Shannon Entropy Applied to the Productivity of Organizations. Why Big Organizations Can Seem Stupid

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1 The Aalytic Solutios Group, LLC Shao Etropy Applied to the Productivity of Orgaizatios Why Big Orgaizatios Ca Seem Stupid Dr. Rich Jaow November 4, 2003 New Jersey Istitute of Techology, Departmet of Physics Newark, New Jersey Pricipal, The Aalytic Solutios Group, LLC 514 North Wyomig Aveue, South Orage New Jersey, Copyright 2003 by R. Jaow

2 Itroductio ad Summary The Aalytic Solutios Group, LLC Whimsical origi: big, stupid orgaizatios Aecdotally, size seems to kill decisio efficiecy Legtheig decisio times with growth Culture shock goig from small -> large, especially M&A Idividuals ca seemigly over-ru orgaizatio s capacity to respod. Maybe effects are a symptom of some fudametal limit? Cojecture: The maximum rate at which a orgaizatio ca assimilate ad use kowledge (decisio flow rate) is limited by the structure. Fudametal limit due to structural etropy of decisio / cotrol etwork. Maximum decisio flow rate grows slower tha orgaizatio size. Per capita rate falls with size as 1 / log 2 (). Simple model, odes. Potetially importat for orgaizatios domiated by complex cogitive tasks & teamwork. May drive competitiveess i certai markets. Objectives: Quatify orgaizatioal etropy ad max decisio flow rate. Develop quatitative tools to help re-egieer structure for more efficiet kowledge- maagemet work Validate model. Whe is the limit actually reached i practice?

3 Some Iformatio Theory (Shao) The Aalytic Solutios Group, LLC Where is a upper limit o capacity tied to a etropy? Iformatio theory: Shao s fudametal theorem for a oiseless commuicatio chael* A commuicatio chael drops symbols if it is ru above a maximum trasmissio rate. S = max symbol trasmissio rate (symbols/secod) bits = elemetary quata of iformatio C = chael capacity (bits/secod), raw data trasmissio H = etropy of source or sik (bits/symbol) usig best codig Iformatio, etropy, ad choice: Physics: etropy measures choice of states (Boltzma H Theorem) Iformatio theory: etropy measures choice i symbol occureces Classic fuctio: H = - k S = C / H pjlog 2(p j) *Shao, Claude E. ad Warre Weaver: The Mathematical Theory of Commuicatio, Uiversity of Illiois Press, 1998, Reprited from the Bell System Techical Joural of July ad October j= 1

4 Model for decisio processes The Aalytic Solutios Group, LLC Orgaizatios are aalogous to commuicatio chaels but decisios flow rather tha symbols. Decisio etwork of maily huma odes. NO relatio to PHYSICAL comm. etworks Maagemet decisios related to complex cogitive tasks flow betwee odes. No differetiatio amog decisios based o importace or impact. Dits = quata of actioable iformatio. Decisios ca be reduced i priciple to biary choices. No coectio to represetatio as symbols. Assume: humas ca assimilate choices oly so fast; i.e., they have fixed maximum dit rates R() is the maximum rate of trasmittig biary choices i [dits/uit time] for the whole orgaizatio. Orgaizatio structure offers choice i collaboratio (etropy) Large decisio flows ted to require may collaborators (cotet iformatio flow proportioal to structure iformatio). A() is the average umber of dits/decisio icludig structure ad cotet factors ( decisio complexity ) The maximum decisio rate measures what ca flow, ot what idividuals produce i isolatio: M() Per capita: µ( ) R() A() M() Orgaizatioal etropy: Is extra iformatio used by the choice i collaboratio partitioig tasks to kowledge maagemet odes Icreases as orgaizatioal structure grows i size ad complexity, eablig broader collaboratio Large etropy is the price of a broad, geeral purpose orgaizatio Smaller etropy improves efficiecy but arrows the scope of tasks.

5 Proposed Quatificatio The Aalytic Solutios Group, LLC Maximum raw decisio flow rate for the orgaizatio [dits/uit time] R () = i= 1 R i () = i= 1 j= 1,j i ρ i,j Orgaizatio structure switch toggles flow from i to j o or off R 0 i, j i= 1 D i Maximum dit flow rate over path from i to j, may deped o experiece Saturatio limit for i th ode: idividual s limits reached, all effort possible spet o collaborative decisio flow Average decisio complexity for the orgaizatio [dits/decisio] Coditioal probability of choosig to sed a message to ode j from ode i Quatity of structure iformatio for the choice A() = A () = A H = A pi(j) log 2(pi(j) ) i= 1 i i= 1 0i i 0i i= 1 j= 1,j i Average decisio complexity of tasks at ode i icludes collaboratio frequecy over the orgaizatio etwork [decisio -1 ] assume rough proportioality of cotet flow ifo to structure ifo Etropy of the probabilities that ode i sees: measures dits of structure iformatio. Tedious to evaluate: requires may parameters plus structure detail

6 Approximatio: Equivalet Nodes The Aalytic Solutios Group, LLC Approximate the orgaizatio as a set of comparable decisio-makers collaboratig o comparably complex tasks Structure effects separate, absolute measuremets of coeffciets ot eeded (comparative studies) Oe specific topology (defied by ρ ij ) used whe evaluatig M. M() = M Dimesioless form factor depeds oly o orgaizatio structure (effective umber of odes) 0 i= 1j= 1,j i pi (j) i= 1j= 1,j i ρ i,j log (pi 2 (j) ) where M Maximum decisio flow rate per ode, measure of task complexity 0 R A 0 0 Approach Split real orgaizatios ito layers ad subets cosistet with above Develop stadard sets of decisio rates M 0, M 1, M 2 & assig to layers

7 Further approximatio: Fully Coected Orgaizatio The Aalytic Solutios Group, LLC All decisio makers collaborate with equal probability Exactly solvable Maximizes the etropy Realistic for small groups Etropy ~.log 2 () is proportioal to average sortig time M () = M 0-1 log 2(- 1) S - 1 log ( - 1) M0 log 2 () for large S UNSATURATED {M0 S M0 for large > S SATURATED 2 log 2() Per capita cap o efficiecy falls off as 1 / log 2 () due to etropy whe saturated it falls off as 1/.log 2 () [collapse] Growth of a orgaizatio ca impair productivity, adjust structure to limit etropy impact = 3 is smallest orgaizatio for which model works Saturatio meas most idividuals ca ot keep up with flow of choices. Oset for > s ~ D 0 / R 0

8 Relative values of max decisio rate per capita versus size fully coected The Aalytic Solutios Group, LLC FACTOR OF Per capita decisio rate (relative) No Saturatio Saturatio at N = 10K Saturatio at N = 1000 Saturatio at N = 100 Saturatio at N = 100K ,000 10, ,000 1,000,000 = Number of decisio-makers

9 Applicatios The Aalytic Solutios Group, LLC Qualitative isight, support for familiar re-egieerig rules (see ext slide) Relative but quatitative measures used with rules ad guides.* Fully quatitative tool, optimizig structure for efficiecy Use as compoets of cost fuctios (LP techiques)* Need absolute measuremets, detailed structure Outlie of a process to apply*: Map the structure; break orgaizatio ito homogeeous layers if applicable. Evaluate tasks by type, fit ito a taxoomy. Evaluate limit M() usig approximatios as applicable ad M 0, M 1, M k kow from bechmark studies Estimate actual average decisio rates by task, via observatio. Add all the terms to estimate actual total decisio rate Compare: Is real orgaizatio pushig the limit? If so, apply re-egieerig rules (see list) or possibly optimize structure. *Patet applied for

10 Some re-egieerig rules ad methods (overlappig) suggested by the model The Aalytic Solutios Group, LLC Reduce choice, sparsify decisio paths, streamlie processes. Create dedicated, stable workgroups with commo task & culture Defie workflows, cross "silo" boudaries, follow customer-cetric processes. Match orgaizatio size to task complexity Critical mass is eeded but oly as decisio complexity demads. Multi-purpose orgaizatios give up efficiecy Use differet orgaizatio structure for kowledge-based versus productio or operatioal activities. Idustry architecture i KM sesitive fields may require small uits. Use "iformatio hidig" aggressively. Icrease abstractio so that idividuals work more idepedetly ad make less frequet but higher-level decisios. Layer orgaizatio by level of decisio abstractio Use kowledge maagemet systems (KMS) to offset large-firm etropy. Share to avoid repetitively coverig the same groud. Retrieval efficiecy essetial to achievig gai Alter the rewards system: decouple maager's rewards from orgaizatio head-cout..

11 Ogoig Iterests The Aalytic Solutios Group, LLC Broade experiece with practical applicatios Measure ad/or estimate modelig coefficiets Taxoomy of task complexities ad decisio rates via ratigs Use small groups to measure the model costats (M 0, A 0 ) Methods for measurig dit rates (R 0 ) Recogize whe the effects are beig observed Sigatures, estimates Work with potetial beeficiaries: Military C 3 I, sesor fusio, battle maagemet. Well structured, clear decisio structure. Cosultig, egieerig, R&D, firms whose product is itellectual property. Those eedig to use skilled huma resources efficietly. Receptive to: Ogoig opportuities for validatio, practical experiece, advacig theory Cliets, applicatio parters, R&D cotracts, & licesees

12 About the author The Aalytic Solutios Group, LLC Rich Jaow is the pricipal of The Aalytic Solutios Group, LLC, cosultig with govermet, idustry, ad academic orgaizatios. He ejoys cross-discipliary problems at the itersectio of busiess ad techology strategy, R&D, iformatio systems, ad physical sciece. He is also a faculty member i the Applied Physics Departmet at New Jersey Istitute of Techology. Dr. Jaow s associatio with advaced techology markets, roadmaps, strategy, assessmet, techological forecastig, ad futures icludes 18 years at Bell Laboratories, 4 years as a executive i a high techology compay, ad applied research i computer sciece, codesed matter ad surface physics. He holds a Ph. D. from CUNY ad a A. B. degree from Columbia College, both i Physics, ad resides i South Orage, New Jersey. He may be reached at jaow@att.et, jaow@jit.edu or by phoe at (973) The Aalytic Solutios Group, LLC Techology Strategy ad Assessmet Market Impacts Roadmaps Rich Jaow, Ph. D., Pricipal 514 North Wyomig Aveue, South Orage NJ jaow@att.et