Application ofQuantitative Optimization Techniques to
. Small Businesses1
Miroslav Plevny 

University ofWest Bohemia, Faculty ofEconomics 

Hradebnf 22, 350 11 Cheb, Czech Republic 

E-mail: miroslav.plevny@fek.zcu.cz 

Abstract
In the paper, we discuss the possibilities, which offer solutions of decision-making problems in
small businesses. Although small businesses vary so much in their size, type of clientele, and the
market served, they deal with common problems to be solved in various stages of their life cycle.
A study concerning the extent of usage of quantitative methods showed that these methods are
used in Czech small and middle-sized enterprises only seldom. The reason ofthis situation consists
first of all in unfamiliarity with these methods including possible effects that may be gained by
their use. Certain operations research/management science (MSIOR) approaches can help small
businesses to survive and to compete effectively on the market. It is essential at any time to know
the right technique for each concrete situation and to know how to use such a technique. This
requires certain knowledge, a sense ofhow to model a specific decision problem, and surely some
practice.
Ke)'words
Optimization, modeling application, heuristics algorithms, MS/OR tools in management,
quantitative methods in management, small businesses
1 MS/OR Techniques and Small Businesses
The use of operations research tools and techniques in a small business environment can appear _ .
very doubtful from the economic point of view. Large businesses usually have resources for··
implementation ofcomputer techniques and quantitative approaches when supporting decision-making
processes. Nevertheless, small businesses also have to face complex problems that require the use of.
quantitative techniques in order to solve them efficiently. 1bat is why small businesses not only can"
but also should, use these decision supporting techniques and tools to solve their problems effectively.
All businesses, i.e. small, middle and large, have to solve a variety of decision problems in their daily
operations. In many cases, these problems are similar to both.small and large businesses.
Certain MS/OR methods and techniques can be applied selectively to solve the problems arising in.
small businesses. Respecting the fluctuating environment within which small businesses operate, and
the varied patterns of the problems, users must consider the aspects ofsensitivity analysis before using
the MS/OR models. This enables a manager to analyze what-if questions more efficiently.
Small buSinesses can encounter the following problems in their operations (Mehra, 1990):
• Demand forecasting for their products or services;
• Product mix determining;
• Distribution planning;
• Inventory controlling;
• Resources allocation;
• Layout of facilities planning;
• Quality controlling;
• Customer service improving;
• Scheduling,
I The paper is supported by the Grant Agency ofCzech Republic grant No. 402103/668.
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• Capacity planning;
• Failures predicting; etc.
There exist a lot ofvarious techniques that can be used to solve these problems. It is a serious task .
i fOr manager to find a match between a problem area and a specific technique. With personal
computers easily available, manager can now use a number of tools supporting the decision-making
, process. We suppose herewith all sorts of forecasting procedures, inventory control systems, material
requirements planning systems, statistical analysis techniques etc., but also the use of linear
i 	 programming, transportation and assignment methods or scheduling rules and line-balancing
procedures, which can be helpful by solving problems as determining product mix, allocation
resources, planning capacity, locating facilities, and distributing products. To apply and adopt any of
above techniques for a small business, its staff must have some minimal training in quantitative
methods.
However, sinall businesses may not be able to solve these problems the some way, as can do large
businesses. Financial and other resources are easily available in larger companies usually. Smaller
businesses can choose between two principal possibilities:
1. they may have to seek free or subsidized external consultancy;
2. they can attempt solution of these problems by means ofin-house resources.
Of course, there exists the third possibility too - to do nothing. This third way in today's changing
competitive environment has not much chance of success, especially for small companies. Further, we
will discuss the first two mentioned possibilities.
1.1 External consultancy
There can be considerable competition over how to deliver MS/OR services among internal specialists
and external consultants - even within larger firms that have high potential demand for MS/OR
services. A realized'UK study (Ormerod, 1998) showed that the dominancy of the internal OR groups
of the '70s and '80s changed. Today, MS/OR services are delivered primarily by external OR
consultants in large companies. These organizations focus on core competencies, and many specialist
activities including OR services are outsourced.
It is not aim of this paper to discuss in detail the advantages or disadvantages of both the external
and internal consultancy. This topic is discussed for instance in (Fildes, Ranyard, 2000). As we
mentioned above small businesses often fail to reach the benefit of external consultancy considering
their available financial resources. They have to seek free or subsidized external assistance from local
or state agencies. Other not yet fully exploited source of help may be the universities with their
potential of staff and students, which often seek for practical problems for instance for educational
purposes or diploma work submission. Some universities house small business development centers,
which can provide training for small business managers in MS/OR techniques.
1.2 Internal problem solution
Even if the small business can afford external consultants, this service requires certain time. The need
ofprompt implementation of the [mal decision inhibit from this requirement usually. A very short time
period is available for most decisions necessary to execute in smaller businesses, even for decisions of
fundamental and existential meaning. If some decision concerning a concrete situation or opportunity
is not realized in a very short time, this opportunity and the relevant economic effect usually vanish
beyond recovery. This leads to the conclusion that if small businesses use quantitative techniques,
these techniques are frequently implemented not by ORIMS specialists but the skilled firm managers.
It is essential especially for the small businesses to know the right technique for each situation and
to know how to use it. Wrong or poor-underlaid decisions can threaten the further company's
existence. On the other hand, well-done decision analysis supported by the result of corresponding
quantitative procedure can help to open an unexpected possibility for the next company's activities.
Now, because these procedures in smaller companies usually will be not performed by specialists
in OR methods solution, it is possible to deliver a basic presumption for the use of quantitative
methods in smaller businesses:
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In smaller businesses practice such methods are applicable, that are:
• 	 simple - also the manager who is not a professional OR specialist is able to apply them;
• 	 inexpensive preferably without any additional financial demand;
• 	 able to implement by means of computer technique and software in common use (pC and
modules of common PC-software or commercial available and inexpensive user-friendly
software products).
2 MS Implementation Problems
A successful application of a MS/OR technique depends closely with the implementation of the
method. It was presented in (Watson, Marett, 1979) that only about 40% ofMS projects are ever fully
implemented. The study analyses the major problems in implementing MS method from management
scientist's point of view. The problems as the lack of goQd clean data, not enough time to analyze a
real problem using a sophisticated approach, difficulty in defining problems for applications etc. were
presented.
Our research from the manager's view (closely described in chapter 3) shows that the major
reasons for non-using the MS methods are the poor educational backgroWld to appreciate MS methods
by the top and middle management, the cost of developing and using models, and the lack of time to
implement the MS methods because ofactual problem solving.
It is obvious there are differences between the management scientists and managers opinion to this
problem. It may often be that the management scientists do not Wlderstand the infonnation needs of
management. The management frequently requires so-called "quick and dirty" analysis. This kind of
analysis of the problem is inexpensive, does not have extensive data input requirements, and is
available within the acceptable time for making the decision. There is necessary to understand what
infonnation is needed and how much money and time can be spend on the analysis effort.
The recommendation, which in our opinion suits well to the small business practice, is the initially
building of small, tentative models with involvement by the end user. The building of more
comprehensive models is advisable only when clearlyjustified. Similar recommendation can be fOWld
for instance in (Watson, Marett. 1979):
"In developing planning models it pays to think big but stat small. Initial cost should be
minimized until the benefits ofa model can be demonstrated through some concrete results. The'
natural initial tendency to incorporate everything one can think of into the model should be
avoided."
3 Study on Czech enterprises
Recently we finished one period of the research project concerning the survey of the applications of
models, quantitative methods and rational procedures in Czech companies. Partial results of this
research we presented in (Plevny, 2004). The objective was to obtain infonnation concerning:
• ~e knowledge and awareness ofvarious types ofoptimization methods;
• the use of quantitative procedures that supports decision making in companies (application
types, methods and software used); respectively
• 	 the disuse of these procedures (disuse reasons, eventual usage motivation, fonn of the
access to the necessary information).
With respect to the objective of the research project only the companies stating manufacturing
activities were selected. On the whole we obtained 103 duly filled-out questionnaires from the
addressed companies (more details about the respondent selection and return rate see in (Plevnj»
2004».
The research provided a range ofinteresting information. The familiarity with particular methOds in
Czech companies is generally lower compared with west European and north American cOWltries. 1he
awareness structure about particular types ofmethods is similar. The high ratio of real applications in
the field of quality control in Czech companies is very positive as a relatively new trend in
258 

implementation oftools supporting decision-making. The use ofwidely available software products by
the help of common computer technique (PC) dominates in the investigated (mainly smaller-sized)
companies. The well-known and user-friendly environment and quick and operational accessibility at
requested record computing is their primary advantage. Es example of the results we present here the
Table 1 summarizing the main areas in which the respondents have applied the ORIMS techniques.
The most popular areas of application seem to be Production scheduling, Inventory management
and Quality controlling. Transportation problems and Depot allocation were used minimal, which
logically results from the focus of the research not to transportation, logistics or service but
production-oriented fInns.
On the whole, only 13% companies use the MS/OR tools regularly. On the other hand, nearly three
quarters of companies have never used these instruments. This state is not positive compared with
economic advanced western countries. It is possible to state that these methods are used in Czech
small and middle-sized enterprises only seldom. The reason of this situation consists first of all in
unfamiliarity with these methods including possible effects that may be gained by their use. A great
deal of responders affrrms that they disuse quantitative methods because the nature of their activities
do not allow it. However, it is paradoxical, that great deal of them at the same time declares they do
not know any ofthese methods for decision-making support.
The mathematical optimization methods have been known in the company's practice a couple of
decades already. Nevertheless, the Czech enterprises often cannot utilize these management tools
efficiently. It is possible to examine a number ofpossible causes ofthis state. We can spot one ofthese
causes according to how the strength of the quantitative optimization methods is presented in various
courses or in the literature available in the Czech RepUblic. An effective aid with a list of relatively
simple exact approaches and rational techniques, that could be applicable to solving decision-making
problems in companies, is seldom available to senior managers in Czech companies.
4 Conclusion
Managers in all types of organisations - large or small, private or state, profit or non-profit,
production or providing services use exact methods to help them in their decisions. In consequence
ofincreasing complexity, intensity and quantity ofinternal and external influences, managers meet and
have to solve a large quantity of problems from operational problems to difficult and important
strategic ones. The managers are more and more expected to be able to make decisions based on
logical thinking and complete analysis, and not only on their experiences and intuition.
The power of quantitative methods grows with regard to using of personal computers. The PC
become as a very effective managerial tool, which enable to managers not only to get and to dispose
immediately actual infonnation (for example thanks to the internet), but also to process this
information (thanks to relative cheap software) and to realise (on the base ofgained results) measures
and decisions.
259 

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These procedures in smaller companies usually will be not performed by specialists in OR methods
solution. Therefore for the smaller businesses practice we can recommend the simple methods, which
are inexpensive in their requirements, and can be implemented by means of computer technique and
software in common use.
Finally, the philosophy "think big but start small" seems to be appropriate if solving the problems
with the help of the quantitative tools in small businesses. It is recommended to gain some
approximate or fractional solution at the early point in project development (so called "quick and
dirty" solution) and keep the orientation ofthe project according the user's goals.
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260