of SomeAspects of fhe Analysis MultipleAlternatives
The logical order of procedure in the case of any new enterprisewhich is, ftrst, to determine whether or not the proiect is a sound one, and to be carried out; and secondly, to make the necessary studies as to the manner of carrying it out-is not necessarily followed in order of time: often it cannot be, for the fnal decision as to the former often depends on the results of the latter, or on un' known future events. Nevertheless, although subsequent events may cause a revision of such assumptions,the mere initiation of the study of details implies a pro-forma conclusion, that the proiect as a whole is a wise one if wisely carried out, and can only fail by bad judgment in details. This premise must be from the beginning, therefore, under all circumstances,the basis of the engineer's action. From this it follows: No increase of expenditure over the unavoidable minimum is expedient or justiffable, however great the probable pro6ts and value of an enterprise as a whole, unless the increase can with reasonable certainty be counted on to be, in itself, a profftable investment. Conversely, No saving of expenditure is expedient or iustiffable, however doubtful the future of the enterprise as a whole, when it can with certainty be counted on that the additional expenditure at least will, at the cost for the capital to make it, be in itself a paying investment.-A. M. Wellingtonl A ffrst step in learning how to reason clearly about choosing among many possible courses of action is to learn how to choose between ftoo alternatives. Moreover, general principles of decision making often are clearer when only two alternatives are involved. For these reasons most 14. M. Wellington, The Economic Theorgol RailwagLocatiur,2d ed. (New York: Inc., 1887),p. 15. fohn Wiley & Sons,
TECHNIOUESFOR ECONOMY STUDIES
ch. 12
Ch. 12
SOME ASPECI!
of the examples and problems up to this point have deart with alternatives in pairs.
special problems or difficulties that difier in any way from the analysis of only two possibilities? The answer to this question ..yes is and no.,, The answer is "No" in the sense that th-e same principres of anarysis apply to multiple alternatives that apply to comparison of only two arternatives. Any multiple-alternative probl"* car, .be analyzed by'considering alternatives in pairs. But the answer is "yes" because it is herpfur to use various mathe_ matical techniques to find optimal solutions f& multipre-alte;native types ^be of problems and because it is desirable for analysts to aware of certain pitfalls and limitations in the use of such t""h.,iq,r"r. err" the answer "Yes" is because certain types of errors in reasoning have been common when either the rate-of-reiurn method or the benefit-cost-ratio method have been used in the analysis of multiple_alternative p-Uil*r.
why Discuss MurtipreArternatives?obviousry, many decisions cail lor a choiceamonga-numberof difierentpropoiars.Dl theseinvolve
2. Cases in which more can be accepted or a limitation in
can be accepted. Sore problem were discussod subsequent chapters. The present chapter
namely, the case in
EXAMPLEI}I. THE Facts of lhe Gaca tions of annualcosts in eters of pipe are unde the lower the friction reduces the necessary amountof energyto In this preliminary pumping stations taksr is attractive rate of return are computed using tho Estimated averageannud The comparison by 12-1. The table indicates equal annual costs. Bdr 14-in.sizes. The choice madewithoutcareful
alternativeproblems into two classes: 1. cases where onry one of the arternatives wi' be serected, usuary (although not always) becausethe arternatives are physicaily mutualry exclusive,A convenientsubclassification is: ( a ) cases where difierencesin estimated cash flows are entirery (or almost entirely) in disbursements. Many design "tt"rn"iiu", and many cost-reduction alternativesare of this type. nxampresr2-1 and r2_2 fall within this group. Although Example I2-r does not invorve any speciarcomplications, it does illustrate a cJmmon state of afiairs in which in in"r"^r"-in required investmentin one praceis acco-mpanied by a decrease required investin t":l i: anotherplace. It arsoiiluitrates the treatmentof incometaxesin a multiple-alternativeanalysisthat is b"r"J o' equivarent uniform annuar costs. Example l2-2 deals with problems that are of great historicarinterest (as well as of continuing applied interese in economy. This exampleis simplified by "ri"g co-parisons -engineering before income taxes. It serves here as an introduction to the use oi mathematicar modelsin dearingwith multiple alternatives. (b) Cases wher..ah"l" are also prospective difierencesin cash re_ ceipts (or in benefits). p""lrig", "-J'g llter.,ate t"u"t, oi development in a new project generaty fat into thii "turr. r*u-pi", rzJ o"a rz_a illustrate,respectively, rate-of-retur' urruiyri, and beneht-"nrt-ruiio ranalysis as applied to this type of problem.
A classificationof Murtipre-Arternative probremsin Engineering Economy. For purposes disc.rssi.n, is helpfur of it to divide murtipre_
Comparloo d
Pipe
A. First cost of pipe line . - -. B. First cost of pumping atrlr C. Total investment
D. Capitatrecovery cost (l. = E. Annuatpipe line mainieid F. Annual pumpingstaton H, Annualproperty taxes l. Extra annualincome J. Total equivatent annualod
-----------
Ch. 12 SOME ASPECTS THE ANALYSIS OF OF MULTIPLE ALTERNATIVES 203 2' cases in which proposals are sufficiently independent so that two or more can be accepted but some constraint (such as u li*it"tion in ffnances or a limitation in manpower ) controls the aggregate of the proposals that can be accepted. some aspects of this common type of capital-budgeting problem were discussgd in chapter rl; other aspects are considered in subsequent chapters. The present chapter is limited to consideration of the ffrst class of case, namely, the case in which only one alter'ative is to be selected.
I ) f
EXAMPLE 12-1. PRELIMINARY STUDYTO DETERMINE THE ECONOMIC DIAMETER AN OIL PIPE LINE OF Factsof the Gase. Tabre12-1 showspreriminary estimates and carcurations of annualcosts in connection with a proposedpipe rine. Four diametersof pipe are underconsideration. The rargerthe diameter the pipe, of the lower the friction loss in the line. An incrlased size ot pipl therefore reducesthe necessaryinvestment pumpingstations and' ieouces in the amountof energyto overcome friction in the line. ln this preliminary study the estimated of both the pipe rine and the rife pumping stations takenas 15 yearswith zerosalvage is vatue. The minimum attractiverate of return is ,13"/" atler income taxes. Incometax differences are computedusing the simprified assumptions exprained chapter 10. in Estimated averageannualpropertytaxes and insuranceare 3o/o lirst cost. of The comparison equivarent by unlformannuarcash frow is shown in Tabre 12-1. The table indicates that the 10-in.and 12-in.pipes have approximatery equal annualcosts. Both are clearrymore economicar than the g-in. and 14-in.sizes. The choice between tne to-in. and 12-in.sizesshourdnot be madewithoutcarefuldetailed cost estimates both. lf such estimates for con_ TABLE 12-1 Comparisonof Annual Costs for Different Diameters of Proposed Oit pipe Line
(All figuresin thousandsof dollars)
PipeDiameler
A. First cost of pipe line B. First cost of pumping stations C. Total investment D. Capital recovery cost (l- - 1}o/o) E. Annual pipe line maintenance F. Annual pumping stalion maintenanceand a t t e n d a n c e. . . . . .
8-in.
10-in.
12-in.
l&in.
$ 9,600 $ 1 2 , 0 0 0 1 4 , 3 0 0 1 6 , 7 0 0 $ $ 3,600 2,400 1,360 700
$13,200$14,400$15,660$17,400 $ 2,043 $ 2,228 $ 2,423 $ 2,693 314 350 350 390 340 820 396 0 225 500 432 142 108 275 470 252 70 140 522 234
G .A n n u au e i t o . i l " t p r . p i " g : : : : : . : : : : : tt
J. Total equivalentannual cost
H . A n n u a lp r o p e r t y a x e s a n d i n s u r a n c e. . . . . t l. Extra annual income taxes over g_in. line
$ 3,913 $ 3,877 $ 3,878 $ 4,049
STUDIES FOR ECONOMY TECHNIOUES
ch. 12
ch. 12 SOME and let
the tinue to show the two sizes as having almostthe same annualcosts, matthe basisolirreducibledata. one important choiceshouldbe madeon in or of would be the possibility an increase decrease flow ter to consider duringthe life of the PiPeline. involvof a ilfusfiaies characteristic many designproblems This example lt investment. will be noted that the larger the levels of ing alternative pumpingplant' in in iniestment the pipe line,the smallerthe investment the are increasedby incosts certain operationand maintenance Moreover, creaseddiameterwhereasothers are decreased' in investment one place will It is a commonconditionthat an increased this else. wheneverpossible, somewhere investment the necessary reduce as total investment has of directlyin the cost estimates shouldbe indicated beendone here. Formulas lor Minimum-Cost Point. Example 12-1 dealt with a case in which cost varied with a certain variable of design, namely, pipe diameter. Some elements of cost increased and others decreasedwith an increasein the value of the design variable. In this common type of case there is presumably some value of the design variable that makes the sum of all costs a minimum. Wherever the variation of cost as a function of a design variable can be expressedby an algebraic equation, it is possible to use calculus to find the value oi the deiign variable that results in minimum cost. During the past two decadesanlntire fteld of scientiffc literature has developed "ro,Iird the simple model illustrated in the following paragraphs. It is referred to as inventory control theory, but it might more properly be called economicinventory management.z The simplest case is one in which one element of cost varies in direct proportion 1o the variable of design, a second element of cost varies in,r"tr"ty as the variable of design, and all other costs are independent of this variable. Although minimum-costpoint formulas may, of course,be developed for situations much more complex than this, some of those that have tiaditionally been used by engineersdid actually deal with situations of this type. A general solution of the problem of ftnding the minimumcost point in such circumstancesis as follows: Let / = total cost
2 The primary emphasis in this text is the presentation of the basic principles and technique-sof "apital expenditure analysis. Since inventory and-lot-size decisions are very "o-p|"" and tecinical iperating deciiions, it would be impossible-to present a deffnitive ""poiritiol of the ffeld here. However, since the basic principles discussed in Chapte-r I "frirty t" both types of rlecisions, and, as Example l2-2 illustrates, since the general fortiut"tion -"y b" applied to investment decisions of certain types, a brief discussion of both the advantagei-and disadvantages of such formulas is considered desirable at this point. -"-l.l*, texts on production and inventory control contain extensive developments of procluction quantity and purchase quantity models. One excellent example is ""orl-i" G. Hadley and T, M. Whitil, Analgsis of Inrsentory Sgstems,Prentice-Hall, 1963'
The situation of equation
Taking the ffrst
Equating this b
This is the valuc When r:
costs. This f act is as followsr
\l;'
tb
The formula, r = of problems, but it
taken in the a cost point occunt
varying costs is mi ing costs goes actually vary
vary inversely. In
be the same for all and the costs of variable rate for loss (such as occur second assumption verse consequenoes ment. A lower liml requirements.
Ch. 12
SOME ASPECTS OF THE ANALYSIS OF MULTIPLE ATTERNATIVES
and let
r = the variable of design
The situation of cost variation just described may be expressedby the equation
'u
= e x +. b + " x
Taking the ffrst derivative, we ffnd d= r dr
a - _
q
b x2
Equating this to zeio, and solving for r,
This is the value of the desig'variable that makescost a minimum. th When * = ,l;, the directly varying costs equal the inversely varying costs. This fact is illustrated in Figure I2-l and may be demonstrated as follows;
Q x , = a tb; = v o o 1 b b
i=
F= 1;
vab
The formula, * = can be applied to a number of different kinds e, of problems,but it should be obvious that certai' precautionsshould be taken in the applications. For example,the statementthat the minimumcost point occurs when the directly varying costs equal the inversely varying costs is not correct unless the line representing the directly varying costs goes through the origin. Also, the cost representedby ar must actually vary directly with r and the cost representedby 4 *rrst actually vary,inversely. In the following examplethe cost per pound of wire must be the same for all difierent sizes of wire (which u-suallyis not true), and the costs of energy lossesmust vary inversely with the wire size. A variable rate for electric energy or the existenceof leakageloss and corona loss (such as occur in high voltage transmission lines) Interfere with the second assumption. Moreover, the analysis disregards any possible ad_ verseconsequences voltage drop on the operation of electrical of equipment. A lower limit on wire size may exist becauseof electrical code requirements.
TECHNIOUES FOR ECONOMY STUDIES
ch. 12
ch. 12 SOME
SIZE OF AN EXAMPLE12-2. ECONOMICAL CONDUCTOR ELECTRICAL F a c t s o f t h e c a s e . T h e g r e a t e r t h e d i a m e t e r o f a n e | inwatts iscl2R' u c t o r ' ectrical ond loss ro""'in"i*irt take placein it. (Power the lesstheenergy in and R : resistance ohms' This may be conwhere/ = cullnt in amperes by the ov J[ioi"s by 1,000.power loss in kw. multiplied vertedto kilowatts wiil give energyloss in kw-hr.) numberof hoursit occursin a given period Thusanincreasedinvestmentinconductormetalwi||saveanoperatingexpensefor electricenergy. 50 ampereslor 4'2OO Assumethat a condJctor is to be selectedto carry hoursperyear,withtn""ostofwireat$1'T5perpoundandelectricalenergy p u r c h a s e d a t 3 . 4 c e n t - s p o r . * . n ' T h e | i f e i s e s t i m a t e d a s 2income s w i t h 5year return before zero salvagevatue. ine minimumattractiverate of ol al annualpropertytaxesare estimated 1'75o/" average taxesis 14o/o,etnd capitalrecovto first cost. These"n"igei-proportional investment-namely, together as lumped "iJ ery cost ot 14.55o/o piop"tty taxes ot 1'75o/o-are of charges 16'3%. investment in area of a copperconductoris expressed circular The cross-sectional to proportionar the crossmirs,and the weightof the conductoris directry proporinversely to area and the resistance the flow of currentis sectional t i o n a l t o t h e a r e a . T h e r e f o r e , | e t x r e p r e s e n t t h e c r o s s the c t i o n a | a r e a i n . s e stated size lor circular mils, and xc representthe most economical 1,000ft. in lengthand 1 i, conditions.rne resiStani", to, a conductorof circularmilincross-sectionalareaisapproximatelyl0'580ohmsat25oC'and pounds' 0'00302 will the sameconductor weighapproximately will be in the conductor The investment $1.7s(0'00302)x Let The annualcost will be $1'75(0'00302X0'163)x' - a = $0'000861 $1.75(0.00302X0.163) The annualcost of Powerloss is
,2F(4,200x$0.034) 1,000
Fromthe value economical
By examinirA closest availff
Gommarl
ductor was
available art
rate of f.UXf h' sizes of wire sectional arl, d attractive-
In Tatile ll'f application hc
computed. Thc cost. Tbis hfrlc as the otter dternatirrcs. the inteffi
b chfell,r.ft
ht ttr
"r1,.$
F = 10,580/x
the cost of Powerloss is Therefore,
0'580) (502X4,200X$0.034X1
@
A_ (50:x4,200x$0.934x10'580) = $3,777,060 1.000
Ch. 12 SOME ASPECTS THE ANALYSIS OF OF MULTIPLE ALTERNATIVES 2O7 From the formula developed in the previous article we know that the most economical value of x, x", occurs when
t :
l b
{ ;
r, ='J*#i
- 66,216 circurar mirs
By examining a table of wire sizes (American Wire Gage, B & S) the closest available conductor is Gage No. 2, with 66,400 circular mils.
Comments on Example 12-2. In this example the size of the conductor was treated as a continuous variable. Actually, the conductors available are discrete sizes, increasing by a geometric progression at the rate of 1.1232for the cross-sectionalarea. The fact that there are speciffc sizes of wire available and that tables giving the resistance, weight, crosssectional area, etc., are also available makes another method of solution attractive. In Table l2-2 five successive wire sizes that might be used for this application have been selected and the annual cost of each size was computed. The table shows that wire size No. 2 gives the lowest annual cost. This table also emphasizes the fact that one type of cost increases as the other decreases,as happens in many problems involving multiple alternatives. Furthermore, note that at the most economical alternative the investment charges approximately equal the cost of lost energy. This is characteristic of problems in which the total costs can be represented by the equation
q = Q . r +b + c x
TABLE 12-2 Comparisonof Annual Costs of Various Wire Sizes in the Selection of an Electrical Conductor
(lnvestmentin wire at $1.75llb.; current of 50 amperes for 4,200 hrs./yr.; all calculationsbased on 1,000tt. of copper wire) A. Size of wire (AWG) . B. Weight of wire in lb. . . c. lnvestment in wire . D . R e s i s t a n c ie o h m s n ....... E . P o w e rl o s s - k w . ... F . A n n u a le n e r g yl o s s i n k w - h r .. . . . . . G . l n v e s t m e n th a r g e s t 1 6 . 3 % . . . . . . c a H. Cost of lost energy at 3.4 cents/ kw-hr. . L Total annual cost assumed to be variable with wire size . . . O0 0 i 2 3 403 319 2Sg 201 159 $705.25 $558.25 $442.75 $351.75$278.25 0 . 0 7 9 5 0 . 1 0 0 0 . 1 2 6 0.159 0.20'l 0.1987 0.250 0.315 0.398 0.503 g3S 1,OSO 1,323 1,670 2.111 $ 11 4 . 9 6 $ 9 0 . 9 9 $ 7 2 j 2 $ 57.34 $ 45.35 28.99
35.70
44.98
s6.78
71.77
$143.35 $ 1 2 6 . 6 9$ 1 1 7 . 1 5$ 1 1 4 . 1 2$ 1 1 7 . 1 2
STUDIES FOR ECONOMY TECHNIOUES
ch. 12
ch.12 SOME
It was first pointed out by Lord Kelvin in 1881 that the economical size of conductor is that for which the annual investment charges just equal the annual cost of lost energy. This is well known in electrical en^gineeringas Kelvin s Law. The costs in Figure l2-l illustrate its application.
variable. Such costr parts costs required includes those whicl illustrated by coslr
tions to
$r60
$l 40 $l 20 $100
o
U
ration will be crt I Costsof tbe units in the lC surance,and inventory that the mnqt
be double4 enil
ftnancing of it must yield e
In applying fu
previously rr, the ecom* and e pmpirb mffi
E 3
E
$80
< $oo
$40
Arr
b
rtl
$ol 0 300 ft' lb' per1,000 in of Weight conduclor
r00
of Figure12-1. Gomparison Annual costs in the selection of an Electrical Conductor Minimum-CostPoint Formulas in Production and Invenlory Control. One of the maior operating problem areas faced by industry and commerce is that of determining purchase order quantities and manufacturing lot sizes. Possibly there has been more written about methods for determiDing appropriate economic values for these quantities than about any other iingie class of problems dealing with analysis for economy. This common problem arises whenever production, spacial, or ffnancial resourcesmay be shifted from one part or product to another. Many solutions to lot-size problems employ some version of the minimum-cost point formula previously discussedwherein the decision variable, r, is the order or production quantity. In general, costs may be divided into three classes. The first includes those costs which vary directly with the total number of units required during a given period of time, usually a year, and are independent of the value of the decision
Ch. 12
SOII'IE ASPECTS OF THE ANALYSIS OF MULTIPLE ALTERNATIVES
209
variable. such costs are illustrated by the direct labor, material, and/or parts costs required to produce or acquire the unit. The second class includes those which vary inversely with the value of the decision variable illustrated by costs associatedwith the ordering processor with preparations to manufacture-for instance, where annual expenditures foi pieparation will be cut in half if the sizesof lots are doubled. costs of the third classare those which vary directly with the number of units in the lot size and include such costs as storage, valuation taxes, insurance,and interest-for instance, where storage space requirements and inventory valuations will be doubled if lot-size is doubled. It also means that the money outlay at the time a lot is procured or manufactured will be doubled, and thus more of the concern's funds will be used for the ffnancing of inventories. If such extra investment of funds is to be justiffed, it must yield a return commensuratewith the risk involved. In applying the explanation of the simple minimum-cost point formula previously developed,the decision as to the value of the deciion variable, x", the economic lot size, involves a trade-ofi between preparation costs and a combination of storage, tax, insurance, and interes-tc-osts.The appropriate interest cost in this classof decisionsis the desired rate of return on funds invested in working capital. As was the casewith the analysisof Example l2-3, practical considerations may dictate the use of some Iot size difierent fiom that found by application of the minimum-cost point formula. Thus total costs for some range of values about the minimum-cost point may be of more value to the decision-makerthan simply the single value. some comments About the Use of Mathematical Models in Engineering Economy. Many mathematicar modershave been deveropedlo guide decisions among investment alternatives. certain generar statements may be made that are appricabre to many of the colpre* moders as well as to simple models such as the one leading to Kelvin,i Law. one generalization is that whenever a particuLr type of problem of eco-nomic comparisonoccurs fairly often, a rule or formirla is i timesaver in ffnding the most economicvalue of a variable of design. In such cases, it has been fairly common to use a nomographic chart ir special-prrrpor" slide rule as a tool for timesaving. with ma-"y of the complex^mathematical models developed by operations researchersand systJms analysts, the modern high-speed electronic computer takes the pia"" of t'he chart or slide rule that could be used to solve the simpler firmulas. The saving of time through the solution of a-formula that gives __ a single "optimal" value for a variable sometimeshas a hidde' p"rr"ity associated with it. The single value has the limitation that it does "ot ,rro* the range of variation of the design variabre through which "ort some other chosen economic measure wilr change veiy littre. what fo, ) often is needed is a minimum-cost range rather than a minim.,m -costpoint. If this range
210
STUDIES FOR ECONOMY TECHNIOUES
ch. 12
ch. 12 soME ASPECTS
weight to the irreducibles that enter is known, it is much easier to give relatively Thu"s Table 12-2, *hi"h indicated a into most economy ,,oiJ sizes 1' 2' and 3' gave wire conductor gage small variation in "oriU"t*een Example l2-2, than the solution of the formula in more useful information wire size of 66'216 cost required a which told us only that the minimum circular mils. guide an eco-nomic.decision ought The analyst who uses a formula to underlpng the mathematical model that to understand the "r*-ftto"t economic matters his formula. Mlathematical models describing ;;";J compromises with irt" model builder to make some t"q"*" ;#;;itt made so that the mathematics reality. Sometimes these compromises-are canbesimplified;,o*"ti*"'amathematicaltreatmentisimpossible are found in complex without a few compromises' These compromises as in simple ones' models as well -*tt "-"ti""l the omission of certain matters' Compromises may take the folm -ofForexample,thederivationofKelvin,sLawdisregardedthepossibleexistenceofleakageandcoronalossesandalsodisregardedanypossible Compromises may also take the adverse "onr"q,r".r""s of l'oltage drop' certain relevant quan"f a simpiification of the relationship between i-* titiesthatappearinthemodel.Forexample,inthederivationofKelvirr's Lawitwasassumedthattheinvestmentinaninstalledconductorisa lineurfrrr,"tionoftheweightofconductormetalandthattheappropriate all wire sizes. These assumprate of investment "harg"! is the same for it was asparticular cases. tions do not necessarit/nt the facts of -Also sumedthatwire,i""is,acontinuousfunctionwhereasinfactthefunction is discontinuous. use a particular formula' When an analyst decides whether or not to therealissuethatheshouldcorrsideriswhetherornothisdecisionwiJl| that exist in the mathebe sensitive to the omissions and/or simplifications is discussed in chapmatical model. The topic of tests for sensitivity ter 13. describe a type of The attempt to devise a mathematical model to to a clearer underprout".n laling for an economic decision can lead relevant matters that need standing of the nature of the problem and the where this has occurred; to be considered. There ha"e be"n many cases in chapter 17 and is concerned with mathematical one of them is disc.rssed models for equipment replacement'
by operations matics. Chapter 15 on i ffrst mentioned in this prospective differenms
parison. Over the
problems in
guidance to decision not recognized this speaking, made
systemsof business Chapter 17 systems"for i George Terborgh, ucts Institute, with the of MAPI publicatior MAPI models were industrial assets,this writings by T systemsover a period that seemlikely to
making that are i
Some Special
AlternativesUsing
examples Chapters8 in
mutuallv exclusive its economic challe.ge
Specifically,it was
change to be co
In using the rate method. there seems weight to comparisoc tion seems to be Example 12-3
method in examining investment. Example
benefft-cost ratio proposalsfor a EXAMPLE OF
Facls and
Chaptersand Appendixesto the Conof Relationship Subsequent ModelsDealingwith Inof structionand Interpretation Mathematical vestmentDecisions.Chapter13onsensitivityanalysisdealswitha
models and topic of great importance f,oth in the design of mathematical The application of in the interpretation of formulas derived from them. the subject the mathematics of probability to investment-type decisions-is models developed matter of Chapter i4; u ,r.,*ber of the mathematical
construction a of As shownon
,72 rter 'ely ave
Ch. 12 SOME ASPECTS THE ANALYSIS OF OF MULTIPLE ALTERNATIVES 21'' by operations researchers and systems analysts involve probability mathematics. chapter 15 on increment costs and sunk costs develops the concept, first mentioned in this book near the end of chapter l, that it is only prospective differences among alternatives that are relevant in their comparison. over the years, many published formulas for the solution of problems in engineering economy have given dangerously misleading guidance to decision makers because the authors of the formulas havi not recognized this concept. such misleading formulas have, generally speaking, made uncritical use of ffgures derived from the accounting systems of business enterprises. chapter 17 contains a brief discussion of one of the various 'MAPI systems" for investment evaluation. These systems were developed by George Terborgh, Research Director for the Machinery and l\llied products Institute, with the aid of his associates; they are described in a series of MAPI publications issued from lg49 to Ig67. Although the original MAPI models were aimed particularly at decisions about replncements of industrial assets, this obiective was broadened considerably in the later writings by Terborgh. An examination of the changes in the MAPI systems over a period of years throws light on certain types of problems that seem likely to arise in the design of mathematical models foi decision making that are intended to be widely useful in industry.
t2,
2L6 ght hat ters /ith tics ible llex ers. xisible the |anin's s a iate npasion ula, will :herapof lereed :ed; ical
somc,special Aspects of comparing Mutually ExclusiveMultiple AlternativesUsing Rates of Return or Benefit-cost Ratios. certain examples chaptersB and g broughtout the point that in comparing in three mutually exclusive proposals, each proposalshould be able to sustain
its economic challenge as compared to the best of the other two proposals. specifically, it was pointed out that it is insufficient for each propoial for change to be compared only with the continuation of a preserit condition. In using the rate of return method of analysis or the benefft-cost ratio method, there seems to be a special temptation for anarysts to give undue weight to comparisons made with inappropriate alternatives. Ttis temptation seems to be greatest when there are many alternative proposals. Example l2-3 illustrates the use and possible misuse of the rate of return method in examining a number of mutually exclusive proposals for private investment. Example 12-4 illustrates the use and poisible misuse of the benefit-cost ratio method in examining a number of rrmtually exclusive proposals for a government project.
onlnl a
and rof iect ped
EXAMPLE12-3. RATE OF RETURN ANALYSISOF A SET OF MUTUALLY EXCLUSIVE ALTERNATIVES Factsand Estimates. Ten different plansare under consideration the for construction a buildingfor commercial of rentals a pieceof city property. on As shownon line A of rable 12-3,the investment land will be in $400,000
212
TECHNIQUES FOR ECONOMY STUDIES
ch.12
d
ch. 12 SOME
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6
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att(\t
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(?
.lo
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a
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@
8
3 cs
I
bQ q
regardless which of estimatedfor each single-story bui
ing in Plan 10. and building The
t
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o
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_ l o l t t t a
3
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tr{lao oI
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213 ALTERNATIVES OF OF ASPECTS THEANALVSIS 'TIULTIPLE Ch. 12 SOME investment as of regardless whichplan is selected.Line B givesthe required for vary from $204,000 a the investments for estimated each buildingdesign; multi-story buildfor buildingin Plan 1 to $3,000,000 a luxurious single-story shownin line C is the sum of the land ing in Plan 10. The total investment and buildinginvestments. for from rentals each planare shownin line annualreceipts The estimated and maintenance, for total annualdisbursements operation D. The estimated propertytaxes, and insurance-in fact, all items except income taxes-are life shownin line E. The estimated of the projectis 40 yearswith an estimatedzero net terminalsalvagevalue for the building.The incometaxes describedin using the simple assumptions bhown in line F are calculated depreciation tax incremental rate, the use of straight-line Chapter10 (a 50o/o value used in the life for tax purposes with the sameestimated and salvage economystudy,and financingentirelyfrom equity funds). The annualnet the positive cash flow in line G is found by subtracting total disbursements (line D). (linesE and F) from the receipts GalculatedRatesof Return. The rates of return shown in line H assume at that the landwill be sold for its originalcost,namely, $400,000, the end of about income tax mattersthat we 40 years. (With the simple assumptions assumption are makingat this point in the book,this is the only practicable for study. consequences an after-tax of that will permitcalculation income-tax to ratesof returnare relatively insensitive fairly large However, calculated the terminal valueof the land.) in changes the estimated The ratesof returnin line H are found by computingpresentworthsand in 8. that was explained Chapter For exin makinginterpolations the manner ample,for Plan 6: - $1,664,920 = PWat18olo $300,000(P/A,18o/o,40) + $400,000(P/F,18Vo,40) / F,16!o = $1 / A,16o/o + $400,000(P PWat 16% : $300,000(P ,870,940 ,40) ,401 investment indicates that the prospective using the $1,684,000 lnterpolation 17.9oh. rate of returnis approximately of calls for consideration A rate of returnanalysis multiplealternatives of incremental ratesof returnas well as total ratesof return. LinesJ and K give theserates. Line L givesthe proto the cash flow figuresneeded calculate Becauseall the spectiverate of return on each incrementof investment. havezero apply only to the buildingand therefore increments investment of ratesby it to terminal values, is possible computetheseincremental salvage to the factors. For example, compute interpolating between capitalrecovery incremental rate of return of Plan 6 over Plan 5: = 0.16591 A/P = $43,800/$264,000 An interpolationbetweenthe 40-yearcapital recoveryfactors for 18% and gives an approximate incremental 16% (0.18024 and 0.16042, respectively) rate of return of 16.60lo. that We shalldraw our conclusions from Table12-3on the assumption the primarycriterionfor the choiceamongthe alternatives that the minimum is aller income taxes. Of course this criterion attractiverate of return is 15o/o shouldbe appliednot only to the total investment also to each separable but increment investment. of However,none of the figures for rates of return in lines H and L depend
-
'i'eu i" .r"""""iJi'ir,-i.-"n"rrenge Plan because extra 3 ro the 1 zz.ly" szro,ooo rirr andtheou"r"ttrateof re_ turnis 16'6%; bothof rheser;'t* ";;;;tire stipurateo is.z_--sirirarry, 5 succeeds its chatens" pli';'tJr: pran in to the incrementar of return ot 24'4o/o the overarr rate and rateof i"iu'ioiia.z" bothexceed ln spiteof the fact that *re-ou"r"rr"rii" 15%. of return;;;;;;; Plan6 succeeds ,,: lrter prans, 'n 7 succeeds its chattengeto pran6. The :!:l,"ls; ;;l;;';, in 11!.p_tan extra i'iu""ir.ni'oi q1o1,9oo pran in hasa prospective o ou",,pran5 after-tax.rate the stipulate 150/o, extra oi r"irrnlr 16...60/o;because exceeds 16.6% d this ln;;;rr;;, ,yi attr""tiue.simirarry, the 18.40/o of $z2e,ob-o ii'i;r"i 7 meetsthe :lr::ffii:.invesrment sivenstandard of
Beyondplan 7. the
TECHNIQUES ECONOMY FOR STUDIES Ch.12 on the stated i'or^150/o. Nevertheless, becausethe incrementar Ptans 3' 9' and 10 are ""i 2' ;qr;;"ii'apprying this i. criterion, rates for havebeenshownin parentheses theserates in line L. The chatenger'D-efender viewpoint in Anaryzinga set of Mutuary Excrusive Mutripteo,,^":ili::: ;-;;;; iaore 12_3 as a guide to making, needsto be recognized it decision that"an untaburated artern-atiie to accept noneof the prans. pranr is clnnot sr"i"i" i," charrenle atternative il;;;;ili. do_nothins because p-"p""ti;;;;.;i"';"te or ,et-urn i;;";"" 1t" is tatedi* ot 1|o/o. Neither"ilpi;;;';;""r" the sripu_ 13.27o 1ro/o. { The do-nothinq arternatiu" rr,orroil il defender against pran 2because Pran1 was erimiiatedwhen it r"ir"o tl .,5t"1., its chatenge. elimination pran2 simirarry, of the T3k"" ,n"-Oo-ioini"ga.rternative theiefender against Plan 3. But plan S, with i,, is.+r" "".r"li ,"," of return, eliminates do_ nothing the arternative from competitioi'["""r"" the 15.40/o 150/0. > At this point in the ii.t"r"r"riir rates of return .anarysis, Ptan3 nowbecomes becomererevant. trre-iereniei.;'".'
214
ch. 12 soME ASi
In applying these in order of incrrd rncrement of invt by evaluating rl,
vestment levels, ing when the acceptablc
A diagram rate of return L2-2,
foregoing analysis that thestipuration ^_ after_tay i, at ]'rot ,_ i, ^{ arter-taxot 1so/o th".r"ir,",;;l;",ili#,i,ji is jl", the stinrrtari^h or an rc"j.
oa '..;:q'i i ;',:Y,'';f J:.Tii-1l.U'; ;il n roorattracriveness because The conclusionof
rnvestment yierds onrv1,0%.rr*" ""i"ir"i:g the tastsuccessful g as a chatenger etanz, to crrarr.enger, a;;;i;;;.^tr"nt of $888,000 required obtain extraannuar i-s an to "rt"it"* r""r, ;];;';; see,soo-roi a;r"*.i,n" approx_ imate rateof return is,9.07o. r*'" ii.z."r"" of return snown extrainvestment in.pran ou"i Frln"aTJ""J.rerevant on tineL for the 9 pran8 was because efiminated whenit wascompared with ptan Z.)
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ized at the conctusi"" "t;;;;;;:T"*r: "#ilji""" lr.l^:-1
u.lT,:':nl'J"rtl**::'i,.lti jliltT:Til:"#Hlf ;Iffifl sixth basio o at theconcrusion pffi;nff:"mmar_
This approach stems I benefit-cost ratio method.
"'n:,:",:',lT,y*i:s,::rp",,isons.A.monr,il upp,o i"' a""'*i:T"#-:#"fl .ilT,,"'"'ib"d " "h#ig".th ""h a"ru,,a ", 9
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the d'iferences among alternatioes are rer.eoant ,ol*of;."'o in their com_ 6' Insofar as practicable, separabre d.ecisions shourd, made separatery. be
Ch. 12 SOME ASPECTS THE ANALYSIS OF OF MULTIPLE ALTERNATIVES 215 In applying these principles, it is first necessary to array the alternatives in order of increasing investment magnitude and then insure that each increment of investment carries its own weight. This is accomplished by evaluating the differences between successive pairs of alternative investment levels, beginning _with the do-nothing alternative, and concluding when the last alternative in the array is compared with the last accep t abl,e alternative. A diagram of the appropriate steps in the analysis applicable to either rate of return or benefit-cost ratio methods of analysis is shown in Figure
r2-2.
l. Arroy ohernolives in order of increosing copitol I investmenl (increosing onnuol cost for B,/C rotio onolysis).
2. Defenderis the do-nothing olternofive (or present condition). Firsl qhernotive is the chollenger.
3. ls $e chollenger occepfobleover the defender? (i 2i*, or B/C>14 Yes No
4. Defender remoinr the do-nothingohernotive Nexl ohernqlive becomes the chollenger.
5. Currenl chollenger becomes fhe defender. Nexl ohernofive becomes the chollenger.
6. lr the chollenger occepfobleovar ths dafender? {i>i*, or BIC>l?} Yes No
7, Currentdefenderremoins the defender. Nexl ohernolivebecomes the chollenger.
Figwe 12-2. Flow Diagramof Procedurefor Analysisof Multiple Alternalives
216
TECHNIOUES FOR ECOI{OMY STUDIES
ch. 12
ch. 12
Two Possible Types of Erlor in Interpreting prospectiye Rates _ of Return on a set of Mutually Exclusive Alternatives. Ii lines K, and L J, had been omitted from Table l2J, the rates of return in Line H would not have been a sufficient guide for making a choice among the alternatives. There are two types of error that sometimesare made in drawing conclusionsfrom such a curtailed table. some personswho examine such a table will make the mistake of selecting th! alternative that has the highest total rate of return; this is pran 5 in Table r2J. other persons will make the mistake of selecting the arternative with the highest investment that will yield at least the stipurated ii; this is plan g in"taute u_g. If it is stipulated that the minimum attractive rate of return is r5%,presumably it is believed of Fl, the consequences reiecting a proposed in-crement of investment will be to accept "n .rnrp""ded in-vestire.rt elre*h"re that will yield l5%. If plan 5 shourd be s-electedi' n""*fle l2-3 on the grounds that it has the highest over-afl rate of return, thJreiection of Plans 6 and 7 is, in efiect, a ct-r9ice unspeciffedinvestments of yierding rE% rather than speciffed ones yielding, respeitively, 16.6%and, tl. g. Also an ia of L5% implies that the "oirr"q.r"rr"" of accepting a proposed increment of investment wilr be to reiect an unspeciffed invfstment erseyhe-re that will yield, LS%.If plan g is chosen on the grounds that it has the highest total investmentwith an over-all yield of *t rJ"rt isa an implied consequenceof this choice is to reject an investment of $gdg,000elsewhere that will yield 15%in favor of an avoidable extra investment in this project that will yield only g%. when a calculated Incremental Rate of Return is lrrelevanr. The discussion of- Example l?-3 pointed out that certain ,"t", oi return on increments of investment in line L of Tabre 12-3 were shown in parentheses to emphasize the point that these rates were not relevant in the choice_amongthe stated alternatives. In general, if an alternative is rejected becauseit fails to meet the decision criteria, it should not be viewed as the defender against subsequent arternatives that require higher investments. occasionally there are irregularities in the patterns of rates of return that may lead to error in intlrpretation. such- a pattern "ff""r, in the incremental rates of return in rine L for prans 5, 6,'and z. ifesol rtion of 'an this pattern is requested in probrem rH.) As "*^rr,ft" consistent with the analysis of Exampre r2-3, add a pran 7a; this ft'"r, ,"q.rir", " total,investment of gz,L!:O,w ($400,000for Iand and or,-ga0"000 the for building) and has an estimated annuar net positive cash fow of g3bg,700. The rate of return on the totar investment wliu be approxim^ouly t6.0%, ^n acceptable ffgure. But the rate of return on the $5gg,000increment of investment over Plan 7 will be onry 4.s%,crearry "n ,rrr""""pa"ui" ng,rr". Now imagine that Tabre r2-3 is changed to add pr"" f"; "rrd that in
Iines f, K, continuc will not
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ALTERNATIVES 217 OF MULTIPLE OF Ch. 12 SOME ASPECTS THE ANALYSIS lines J, K, and L, Plan 8 is compared with the new Plan 7a. Plan 8 will continue to have a 16.4%rate of return on the total investment, and line L will now show a rate of return of 25.4%on the increment of investment. A superRcial view of the matter might lead to the incorrect conclusion that Plan 8 is acceptable because both of these rates exceed the stipulated i* of l5%. Such a conclusion would be incorrect because an incremental rate of return over an unacceptable alternative is not relevant. The defender against the challenger of Plan 8 should be the plan with the next lower investment that is acceptable, namely, Plan 7. The addition of an unacceptable Plan 7a does not change the fact that Plan 8 is an unattractive alternative to Plan 7 because .its $432.000 increment of investment over Plan 7 promises an after-tax yield of only 10%.
EXAMPLE12-4. USE OF BENEFIT.COST RATIOSIN ANALYSIS FOR A EXCLUSIVE ALTERNATIVES OF A SET OF MUTUALLY 3 PUBLICWORKSPROJECT Facts and Estimates.A certain section of highwayis now in locationA. A number proposed improvements of designs new locations at and proposed at the present of with a continuation the present location to be compared are condition A. For purposes analysis, at is of the condition continuing present designated A-1. as Threepossible to are referred as A-2, new designs the present in location A-3, and A-4, respectively. Two new locations and C are also considered B for this sectionof highway.Thereare five new designs be analyzed loto at cation B and four at locationC. These13 proposals, A-1 to A-4, B-1 to B-5, and C-1 to C-4, are mutually in exclusive the sensethat only one proposal will be selected.Of coursethe variousdesignsat each locationcontaina number common of elements. Table 124 givesthe investments the estimated and annualmaintenance costsfor the various locations and designs. lt also givesestimates the anof nual costs to the road usersfor each alternative. is assumed that there lt are no differences other consequences can be expressed money in in that terms. In orderto concentrate reader's the inattention the specialproblems on volvedin the comparison multiplealternatives a publicworks project, for of the factsof this example in havebeensimplified certainways. lt is assumed that road user costswill be uniformthroughout 30-year a study periodand that all alternatives havezero terminalsalvage will valuesat the end of that period. (The readermay recall that when we used a highwayexampleto introduce benefit-cost the that annualtrafratioin Example , we assumed $1 fic and road-user costs would increase and that certainalternatives would
3 This example is adapted from one given in a paper "Economy Studies for Highways" by E. L. Grant and C. H. Oglesby published in Highway Research Board Bulletin 306, Studies in Highwag Engineering Economg, Washington, D. C., National Academy of Sciences-National Research Council. 1961.
218
FOR STUDIES TECHNIOUES ECONOTIIY TABLE 124 Estimatesand Annual Cost Comparisonfor Certain Mutually Exclusive Highway Alternalives (Allfigures thousands dollars) in of
Annual ltlainlenans! Cost $60 35 30 40 30 20 30 40 45 40 30 40 50
Annual Road User Costs
Alternalive A-la | A-2 A-3 A*4 B-1 B-2 B-3 B-4 B-5 $
Flrst Gost 0 1,500 2,000 3,500 3,000 4,000 5,000 6,000 7,000 5,500 8,000 9,000 11,000
Annual CR Cost $r - 7o/ol $ 0 121 161 282 242 322 403 484 564 443 645 725 886
Annual Hlghway Costs
Total Annual Cost! lnfluenced by Choice $2,260 2,076 2,051 2,132 2,062 2,O32 2,013b 2,O94 2,089 2,103 2,145 2,165 2,276
c-1 c-2 c-3
C-4
$ 60 156 191 322 272 342 433 524 609 483 675 765 936
$2,200 1,920 1,860 1,810 1,790 1,690 1,580 1,510 1,480 1,620 1,470 1,400 1,340
I Continuationthepresent condition. of b Minimum annual total cost. period.) Our ecohavesubstantial valuesat the end of the analysis residual are nomic comparisons the 13 alternatives made assuminga minimum of attractiverate of return of 7%. AnalysisBasedon MinimumAnnual Costs. The total annual costs of the 13 alternatives comparedin the final columnof Table 12-4. For each are alternative, total is the sum of the capital recoverycost of the investment this usingan n of 30 and an i' ol 7/o, the annualhighwaymaintenance cost,and the annualcoststo roadusers. The total annualcost is a minimum design for Br3, which requiresan investment $5,000,000. of AnalysisBasedon Benefil-Cost Ratios. In Table 12-5 the 12 alternatives to A-1, a continuation the present in of condition, arranged order of inare creasing highwdy first to costs. Because each alternative is to be compared A-1, the highwaycosls shown are the annualcosts in excessof the $60,000 maintenance cost for A-1; for example,the highwaycost figure lor A-2, shownat $156,000 Table 12-4, is $96,000 the third line of Table 12-5. in in The benefits shownin the secondline of the table are the estimated reductions in annualroad usercostsbelowthe $2,200,000 will continue A-1 that if is sefected;thus the beriefitfigure of $280,000 shown lor A-2 is found by subtracting$1,920,000 from $2,200,000.
l*i,i
GT. 12
SOME ASPECTS OF THE ANALYSIS OF MULTIPLE ALTERNATIVES
219
The fourth line of Table 12-5 gives the B/C ratio for each alternativeas c-4 to eompared A-1. All except the $11,000,000 design show B/C ratios greaterthan unity. to However, is necessary comparethe 12 designswith one anotheras it of rell as with the continuation the presentcondition.The relevantincrein are B/C ratiosfor this compdrison developed the final five lines of nrental ratios leads to of Table 12-5. Of course,a consideration these benefit-cost lre sameconclusionas the annualcost comparisonin Table 124; B-3 turns ost to be the best of all the alternatives. in and defenders the incremental to It is of interest note the challengers in its challengeto A-1 with an incremental @mparison. A-2 is successful B/G ratio A-2 with an incremental !/G ratio of 2.92. Then A-3 eliminates to d 1.71. NeitherB-1 nor A-4 can sustaintheir challenges A-3; their reratios are 0.86and 0.38. Then B-2 eliminatesA-3 and Tective incremental B-3 recomparisons, by b in turn eliminated B-3. In all of the subsequent no rJns the defender; designthat has higherhighwaycosts than B-3 can them by an increasein benefitsthat is greater than the increasein luEtaty Igftway costs.
Some Commentson the Use of Rates of Relurn and Benefit-Cost |1[os in ComparingMutually Exclusive Multiple Allernatives. Even were different,the reader will doubtof lhrgh the techniques analysis used in Lrs have observeda similarity betweenthe types of reasoning
12J and I?A.
res
ln the rate of return analysis in Example 12-3
not enough to compare each plan with a do-nothing alternative;
plans also needed to be compared with one another. And in using B/G ratios in Example L2-4, it was not enough to compare each design
a continuation of a present condition; the comparison of the designs each other was also essential. The same general type of reasoning
to choosing the appropriate challengers and defenders in the comparisons. The temptations to incorrect reasoning were in the two examples. lae reader should recognize that the selection of a minimum attracrate of return is of critical importance in analysisbased on the benefftratio just as in the various other types of analysis. Problems 12-11 12-16 illustrate certain aspectsof the importance of the chosen value f in Example L24 as well as some other aspectsof beneftt-costanalysis hought out in the example.
Qrrlderation of Mulliple lrreducibles in the Analysis of Multlple
Even with only two alternatives to be compared, it often
that certain irreducible data favor one alternative whereas other favor the other alternative. (This was illustrated in the story 6e end of Chapter 2 about the choice between two proposed total systems. When there are many alternatives to be compared and )
220
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ch.12soMEAsPEcTsoFTHEANALYS|SoFMULTIPLEALTERNAT|VES221 when there are a number of irreducibles with difierent impacts on the clifierent alternatives, the problem of giving suitable weight to irreducibles may be particularlY troublesome. alternatives and if irreducibles need to be given if tn"t" "r" *oitipl" weight in the ftnal choice, it is helpful to examine alternatives in pairs. It is much easier to reach a conclusion about the impact of a variety of irreducibles, some favorable to one alternative and some favorable to another, when the decision maker looks at only two alternativ_es at a time. In Example 12-3, which applied the rate of return method, and in Example l2-4, wliich applied the B/C ratio method, we illustrated the technique of considering multiple alternatives in pairs, always viewing one as a defender and anothei as a challenger. Whenever a number of irreducibles are present, a similar technique can be applied with any method of analysis of multiple alternatives. A systematic procedure for organizing and using data regarding multiple iireducibles is discussed at the end of Chapter 19. This is in cotr"community factor proffle" developed by C. H. Oglesby, niction with the A. B. Bishop, and G. E. willeke to help with the problem of comparing alternate locations for urban freeways.
The system viewpoint in a choice among Multiple Alternatives.
In a choice among major altematives, it is common for each alternative to have subalternatives, for each subalternative to have subsubalternatives, and so on. This point was stressed in the presentation of basic concepts in Chapters t and 2. To ieach sound decisions about the subalternatives, an analyst needs to recognize the interrelationships between the choices among subalternatives and the choices among maior alternatives. Insofar as practicable, it is desirable to take a system viewpoint in making decisions about subalternatives. Where a choice among major systems must be made, one difficulty may be the existence of too many possible alternatives for an economical and convenient analysis. Often a complex problem of making a choice among possible systems can be reduced to workable dimensions by ftrst considering the component subsystems. An instance where this was done is described in Examples 12-5 and 12-6.
SUBSYSTEMS OF EXAMPLE12-5. CONSIDERATION RELEVANT OF STUDYFOR THE SELECTION IN PLANNING ECONOMY AN HANDLINGSYSTEM A MATERIALS drug distribuFactsof the Case. One of the nation'slargestindependent a centers covering majorpartof the country' lt is now lors has8 distribution centerof planning remodel that to one of its warehouses servesa population peoplein an area about200 mileswide by 500 miles long. about10 million itemsin stock from which it Eachdistribution centercarriesabout30,000
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ch. 12 fills severalthousandorders per day. Most of the orders involve less-thancase lots of 10 to 50 differentitems. About 2,000items accountfor 50% of its volumeand another2,000items accountfor the next 30% of its volume. The cornpanymaintainsits own fleet of trucks on which it delivers all its orderswithina radiusof s0 mires(about6 miilionpeopre) a daily basis. on Daily shipments are madeto more distant points oy way of commercialcarriers. About 80o/o its volumeis derivered its own irucks. of by The companyhas experimented with a numberof ditferentmaterialshandlingsystems fillingordersand has warehouses whichthe order selecfor in tion is performed entirety hand,othersinvolving by somemechanization, and one in which the most important2,000itemsare stored in a completelyautomatic,electronically controlled order-picking machine, with the other items beingpickedby handand praced a conveyor on system accumurating for orders. Thegompany now tryingto decidejust whatcombination methods is of to use in this installation. The majorityof the orders to this distributioncenter are terephoned in by the individualdrugstores.A clerk typesout a temporary invoiceas she takes the order over the telephone.The itemson the preliminary invoicemust be pickedfrom the stock in the warehouse and movedto the jacking area. The itemsare checkedagainstthe invoiceand any unfilteditemsare marked off. A final invoicein four copiesis typed,with one copy servingas a shipping list,one as a receipt be signedby the receiving to ciert at thJdrugstore, one for the accountsreceivable office for billing purposes, and the fourth for the inventory controlsectionfor use in maintaining stock revers. It is important visualize interrelationsnips the variousactivities. to the of Promptand completeshipments are essentiar customersatisraction.Erfoi rors,short shipments, delaysdrive customers competing and to distributors. 'Drugstores typically maintain only timitedstocksof drug itemsind expectto be ableto replace stock withins to 10 hoursfrom locafdistributors. Thisexample dealsprimarily with the matedals handling .yrt"r,-brt it was found that the paperworksystemswere so crosery tied t;th; materialsnandling system that they must be considered simurtineously. Threemajor systems mustbe integrated: the materiars (1) (receiving, handring storing, order picking,and packing).; customer (2) paperwork (ta-king oraei'preparation of invoiceand shippingrist,and end-of+nonth biiling);and (3) inventory control (maintaining perpetuar inventory, determination Ji'oroer' joints, ano writing purchaseorders). ldentification the alternatives of availablecan best be done for the ditferent subsystems individually. The physical handling system can be subdivided into three subsystems: A. Receiving and storing B. Order pickingand assembly C. Packingfor shipment subsystem A. The productsare arwaysreceivedin casesor in murti-case lots, and must be transportedto the proper storage area in the warehouse and stacked in the shervesand bins. The alternalive methodsthat appear feasible are: A1' A completery manuar system, using 4-wheered shop trucks for transportation
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22 ALTERNATIVES OF OF ASPECTS THEANALYSIS MULTIPLE Ch. 12 SOME A2. A pallet-forktruck system;manuallypalletizeat the dock; smalland stackingat point volumeitemswould requiremanualseparation of storage A3. Under floor tow chain towing 4-wheeledtrucks through the wareand stacking house;requires manualloading,unloading, A4. Powergdbelt or roller conveyorsrunningfrom dock to storagearea; unloading, and stacking requires manualloading, system,employinglive storageof automaticconveyorized A5. Completely and condispatching and electronic caseson gravityrollerconveyors trol SubsysfemL A typical order consistingof from 1 to 12 bottles, jars, tubes,small boxes,etc.,of 10 to 25 items. Most of the items are relatively in can be performed a numberof small. The order pickingand assembly ways: shop trucks, with 81. Completely manualsystem,employing4-wheeled one personpickingall the itemsfor one order with nonautomatic, manualpickingand man82. A belt conveyor system, ual regulationof the placementof orders on the belt for transportto the packingtables 83. Under floor tow chain with 4-wheeledshop trucks, performingin sameway as conveyorsin 82 cardispatchable 84. Overhead chain conveyor systemwith independent, riers,but with manualpicking items and automaticorder picking of the large-volume 85. Completely items for any of the other alternatives the low-volume Subsystam The packingfunctionis basically manualjob, allowing C. a in only minorvariations the arrangement the work placesto accommodate of the order-picking system selected.The packing operation shouldincludethe final accuracycheck on the shipmentand the initiationof the customer paperwork. Subsystem The recordssystemdealingwith the customercan be operD. ated in a numberof ditferent ways,with a wide choiceof actualequipment undereach general alternative: D1. Completely manualsystem process eliminate to the D2. Basically manual, including duplicating but a retyping invoices multiplecopies of in D3. Basically machine manual, including but accounting to semiautomatic prepare invoices, bills shippinglists,and monthly D4.An automatic systeminvolving electronic data processing equipment, punched printers, cards,automatic etc. Subsysfem The inventorycontrol systemmust maintaina perpetualinE. ventory eachitemand seethat an adequate for supplyis on handat all times. Thus,it mustnot only havedaily recordsof receipts and salesof each item, but mustcontinuously analyze marketfluctuations, pricesin and salestrends, policies.The available orderto set the best purchasing methods similar are to thosedealingwith the customer: E1. Completely manualsystem
TECHNIOUES FOR ECONOMY STUDIES
E2' Basica'y manuar, but incruding some semiautomatic accounting ma_ chines to summarize daity saLs ano computeinventories, .receipts, gnd compare.balances order points with _^ E3' Futy automatic system' ,.ing "rJ"tronicdata processing equipment to performthe operations The comprete systemin this warehous_e_ contain -ivitn must one of the arterna_ tives from each of th: f,J9 "ro"v"ier". s arternaiiveJJ"ln to,' sybsystemsA and B, 1 for c, 4 tor D, ""JJ ilr'e, tnereareii;i"i;;300 possibre combinations from which the rori ""onoricar -eipenses shourdbe chosen. rt is theoreticaily possibreto esJimate tre invorved receiptsof each of the 300 possibre-aitJrnatives, and the effects on but it is doubtfurthat at_ temptingto do so woutd be *orth-it " "flrt. rn the first prace, manyof the 300 comoinations can be eriminated im_ practicabre' as For exampre, wourdooviousry it be foorisht" i"li"lr subsystem A3, the underfloor tow chain,ror nanoiing incoming materiars ancrthen use subsystem the bert conveyor, 82, toi oiolr picking. This wourdinvolve two separatesystemscovering the same ttLL,' "r"", two equipment, and would inirease-*,"-"im*pri"ations rarge investmentsin of layout,becausethe conveyor would perm"rgnl]y occupy spaceand interfere'with the rayoutof the tow chainsystem.similarty,,n,ilff"" of subsystem the useof semi_ D3, automaticaccountingmacnines ror-pio""raing orders and in_ voices, wourdmakesystemE1 a foorilh-cnoice,customers, because great dearof the a information needed oy inventoiy;;i;J'woutd be readityavaitabte from subsystem in a form that "o;o D3 o""i oe by chinesratherthan by.hand. F;rth;r;;;;,*the handred semiautomatic ma_ serection a futy automatic of order-picking systernfor the h;g;_;;;r;; itel3, sulsvstem A5, woutd prac_ ticaltvdemandthe u:" ol eitnei suoslsilm os or oi;J ;iil", E2 or E3, becausethe informatioi r-o^lly oil4;;.g machinewoutd have to be in a form that the machine courd undersiand and be avairabre speedsthat at coutd not be possibte with manuat-i;;i;". consequently, selectionor in" the .-v"i!r to1. centercan best be mSdeoy making-up'"-"", this remodeleddistribution ot combinations the mate_ for rials handring probrem and another""i roi.*," paperwork. Each arternative combination the mate.rials for rranoring shluld be chosenso that the two systems subwit be compatibre "no "o t"n"litie speciricintormation'needs (re_ strictions imposed the..handril.ilrr';n by the information system) Known' Thenthe arternative wi, be "or6inition" t,. *," inrormation l'n-Jp"p"r,or* systems shourd serected mate most-rconoric"r be to use of *n"i"u", equipment is invorved that combination. in on" t,, more combinations shourdbe devisedto meet the information neeos-oieacn handring "iteinltiue. rnrs, suboptimization be,employed can to .irprirv the problem. Equivalent annual
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ALTERNATIVES 225 OF MULTIPLE OF Ch. 12 SOME ASPECTS THE ANALYSIS plete systems that would be feasible, it is unlikely that all the alternatives would have been recognized. By breaking the whole system into subsystems and examining each individually, the analyst helped assure that he would not overlook some important alternative. Furthennore, the analysis of the subsystems tends to bring the requirements of an acceptable whole system into proper focus. The company had other distribution centers and many of the alternatives had been used in various forms. Cost data were available from the other centers, but the data could not be used in the existing form. Differences in such items as taxes, labor rates, insurance rates, and volumes to be handled among the different locations required adiustment of the cost data to suit the conditions at this location. None of the other distribution centers have a system that is cbnsidered to be ideal, and this remodeling presents another opportunity to try to develop the best possible system. Consequently, the new system should be a composite of many of the ideas from difierent plants in addition to some entirely new ideas. This is really a new problem and requires a complete analysis rather than dependence on past solutions. The ffnal analysis of this problem is summarized in Example l%-6.
EXAMPLE12-6. ECONOMYSTUDYTO SELECTA SYSTEM MATERIALS HANDLING combinations of Estimates Analysis.After studyof the manypossible and were describedin Example12-5, eight differentcombinations subsystems were analysis.Threeof thesecombinations for economic chosen preliminary five combinations weresethis initialanalysis and the following by eliminated lectedfor detailedanalysis: 4-wheel shoptrucksfor both 7 of operated Combination consists manually alongwith a manual and order picking, handling incoming shipments control. lt includesa duplisystemfor recordskeepingand inventory catingprocess multiplecopies. for shop trucks tow chain with 4-wheel 2 of Combination consists underfloor accounting equipment and semiautomatic for both handling operations control. for all recordskeepingand inventory trucksfor intow 3 Combination employs underfloor chainwith 4-wheel an disan chain conveyorwith independent coming materials, overhead patchable electronicdata carriersfor order picking,and an automatic processing control. systemfor recordskeepingand inventory 4 Combination employsfork lift trucks for handlingincomingmaterials, a completely order-picking systemfor the 2,000high volume automatic items and manualpicking for all other items,and an automaticelectronic data processing system. 4 Combination is the same as combination except that it has automatic 5 order pickingfor 4,000high volumeitems. i* The monetary is comparison shownin Table12-6 usinga before-tax of doesnot affect 25%. This is a casewherethe choiceamongthe alternatives the estimatedrevenues the enterprise. of
::-ch. 12 SOIE
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STUDIES FOR TECHNIOUES ECONOMY TABLE 124 Ma!9ri-a::Handling Systsms Cost Comparisonof Alternative Distributor for WholesaleDrug
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final in to be considere-{ the of orders' area number irreducibles.thatrteed oirrt'purchase There tneiioit"t' The comWithcombilr;;;"-;;;' "no's' *iin a manual system' decision. dav with be *;'';;;"riier.than witl and reports to.i"noi" tore' orders -per be ex4 and 5 *"ii'J"ij"-canacrJv othei* can.only binations comoinations tn'e laborcosts)'The auto' vervlitile added"*p",i"J,'ilnirl-irr (ano in-"t"-"ting and *ffii;;i";Jopte by oandeo adding i*"t91 d-eveluoPment ol errors *irr nJ'iouut'require? ":;;;;i maticsvstems nito' "-gt"uternumber period' tiai-tn" otnersystems"debugging" period initial "nil-iiringiu'ing.the errorsthan orJ", iirring o" tewer probabty ,"o"ln Uoin witn will ,yrt"r, .n"rii"o"iaie tn" but eventuarty "uiorlti" annual the othercombinations' 4-hasthe lowestgro-sq:ctive taxes' income 12-6'"u""'l'in"t combination Table or t"t;;; ;ieiy' oeiore and conwith a minimuni;il;;tdrate tnan Jomuination howerer' s' cost L"'t"' o Combination '' oni'Giii in"t""""t' il' ?y"in"ss' less such 'it"'itj"'0r""-"t p'o"g3""iuJ errorsmishtreadthe manof sideration "^ dependence hbJ;:";i-;;-e;J;;i;;i;*;r 5'
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aspects of economic has dealt with certain to Summary. This chapter with special reference in comparis;;"J;;ilp1"-"tt"*"tives' of the chapter part analysis ;; b" chosen' The ftrst where only one ;ii;"* cases
ALTERNATIVES 227 OF I'IULTIPLE OF Ch. 12 SOT{EASPECTS THE ANALYSIS illustrated and discussed the use of simple mathematical models to obtain an optimal solution in this type of problem. The second part of the chapter illustrated and discussed certain dangers of misinterpretation of an analysis of multiple alternatives whenever rates of return or benefit-cost ratios are calculated. The ffnal part of the chapter illustrated a complex problem in which it was desirable to recognize a variety of subsystems before selecting the particular combinations to be compared in the detailed economy study. It has stressed the fundamental principle that each increment of investment in a proposed project should be expected to yield a return commensurate with the value of ii stipulated by the decision maker or decision making authority. When a decision is made based on the stipulated io, either the decision maker has another opportunity of equal risk at which he can invest any available funds at i* or he has made a conscious decision thag for the risk involved in this set of proposals, he is not willing to make an investment that does not have the prospect of earning i*.
PROBLETIIS 12-1. A manufacturing company has been eited by the local air pollution authority for allowing too much smoke to issue from its chimney. Investigation shows that there is no chance to meet the authority's requirements by better con"smoke" is a form of dust inherent in the trol of combustion becausepart of the process. It will be necessaryto install a precipitator to remove the manufacturing solids from the hot gasesbefore they leave the chimney. The plant engineer has made the following estimates: A $6,000 't0 0 $ $1,280 1,200 600 4OO 120 $3,600 Preclpltatora B C $7,600 $9,000 10 10 $ 0 $ 0 $1,280 'l,200 500 370 150 $3,500 D $10,300 10 $ 0
First cost installed Llfe (years) Salvagevalue. Annual operating disbursements: Powerand water . Cleaning Maintenance Labor extras Property taxesand insurance
$1,000 $ 950 800 860 600 500 260 240 210 180 $2,900 $ 2,700
Estimate the annual income tax differencesusing the simple assumptionsillustrated in Chapter 10. Compare the economy of the four precipitators using an after-tax i* of.8% Which one would you recommend? (Ans. = Precipitator C.) 12-2. Prcpare a table similar to Table 1%-2 comparing the annual costs of wire sizes 00 to 3, both inclusive, assuming the investment in copper wire at 12.25/1b., the price of electric energy at 4.2 cents/kw-hr, investment charges at for 18.5%, a current of 60 amperesfowing for 6,000 ht/year. Which size has the lowest annual cost? (Ans. : Size l.) 12-3. In a certain manufacturing plant, schemesfor cost-reducing machinery "gross are iudged on the basis of the retum," which is computed as the ratio of the annual saving in direct materials and labor to the investment. To justify the investment of funds in such projects, there must be a gross retum of 30%. This