A Stochastic Analysis of Static Complexity in Manufacturing Systems



H. K. Ilter and A. A. Bulgak
12.12.2014
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Abstract

This paper presents static complexity in manufacturing systems. Static complexity can be viewed as a function of the structure of the system, connective patterns, variety of components and the strengths of interactions. We seek the acceptable static complexity levels for different types of manufacturing systems by means of their system performances. In general, deterministic processing times or expected values of processing times are considered to measure the complexity and related system performance in the production and operations management field. We consider stochastic processing requirements with a number of different processing distributions and levels of variability on the static complexity measurements. The objective of this paper is to reveal characteristics of the static complexity by making observations about the behavior of different systems in a hypothetical manufacturing environment. This would help in analyzing the properties in different manufacturing systems due to static complexity and system performance.

Keywords: Static complexity, Stochastic analysis, Manufacturing systems

Introduction

Static complexity is a characteristic associable to the systems - and so also to the production processes - that refers to the structure of the facilities or to the structure of the plant and considers the degree of difficulty for their management and control. Such type of complexity becomes important when the possible design of a facility or plant is studied. On the other hand dynamic complexity refers to the analysis of the systems along the time, in other words it studies the trend of the real states that the process assumes within the considered time. However from the point of view of the entropic measures we can consider the trend of the waiting queues (or the warehouses). In fact they absorb the variability of a system unit along the time. [1][2]

Static Complexity Index

The static complexity starts from the competition between products and resources; it is an index that represents the potentiality inside the structure to cause operative critical states. The Static Complexity index[3] is associated to the system variety linked to the planned state. The mathematical formulation is the following:

File:Static-complexity-index.png

where M is the number of resources (that is the number of machinery, equipments), [math]N[/math] N represents the number of possible states the resource j can be found and pij is the probability that the resource j is found in the state i [4]. The authors define "planned state” the association between the product i and the resource j which will work according to the scheduled plan.

Separating the complexity measure into two components simplifies the computation of the measure. One is used to measure the system structure and the other to measure the system uncertainty. Frizelle and Woodcock [5] [6] used static complexity as a measure of complexity due to the system design, while dynamic complexity was seen as the result of the uncertainties in the system while it is operating (e.g., machine breakdowns).

Deshmukh, Talavage and Barash [7] provided a clear definition of static complexity and dynamic complexity. Static or structural complexity is a “function of the structure of the system, connective patterns, variety of components, and the strengths of interactions”. So, static complexity measures how the factory is structured (e.g., number of products, number of processes/machines). On the other hand, dynamic complexity is a measure of “the unpredictability in the behavior of the system over a time period”. A common example of dynamic complexity is a machine breakdown. This means that dynamic complexity is an obstacle to achieving the system’s goals [8][9]

Conclusion[10]

This paper presented a measure for quantifying static complexity in manufacturing systems, studied characteristics of the static complexity measure, and observed the behavior of system performance with respect to the static complexity measure,and observed the behavior of system performance with respect to the static complexity measure. The static complexity measure introduced in the paper is applicable to systems manufacturing discrete parts, without assembly/disassembly operations. We study the effects of managerial decisions on the complexity of the system and present guidelines for improving system operations. We argue that increase in static complexity results in an improvement in the system performance, if the system is operated optimally. This implies that it is not always detrimental to have excess static complexity, even though the decision making di culty in such systems is increased. Therefore, the system planner or manager has to make decisions about how much static complexity to add to the system, since there is a tradeoff between increasing decision making or hardware costs, and improved system performance.

The proposed measure can be extended to include multiple part precedences, for modeling assembly/disassembly operations, in addition to the operation precedences for individual parts. Another extension of the work presented in this paper would be to study the costs associated with increasing static complexity with respect to different cost structures for the elements that contribute to static complexity. This would help in analyzing the tradeoffs between different cost structures due to static complexity and improved system performance. The proposed measure can also be enhanced by considering stochastic processing requirements, instead of deterministic processing times or expected values of processing times. Effects of different processing distributions and levels of variability on this measure can be studied.



References

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  2. Toni et al., Complexity measures in manufacturing systems, http://www.dis.uniroma1.it/~nonino/Publications/CI3.pdf
  3. Frizelle G., The Management of Complexity in Manufacturing, Business Intelligence, London, 1998.
  4. Calinescu A., Efstathiou J., Sivadasan S., Schirn J., Huaccho Huatuco L., Complexity in Manufacturing: An Information Theoretic Approach, Proceedings of the International Conference on Complex Systems and Complexity in Manufacturing, Warwick, pp 30-44, 2000.
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