Consistency and Optimality in Managerial

8/12/2019 Consistency and Optimality in Managerial

1/13

CONSISTENCY AND OPTIMALITY IN MANAGERIALDECISION MAKING*'*E . H. BOWMAN

atsachuse a nstitiUe of Techn ologyThis pai>er reports some research, ideaa, and theory about managerialdecision making. The first research projects dealt with are aggregate produc-tion and employment scheduling. From this is developed the idea that man-agem ent s own (p ast) decisions can be incorporated into a system of imp rovingtheir present decisions. D ecision rules are developed, w ith the coefficients in therules derived from m anagement s pas t decisions (rather than from a cost orvalue model). Half a dozen trat cases are used to illustrate and test these

ideas (theory). Some rationale about decision making in organizations andcriteria surfaces ia supplied to help interpret th e major ideas presented .This paper reports some research in managerial decision making, as well asthe ideas and a theory stemming from this research. Presented here is a combi-nation of description and prescription. It combine the talents of the managerwith those of the analyst in a method and in a theory. The method is pragmaticrather than Utopian in that it offers one way of starting with the managers'actual decisions and building on them to reach a better system.A referee has summarized this paper as follows: th a t managerial decisionsm i ^ t be improved more by mairing them more consistont from one time toanother than by approaches purporting to give 'optimal solutions' to explicitcost m o d e l s . .. especially for problems where intangibles (run-out costs, delaypenalties) must otherwise be estimated or assum ed. Though this is a norma-tive statoment, it is derived from a number of descriptive concepts (about theworld in which we live) which may be of equal interest.The paper is organized essentially in the sequence in which the research wasperformed and the ideas generated. The problems, research, and decision rules

of production scheduling are set forth first. They introduce the cause of thispaper. Next, the approach of usii^ management's own past decisions in orderto improve present decisions is described. The theory is then set forth in a moregeneral form, after which several additional empirical tests of the theory aredescribed. Finally, the ideas are summarized. Further questions of validity,generality, and operationality must be answered by future research.* Received M ay 1961. Draft of a paper given at the Conference on Factory Scheduling at Carnegie Institute s

Graduate School of Industrial Administration, May 12,1961. The research underlying this paper was in part sponsored by the MIT Operations

Research Center contract with the Army Office of Ordnance Research (DA-19-Q20-ORD-


2/13

AND opmiALiTr IN UANAGEBIAL DECISION UAKING 311Praduc t io i i Schedolmg Dec i s ion Rules

The research which led up to tiie more basic ideas presented here dealt withthe general problem of production and employment scheduling. This work isset forth in some detail in order to convey the spirit of the research.A very simple decision rule for production scheduling might be:

P . = -S,where Pt represents production scheduled in time period t, and St representssales expected in time period /. In this case production would match all fluctua-tions up and down in sal^, and the rule might not be considered a very goodone. An extension might, be:

Pt= St + xiP^i - St)where is a decision rule coefficient to be specified between zero and one, andPt_i represents production in the previous time period. Ifa = 1, then the salesterms cancel out, a nd production ia th is period equals production in the previoustime period (i.e., w ith no fluctuation). A value for xbetween zero and one willsupply a damping mechanism in this case, where production does change butnot a s qu ickly as sales.*

However, Siog this iU e (where production d o ^ no t necessarily matc h saleseach period) would cause inventories to fluctuate. In order to offer some con-trol of these inventory levels the rxile may be further extended:P, = S, + xiPt-i- St)

wherey is also a decision rule coefficient to be specified between zero and one,IK represents a concept of N or m al inventory (possibly an easier label tha noptimum inven tory), andIt-i represents the amount of inventory at the end ofthe previous period.Because it is desirable to take into account the anticipated future sales (inthe near term), the rule should be extended further:P. = i:Zl* aiSi+xiP^i - St)

with the Oj's representing weighting coefficients of the sales forecasts, i, forfuture periods.While such a decision rule could be further extended and elaborated, thiswill suffice for our introduction. The production scheduling behavior of a firmfollowing such a rule would be critically influenced by the numbers suppliedfor the coefficients, Oi a, a;, y, and In (which m ay be conceived of as anumber for the moment). Different sets of numbers in the coefficients wouldresult in different behavior patterns through time. Some patterns would un-doubtedly be preferable to others. The challenge, of course, is to determine the


3/13

3 1 2 E. H. BOWMANpr^erred set of coefficients. Three methods for making this determination arelisted bdow:1) Simulation (experunentation)2) Analysis3) Management DecisionsSimulation seems to require no justification at present. Many uses are beii^made today of this activity in universities and in industry,^ particulaiiy wherethe mathematics of a more deductive solution scheme break down. Mathe-matical analysis may be possible even in problems as complex as this.' Forindustrial problems which are framed in less complex form ma them atical analysisis not imcommon. A different source (management decisions) for these decisionrule coefficients is developed later in this paper.

The HMMS Dec is ion RulesThe production and employment scheduling problem faced by most manu-facturing firms, where in each scheduling period bo th a production qua ntityand an employment level must be chosen, has been analysed in researeh workby H olt, M od^ liani, Mu th, and Simon (HMM S) on a paint company. Workingwith quadratic cost forms, and a long term scheduling horizon the followingproduction and work force rules were derived:Ft = -f .463Ot + .993Wt..i + 153 - .464 It-i

-f.234Ot i+.111Ot i

: Ot nW, = +.0101 0 , +.74 3Wt-i + 2.09 - .010J ...i

+.0088Ot i+.0071Ot i

: Ot+nwhere the subscripts are time period notation, P stands for production, W forworkers, 0 for sales oMers, and I for inventory. The analyses leading to thesedecision rules are quite involved and will not be described here, as it is notessential to the major ideas presented in this paper. They may be found in theliterature.

See for a large example Jay Forrester, Industrial Dynamics, M IT Press and JohnWiley, 1961. See especially Ho lt, Mod igliani, Muth and S imon, Planning Production, Inventories,and Work Force, Prentice-Hall, Inc., 1960.* A Linear Decision Rule for Production and Elmployment Scheduling , by Holt,Modigliani, and Simon, Management Science, October 1955, and D eriv atio n of a LinearDecision Rule for Production and Em ploym ent, by Ho lt, Modigliani and Mu th, Manage-ment Science, January, 1956. Reprinted inAnalyses of Industrial Operations, Bowman and


4/13

CONBKTBNCT AND OPmC ALITT IN HANAGEBIAL DECISION i fAK INa 3 1 3It is important to explain, however, that the rule nd the coefficients^thenumbers .463, .993, 153, .464 ^werederived by mathematical analysis fromthe cost structure model of this one paint factory studied. Had the companyfollowed these rules, the physical behavior pattern and, therefore, the costs ofthe behavior would hav e been different. Th e H M Ik ^ group present th e followiognormalized summary cost data for thrte cases:

Paint Company

Decision Rule (perfect forecast)Decision Rule (moving average forecast)Company Perfonnance(cost base about 13,000,000)

1M9--53(Korean War induded)

100%110%139%

1952-54

100%108.5%

Since the decision rules require estimates of future sales over the next 12months, both the actual sales (now known and entitled perfect forecast), and amoving average forecast (entitled naive forecast) were used to reconstruct thebehavior of the system over the years listed. The total costs (normalized to100 ) for the company 's own behavior, and th a t from the decision rules, is^v en . It can be seen tha t th e decision rule consistently used would have shownan appreciable cost saving.

uc-Other App l i ca t ions

In our research, we applied the H M M S analysis previously cited to the produc -tion and employment scheduling problems of an ice cream company,^ a chocolatecompany,* and a can dy com pan y.'The results, in the same form as before, were as follows:Ice Cream Chocolate C u d y

Decision Rule (perfect forecast)Decision Rule (moving average forecast)Company P erfonnanceApproximate Cost Base

100%104.9%105.4%$500,000

100%102.0%105.3%(150,000

100%103.5%111.5%$1,500,000

With less mai^in of improvement, it appeared that the linear decision rules,derived from the q uadra tic approximations to the costs structures of each fr mmight have r^ulted in the cost savings shown.' An App lication of a Linear Decision Rule for Production and Em ployment Schedul-ing by Rien T. van der Velde, an M IT Master's thesis, 1957.' An Empirical Stud y of Actual and Optimum Decision Rules for Production and Em -ployment Scheduling, Wallace Crowston, MIT Ma ster's thesis, 1958.


5/13

314 E. H. BOWMANBehavicn* an d St at i st i ca l R egrm sion

Hie author of the chocolate comfMtny thesis was requested to do a statisticalleast squares r^ression of the company's actual scheduling behavior against thelinear decision rule. He added another variable, sales contracted iat the next6 m onths, and used a sales lev d which was derived from exponentially w e i^ te dpast sales. For the Wt rule he obtained a multiple correlation co^cient ofr = .971. For the P rule he obtained a multiple correlation coefficient of r =.87. In other words, theform of these rules gave a pretty fair indication of thechocolate company managers' decisions. That is, the managers were sensitiveto these same variables in their decision be havior.

We then did a graphical multiple r^ression for the candy company usingthese rules (with a single sales leve l figure). Again we obtained a fair correla-tion with the addition th at more inventory was tole rated in the busy half oft h e y ^ r .

Next for all four companies^paint, ice cream, chocolate, and candy^wedid a statistical least squares regression for the company management schedulingbehav ior on tiie open form of the decision rules, e.g.,P , = o + 6i^i + hSt + hSi + 54^4 + hSt + htWL 1+

regressions gave us rather poor results. The sales estimates, ,werehighly correlated, and thettests on the coefficients came ou t pooriy.W ith advice concerning regression, Use all the good restrictions you haveyou 'll get bette r estim ates, we were able to use the feed back form (modified)of the original decision rules.'The versions of the decision rules developed for r^ression were:

AWt= bi[B^ - {SlW)Wt..i]+ h[St{Il8) -Ft = bzWt+ b4[(Tr/S)Sw - Wt]

where W, F, and J are as given before, Strepresents actual sales in the currentperiod, 8t-* represents average actual sales in the next three periods, and S,W , and / represent averages of th^e variables over the total period of invrati-gation. These rules are a bit simpler though they follow from the feed backrules which Yance provra equivalent to the Carnegie rules. Th e exact form of therules is not important for this paper, though the modification using variableswhich are the normalized differences between variables, e.g., [


6/13

AND O F H U A U T T I N MANAGEKIAIi DECISIO N MAKING 315CostibngT he Regression R ules

With tbe feed back production and employment scheduling rviks and withthe coefficients developed from managem ent s own schedu lii^ behavior, i t waspossible to reconstruct (mmulate) the companies scheduling behavior followingthese rules (with moving a v e n ^ forecast) as was done in the oH ^nal work.The r^ u lt s are as shown in the table.Ice Cream Chxxdate u y Paiot

Decision Rule (perfect)Decision Rule (move.av.}. . .Company PerformanceManagement CoefficientsCorrelation

100%104.9%105.3%102.3%Wt,r- .78Pi.r- .97

100%102.0%105.3%100.0%Wt,r~ .57P,,r - .93

100%103.3%111.4%124.1%t,r .73, , r - .86

100%110%139.5%124.7%I T , , r - .40P . , r - .66

As can be seen from the table, in all cases bu t th e candy company, using th edecision rules with the coefficients supplied by regression of mana^ment s ownbehavior, and a rath er simple estimating scheme for future sales, the costs wouldhave been less than the company s actual behavior. In the Ice Cream Companyand the Chocolate Com pany, it would hav e been even cheaper tha n th e decisionrule derived from the standard quantitative analysis and the same sales fore-casting scheme.Several points of explanation may help. It is suspected that the somewhatsurprising results of better performance with the m a n a ^ rs coefficients than th a tsupplied by the analysis is due to the fact that the analysisis optimum only inthe sense that the quadratic cost models from which the rules were derived is aperfect fit for these costs. Th is, of course, is no t the case. I t is impor tant to keepin mind that optimiz tion is always of a (mathematical) model, which hopefullybears some resemblance to important facets of the real world. The graphicalmultiple regression done earlier on the candy company (the refuting case here)suggests that had the split inventory policy between slack and busy times ofthe year been permitted in the rule, the then adjusted m ana ^m ent coefficientsrule would have been better.

The Management Coeff ic ients TheoryAn attempt at something like an axiomatic treatment of these concepts ispresented in order to stimulate more ideas:1) Experienced managers are quite aware of and sensitive to the criteria ofa sj^tem. U sing a perfect sales forecast would have reduced this to 112.5%. T his figure must be viewed with some reservation as we were working w ith the publica-tions and working papers from H MM S, not the data as such . We could not reconstruct some


7/13

3 1 6 E. H. BOWUAN2) Experienced managers are aware of the ^jrstem 'variables which influencethese criteria.3) Managers, in their present podtion through a process of natural screenii^,make decisions, i.e., implicitly operate decision rul^, with a sense and intuitionwhich relates the variables to the criteria imperfectly but more err tic th n

bi sed4) Most cost or criteria surfaces as a function of the decision variables areshallow, dish-shaped at the bottom (top) and even with bias in the mana^r'sbeha'vior, it is the far out (variance) examples of beha'vior which are reallyexpensive or da m ^ ii ^ .5) If manner's behavior had paralleled the decision rules with their averageor mean coefficients, their experience would have been better according to thetheir) criteria.It seems useful to attempt an explanation of why decision rules derived frommanagement's own avera^ behavior might yield better results than the aggre-gate behavioritself M an seems to respond to selective cues in his environmentparticular things seem to catch his attention at times (the last telephone call),while at other times it is a different set of stimuli. Not only is this selectivecueing the case, but a threshold concept seems to ap ply. He m ay respond n ot a tall up to some point and then overrespond beyond that. It is this tjrpe of be-havior which helps explain the variance in the organization's (or its manage-ment's) beha'vior.Departure of the decision making behavior of management from the pre-ferred re sults, in this sense then can be divided or factored into two com ponents,one which in the manner of a grand average departing from some preferredfigure, we call bias (which causes a relatively small criteria loss due to the dishshaped bottom of the criteria surface), and one which representing individualoccurrences of experience departing from the grand average, we call variance(which causes larger criteria losses due to the individual occurrences up t he sidesof the criteria dish-shaped surface). It is the latter and more important com-ponent which seems to offer the tempting possibility of elimination through theuse of decision rules incorporating coefficients derived from management's own

recurrent behavior.What can be done with this management coefficients theory?1) It may jdeld fresh insight into a m anagement problem or a decision processit may lead to further ideas. (This is operational in an academic world.)a) Several approaches to the same problem are often of benefit.b) Pa tte rn s of behavior ^^Jiance against the decision rule may point to missedelements in th e analjrsis.c) It pves us a chance to see (indirectly) the criteria through the manager'seyes (or action). Harlow Sha pely, the Harvard astronomer, in reviewing The Universe at argeby H er-mann Bon di, includes It is not the purpose of any scientific the ory , 'vrisely remarks Dr.


8/13

CO N8IST ENC T AK D OFTIMAJUTT IK MA NAGE BIAL OEK IBION MAKING 3 7

2) Sampling in the current system may be possiblee.g., with 10,000 itemsin inventory, maybe the managers will look carefully at 100, and make theneceâry decisions for these 100; the n t h ^ e 100 items (along with their relevantvariables) m ay be used in estimating the coefficients in th e decision rules for the10,000-100 items (an inventory t ^ t case is ^v e n late r in the p ape r).3) Balance the present system stmcturee.g., with many branch plants,it may be possible to arrange a better configuration of plant W K S (a plant sizetest case is given later in the paper).4) Let the manager look at the decision rule with his regression coefficientsand then decide what his decision will be, e.g., run in parallel with joint feedback between manager and rules.5) Decouple the manager, but record his decisions. (This is not seriouslyoffered as a suêstion but just to stimulate ideas). The manager has continualaccess to his changing enviroimient^he makes his decisions^these are filedand this operation (e.g., production and employment scheduling) is deternainedby the decision rule (not his decision). Then periodically the decision rule isupdated from the file of recent decisions. The idea he re is to eliminate t he effectsof the variance in decision behavior, while at the same time permitting thedecision rule to reflect the current environment.6) If the theory can be verified where it is felt that the system criteria canbe measured (as in the cases presented in this paper), then some assurancemight exist for using it where the criteria can't be measured.*'7) Automatic decision making (by computer) to save executive time will re-

quire decision rules with coefficients^these may be supplied by regression.8) At the boxmds of analysis, the new theory may help structure the system.Where aggregation is used in th e analysis and the question is raised a s to whathappens when the clerk breaks open the aggregate, rules with regression coeffi-cients can be supplied. March and Simon,Organizations John WOey and Sons, 1958, p . 209, st at e: ... sincethere is no reason to suppose that anytechnique of decision-making, whether centralized

decentralized, will bring the organization into th e neighborhood of a genuine 'optim um ',the search for decision mechanisms cannot take criteria of optimization too seriously,but must seek 'workable' techniques for satisficing. The exploration of decision-makingtechniques along these lines is stUl in a very undeveloped state... A number of decisionrules for production control and scheduling decisions in individual firms have been de-velopedbut again with only small forays beyond the familiar terrain of optimization.The new theory departs a bit from this familiar terrain. Herbert Simon inThe New Scienceof anagementD ecision Harper Bros.,1961,makesseveral statements relevant to this idea. If the new theory offers anj^thing then the firstquotation is not necessarilytruep.17, (talking abou t operations research) .. . The modelwill call for certain parameters of its structure (the system) to be estimated before it canbe applied in a particular situation. Hence, it is necessary that there be ways of makingactual numerical estimates of these parameters (he is talking about the system not thedecision rules derived therefrom) of suflScient accuracy for the practical task at hand.The second quota tion, however, is cited for reinforcement herep. 18. Fo r the opera-tions research approach to work, no thing ha s to be exactît jus t has to be close enough t o


9/13

3 1 8 E. H. BOWUANThe management coefficients theory is, of course, not without its problems.I t may kill the goose th at lays the golden eggs. Th e manager m ay follow th e rulewith his past (average) coefficients, and not adjust to new conditions as theytake place. M arch andSimon^'make the distinction between a) short run adapta

tion as problem solving (here, using the decision rule as fulcrum), and b) longrun adaptation as learning (here, using the manager to modify decision rules).The problem is how to bypass (a) without inhibiting (b).P lan t S ize

As an additional check on the theory presented here an analjrsis d^cribed inthe perations Research journ al was reexamined. Th e stud y concerned question of the optimum size ice cream plant for a pa rticular company operatingten plants over a seven state area. For purposes here, the analysis need not berepeated, b ut i t led up to a decision rule for th e optimum volume p lant :whereK was the sales density in thousand g^ons per square mile (per year)and b and c were particular cost factors relevant to the ice cresun productionand distribution system. Had the system been restructured accordii^ to theanalysis and decision rule, gross cost savings appeared to be available. Thesealong with t he results of the new theory a re presented in the tab le.

OriginalRegression (first model)Regression (naive model)F. P. = (^)(26/c) V - (^) diV ~ a + d^

Savings

$207,000$133,000$20,000Using the sam e decision rule from (with iK)^ * as the Independent variableand p ermitting no intercept, a = 0), the company's actual plant volumes wereused to estimate di , th e decision rule coefficient. Had t he plan t system thenbeen restructured using their own (behavior) coefficient in the decision rule, the

projected gross cost savings would be $133,000.For test purposes a naive decision rule, V a + dtK, was used in the samemanner^it included the relevant variable, sales density, bu t not to th e righ tpower, as well as permitting an intercept o. Here aand dtwere estimated fromthe actua l plants, an d a s can be seen the savings are q uite small. In othe r words,anyold decision rule will not do.I t is certain t ha t th e most simple, V = V,i.ehave all plants th e average size, would ha ve been m ore costly for th e firm thanthe present arrangement.It is interesting to note that the naive rule actually gave a better fit to thedata. While it is the cost savings rather tiban the good fit which is the choicehere, if a collaboration were now in existence between the analyst and the


10/13

CONSISTENCT AND O P T H C A L I T T IN K N GEBI L DECISION M KING 3 1 9

managers, this point would be worthy of discussion and reflection for bothparties. TTiat is, the new theory might be a very useful part of a more generalanaljrtic procedure, rather than beingdire tlyprracripthre.Idlewild Aircraft Spares further check was made on the new theory using the basic work of a thesisdealing with a spsire parts inventory maintained at Idlewild Airport. Waitingline theory had been used for the inventory analysis with an n channel servicefacility for n pieces of an item. An idle channel corresponded to an item instock; a busy channel corrraponded to an empty space; no queues were allowed.For the management coefficients theory test, an extremely simple decisionrule was developed:** Spares = a hx

, useage during repair cyclewhere: x = ..T , . , umt pnce of itemThe thesis studied in some detail ten stock items of widely scattered char-acteristics. For our purposes, the results are shown below.

InvestmentStock-outs in 6 years

Compuij Actual$17,000186

Thesis Analytis$16,00069

New Theory$16,500143

From this small sample, at least, the simple decision rule with the coefficients(a and b) would have saved half as much investment and one third as manyrun outs as the analysis. No more detailed analysis was made here.Other AppUcations

In a very detailed study of equipment replacement policies in the truckingindustry,^ a number of conclusions supporting ideas presented here are found.A well accepted modeF was used witii empirical data from industry studio.The following items were determined:A. Estimates of obsolescencea) carrying capacity of trailerb) internal combustion engine technology Giyora Doeh, Overhauled Spares Inventory for Aircraft Components, MIT Mas-ter's thesis, 1958. For an incremental approach:A Cost - A GainUnit Cost (A prob) (run out cost)Let A proba (I/spares) (useage), with tail of hyperbola a rough approximation to tailof poisson distribution.Then, Unit Cost a (useage/spares) (run out cost) and Sparra a (useage/unit cost)(run out cost)


11/13

E H BOWMAN

B . Estimates of operating costa) fuelb) maintenanceThe study resultod in very fiat curves of total yearly average value as a func-tion of equipment life. Replacement anywhere between 2.2 years and 4.4 yearswill lead to losses of a t most $50 sho rt of ex ac t optim um. Sm ith reports: Th is is a remarkable result especially when one considers th at on the averageabout of the total investment of trucking firms is in the form of tmcldngequipment (i.e., capital goods of intormediato durability requiring regularmaintonance). I t would seem th at this of aU industries would find equipmentrepl cement policies of considerable importance, yet precision in such policiesturns out to be of minor significance. It is not argued that it makes no differ-ence when equipment is replaced. Rather the point is that profits are not suffi-ciently sensitive to replacement that the firm is likely to miss the optimumby a costly margin even when using relatively crude methods of analysis.He also states that an optimum service period of 3 to 4 years is about 1 to 2years shortor than the actual replacement behavior of the firm in question.He then goes on to explain that delayed replacement in ^ect is a relaiively cheapsource of c pit lforthisfirm This is equivalent to saying that the managementsenses a somewhat different critoria surface than his analysis explicitly considers.Regression of behavior should permit this sensing to be incorporatod in thedecision rule.A good deal of interest today seems to exist in heuristics and managementproblem solving. While these processes may be largely programmatic andqualitative, some coefficients are embedded therein. The question of how far togo down some path or how many of these parts to combine may still requireparameters. Where this is so, observation and regression of experienced problemsolvers may be helpful.For a case in point, a thesis student has been working on heuristics for a dis-patch ing rule to be associated with a key process in an aircraft pla nt. Thequestion involves the order in which waiting parts should proceed through theequipment. He has identified four characteristics (e.g., cost, due dato) of thepa rts w hich are relevant for thi s sequencing (dispatching ). He needs coefficientsto weight these charactoristics. Simulation had already occurred to him. Heagreed that analysis, at least conceptually, might be possible. The new theorysu^ests to him that he might obtain from the shop the actual dispatching de-cisions by the men directly involved on a long list of parts along with theircharac teristics in o rder to do a regression for the weighting coefficients.

Th e managem ent coefficients theo ry says something about t he behavior ofmanagers and their organizations. There seems to be no apparent reason whythese ideas should apply to production only and not marketing, or industrial


12/13

CONSISTBNCT AN D OPTIMALITT IN MANAGERIAL DECISION MAKING 3 2

S u n u n a r yThe gist of the management coefficients theory is a relatively simple notion:a) In their decision making behavior, managers and/or their organizationscan be on eived of as decision rule coefficient ^timators, (not that they ex-plicitly recoefficient es tim ato rs).b) I t is the variance ia the decision making rathe r th an th e bias th at hu rts dueto dish-shaped criteria surfaces.c) A decision rule with m ean coefficients estim ated from manag em ent s be -havior should be better than actual performance.d) It may be better than a rule with coefficients supplied by traditionalanalysis.e) Systematic and comparative studies using this idea may lead to furtherideas.


13/13

Consistency and Optimality in Managerial

Documents

Transcript of Consistency and Optimality in Managerial