The Use of the Generalised Knapsack Problem in Computer Aided
Strategic Management
Dorota Kuchta
, Radosław Ryńca
, Dariusz Skorupka
and Artur Duchaczek
Faculty of Computer Science and Management, Wrocław University of Technology,
Smoluchowskiego Street 25, 50-372 Wrocław, Poland
Faculty of Management, The General Tadeusz Kosciuszko Military Academy of Land Forces,
Czajkowskiego Street 109, 51-150 Wroclaw, Poland
words: Portfolio Planning Methods, Strategic Management, Generalised Assignment Problem, General Knapsack
Problem, Computer Decision Aid.
Abstract: There are many methods and tools in the literature that are helpful in strategic management. Some of them
are related to the aspect of sustainability in terms of controlling and balancing the level of fulfilment of the
different, sometimes conflicting, objectives which must be considered while building strategies. These tools
include product portfolio methods. However, their use is often intuitive and detached from the quantitative
aspects of management, such as cost-related restrictions or other quantitative restrictions imposed by the
market or by internal circumstances. This article presents a proposal for the modification of portfolio methods
aimed at enforcing the portfolio’s quantitative aspect through the use of a discrete optimisation problem,
namely the knapsack problem. Interacting with the decision maker, the quantitative parameters of the situation
and the strategic goals are determined. Following this, a proposal solution is generated by a computer system
in which the respective algorithms for the generalised knapsack problem (also called the generalised
assignment problem) are embedded. The decision maker can accept the solution or change the parameters if
the solution does not suit them or if they simply want to have other solutions for comparison. The outline of
the system and the interaction between the decision maker and the system is illustrated by means of an
example of constructing strategies for a university.
There are many portfolio planning and control
methods (also known as the growth–share matrices)
in the literature. These methods help to control and
specify companies’ current and future market
position and generally help to make strategic
decisions. They make it possible to assess the
directions in which organisations may develop; in
particular they help to control which products,
technologies, or strategic units the company should
concentrate on and which ones should be abandoned
or treated with less attention. This analysis is a good
basis for strategic planning.
The idea of the application of the matrix methods
consists of defining several (approximately 4–20)
areas in the plane and identifying which areas the
objects to be examined (they may be products,
customers, departments, branches, etc.) belong to for
the time being. Next there is the question of ranking
the areas on the basis of a multicriteria analysis.
Obviously, the areas that have the highest position in
the ranking are usually preferred. Then, the decision
maker should decide whether he or she is happy with
the current distribution of the objects. The answer is
usually negative. To address this problem, the
decision maker has to identify which objects could
and should be moved into which areas and which
objects could and should be abandoned (i.e. taken out
of the matrix (and thus the organisation) completely)
so that the overall situation of the organisation with
respect to the specified criteria becomes better than it
was at the control moment, while the circumstances
in which the organisation is operating are respected.
The practical application of the matrix methods is
usually detached from its quantitative aspect and is
rather intuitive. Not taking the quantitative aspect
explicitly into account may prove decisive to the
credibility of the control and of the selection of
available possibilities for improving the current
Kuchta, D., Ry
nca, R., Skorupka, D. and Duchaczek, A.
The Use of the Generalised Knapsack Problem in Computer Aided Strategic Management.
In Proceedings of the 18th International Conference on Enterprise Information Systems (ICEIS 2016) - Volume 2, pages 39-46
ISBN: 978-989-758-187-8
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
situation of the organisation. In particular, the aspect
of the cost of potential actions to be taken and its
relation to the projected budget for said actions may
have a decisive influence. Moving objects into
“better” areas requires concrete actions and creates
cost –as may moving objects into “worse” areas (to
make room for other objects), removing objects from
the matrix (i.e. from the organisation), or making an
object stay in the same area in the next period. The
actions are also usually limited by several quantitative
restrictions of an internal or external nature. These
restrictions might, for example, be due to the fact that
a good area will not accept any more objects, as the
market is saturated. There may also be a restriction
related to certain types of actions for which the
organisation may only have a limited quantity of
financial or human resources. Only attempting to take
these restrictions into account in an intuitive way may
mean that the optimal solution (according to the
optimality criteria defined by the decision maker) is
not always determined.
On the other hand, as the application of the matrix
methods in fact reduces itself to answering the
question of how to “pack” the available objects into
the various areas in the matrix in an optimal way, it
seems natural to combine the application of the
matrix methods with the quantitative optimisation
problem of packing, and more exactly with that of
packing several knapsacks (backpacks). This
combined proposal, together with the concept of a
computer system which would support the decision
maker in the control of the current situation and in
strategic decision making, in which the quantitative
restrictions and requirements may be introduced and
interactively modified, is the main product of the
paper. To illustrate the proposal, its application to the
control and to the elaboration of a modification
proposal of a university’s situation is described.
The outline of the paper is as follows. In Section
2 we briefly describe the main matrix methods. In
Section 3 we present the optimisation problem used:
the generalised knapsack problem (also called the
generalised assignment problem) in the form in which
it can be applied to the control of the organisation’s
current situation and to the strategic decision making.
In Section 4 we illustrate the combination of the
matrix methods and the generalised knapsack
problem as well as the concept of the computer
system that supports the proposal by means of an
application to a university’s situation. Screen shots
are shown from the prototype of the system we have
developed. The paper finishes with conclusions.
The Boston Consulting Group (BCG) matrix (Udo-
Imeh, Edet and Anani, 2012) is one of the best-known
methods in portfolio analysis. The method helps to
determine the strategic position of the company by
indicating its possibilities for development. The idea
of the BCG method involves the controlling and
planning of a product portfolio or a portfolio of
services in order to ensure a long-term balanced
relationship between the products/services that are
characterised by high competitiveness and
profitability as well as new products/services, often in
the development phase, which are not highly
competitive or profitable. The BCG matrix helps to
determine which products should be withdrawn from
the range of production and which should bring more
profit in the future (Fig.1).
Figure 1: BCG matrix (Adapted from (Porth, 2003)).
As shown in Fig. 1, the BCG matrix is based on
two criteria–relative market share and market growth.
The relative share of the market helps to evaluate the
degree of competitiveness of the company. The
second dimension relates to the attractiveness of the
market in which the company operates. The two
dimensions (criteria) define four areas in the matrix.
In the late 60s and early 70s, when the BCG
method was first presented, the division between the
high and low market growth rate was determined to
be 10%, which is often diminished today to 5% (Udo-
Imeh, Edet and Anani, 2012) and may be changed by
the decision maker.
The second dimension – the relative market share
allows the decision maker to evaluate the
competitiveness of the products and/or services. This
indicator, because of its specificity, indirectly takes
into account the competition, and, in contrast to the
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
market growth rate, is measured in terms of current
values. “Relative market share“ enables the
competitive position of the company to be compared
with its largest competitor, whose position
determines the limit seen in the matrix.
Products/services placed in Fig. 1 on the left side of
the border reached a leading position in the market.
For example, a share equal to 4 means that the sales
of a particular product are four times greater than the
strongest competitor.
The four areas in the BCG matrix define four
product groups. The first group is called “Stars”,
which represent a valuable investment and have a
good outlook for the future. The second group of
products is “Question marks” (also called “Problem
children”), which are characterised by an unknown
future. Just like “Stars”, these units are characterised
by high market growth. However, the attractiveness
of the market, high returns, and low entry barriers
may allow the competition to gain strength. This
situation requires significant outlays in the fight with
the competition, including marketing activities. A
small market share may be the reason for the late
introduction of these products to the market.
“Question marks” are unprofitable products that
require funding from other sources. The third group
of products, known as “Cash cows” (also called
“Hosts”) is a group of profitable products with an
established competitive position which generate a
financial surplus that can be used to finance other
product groups (especially those which currently do
not generate profitability, but provide opportunities
for development in the future). The low market
growth rate associated with this product group makes
the market less attractive to new investors. The
company has wide discretion in determining the
prices and quantities of products produced, but
significant investments in the modernisation and
improvement of products cannot be made. The last
group of products are so-called “Balls and chains”
(also called “Dogs” or “Pets”).“Dogs” do not
generate high surpluses or incur significant capital
expenditures. They are typically characterised by low
profitability. They are not progressive and do not
bring the profits expected of them (Wilson and
Gilligan, 1992).
Factoring in these considerations, the user
conducts a ranking of the four areas. Seeing the
matrix with the present products located in the
respective areas, the decision maker evaluates the
current situation and plans to take, if possible, actions
to move the selected products from one area to
another one or make the effort the keep them in the
area where they are or to take them out of the
organisation completely. Thus, we are faced with the
problem of packing four knapsacks in an optimal
way; while the knapsack “Balls and chains” should of
course be avoided, the other three knapsacks are more
desirable. All these decisions may be limited by some
quantitative requirements. The decision of where to
put the limits that define the four areas (how to choose
the thresholds for the two criteria) is of a quantitative
nature. These requirements and preferences of the
decision maker will be able to be taken into account
explicitly in the quantitative model that we propose
later in this paper.
Other matrix methods will be described in less
detail. The General Electric(GE)matrix, also called
the McKinsey Matrix or Business –Industry
Attractiveness Matrix (Udo-Imeh et al., 2012), is
based on the assumption that the company should
operate in more attractive sectors and focus on
investing in products that have a strong competitive
position (Fig. 2).
Figure 2: GE matrix (Udo-Imeh et al., 2012).
The GE matrix model is based on two criteria: the
competitive position of the company and the
attractiveness of the sector in which its products are
offered. For each of the variables there are three
options (high, medium, and low) of assessment
provided. In this way 9 areas are distinguished in
which products under evaluation may be placed.
Symbols A,B, and C (Hax and Majluf, 1990) in Fig.2
represent a possible basis for the ranking of the nine
areas (the areas marked with A form the group of
areas with the highest ranking, followed by the areas
marked with B, etc.), whose details will have to be
resolved by the decision maker. All the areas marked
with one letter may also form one area (one knapsack
in our approach). Following this, the decision maker
would have to resolve the optimisation problem of the
optimal packing of the nine areas, where the areas
ranked the highest would be preferred. Our
The Use of the Generalised Knapsack Problem in Computer Aided Strategic Management
proposition in Section 4 would help to formalise this
decision and to find the best possible solution. The
limits (the threshold for the criteria) may also be
defined in a quantitative way, in which case our
proposal would help to examine the sensibility of the
various solutions to the decision of what the notions
“high”, “medium”, and “low” are chosen to mean.
Here fuzzy thresholds may be used.
The ADL matrix, also called the Maturity Matrix
(Mason, 2010), helps to assess company products on
the basis of two criteria – the competitive position of
a product in the sector and the maturity of the sector.
Five different competitive positions and four phases
of the industry life cycle are distinguished, which
gives 20 areas, usually grouped into three categories
– A,B, and C – as in the case of the GE matrix.
The Hofer and Schendel matrix (Ionescu et al.,
2008) is a development of the GE and the ADL
matrix. Its authors suggest that the assessment of
strategic units must take into account the size of their
competitive position and the phase of the business life
cycle that they are in. Hofer and Schendel also
introduce other criteria in order to assess life-cycle
phases, such as the embryonic, market entry, growth
and shocks, maturity, and decline phases. They also
propose various strategic options ranging from
strengthening the market position, through finding a
market niche, to withdrawal from the business.
The Ansoff matrix (Ansoff, 1957) focuses on the
selection of strategic options based on the criteria of
the market and product newness. Ansoff assumes four
possible strategies for business development, i.e.
market development, product development, market
penetration, and product diversification.
To sum up the usage of matrix methods in the
control of a company’s current situation and its
strategic management, we can say that various criteria
and criteria threshold values are used in order to
define areas which we can see as knapsacks
(backpacks).These knapsacks are filled in in the given
moment in a certain way (each product or each
customer belongs to one knapsack). The objective of
the decision maker may be – and usually will be – to
change the assignment of individual objects to the
knapsacks, as some of the knapsacks are considered
to be better and some worse from the point of view of
the overall situation of the organisation. Following
this, the problem of the optimal packing of the
knapsacks in a given situation is in fact considered,
without being explicitly seen and formulated. It is
usually solved intuitively, without explicitly
considering the quantitative limitations. The
approach we propose in Section 4 will make it
possible to formulate an adequate quantitative
optimisation problem, with the participation of the
decision maker, and implement it in a computer
decision support system, which allows better
solutions (because they are formally optimal) to be
In the next section we will present the generalised
knapsack problem, also known as the generalised
assignment problem, in the form in which it should be
used in our proposal.
The methods described in the previous section help to
evaluate the current situation of an organisation’s
products, customers, or departments and help users
make decisions about how to improve their
organisation’s current situation. However, in our
opinion they would do this more effectively if the
quantitative aspect, quantitative objectives, and
quantitative requirements were incorporated
explicitly into the methods. The optimisation problem
based on the knapsack (backpack) problem with
multiple knapsacks, also called the generalised
assignment problem, might in our opinion constitute
a useful basis for this step. An incorporation of this
kind, together with a computer system that allows the
decision maker to shape the formulation of the
optimisation model according to his or her wishes,
would constitute a considerable form of assistance in
making strategic decisions.
In the single knapsack problem (Martello and
Toth, 1990), we ask the question of which objects
(each of them having a certain volume and a certain
value) from a given set of objects can be put in the
knapsack, so that their total volume does not exceed
the knapsack capacity and their total value is as high
as possible. If we have several knapsacks (the
problem is then called the generalised knapsack
(assignment) problem (Haddadi and Ouzia, 2004)),
the value of each object may depend on the knapsack
it will be placed in. Next, this assignment of objects
(some of which may remain unassigned because of a
lack of knapsack capacity) to the knapsacks is
explored to determine which assignment would
maximise the total value of the objects placed in the
knapsacks while not exceeding the capacities of the
knapsacks and respecting other constraints. Such an
optimisation problem suits our needs well. We have
various knapsacks–various areas in the matrices, each
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
of which may give another value to the object placed
in it. The volume may be represented in our case by
cost, which would be generated by the decision to
move the item from one knapsack to another, and, if
so desired by the decision-maker, by the decision to
leave an item in the knapsack. The limitations (the
equivalent of the knapsacks’ volumes) would be the
budget available for implementing strategic decisions
or some other limits. For example, we might have a
limited budget or limited competences for certain
types of actions (e.g. promotion actions). The
equivalent of volume may also be simply the number
of objects. This would be the case if the market did
not allow a matrix area to absorb more objects than a
certain number. All constraints of this type and many
more could be introduced into the model and
modified if necessary in cooperation with the decision
maker. The model presented below and implemented
in the computer system prototype we present in the
next section can be expanded in many ways,
including the introduction of fuzzy divisions between
knapsacks/areas and other soft (fuzzy) elements.
The basic model, based on (but not identical to)
the generalised knapsack problem, would be as
follows: we assume that in the matrix we have M
areas or domains, denoted as
area has a certain ranking position in the eyes of the
decision maker, denoted as 
, 1, , , while
function R does not have to be injunctive. There are
also N objects
,1,…,. If object
is in
, it has value
, where this value is
determined by experts and takes into account the
ranking of the domains. In some cases we may simply
, 1,…,,1,…,. We also
assume that we have a function that evaluates the
overall situation of the organisation at a given
moment, called the satisfaction function (SF), which
we assume to be as follows:
is the binary variable that takes on a value
of 1 if the i-th element is in the j-th area, and takes on
0 if otherwise.
At the moment of the control of the organisation’s
current situation, the decision maker has to identify
the area that each object belongs to at that moment
and calculate the current value of function(1). If the
value of function (1) is satisfactory, there is no
problem to be solved. However, if it is not, we change
the meaning of variables
. They turn into decision
is equal to1 if the i-th element should be
placed in the j-th area, and equal to 0 otherwise. For
,1,…,, the decision maker has to determine
which areas it might be moved potentially to, and
evaluate for each area the cost of moving object
into area
,1,…,or of keeping it in this
area. This cost will be denoted as
, 1,,,
1, , . If object
cannot be moved into area
the decision maker wants to forbid such a move, then
is given a very high value. Function (1) becomes
an objective function which should be maximised.
We will have in the model the basic constraints of
the generalised knapsack problem (Martello end
Toth, 1990), assuring that no object is placed in more
than one knapsack. The equality sign is also possible,
if we require all the objects to be in one of the
domains, thus if we do not want to eliminate any
object from our activity:
1for 1, ,
On top of that, all the budgetary or other resource
limit-based constraints have to be identified. For
example, if there is a budget B which can be used for
the realisation of the strategy identified by the
optimisation problem, we will have the constraint:
 (3)
We might also have, for example, a budget
all the activities related to object
beingoneofthenumbers1, , ). This
might happen, for example, in the case where each
object has a budget assigned to it and no money
transfers among objects are allowed by the
organisation’s management. Then we would have the
Another type of constraint could be due to the fact
that it is not possible to place more than a certain
number of objects in a “good” area, as the market
does not allow it. If the area in question has index
and the limit is
, we will have the constraint:
Constraints (4) and (5) might have further
variations according to the wishes of the decision
maker. Some of these variations will be illustrated in
the next section.
The solutions of models (1) to (5), found by means
of any software that provides solutions to integer
linear programming problems (for example the free
software “Gusek”, [
k.html]), will deliver the values of the decision
The Use of the Generalised Knapsack Problem in Computer Aided Strategic Management
variables, which in turn ensuring the highest possible
value of objective function (1) in the given
circumstances. If the decision maker is not happy
with this value, he or she may consider modifying the
The following section contains an example of the
application of the proposed concept to the strategic
management of a Polish university. At the same time
it shows screenshots of the prototype of the proposed
computer system in which our proposal has been
The example discussed here concerns a Polish
university. The university faculties (there are seven of
them, denoted by
,1,…,7) will be the objects
of the analysis and of the strategic decisions. They
can be assessed from the point of view of different
criteria. In the discussed case, we propose the use of
two criteria, i.e. the attractiveness of the faculty and
its profitability (other criteria would be also possible).
Figure 3: A screenshot showing the assessment of one
faculty’s attractiveness.
While profitability is a rather unanimous measure
(although there are serious problems linked to
university costing (Cox, Downey and Smith, 1999;
Klaus, 2008; Klaus-Rosińska and Kowalski, 2010)),
attractiveness may be measured using various criteria
and from various points of view, which have to be
aggregated in a certain way, e.g. by means of
weighting. Figure 3 gives an idea how this can be
done in the computer system we propose.
We do not enter into details here, although more
on the subject of faculty attractiveness assessment can
be found in (Ryńca, 2014).Here we give the final
results of the calculations:
Table 1: Assessment of the university faculties.
o Criteria
1 attractiveness 3,46 3,44 3,10 3,28 3,56 3,80 3,42
2 profitability 138,6 60,2 68,1 89,9 45,8 19,3 101,56
First, the current university situation was subject
to a control. In the prototype of the computer system,
in which M=4 and the threshold values were chosen
by the decision maker, taking into account Table 1,
we can see the following screen, where all the
faculties have been placed in one of the four areas,
illustrating the current situation of the faculties:
Figure 4: A screenshot showing the positions of the
The profitability of the faculties is marked on the
X axis (the horizontal axis), while the attractiveness
of the facilities is displayed on the Y axis (the vertical
Function R was entered (R(1)=0, R(2)=4, R(3)=5,
R(4)=8), and it was assumed that
1, ,7, 1, ,4. The current value of objective
function (1) was calculated and found to be equal to
22. The maximum possible value of (1) (in the ideal
case where all the faculties are in the 4
area) is 56.
The relation of 22/56 was found to be unsatisfactory.
Thus, the decision maker was asked to use one of the
empty matrices in Figure 4 to define the cost of all the
transfers possible and desirable for the departments
between areas. It was assumed that keeping a
department in an area where it was at that moment
would not generate any cost and that transfers to
lower-rated areas were not allowed. The results
entered by the decision maker are given in Table 2.
ICEIS 2016 - 18th International Conference on Enterprise Information Systems
Table 2: Cost of actions which would move a faculty to
a higher-ranked area.
Faculty W
Cost of
to Area 1
Cost of
to Area 2
Cost of
to Area 3
Cost of
to Area 4
---------- 0 40 50
0 10 20 30
0 20 20 25
---------- 0 10 10
---------- ---------- 0 60
---------- ---------- 0 70
---------- 0 40 60
Later, several constraints of the type discussed in
Section 3 were introduced (the basic knapsack
problem constraints (2) are included in the model
automatically). All this can be seen in the next
screenshot of the computer system (see “Cost
Figure 5: A screenshot showing the costs of the transitions
between areas including additional constraints.
The additional constraints seen in Figure 5 are:
one concerning the total budget for
improvement actions (3)
those concerning limited budgets for groups
of actions, crossed in the matrices on the
right-hand side of the screen, of type (4) (e.g.
constraint number 1 is 40
those concerning the absorption possibilities
of the individual areas (of type (5)).
Then aGusek file with the integer linear
programming model is automatically created,
exported, and solved The solution, visible in the right-
hand side of the screen in Figure 6, is then imported
and shown to the decision maker in the system
(Figure 6):
Figure 6: A screenshot showing the optimal solution.
The decision maker can see that it is possible to
improve satisfaction with the university’s position
from 22 to 38, thus from 39% of the ideal satisfaction
to 68%. The total budget for improvements will only
be partially used (due to the other constraints – out of
120 monetary units available, only 105 are needed).
The transfers that should be implemented are marked
with OK in Figure 7. Thus there would finally be no
departments in area 1, which is ranked as the worst
area, departments
, and
would be in area 2
(where they were before), departments
in area 3) and
(currently also in area 3) in area 3,
and department
(currently in area 1) and
(currently in area 3) would be in the best area, area
4. If the decision maker is satisfied with this solution,
he or she may agree to it; otherwise, the model may
be modified.
This paper proposes the calculation of matrix models
known from strategic management, which support the
evaluation of products, units, clients, or units of
organisations, with a quantitative component using
discrete optimisation methods, and proposes
embedding all of this into a computer decision aiding
system, allowing the decision maker to find the best
solution according to his/her criteria. The use of
mathematical models by decision makers forces a
deeper reflection and a more systematic analysis
aimed at a quantitative assessment both of the
parameters of the controlled objects, as well as of the
costs of various activities which may be undertaken
The Use of the Generalised Knapsack Problem in Computer Aided Strategic Management
to implement the adopted strategy. Even if the
quantitative assessment is difficult in some cases, it
fosters an objective analysis. In the case where crisp
values are difficult to give, fuzzy numbers (or even
linguistic expressions, modelled by fuzzy numbers)
can be used. The generalisation of the proposed
concept to the fuzzy case would not be complicated
and is foreseen in future research, as fuzzy versions
of the knapsack problem are discussed in the
literature and corresponding algorithms exist (Lin and
Yao, 2001; Kuchta, 2002; Changdar, Mahapatra and
Pal, 2015).
Undoubtedly, the proposed model requires further
verification in practice and the computer system
prototype requires a large amount of testing. Further
extensions should also be taken into consideration, in
particular the introduction of fuzziness.
As far as the computational aspect is concerned, it
must be noted that the knapsack problem belongs to
computationally difficult problems (Haddadi and
Ouzia, 2004), which means that if it were to deal with
a problem of a large size (usually measured by the
number of evaluated objects) the generation of an
optimal solution may take a long time (this time can
even be hours long). If a given organisation has
several thousand products and wants to generate an
appropriate strategy for them, then the determination
of the solution may take more time. However, there
are numerous references in the literature proposing
approximate algorithms for such cases, which are
much quicker (Haddadi and Ouzia, 2004;
Michalewicz and Fogel, 2004). Additionally, the
control of a company’s current situation and strategy
building is not an everyday activity, so even if it takes
more time, this is usually not a serious obstacle and
the type of free software we propose for use in this
matrix should be satisfactory for practical purposes in
most cases.
Ansoff, I., 1957. Strategies for Diversification, Harvard
Business Review, Vol. 35 No.5, pp.113–124.
Changdar, C., Mahapatra, G.S., Pal, R.K., 2015. An
Improved Genetic Algorithm Based Approach to Solve
Constrained Knapsack Problem in Fuzzy Environment,
Expert Systems with Applications, Vol. 42, No. 4, pp.
Cox, K.S., Downey, R.G., Smith, L.G., 1999. ABCs of
Higher Education. Getting Back to the Basics: An
Activity-based Costing Approach to Planning and
Financial Decision Making, Presented at the 39th
Annual Forum of the Association for Institutional
Research, Seattle, WA, USA, 30May–3 June, 1999.
Haddadi, S., Ouzia, H., 2004. Effective Algorithm and
Heuristic for the Generalized Assignment Problem,
European Journal of Operational Research, Vol. 153
No. 1, pp. 184–190.
Hax, A.C., Majluf, N.S., 1990. The Use of Industry
Attractiveness–Business Strength Matrix in Strategic
Planning. In R.G. Dyson (ed.), Strategic Planning:
Models and Analytical Technique(pp.73–92).
Chichester, England: John Wiley & Sons.
Ionescu, F.T., Căescu, Ş.C., Cruceru, A.F., 2008. Business
Portfolio Analysis – Hofer Method, Annals of the
University of Oradea, Economic Science Series, Vol.
17 No. 4, pp. 913–917.
Klaus, A., 2008. Activity based costing - a response to the
increased needs of Polish universities in the field of
information cost. In A. Matysiak (ed.), Prace Naukowe
Uniwersytetu Ekonomicznego we Wrocławiu, Nr. 15.
Rachunkowość zarządcza w warunkach globalizacji
(pp. 152–161).Wrocław, Polska: Wydawnictwo
Akademii Ekonomicznej, (in polish).
Klaus-Rosińska, A., Kowalski, M., 2010. Activity Based
Costing in Universities – A Calculation of Teaching
Costs, Proceedings of the 3rd International Conference
of Education, Research and Innovation
(ICERI2010),Madrid, Spain, 15–17 November, 2010,
Kuchta, D., 2002. A Generalisation of an Algorithm Solving
the Fuzzy Multiple Choice Knapsack Problem, Fuzzy
Sets and Systems, Vol. 127 No. 2, pp. 131–140.
Lin, F.-T., Yao, J.-S., 2001. Using Fuzzy Numbers in
Knapsack Problems, European Journal of Operational
Research, Vol. 135 No. 1, pp. 158–176.
Martello, S., Toth, P., 1990. Knapsack Problems:
Algorithms and Computer Implementations.
Chichester, England: John Wiley& Sons.
Mason, M., 2010. ADL Matrix by Arthur D. Little. All
About Economies on the Web. Retrieved 8June 2012
arthur-d-little , (access: 13.02.2014).
Porth, S.J., 2003. Strategic Management: A Cross-
Functional Approach, Pearson Education, Inc., Upper
Saddle River, New Jersey.
Michalewicz, Z., Fogel, D.B. (2004), How to Solve It:
Modern Heuristics (2nd ed.). Berlin, Germany:
Ryńca, R., 2014. Application of selected methods and tools
in the evaluation of universit, Wrocław, Polska:Oficyna
Wydawnicza Politechniki Wrocławskiej, (in polish).
Udo-Imeh, P.T., Edet,W.E. Anani, R.B., 2012. Portfolio
Analysis Models: A Review, European Journal of
Business and Management, Vol. 4 No.18, pp. 101–120.
Wilson, R.M.S., Gilligan, C., 1992. Strategic Marketing
Management: Planning, Implementation and Control.
Oxford, England: Elsevier Butterworth Heinemann.
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