A STOCHASTIC ANALYSIS OF STATIC COMPLEXITY in Manufacturing Systems Akif A. Bulgak, Ph.D., P.Eng. Department of Mechanical and Industrial Engineering, ENCS, Concordia University H. Kemal İlter, Ph.D. Department of Management Information Systems, SB, Yildirim Beyazit University YAEM June 2014 

CONTENTS Introduction The Problem Theoretical Systems vs Real Systems Complexity in Operations Management Brief Literature Types of Complexity in OM Measuring Complexity Critical Factors Entropical Measurement Simulation and Results Simulation Results References Discussion Questions 

INTRODUCTION The Problem 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. 

INTRODUCTION The Problem Mass Customization Product Variation Complex Manufacturing Systems Less initial investment Relatively low demand irregularities 

INTRODUCTION Theoretical Systems Non-modular Assembly Modular Assembly 

INTRODUCTION Real Systems BMW 7 Series 1017 Complex 

INTRODUCTION Real Systems Airbus A380 1021 Over-Complex 

COMPLEXITY IN OPERATIONS MANAGEMENT Brief Literature Supply chain complexity (Frizelle and Woodcock, 1995) Product variation complexity (MacDuffie et al., 1996) Entropic complexity (Deshmukh et al., 1998) Complexity interactions of different processes (Fujimoto et al., 2003) Complexity measurement (ElMaraghya et al., 2005) Supply Chain Complexity Manufacturing System Complexity Product Variation Complexity 

COMPLEXITY IN OPERATIONS MANAGEMENT Types of Complexity in OM The complexity of a physical system can be characterized in terms of its static structure or time dependent behavior. Static complexity can be viewed as a function of the structure of the system, connective patterns, variety of components, and the strengths of interactions. Dynamic complexity is concerned with unpredictability in the behavior of the system over a time period. The manufacturing environment consists of physical systems in which a series of sequential decisions need to be made in order to produce finished parts. The sequence and nature of these decisions are not only dependent on the system capabilities but also on the products being manufactured in the system. Any measure of system complexity should be dependent on both the system and the product information. Static Complexity (Structural) Dynamic Complexity (Operational) Associated with the variety embedded in the static system Associated with the uncertainty of the dynamic system 

MEASURING COMPLEXITY Critical Factors •  Number of suppliers •  Variety of interchangable parts •  Number of work stations •  Structure of the assembly line •  Structure of the manufacturing system 

MEASURING COMPLEXITY Entropical Measurement Supplier A Supplier B Station 1 Station 2 A1 , A2 , A3 B1 , B2 A1 B1 A1 B2 A2 B1 A2 B2 A3 B1 A3 B2 Assembly Line 

MEASURING COMPLEXITY Entropic Measurement Station 1 j-1 H0 j j+1 Station n H1 Hj-1 Hj Hj+1 Hn C0,j C1,j Cj-1,j Cj,j+1 Cj,n 

SIMULATION AND RESULTS Simulation 

SIMULATION AND RESULTS Simulation Modular Non Modular 

SIMULATION AND RESULTS Results 

SIMULATION AND RESULTS Results Modular Non Modular 

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DISCUSSION QUESTIONS 

A STOCHASTIC ANALYSIS OF STATIC COMPLEXITY in Manufacturing Systems THANKS Akif A. Bulgak, Ph.D., P.Eng. [email protected] Department of Mechanical and Industrial Engineering, ENCS, Concordia University H. Kemal İlter, Ph.D. [email protected] Department of Management Information Systems, SB, Yildirim Beyazit University YAEM June 2014