analysis of information flow in hierarchical organizations

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Analysis of information flowin hierarchical organizationsDavid Ben-Arieh & Moshe A. PollatscheckPublished online: 14 Nov 2010.

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int. j. prod. res., 2002, vol. 40, no. 15, 3561±3573

Analysis of information ¯ow in hierarchical organizations

DAVID BEN-ARIEHy* and MOSHE A. POLLATSCHECKz

It is commonly accepted today that competitive, service-oriented or manufactur-ing organizations are overloaded with information to an extent not experiencedbefore. Moreover, technical employees as well as managers at all levels of anorganization devote increasing resources to handling this ¯ow of information.While the inundation of information may be useful in an organization, it reducesthe productive time of all the members of the organization. This paper presents amodel that links the productivity of hierarchical organizationswith the amount ofinformation processed and generated in the organization. This model is used to®nd the optimal conditions and optimal amount of information that needs to ¯owin three types of hierarchical organizations: homogeneous, semi-homogenousandnon-homogenous organizations. The model de®nes the information processingparameters that lead to optimal productivity at each level and each type of organ-ization. Dynamic programming is used to solve the model. The paper provides apioneering e� ort in linking the amount of information processed in an organ-ization to the productivity of the organization. In addition, the paper provides anew approach to linking the productivity of the individual functions to the overallproductivity of the organization.

1. Introduction

Modern manufacturing and service-based companies face a more competitiveworld than a decade ago. The fast development of technologies, worldwide competi-tion, the ever-increasing rate of product introduction, and higher customer demands

cause companies to be more e� cient and productive. These demands cause organi-zations to become information intensive. Such companies generate large amount ofinformation internally, usually in the form of electronic messages (e-mail). These

messages can contain direct information about the product (such as CAD ®les) ordirectives, instructions and support data related to the operation of the ®rm (ven-dors’ data, parts lists, quality reports, etc). These internal data have to be handled by

a number of management levels as well as the technical sta� at the organization. Ithas been observed that, in some technology-oriented companies, engineers have toprocess about 50 e-mail messages every day in addition to their day-to-day assign-ments.

The additional pressure of information overload comes from the adoption ofdownsizing described as the 1/2-by-2-by-3 rule, in which half as many people arepaid twice as much to produce three times as much (Handy 1995).

International Journal of Production Research ISSN 0020±7543 print/ISSN 1366±588X online # 2002 Taylor & Francis Ltd

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DOI: 10.1080/00207540210137611

Received October 2001.{ Department of Industrial & Manufacturing Systems Engineering, Kansas State

University, Manhattan, Kansas, 66506, USA.{ Faculty of Industrial Engineering and Management, Technion, Haifa, Israel 32000.* To whom correspondence should be addressed. e-mail: [email protected]

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In addition to their roles as information producers and consumers, employees ofsuch organizations have to maintain their value-adding activities. By processing theinformation the employee can add value to the company; however, this processingalso decreases the productivity of an employee. Thus, the problem of deciding howmuch information each employee should process is not trivial.

This paper explores the e� ect of the information ¯ow within an organization onits productivity. More speci®cally, it identi®es the optimal amount of informationthat has to ¯ow across the levels of a hierarchical organization in order to maximizeits productivity. The objective of this analysis is to prevent a situation in which somelevels of the organization will be overloaded with information and hence spend theirtime resources processing that information. However, unprocessed information mayresult in a reduction in productivity. The analysis of the productivity is conductedusing a production function that represents the productivity of the organization withtwo parameters: information and productive time. This function represents thetrade-o� between gain and loss of productivity due to information ¯ow.

Three types of organization are analysed in this research: fully homogeneous(type I), semi-homogeneous (type II) and non-homogeneous organizations (typeIII). In fully homogeneous organizations, the processing of the information is iden-tical at all levels, while in semi-homogeneous organizations each level has a di� erentusage of the information but with the same production function. In non-homoge-neous organizations, each level has its own utility function of the information (dif-ferent production function) combined with individual processing of the information.

The contribution of the paper is in creating a link between the information that¯ows in an organization and the productivity of the organization. This link isexpressed as a mathematical model that can be useful to any hierarchical organ-ization that processes information intensively. Military intelligence and Researchand Development organizations are just two examples. In addition, the paperpresents a pioneering view of analysing productivity of an organization based onthe individual contributions of the employees.

This paper is structured as follows: section 2 presents a brief background andliterature review regarding the information explosion and parametric productivityfunction of organizations. Section 3 provides notation and introduces the problemformulation for the three organization types. Section 4 presents a dynamic program-ming formulation and optimal results for organizations of types I and II. Finally,section 5 provides a summary and conclusions.

2. Background2.1. Information over¯ow

The problem of information overload in organizations is widely recognized(Edmunds and Morris 2000). `The technological development of the last 50 yearshas made more information more available to more people than at any other time inhuman history’ (Feather 1998). Thus, the problem of managing the desired quantityof information is of great interest to both manufacturing and service organizations.Lewis states that `Professional and personal survival in modern society clearlydepends on our ability to take on board vast amounts of new information. Yetthe information is growing at an exponential rate’ (Lewis 1996).

A major source contributing to the over¯ow of information is e-mail. AsWhittaker and Sidner state, e-mail is one of the most successful computer applica-tions ever devised, yet e-mail overload creates problems for personal information

3562 D. Ben-Arieh and M. A. Pollatscheck

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management (Whittaker and Sidner 1997). These authors believe that e-mailincreases the amount of information employees receive and has a positive e� ect ontheir organizational knowledge and commitment.

Individual responses to information overload in organizations include omissionof information (failing to address or assimilate information) and errors (interpretingthe information incorrectly (Vickery and Vickery 1987).

This Information Fatigue Syndrome (as coined by Oppenheim 1997) causesemployees to devote insu� cient amounts of time to their messages or even to stopreading some of the mail (Lantz 1998). Similar ®ndings show that technical commu-nication during tech-transfer projects can cost up to 59% of the total project cost;averaging 19% (von Hipple 1994). The burden of electronic communication causesresistance to information ¯ow (termed `information stickiness’ by Szulanski 1996)and reduces the productivity of the organization in general. This last reference doesnot include, however, the issue of information over¯ow combined with not havingthe right information. This problem, which is described by Katzer and Fletcher(1996), pertains to managers who, on one hand, receive too much informationand, on the other, do not get enough of the relevant information.

2.2. Parametric productivity of organizationsAssessment of the productivity of hierarchical organizations has not been dis-

cussed su� ciently in the literature. Williamson (1967) developed one of the fewexisting models. In this model there are m layers, and each administrator controlss subordinates. This model assumes that production takes place only at the lowestlevel, and all other levels of the organization provide only monitoring and super-vision. Thus, the productivity of such an organization is:

P ˆ ³…¬s†m¡1;

where ³ is a labour productivity parameter, and ¬ is a `control loss’ parameter thatre¯ects the remaining productivity at each administrative layer (productivity loss of1 ¡ ¬ for each additional layer is assumed). (This model is suitable for ¯at organiza-tions that are labour intensive. In such a case, the assumption that the productivityof the entire organization is concentrated at the lowest level may be justi®ed.)

In this research, we developed a di� erent productivity function of the followingtype:

P ˆXm

jˆ1

³ ¢ …s†j¡1:

This function represents the in¯uence of the `support layers’ in the organization inadditive terms. The basic model assumes that each manager has the same contribu-tion (³) regardless of the level in the organization. This assumption will be relaxedlater when the model is developed. The following section explains how to ®nd theindividual contribution to the productivity ³.

3. Problem descriptionThis section presents the assumptions and modelling of the productivity as a

function of the information ¯ow. Three types of organizations are considered: homo-geneous organizations in section 3.1, semi-homogeneous and non-homogeneousorganizations in sections 3.2 and 3.3, respectively.

3563Information ¯ow in hierarchical organizations

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The organization is represented as a tree with a branching factor of n. Each noderepresents a manager/employee with n subordinates. Each node (employee) has toperform a value-adding task, in addition to processing the information. Each such

employee receives X amount of information (in units of e-mail messages, ®le size(KB), number of text lines or any other units of relevance). Processing the informa-tion is done in two steps. In the ®rst step, the user reads and processes the informa-

tion. Also in this step, the user deletes and combines messages, reducing the amountof information by a factor of ¬…0 µ ¬ µ 1†.

In the second step, the user composes new messages, thus increasing the amount

of information by a constant . Following these operations, each node that receivesX amount of information generates ¬X ‡ messages.

The production function of each node considers both the information processed

at the node and the time left for the other productive tasks. In this research, we use aCobb±Douglas (Miller, 1978) production function of the form P ˆ X

a ¢ Tb

where Xis the amount of data processed and T is the time left after processing the informa-

tion.

Notation

¬ information compression factor: ¬ 2 ‰0; 1Š, information expansion factor: ¶ 0,

C1 constant representing the time to read and process the information (in

minutes),C2 constant representing the time to expand the data by 1 message (min-

utes),

T total amount of productive time that each employee has,a constant that represents the production function using the information

resource,b constant that represents the production function using the time

resource,

n branching factor of the organizational tree,k constant that determines the cost of compressing the information,

³…¬; X† information compression function ³…¬; X† represents the time (in min-utes) that it takes to process the information (i.e. read, delete and edit

the messages). This function is de®ned as:

³…¬; X† ˆ C1X ek 1=¬¡1… †± ²

: …1†

In the case when ¬ ˆ 1, C1 represents the time to read each message.This function increases exponentially as the compression functiondecreases, treating information as compressible matter. (This function

can vary between organizations, and currently the authors are conduct-ing a study to de®ne the shape of this function in high-technology

organizations.)F… † the information expansion function F( ) represents the time that it

takes to expand the information (i.e. write new messages). This func-tion is de®ned as follows:

¿… † ˆ C2¢ log2

…1 ‡ †: …2†


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Figure 1. The information reduction function ³…¬; X†.

Figure 2. The information expansion function F… †.

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This function assumes that the e� ort to create new information ismarginally decreasing, as higher amounts of information could beduplicated with less e� ort.

Figures 1 and 2 present the information processing and expansion functions foran example in which C1

ˆ 2:0, C2ˆ 40, k ˆ 1=10 and X ˆ 50. Note that the real

value of the parameters has been estimated from responses that the authors receivedfrom industrial partners. There is still a need to conduct a large-scale survey amongvarious types of organizations in order to estimate the parameters more accurately.

3.1. Case I: homogeneous organization (type I)Two assumptions (that will be relaxed later) are made in this case:

(1) All nodes at all levels of the organization have the same information pro-cessing properties, ¬ and .

(2) The production function is identical at all levels of the organization. Thus,employees at every level produce the same output from each unit of infor-mation and each unit of time available.

3.1.1. Analysis of top levelThe time that the top-level manager is productive, given that this manager

received information volume of X, is:

T ¡ …³…¬0; X† ‡ ¿… ††:Hence the productivity at level [1] is:

P‰1Š ˆ Xa ¢ …T ¡ …³…¬0; X† ‡ ¿… †††b:

The productivity at the second level (level [2]) is:

P‰2Š ˆ P‰1Š ‡ …n ¢ …¬X ‡ †a ¢ …T ¡ …³1‡ ¿1

††b†

where

³1ˆ C1

¢ …¬X ‡ † ¢ …ek 1=¬¡1… ††

and

¿1ˆ C2

¢ log2…1 ‡ †:

The amount of information that the various levels receive, based on this model, is asfollows.

Level [1]: XLevel [2]: ¬X ‡ Level [3]: ¬

2X ‡ ¬B ‡ Level [ j ¡ 1]:

X‰ j¡1Š ˆ ¬jX ‡ …1 ‡ ¬ ‡ ¬

2 ‡ ¢ ¢ ¢ ‡ ¬j¡1† ˆ ¬

jX ‡ …1 ¡ ¬

j†1 ¡ ¬

:

The general data compression function at level j is:

³jˆ C1X‰ jŠ…ek 1=¬¡1… ††:

While the general data expansion function remains the same: ¿jˆ C2 log2

…1 ‡ †.


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The general production function at level j is a recursive equation of the followingform:

P‰ jŠ ˆ …nj¡1…X‰ jŠ†2…T ¡ ³j

…X‰ jŠ; ¬† ‡ ¿… ††b† ‡ P‰ j¡1Š:

The production function at the lowest level (level m) is:

P‰mŠ ˆ …nm¡1…X‰mŠ†a…T ¡ C1X‰mŠ†b† ‡ P‰m¡1Š: …3†

This is due to the fact that the lowest level does not need to generate informationanymore.

3.2. Case II: semi-homogeneous organization (type II)In this case, each level uses di� erent compression and expansion coe� cients. This

is due to two reasons: ®rst, various levels of organization tend to vary in terms oftheir information processing. Higher level management tends to generate more infor-mation than lower level technical sta� . Secondly, by allowing each level to optimizeits behaviour, a better globally optimized organization is formed.

The general production function at level j is:

P‰ jŠ ˆ P‰ j¡1Š ‡ nj¡1…X‰ jŠ…¬j; j

††a…T ¡ …³j…¬j; j

† ‡ ¿… j†††b

: …4†

The only di� erence in this case is that the parameters ¬ and can vary for each level.

3.3. Case III: non-homogeneous organization (type III)In this case, a more realistic assumption governs the production function: the

higher levels of the organization place more importance on generating information(such as instructions and directives) than utilizing the time availability. In the lowerlevels of the organization, it is more important to use the available time productively,than to process the information received.

Thus, in case III, the production function will use di� erent coe� cients a and b ineach level such that aj

¶ aj‡1 while bjµ bj‡1 when j ‡ 1 is one level lower than level j.

3.4. Validation of the modelIn order to support the quantitative description of the information ¯ow, a pilot

study was conducted in a high-technology communication company. The studyfocused on the bottom four levels of middle management in the organization. Thestudy monitored the information that was sent and received by those employees,with the following results:

Level % of information createdTop level 9%Middle Mgt. 46%Field Managers 26%Workers 20%

Most of the information ¯ow was downwards (top to bottom) as described by themodel. Only 28% of the information was sent upwards from the middle managementlevel. Almost no information was sent upwards from the lowest level. Thus, infor-mation ¯ow in this organization supports the semi-homogeneous model.

The information ¯ow consisted of 13 types of information: progress reports,review of competition, new sales information, ®eld updates, activity reports,


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manpower issues, marketing information, new products information, sales reports,schedules, software updates, training information and bene®ts information. Theinformation was roughly divided uniformly among those types.

The types and amount of information varied between spreadsheet applicationswith 1 to 10 pages (average 3 pages), text documents with 3 to 50 lines (average of 20lines) and presentation material with about 20 slides.

An additional indication as to the validity of the model is the interest that themodel has created in the military intelligence community. This community is cate-gorized as a type I organization with homogeneous information ¯ow.

4. Optimal information usage using dynamic programmingThis section presents a dynamic programming formulation, which optimizes the

productivity of the three types of organizations.The formulation is as follows.As seen before:

X‰iŠ ˆ ¬X‰i¡1Š ‡ i¡1

p‰iŠ ˆ Xa‰iŠ‰T ¡ ³…¬i;Xi† ¡ ¿… i

†Šb

³…¬i; Xi† ˆ C1X‰iŠe

k…1=¬¡1†

¿… i† ˆ C2 log2

…1 ‡ i†:

The objective function is the overall productivity of the organization:

Max F ˆXm

iˆ1

ni¡1p‰iŠ:

This equation represents the individual productivity at level i, multiplied by thenumber of employees at that level.

The recursive relation among the levels (stages) for any given amount of infor-mation X‰iŠ at level i is:

Fi…Xi

† ˆ max¬i ;Bi

fXa‰iŠ‰T ¡ ³i

…¬i; X‰iŠ† ¡ ¿… i†Šb ‡ nFi‡1

…¬iX‰iŠ ‡ i†g: …5†

This is the combined production when each node at level i chooses ¬i in theinterval [0, 1] and i

¶ 0, while it receives Xi units.In this formulation, the state variable is X‰iŠ: the information that an employee at

level i obtains from his supervisor. In the uppermost level, X‰iŠ represents the initialinformation used by the top manager. This variable must be non-negative. Thedecision variables are ¬i and i, which de®ne the e� ort spent at each level in pro-cessing the information. The variable ¬ should be between 0 and 1 and should benon-negative. An implicit bound on X, ¬ and is such that the expression for nettime bT ¡ ³i

…¬i; X‰iŠ† ¡ ¿… i†c must be positive.

The algorithm starts at level m (the lowest level in the organization) and pro-gresses upwards until level [0] of the top management.

At the lowest level, the objective function is simply:

Fm…Xm

† ˆ max¬m; m

Xam

‰T ¡ C1…Xm

†Šbg: …6†


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Note: The productivity Fi…Xi

† is normalized (i.e. it becomes productivity peremployee (node)).

4.1. Illustrative results4.1.1. Organization of type I

In case I, all nodes in the organization exhibit identical behaviour in terms ofinformation usage. This means that all nodes have the same compression factor (¬)and expansion factor ( ). This may be justi®ed in an organization with stronghomogeneous culture, or among its levels with similar functions (e.g. levels of topmanagement, etc). The results of numerical analyses show that, in this type of organ-ization, the optimal parameters (¬, ) vary for organizations of di� erent depths. Thisis shown in ®gures 3 and 4. These ®gures show an analysis of an organization with®ve levels, a branching factor of 4, and 25 initial messages (X0).

Figure 3 shows that for a single level organization the optimal productivity isachieved at ¬ ˆ 1:0 and ˆ 0. Reducing ¬ as well as increasing causes a reductionin productivity. Figure 4 presents the productivity of a ®ve-level organization. In thiscase, the overall productivity behaves like a slowly decreasing ridge with optimalproductivity at ¬ ˆ 1:0 and ˆ 2.

4.1.2. Organizations of type IITables 1(a,b) and 2(a,b) present the optimal parameters obtained using the

dynamic programming method for various levels of initial information and various`costs’ of processing the information. Each table presents the optimal parametersthat support optimal productivity, as a function of the amount of initial informationX0.


Figure 3. Productivity of the organization at level 1.

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Figure 4. Productivity of the entire organization.

X0

Level 5 10 15 20 25 30 35 40 45 50

1 1 1 0.91 0.46 0.46 0.37 0.28 0.28 0.19 0.192 0.91 1 0.91 1 0.91 0.91 1 0.91 1 13 0.91 1 0.91 1 1 1 1 1 1 14 1 1 0.91 1 0.91 1 1 1 1 15 1 1 1 1 1 1 1 1 1 1

Sensitivity of

Table 1. (b) Optimal ¬ values under moderate cost C1 ˆ 25, C2 ˆ 10:

X0

Level 5 10 15 20 25 30 35 40 45 50

1 1 1 1 1 1 0.91 0.91 1 0.82 0.462 1 1 1 1 1 0.91 0.91 1 1 13 1 1 1 1 1 1 0.91 1 1 14 0.91 0.91 1 1 0.91 0.91 0.91 0.64 0.64 0.915 1 1 1 1 1 1 1 1 1 1

Table 1. (a) Optimal ¬ values under low cost C1 ˆ 10, C2 ˆ 10:Dow

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4.1.3. Sensitivity of the alpha parameter

Tables 1(a) and (b) show that with low cost (time) of optimal information

processing, the optimal value of the parameter ¬ is higher than when the processing

time is higher. As more information enters the system, the lower the value of ¬becomes.

Tables 2(a) and (b) show that when the initial information is very low (e.g.

X0ˆ 5) is quite large, so that enough information is generated to feed the organ-

ization. As the level of initial information increases, decreases.

The tables show that with the increase of processing cost of information, the

amount of information is generally reduced. This is owing to the high cost of reading

each message, as well as writing new messages. In addition, due to the exponentialgrowth in the cost of reducing the data, it is more e� cient to reduce the information

several times by small amounts than a one-time reduction by a larger amount. The

opposite is observed when X0 is small (e.g. X0ˆ 15). In such a case, a one-time

increase of the information is preferable. Furthermore, when the amount of infor-

mation is very large, a drastic reduction is required in order to prevent overload in

the system.

Note: organizations of Type III exhibit similar behaviour, and are solvedoptimally using the same dynamic programming formulation. The only di� erence

is that the aj and bj parameters of the production function at each level need to be

de®ned.


X0

Level 5 10 15 20 25 30 35 40 45 50

1 36 36 36 36 32 32 24 20 12 82 20 12 8 0 0 0 0 0 0 03 0 0 0 0 0 0 0 0 0 04 0 0 0 0 0 0 0 0 0 05 0 0 0 0 0 0 0 0 0 0

Table 2. (a) Optimal values under low cost C1ˆ 1, C2

ˆ 2.

X0

Level 5 10 15 20 25 30 35 40 45 50

1 36 36 36 36 0.46 32 0 0 0 02 0 0 0 0 0.91 0 0 0 0 03 0 0 0 0 1 0 0 0 0 04 20 12 0 0 0.91 0 24 20 12 85 0 0 0 1 0 0 0 0 0

Table 2. (b) Optimal values under moderatecost C1 ˆ 2, C2 ˆ 8.

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5. SummaryThis paper investigated the problems of information overload in a hierarchical

organization. For such systems, the excessive information load caused a reduction inthe productivity of individual employees as well as the entire organization.

The paper presents a model that links the productivity of an individual in theorganization with the amount of information received and processed. The decisionvariables are the amount of processing that each individual can perform on theinformation. The processing is of two types: reading and deleting information,and composing and distributing new information. The model is expanded to repre-sent the overall productivity of the organization as a function of the informationprocessing activities and costs, and information quantity that ¯ow down the hier-archy.

The model is applied to three types of organizations: a homogeneous, semi-homogeneous and a non-homogeneous organization. For the ®rst organizationtype, employees at all levels have the same `cost’ of processing the information. Inthe second type, each level had di� erent information processing parameters, but withthe same productivity function. The non-homogeneous organization producedhigher productivity of the information resources at higher levels, but higher produc-tivity of the time resource in the lower levels.

This productivity model is solved optimally using a dynamic programming for-mulation. This solution maximizes the overall productivity of the organization, as afunction of the behavioural parameters ¬ and that represent the processing activ-ities of the information. The experimental results clearly show that, with a highercost of information processing (in time units), a lower amount of information should¯ow in the organization.

The results of the model are very general and can be used to ®t many organiza-tions. By changing the information processing costs, and even the cost functions, themodel can be made to ®t many di� erent organizations. By using actual measuredcost parameters (time to read and write information) the model can be tailored to aspeci®c case.

Currently, the project is being expanded and a detailed cost study is being con-ducted in a high-technology communications company and a military organization.

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analysis of information flow in hierarchical organizations

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