), axiomatic theory of D. Savage that enables measure the utility and subjective probability simultaneously; decision tree approach that partitions the tasks into certain subtasks (look the works of H. Reif); multiple-criteria utility theory (developed in the works of R. Keeney); prospect theory methods, Electre methods (worked out by the French School on MCDA headed by B. Roy), hierarchy analysis method proposed by Saaty [3], heuristic methods (for instance, the method of the weighed sum of its evaluation ratings, compensation methods etc.), the models of bounded rationality by A. Rubinstein, the technic for order of preference by similarity to ideal solution

The appearance of a big amount of statistical data encouraged the development of the methods of mathematical formalization used to solve tasks for the management of materials, parts, operations, and choice of suppliers [5] with the consideration of stochastic factors, probability approaches to measure risks taking into account different nature of examined events (joint, correlative, inconsistent and interdependent) used to solve planning tasks taking into account

The consideration of random factors and the use of probability approaches help measure risks with help of models. There are planning risks (the risks related to decision making based on

resources, financial resources, labor competence, and organization resources.

hereafter, can assume a concept of a virtual factory.

76 Digital Transformation in Smart Manufacturing

neering methods [2].

(TOPSIS) [4].

the dynamics of examined processes.

The use of probability models is based on the use of risk metrics [7], Bayes' Theorem [8] or Monte-Carlo Method [9].
