Complexity: Toward an empirical measure Mark A. Jacobs, 2013 , Technovation Name：施旖旎 Student ID：16720774

Generalized complexity index(GCI) Conclusion CONTENTS Generalized complexity index(GCI) Conclusion The nature of complexity Application of the GCI Introduction Existing measures of complexity

Part1 Introduction

Introduction 03 Problem: rising levels of complexity threaten to undermine operational efficiencies and consume profits （3%）。 01 Product complexity and Portfolio complexity is increasing（1:1.7）。 02 Supply chains are also becoming more complex。 （ innovation ） 04 Strategy : quantify complexity so that optional complexity levels can be determined.。

The nature of complexity Part2

The nature of complexity Jacobs and Swink ： It states that complexity is a state manifested by the multiplicity, diversity, and functional interrelatedness of elements.

The nature of complexity Complexity is increased with greater multiplicity of elements 。 Multiplicity Eg: a portfolio containing four pens that are identical except for ink color (a unique feature) is more complex than the portfolio containing only a blue ink pen. Multiplicity is the number of elements, including redundant and replicated elements

The nature of complexity Complexity also increases with increasing diversity in systems, technology, architecture. Diversity Eg: A product portfolio made up of a fountain pen, ball point pen, and pencil is more complex than a portfolio of three ball point pens of differing color Diversity is the degree of differences across elements

The nature of complexity Complexity also increases with the degree of interrelatedness among elements Interrelatedness Eg:The ball point and fountain pens offer consumers the same basic functionality Interrelatedness refers to the common or interacting functions embodied in the elements.

Existing measures of complexity Part3

Existing measures of complexity The marketing literature uses the terms horizontal and vertical differentiation to describe different levels of diversity in product portfolios. Degree of horizontal differentiation indicates product variations within a category. These variations reflect minor differences . 4 2 3 1 Both marketing concepts deal specifically with diversity, minimizing the unique effects of multiplicity and ignoring inter- connectedness. Degree of vertical differentiation indicates changes across categories or changes in features.

Existing measures of complexity Another line of research has been in the context of understanding network complexity. To further this line researchers have developed several coefficients of network complexity (CNC). The dependency index which quantifies element connectivity by tabulating the number of changes required throughout the system as a result of changing one element within the system. 4 2 3 1 A significant limitation to all of the measures published to date is that they do not transcend settings well .Measures developed for products cannot be readily adapted to organizations or supply chains. The complexity index which is the cube root of number of components multiplied by number of different components and number of connections and various approaches to calculating the number of elements per connection.

Generalized complexity index(GCI) Part4

Generalized complexity index(GCI) The product structure diagram:

Advantages Generalized complexity index(GCI) 01 04 02 03 A benefit of product structure diagrams is that they do not necessarily require intimate product knowledge like the design structure matrix. From the product structure diagrams the three dimensions of complexity can be quantified. Advantages 04 02 They can often be constructed using publicly available data. Another benefit is that the diagrams are geometric forms containing network information that can be leveraged for quantitative evaluations. 03

2 1 Multiplicity Multiplicity= variants=V Generalized complexity index(GCI) Multiplicity is simply a representation of numbers of variants 1 Multiplicity Multiplicity= variants=V 2

2 1 Diversity Generalized complexity index(GCI) The commonality index: measures the number of unique components as a percentage of the total components.(U/T) 1 Diversity Diversity=1-(unique elements/total elements)=1-U/T 2

2 1 Interrelatedness Generalized complexity index(GCI) Generate the same number of variants, but with fewer connections, are less complex 1 Interrelatedness Interrelatedness=connections/max connections=A/M 2

2 1 GCI Generalized complexity index(GCI) Advantages: Each complexity dimension be incorporated in the measure GCI=V（1-U / T）A / M 1 GCI Advantages: it is not size dependent. Through the use of ratios 2

Part5 Application of the GCI

Application of the GCI This research uses publicly available data from the same context to illustrate the generalized complexity Index GCI = V*(1-U/T)*A/M GCI = 9*(1-19/45)*(19/720) GCI = 0.137 3*3*4*4*5=720

Application of the GCI This research uses publicly available data from the same context to illustrate the generalized complexity Index GCI = V*(1-U/T)*A/M GCI = 3*(1-12/15)*(12/72) GCI = 0.100 2*2*2*3*3=72

A B C Application of the GCI Providing insight into portfolio configurations, The result is guidance to product design engineers and marketers. There may also be implications for disciplines such as finance This could serve to improve estimates of investment returns. B C A data envelope analysis (DEA) could be performed； Marketing professionals can use the 3-dimensional mapping approach to evaluate the strength of various portfolio configurations

Part6 Conclusion

Conclusion 1 4 2 5 3 6 Conclusion The GCI might be a more precise measure of diversification since it does not incorporate exogenous variables such as pricing. This research provides a means to quantify complexity 1 4 Conclusion New studies incorporating the GCI can validate the earlier findings and subsequently tie them more tightly to future research projects 2 5 Product and supply chain, and its effectiveness illustrated using product portfolios. 3 6 The GCI affords the opportunity to carry out large-scale empirical investigations. From a managerial perspective, the GCI can be incorporated into analytical models to enhance the performance of decision support tools.

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