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Chapter
1
Introduction to Quantitative Analysis TEACHING SUGGESTIONS Teaching Suggestion 1.1: Importance of Qualitative Factors.
Section 1.2 gives students an overview of quantitative analysis. In this section, a number of qualitative factors, including federal legislation and new technology, are discussed. Students can be asked to discuss other qualitative factors that could have an impact on quantitative analysis. Waiting lines and proect planning can be used as e!amples. Teaching Suggestion 1.2: Discussing Other Quantitative Analysis Problems.
Section 1.2 covers an application of the quantitative analysis approach. Students can be asked to describe other problems or areas that could benefit ben efit from quantitative analysis. Teaching Suggestion 1.3: Discussing Conflicting Viewpoints.
'ossible problems in the #$ approach are presented in this chapter. $ discussion of conflicting viewpoints within the organi%ation can help students understand this problem. &or e!ample, how many people should staff a registration desk at a university' Students will want more staff to reduce waiting time, while university administrators will want less staff to save money. $ discussion of these types of conflicting viewpoints will help students understand some of the problems of using quantitative analysis. Teaching Suggestion 1.4: Difficulty of etting Input Data.
$ maor problem in quantitative quantitative analysis is getting getting proper input data. Students can be asked to e!plain how they would get the information they need to determine inventory ordering or carrying costs. (ole)playing with students assuming the parts of the analyst who needs inventory cost costss and the the inst instru ruct ctor or play playin ing g the the part part of a vete vetera ran n inve invent ntor ory y manag manager er can can be fun fun and and interesti interesting. ng. Students quickly learn that getting getting good data can be the most difficult difficult part of using quantitative analysis. Teaching Suggestion 1.5: Dealing with !esistance to Change.
(esistance to change is discussed in this chapter. Students can be asked to e!plain how they woul would d intr introdu oduce ce a new new syst system em or chan change ge with within in the the organ organi% i%at atio ion. n. 'eop 'eople le resi resist stin ing g new new
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GET FULL FILE [email protected] approaches can be a maor stumbling block to the successful implementation of quantitative analysis. Students can be asked why some people may be afraid of a new inventory control or forecasting system.
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GET FULL FILE [email protected] SOLUTIONS TO DISCUSSION QUESTIONS AND PO!LE'S #uantitat tative ive analysi analysiss involv involves es the use of mathema mathemati tical cal equati equations ons or relati relations onship hipss in 1#1$ #uanti analy%ing a particular problem. In most cases, the results of quantitative analysis will be one or more numbers that can be used by managers and decision makers in making better decisions. *alculating rates of return, financial ratios from a balance sheet and profit and loss statement, determining the number of units that must be produced in order to break even, and many similar techniques are e!amples of quantitative analysis. #ualitative analysis involves the investigation of factors in a decision)making problem that cannot be quantified or stated in mathematical terms. +he state of the economy, current or pending legislation, perceptions about a potential client, and similar situations reveal the use of qualitative analysis. In most decision)making problems, both quantitative and qualitative analysis are used. In this book, however, we emphasi%e the techniques and approaches of quantitative analysis. scientific approach to managerial decision making. +his type of 1#%$ #uantitative analysis is the scientific analysis is a logical and rational approach to making decisions. motions, guesswork, and whim are not part of the quantitative analysis approach. $ number of organi%ations support the use of the the scie scient ntif ific ic appro approac achh- the the Inst Instit itut utee for for per perat atio ion n (ese (esear arch ch and /anag /anagem ement ent Scie Scienc ncee 0I&(/S, 3ecision Sciences Institute, and $cademy of /anagement. +hee three hree cate catego gori ries es of busi busine nesss anal analyt ytic icss are are desc descri ript ptiive, ve, pred prediicti ctive, ve, and and 1#&. +h prescriptive.3escriptive analytics provides an indication of how things performed in the past.'redictive analytics uses past data to forecast what will happen in the future.'rescriptive analytics uses optimi%ation and other models to present better ways for a company to operate to reach goals and obectives. #uantitativee analysis analysis is a step)by)st step)by)step ep process process that allows decision makers to investigate investigate 1#'$ #uantitativ problems using quantitative techniques. +he steps of the quantitative analysis process include defining the problem, developing a model, acquiring input data, developing a solution, testing the solution, analy%ing the results, and implementing the results. In every case, the analysis begins with defining the problem. +he problem could be too many stockouts, too many bad debts, or determining the products to produce that will result in the ma!imum profit for the organi%ation. $fter the problems have been defined, the ne!t step is to develop one or more models. +hese models could be inventory control models, models that describe the debt situation in the organi%ation, and so on. nce the models have been developed, the ne!t step is to acquire input data. In the inventory problem, for e!ample, such factors as the annual demand, the ordering cost, and the carrying cost would be input data that are used by the model developed in the preceding step. In determining the products to produce in order to ma!imi%e profits, the input data could be such things as the profitability for all the different products, the amount of time that is available at the various production departments that produce the products, and the amount of time it takes for each product to be produced in each production department. +he ne!t step is developing developing the solution. solution. +his requires manipulation manipulation of the model in order to determine determine the best soluti solution. on. e!t, e!t, the result resultss are tested tested,, analy%ed analy%ed,, and implem implement ented. ed. In the invento inventory ry control control problem, this might result in determining and implementing a policy to order a certain amount of inventory at specified intervals. &or the problem of determining the best products to produce, this might mean testing, analy%ing, and implementing a decision to produce a certain quantity of given products.
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GET FULL FILE [email protected] $lthough gh the formal formal study study of quantit quantitati ative ve analysi analysiss and the refineme refinement nt of the tools and 1#($ $lthou techniques of the scientific method have occurred only in the recent past, quantitative approaches to decision making have been in e!istence since the beginning of time. In the early 1455s, &rederick W. +aylor developed the principles of the scientific approach. 3uring World War II, quantitative analysis was intensified and used by the military. 6ecause of the success of these techniques during World War War II, interest continued after the war. include the scale model, model, physical model, and schematic model 0which 0which is a 1#)$ /odel types include picture or drawing of reality. In this book, mathematical models are used to describe mathematical relationships in solving quantitative problems. In this question, the student is asked to develop two mathematical models. +he student might develop a number of models that relate to finance, marketing, accounting, statistics, or other fields. +he purpose of this part of the question is to have the student develop a mathematical relationship between variables with which wh ich the student is familiar. familiar. interviews with employees and 1#*$ Input data can come from company reports and documents, interviews other personnel, direct measurement, and sampling procedures. &or many problems, a number of different sources are required to obtain data, and in some cases it is necessary to obtain the same data from different sources in order to check the accuracy and consistency of the input data. If the input data are not accurate, the results can be misleading and very costly to the organi%ation. +his concept is called 7garbage in, garbage out8. into the company 1#+$ Implementation is the process of taking the solution and incorporating it into or organi%ation. +his is the final step in the quantitative analysis approach, and if a good ob is not done with implementation, all of the effort e!pended on the previous steps can be wasted. postoptimality analysis allow the decision maker to determine determine how 1#,$ Sensitivity analysis and postoptimality the final solution to the problem will change when the input data or the model change. +his type of analysis is very important when the input data or model has not been specified properly. $ sens sensit itiv ivee solu soluti tion on is one in whic which h the the resu result ltss of the solu soluti tion on to the the probl problem em will will chang changee drastically or by a large amount with small changes in the data or in the model. When the model is not sensitive, the results or solutions to the model will not change significantly with changes in the input data or in the model. /odels that are very sensitive require that the input data and the model itself be thoroughly tested to make sure that both are very accurate and consistent with the problem statement. quantitativee terms that may not be understood by managers. managers. 1#1-$ +here are a large number of quantitativ !am ! ampl ples es incl includ udee '( '(+, *'/, *'/, simu simula lati tion on,, the the /o /ont ntee *arl *arlo o meth method od,, math mathem emat atic ical al programming, #, and so on. +he student studen t should e!plain each eac h of the four terms selected in his or her own words. mathematical models and solving them to find 1#11$ /any quantitative analysts enoy building mathematical the optima optimall soluti solution on to a proble problem. m. thers thers enoy dealing dealing with with other other techni technical cal aspect aspects, s, for e!am e!ampl ple, e, data data analy analysi siss and and colle collect ctio ion, n, comp comput uter er prog progra ramm mmin ing, g, or comput computat atio ions ns. +h +hee implem implement entati ation on proces processs can involv involvee politi political cal aspect aspects, s, convinc convincing ing people people to trust trust the new approach or solutions, or the frustrations of getting a simple answer to work in a comple! environment. Some people with strong analytical skills have weak interpersonal skills9 since implementation challenges these 7people8 skills, it will not appeal to everyone. If analysts become involved with users and with the implementation environment and can understand
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GET FULL FILE [email protected] 7where managers are coming from,8 they can better appreciate the difficulties of implementing what they have solved using #$. aspects of the #$ technique, but they they should 1#1%$ :sers need not become involved in technical aspects have an understanding of what the limitations of the model are, how it works 0in a general sense, sense, the argon argon involved, and the ability to question question the validity validity and sensitivit sensitivity y of an answer handed to them by an analyst. solutions and proofs can be dangerous 1#1&$ *hurchman meant that sophisticated mathematical solutions because people may be afraid to question them. /any people do not want to appear ignorant and questi question on an elabor elaborate ate mathem mathemati atical cal mod model9 el9 yet the entire entire mod model, el, its assumpti assumptions ons and its approach, may be incorrect. break)even point is the number of units that must be sold to make %ero profits. +o +o 1#1'$ +he break)even compute this, we must know the selling price, the fi!ed cost, and the variable cost per unit. 1#1($ f  ;<5
s 1<
v =
a +otal revenue revenue  2501<  >;55 +otal variable cost  250=  >1?5 b 6'  f @0 @0 s sv  ;<[email protected]<  =  <5 units +otal revenue  <501<  >A<5 1#1)$ f  1<5 s <5 v 25
6'  f @0 @0 s sv  1<[email protected]<5  25  < units 1#1*$ f  1<5 s <5 v 1<
6'  f @0 @0 s sv  1<[email protected]<5  1<  B.24 units 1#1+$ f  B55  1,555  1,B55
s <
v ;
6'  f @0 @0 s sv  [email protected]<  ;  A55 units 1#1,$
6'  f @0 @0 sv <55  [email protected] s s ;
<550 s s ;  1B55 s ;  [email protected]<55 s  2.=  ; s  ><.=5 1#%-$ f  2B55 s B5 v 2<
6'  f @0 @0 s s C v  [email protected] C 2<  1?5 per week +otal revenue  B501?5  >?B55
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GET FULL FILE [email protected] 1#%1$ f  2B55 s <5
v 2<
6'  f @0 @0 s s C v  [email protected]<5 C 2<  4? per week +otal revenue  <504?  >B=55 1#%%$ f  2B55
s '
v 2<
6'  f @0 @0 s C v 125  [email protected] s s C 2< 1250 s s C 2<  2B55 s  B< 1#%&$ f  11555
s 2<5
v ?5
6'  f @0 @0 s s C v  [email protected]<5 C ?5 
6'  f @0 @0 s s C v  ;A<@025 C <  2< b f  255 D A< E 2A<
s 25 v <
6'  f @0 @0 sv  2A<@025  <  1=.;;; 1#%($ a /achine 1- f  ?55 s 5.5<
v 5.515
6'  f @0 @0 s C v  [email protected]< C 5.515  1<,555 /achine 2- f  B55
s 5.5<
v 5.51<
6'  f @0 @0 s C v  [email protected]< C 5.51<  11,B2=.A55 /achine 2- *ost E B55 D 5.51<015,555 E ><<5 c /achine 1- *ost E ?55 D 5.5150;5,555 E >455 /achine 2- *ost E B55 D 5.51<0;5,555 E >=<5 d Fet G E the number of copies ?55 D 5.515G E B55 D 5.51<>
s 1= v 15
6'  f @0 @0 s s C v  ?<,[email protected]= C 15  =,12< 'roposal 6- f  ;B,555
s 1= v 1B
6'  f @0 @0 sv ;B,[email protected]=1B =,<55 b 'roposal $ should be chosen.
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GET FULL FILE [email protected] SOLUTION TO .OOD AND !E/EAGES AT SOUTH0ESTEN UNI/ESIT .OOT!ALL GA'ES +he total fi!ed cost per game includes salaries, rental fees, and cost of the workers in the si! booths. +hese areSalaries  >25,555 (ental fees  2,B55  >2  >B,=55 6ooth worker wages  ?  ?  <  >A  >1,2?5 +otal fi!ed cost per game  >25,555  >B,=55  >1,2?5  >2?,5?5 +he cost of this allocated to each food item is shown in the tablePercent
Allocated 2i3ed
revenue
cost
Soft drink
2<>
>?,<1<
*offee
2<>
>?,<1<
ot dogs
25H
><,212
amburgers
25H
><,212
/isc. snacks
15H
>2,?5?
Ite4
+he break)even points for each of these items are found by computing the contribution to profit 0profit margin for each item and dividing this into the allocated fi!ed cost. +hese are shown in the ne!t table-
Sellin5
/ar$
Pro2it
Percent
Allocated
!rea6 ev even
Ite4
7rice
cost
4ar5in
revenue
2i3ed cost
volu4e
Soft drink
> 1 .<5
>5.A<
>5.A<
2<>
? < 1<
=?=?.?A
*offee
>2 .55
>5.<5
>1.<5
2<>
? <1 <
B;B;.;;
ot dogs
> 2 .5 5
>5.=5
>1.25
25H
< 21 2
B;B;.;;
amburgers
>2 .<5
>1.55
>1.<5
25H
< 21 2
;BAB.?A
/isc. snacks
> 1 .5 5
>5.B5
>5.?5
15H
2 ?5 ?
B;B;.;;
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GET FULL FILE [email protected] +o determine the total sales for each item that is required to break even, multiply the selling price by the break even volume. +he results are shownSellin5
!rea6 even
Dollar volu4e
Ite4
7rice
volu4e
o2 sales
Soft drink
>1.<5
= ?=? .?A
>1;,5;5.55
*offee
>2.55
B ; B ; .; ;
>=,?=?.?A
ot dogs
>2.55
B;B ; .;;
>=,?=?.?A
amburgers
>2.<5
; B A B .? A
>=,?=?.?A
/isc. snacks
>1.55
B;B;.;;
>B,;B;.;;
+otal
>B;,B;;.;B
+hus, to break even, the total sales must be >B;,B;;.;B. If the attendance is ;<,555 people, then each person would have to spend >B;,B;;.;[email protected];<,555  >1.2B. If the attendance is ?5,555, then each person would have to spend >B;,B;;.;[email protected]?5,555  >5.A2. 6oth of these are very low values, so we should be confident that this food and beverage operation will at least break even. ote- While this process provides information about break)even points based on the current percent revenues for each product, there is one difficulty. +he total revenue using the break)even points will not result in the same percentages 0dollar volume of [email protected] revenue as originally stated in the problem. $ more comple! model is available to do this 0see p. ;5= Jay ei%er and 6arry (ender, Principles of Operations 'anagement , 4th ed., :pper Saddle (iver, J- 'rentice all, 251B.
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