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Quantitative Methods in Economics CONTENT Beno Rastislav Multicriteria Assessment of the Ergonomic Risk Probability Creation by Chosen Groups of Stakeholders with Using AHP Method within the Context of CSR
Drieniková Katarína 7 Naňo Tomáš Sakál Peter
Borovička Adam The Multiple Criteria Decision Making Method ComputationallyBased on the Assignment Problem 13
Brezina Ivan Hollá Anna Reiff Marian
Stochastic Inventory Location Model 19
Brezina Ivan Gežík Pavel Modeling of Return in Reverse Logistics^22
Čančer Vesna How to Determine and Consider the Weights of Interacting Criteriain MCDN 28
Dolinajcová Miroslava König Brian Lichner Ivan
Value at Risk in Light of Crisis 33
Popović Dražen Vidović Milorad Bjelić Nenad Ratković Branislava
Evaluation of the Direct and Multi-Stop Frequency Based Heuristics for the Inventory Routing Problem 39
Fendek Michal Fendeková Eleonora
Microeconomic Model Instruments for the Analysis of a Competitive Environment State in Slovakia 45
Fiala Petr Models for Combined Overbooking and Capacity Controlin Network Revenue Management 51
Furková Andrea Does Foreign Direct Investment Affect EconomicGrowth? Evidence from OESD Countries 56
Gábrišová Lýdia Janáček Jaroslav Discrete Hamiltonian Problems with IP-Solver^62
Horniaček Milan Expectations of Bail Out and Collective Moral Hazard 67
Hřebík Radek Sekničková Jana Automated Selection of Appropriate Time-Series Model^73
Chocholatá Michaela Relationships Between General Index and its Sectoral Indices: aCase Study for Selected European Indices 78
Ivan Martin Grosso Alessandra Double-Criterion Optimalization of Distributive System Structure^85
Ivaničová Zlatica Rublíková Eva Relations Between Fiscal Policy and Regional Income^92
Jablonský Josef Comparison of Prioritization Methods in Analytic HierarchyProcess 98
Multiple Criteria Decision Making XVI
Janáček Jaroslav Gábrišová Lýdia Regular Polygon Location Problem with IP-Solver^103
Jánošíková Ľudmila Krempl Michal Routing and Scheduling Trains at a Passenger Railway Station^108
Kaňková Vlasta Risk Measures Via Heavy Tails 115
Kopa Miloš Tichý Tomáš Efficiency of Several Risk Minimizing Portfolios^120
Krauspe Kamil An Evolutionary Algorithm for the Mixed Postman Problem 126
Kuncová Martina Sekničková Jana
Multi-Criteria Evaluation of Alternatives Applied to the Mobile Phone Tariffs in Comparison with Monte Carlo Simulation Results^131
Kvet Marek Janáček Jaroslav
Trade-Off the Accuracy for Computational Time in Approximate Solving Technique for the P -Median Problem 136
Michalski Grzegorz Financial Liquidity Management in Relation to Risk Sensitivity:Polish Firms Case 141
Němec Daniel Investigating Differences Between the Czech and Slovak LabourMarket 161
Palúch Stanislav A Simple Solution of a Special Quadratic Programming Problem 166
Pekár Juraj Brezina Ivan jr. Čičková Zuzana
Portfolio Return, Taking into Account the Costs of Financial Transactions 171
Pelikán Jan Černý Michal Some Properties of Graph Flow Problems Used in Logistics^176
Peško Štefan Turek Richard Max-Plus Linear Systems at Bus Line Synchronization^180
Ratković Branislava Vidović Milorad Popović Dražen Bjelić Nenad
A Two Phase Approach to Reverse Logistics Network Design 186
Šedivý Marián Solving Vehicle Routing Problem Using Bee Colony OptimizationAlgorithm 193
Skocdopolova Veronika Goal Programming – History and Present of its Application 197
Sladký Karel Risk-Sensitive and Risk Neutral Optimality in Markov DecisionChains; a Unified Approach 201
Surmanová Kvetoslava Modelling and Forecasting of Wages: Evidence From the SlovakRepublic 206
Szomolányi Karol Lukáčik Martin Lukáčiková Adriana
The Estimate of Parameters of Production Function of Slovak Economy: Econometric Analysis of Nominal Wages 210
Multiple Criteria Decision Making XVI
Quantitative Methods in Economics | 7
MULTICRITERIA ASSESSMENT OF THE ERGONOMIC RISK
PROBABILITY CREATION BY CHOSEN GROUPS OF STAKEHOLDERS
WITH USING AHP METHOD WITHIN THE CONTEXT OF CSR
Beno Rastislav, Drieniková Katarína, Naňo Tomáš, Sakál Peter,
Faculty of Materials Science and Technology, STU Trnava
ABSTRACT
Nowadays in the society more and more resounds the question about corporate social responsibility and sustainable competition of companies as well. The application of CSR (Corporate Social Responsibility) principles by achieving goals of company stakeholders imagines the significant milestone to reach upon mentioned sustainable competition. Despite of possible cross-understanding of stakeholders’ interests on the company management side, shareholders and employees as well, constitutes the adaptation of employees work conditions a place for achieving of synergetic effect. For such an achieving of synergetic effect it is possible to use the ergonomics as a set of tools and methods which goal is to create the appropriate and ergonomics acceptable work environment. In terms of presented facts is this article handling with the multicriteria assessment of ergonomic risk probability creation using the AHP method (Analytic Hierarchy Process).
Keywords: ergonomics, risk, multicriteral decision, sustainable development, corporate social responsibility
JEL Classification: C02, C AMS Classification: 93A30, 97M
Introduction Changing of thinking paradigm of employers in relation to productivity can be achieved by creating appropriate working conditions for employees. Employees thus will be able to submit the required long-term work performance, through which the company can ensure a sustainable competitiveness on market. One of the most effective ways that company can declare a corporate social responsibility is just the application of ergonomics, which solution can reflect in a society-wide scale. Creating an ergonomically acceptable work environment recommend the monitoring of ergonomic risks, which resulting for example in the work environment, nature of work activities, physiological and psychological predispositions of employees. During watching the effects of ergonomic risks, it is necessary to measure and evaluate their acceptable level together with measuring the probability of their occurrence, and assess their effectiveness and mutual pairwise comparison of their effects.
1 ERGONOMICS AND ERGONOMICS RISK
Nowadays we have to deal with situation when companies need to fight with turbulent market conditions, influence of economic and monetary crisis, as well as moral crisis, as well as constantly changing and increasing of costumers demand and technological progress. The companies place more demands then ever before to increase employee productivity. With the increasing level of productivity is increasing the risk associated with the performance of work activities of employees and work environment influences and the level of the technique and technology. The effective way to effectively prevent of risk occurrence is ergonomics, which represent a set of tools and methods, which can be used for its minimization.
Quantitative Methods in Economics | 9
Employees are one of the most important internal stakeholders because of time, energy and efforts they put to company to reach the success and sustainable competitiveness. The relationship between employee and company is considered to be important by society, because employees contribute their efforts and time towards the development of company, which in turn improver society. In return of their work employees’ not only expect wages, but also security and proper working conditions to do their job in friendship and healthy environment. Some specific responsibilities of organization towards their employees are [4]:
- to provide adequate compensation ,
- to ensure open and honest communication with employees that respect each employee’s health and dignity,
- to encourage and assist employees in developing skills and knowledge that are required for accomplishing the task.
- to listen and act to employees’ requests, suggestion, ideas and complaints wherever possible,
- to generate equal treatment and opportunity regardless of gender, age, race and religion,
- to provide optimal working conditions that must be ergonomically acceptable. Both business and employees have certain commitments towards each other. To support company in reaching sustainable competitiveness, company should maintain an ergonomically healthy work environment, where the employees fulfil their responsibilities.
3 AHP METHOD
AHP method is one of the multicriteria optimization methods and exact methods as well. This method can be used within most varied situations where an optimal alternative is searched and a lot of factors are influencing on these possible alternatives – criteria. According to the author of this method Saaty, is composed of three parts:
- Hierarchy – goals, groups of experts, criteria and alternatives are sorted in a hierarchical structure like a tree diagram form and apply a principle that it is going forward from the general to the specifications.
- Priorities – the AHP method is also based on a pairwise comparison always of the two elements between each other, i.e. through the priorities are compared criteria and we are looking for the most important criterion and for the optimal alternative as well. This is done using the scale like it is described in the table 2. The priorities are recorded into the Saaty’s matrix where elements located on a diagonal have a value 1. Reciprocity rule applies: sij = (^1) sji. (2)
⎟ ⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜ ⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
=
(^1111)
(^111)
(^11)
1
1 2 3
13 23 3
12 23 2
12 13 1
K
M M M M
K
K
K
n n n
n
n
n
s s s
s s s
s s s
s s s
S
Table 2 AHP fundamental scale Intensity of importance
Definition Explanation
1 Equal importance Two activities contribute equally to the objective. 3 Moderate Importance Experience and judgement slightly favour one activity over another. 5 Strong Importance Experience and judgement strongly favour one activity over another. 7 Very strong or demonstrated importance
An activity is favoured very strongly over another; its dominance demonstrated in practice.
10 | Multiple Criteria Decision Making XVI
9 Extreme Importance The evidence favouring one activity over another is of the highest possible order of affirmation. 2,4,6,8 Intermediate values between 2 adjacent scale values
Compromise is needed between two levels.
- Consistency – is something like a test of accuracy where we are examining if a pairwise comparison and the final matrix and a result as well are consistent. This is done according to the CI indicator – consistency index CI = ( λ (^) max − n ) (/ n − 1 ). (3) Where “n” is a matrix size. 4 Multicriteria assessment of the ergonomic risk probability creation by chosen groups of stakeholders with using AHP method within the context of CSR
For the purpose of this article we have created an illustrative example of multicriteria assessment of the ergonomic risk probability creation by chosen groups of stakeholders using the AHP method within the CSR context – goal G. As a method for multicriteria decision making was chosen above mentioned AHP method. Ergonomic risk like it is in the table 1 described can take values named by abbreviations: S – small, M – medium, B – big. Selected group of stakeholders are in this case employees of the manufacturing company which most influence ergonomic risks have. Connection with CSR concept is done by the main level of criteria – C1. Technological impact – are hard indicators of the CSR economical pillar, environmental impacts – are indicators of the environmental pillar and last but not least social impacts which are indicators of the social pillar acting on employees. The main criteria level is further divided into the subcriteria – C2 specific for each impact and these are also further divided into the last three criteria C3 : frequency, time exposure and avoid risk opportunity. Alternatives A of the assessment are risk values as described above small, medium and big. Hierarchical structure of this illustrative model is illustrated on the figure 1.
Figure 1 Hierarchical structure of the illustrative model
12 | Multiple Criteria Decision Making XVI
Author’s address Slovak Technical University in Bratislava, Faculty of Materials Science and Technology in Trnava, Institute of Industrial Engineering, Management and Quality, Paulinska 16, 917 24, Trnava, Slovak republic, email: [email protected]
Quantitative Methods in Economics | 13
THE MULTIPLE CRITERIA DECISION MAKING METHOD
COMPUTATIONALLY BASED ON THE ASSIGNMENT PROBLEM
Borovička Adam, University of Economics in Prague
Abstract The paper introduces the multiple criteria decision making method using one of basic problems of linear programming as its computational principle. Thus the method algorithm is based on the assignment problem enabling matching alternatives and rank. The weights of all evaluative criteria set by decision maker are demanded as input information. The approach is proposed in two modifications. One takes into account the differences among criterial values the other no. Finally apart from the theoretical principles the article offers some practical application in investment decision making process in the field of capital market with shares funds.
Keywords: assignment problem , difference, MCDM method, shares fund
JEL Classification: C63, G AMS Classification: 90-
1 INTRODUCTION
In this article a reader can see two important missions. Firstly we propose the multiple criteria decision making method based on the assignment problem. The basic idea is described in some formally modified form compared to (Bouška et al., 1981). This approach does not take into account the differences among criterial values, thus the method modification will be projected. Secondly we can meet the application of proposed method in terms of capital market. Some investor wants to choose suitable investment shares fund^1 from the offer of Investment company Česká spořitelna. We will obtain two different results and compare them.
2 THE MCDM METHOD MAKING USE OF THE ASSIGNMENT
PROBLEM
The assignment method is described in (Bouška et al., 1984 or Hwang et al., 1981). We will use a little (rather) formally modified basic algorithm and then propose deeper modification in order to afflict the importance of criterial values. Firstly we look at the basic idea of this method in the following several steps: First step: Observe the matrix of valuations of all alternatives according to particular criteria Y = ( yij ), where yij ( i = 1, 2,..., p ; j = 1, 2,..., k ) represents evaluation of i th^ variant by j th^ charac-
teristic. Given the vector of criteria weights v (^) j = ( v 1 (^) , v 2 ,..., vk ) defined by decision maker
in agreement with his preferences^2.
Second step: For each alternative we create the ranking vector ai = ( ai 1 , ai 2 ,..., aik ),whereas the
component aij ( i = 1, 2,..., p j ; = 1, 2,..., k ) presents rank of i th^ variant according to j th^ criterion.
In virtue of this vector we identify the set Aij ( , i j = 1, 2,..., p ) containing the indexes of criteria
by which j th^ alternative is placed in i th^ position in the case of no indifferent references according
to all tracked characteristics. Under the indifferent relations specify the sets Eij n ( , i j =1, 2,..., p )
including the indexes of criteria by which j th^ alternative shares i th^ position with the n others^3.
(^1) Shares fund is inside organizational entity of investment company without legal identity (Valach, 2006). (^2) The weight vector can be established on the basis of the points method (see more Fiala, 2008). (^3) For instance: When jth (^) alternative shares 5 th (^) place with two others by kth (^) criterion, so we create three sets for jth
variant as E 5^3 j = E 63 (^) j = E 7^3 j ={ }. k
Quantitative Methods in Economics | 15
Second step: Create the sets for i = 1, 2,..., p , j =1, 2,..., k
Cij l = { , r q (^) ij > qrj ; r = 1, 2,..., p i , ≠ r }, (4) or Cij h = { , r q (^) ij < qrj ; r = 1, 2,..., p i , ≠ r } (5)
containing all indexes of alternatives r which are evaluated worse, or better than i th^ variant by j th
criterion. Then we can define two matrixes Q l^ = ( qijl )and Qh = ( qijh ),where
( ) 1, 2,..., 1, 2,..., ,
lij
ijh
ij rj l r^ C ij (^) l ij
rj ij h r^ C ij (^) h ij
q q q i p j k C
q q q i p j k C
∈
∈
expressing the average distance from alternatives which are evaluated worse, or better than i th
alternative by j th^ criterion. The expressions Cij l^ , Cij h denote the cardinality of sets Cij l ,or Cijh.
Third step: Now the values qlij and qij h must be standardized as follows
max( )
max( )
l l ij ij (^) l i ij h h ij ij (^) h i ij
q t i p j k q
q t i p j k q
Fourth step: Design the matrixes Bh^ =^ (^ bijh ) and B^ d^ =^ (^ bijd ), where the following formulas must
hold
, 1, 2,..., ,
g ij (^) ijn g ij nij
l l v l ij g jg (^) n jg g A g E h h v h ij g jg n jg g A (^) g E
b v t t i j p
b v t t i j p
∈ ∈
∈ (^) ∈
The components bijl , or bij h ( , i j = 1, 2,..., p ) represents the sum of weighted average distances
from worse, or better alternatives in the case of assignment of j th^ evaluated alternative to i th^ place by all criteria. In the case of indifferent relations among alternatives by concrete criteria, the component bij does not include a whole value of weight vg , but only its relative part vg / n ,
where n denotes the number of variants placed in the same position as in the basic algorithm. We
can say again the greater bijl , or lower bij h the major fitness of the assignment of j th^ alternative to
i th^ position.
If there are no assignment of i th^ order to j th^ variant according to all criteria, the values bijl will be
low enough (e. g. -10), on the contrary bijh must be positive (e. g. 10) or at least equal zero as
follows
10 , 1, 2,..., , , 10 , 1, 2,..., ,.
l n ij ij ij h n ij ij ij
b i j p A E b i j p A E
These values are stated in sufficient size in comparison with other elements in the matrixes Bl
and B h not to take place unsolicited assignment of i th^ place to j th^ alternative. Fifth step: We apply the linear problem again for creation the final alternative ranking. But this time we use two assignment problems which are able to do order by average deviations from worse and also better alternatives. Formulate as
16 | Multiple Criteria Decision Making XVI
1 2 1 1 1 1
1 1
1 1
max min
p p p p l l h h ij ij ij ij i j i j p p l h ij ij i i p p l h ij ij j j l h ij ij
z b x z b x
x j p x j p
x i p x i p
x i j p x i j p
= = = =
= =
= =
where xlij , or xijh takes 1 if the alternative j is placed in i th^ position, otherwise equals 0. As we try
to reach the assignment as efficient as possible in the sense of values bijl , or bij h , the objective
function z 1 is maximized, z 2 minimized.
Sixth step: Given two alternative ranks have not to be the same. The whole order will be obtained by the help of simple mean of both ranking as follows
, 2
l h j j j
d d k
whereas d^ lj and d^ hj is the fractional place of j th^ variant according to assignment problems men-
tioned above. The final rank is stated on the basis of descending ordered values kj.
The described method takes into account the differences among the criterial values unlike the basic form. On the other side its computational procedure becomes more complicated. The final order can also contain indifferent relations.
4 PRACTICAL APPLICATION
The investor wants to insert his free financial resources in some open shares funds. As a long term client of Česká spořitelna he chooses the shares funds provided by Investment company Česká spořitelna offering four basic groups of funds, namely money-market funds , mixed funds , bond funds and stock funds. The list of these funds is showed in the following table (Tab. 1).
Table 1 The list of shares funds offered by Investment company Česká spořitelna. Source: Self-designed in MS Excel^5 Money-market funds Mixed funds Bond funds Stock funds
Sporoinvest
Osobní portfolio 4 Plus Fond řízených výnosů Konzervativní MIX Vyvážený MIX Dynamický MIX Akciový MIX
Sporobond Trendbond Bondinvest Korporátní dluhopi- sový High Yield dluhopisový
Sporotrend Global Stocks Top Stocks
The investor wants to gain the ranking of all tracked open shares funds in order to make the right investment decision. Three evaluative criteria are set by the investor (decision maker), in the concrete return^6 , riskiness^7 and costs^8. He determines the weights of all criteria by the help of the points method as follows (Tab. 2).
(^5) http://www.iscs.cz/web/fondy/ (cit. 30. 1. 2012) (^6) We take into account average monthly returns from 1st (^) April 2009 to 1 st (^) December 2011. This period had to be cut
for mixed shares funds Osobní portfolio 4 and Plus because of their later foundation. (^7) The risk is stated as a standard deviation of fund returns. (^8) The costs include the entry fees.
18 | Multiple Criteria Decision Making XVI
connected consequences), thus either take into account the deviations from worse, or better alternatives.
Acknowledgements The work was supported by Grant No. IGA F4/16 /2011, Faculty of Informatics and Statistics, University of Economics in Prague.
References [1] Bouška, J., Černý, M., Glückaufová, D.: Interaktivní postupy rozhodování. Academica, Praha 1984. [2] Fiala, P.: Modely a metody rozhodování. Oeconomica, Praha, 2008. [3] Hwang, C. L., and Yoon, K.: Multiple Attribute Decision Making. Methods and Applicati- ons. Springer-Verlag, Berlin, 1981. [4] Investment company Česká spořitelna, accessible from: http://www.iscs.cz/, [cit. 30. 1. 2012]. [5] Jablonský, J.: Programy pro matematické modelování. Oeconomica, Praha, 2007. [6] Valach, J.: Investiční rozhodování a dlouhodobé financování. Ekopress, Praha, 2007.
Author’s address Ing. Adam Borovička University of Economics in Prague, Faculty of Informatics and Statistics, Department of Econometrics W. Churchill Sq. 4, 130 67 Prague 3 Czech Republic E-mail: [email protected]
Quantitative Methods in Economics | 19
STOCHASTIC INVENTORY LOCATION MODEL
Brezina Ivan, Hollá Anna, Reiff Marian,
University of Economics in Bratislava
Abstract Paper presents stochastic version of the location model incorporating inventory cost in facility location decision making. The goal is to optimize location, inventory, and allocation decisions under stochastic demand described by discrete scenarios. Objective function of proposed model minimizes the expected total cost, including location, transportation and inventory costs of distribution system over all scenarios.
Keywords: stochastic demand, facility location, inventory, optimization
JEL Classification: C AMS Classification: 90B
INTRODUCTION
Logistics technologies and logistics operations are based on the interaction of various subsystems of the distribution system. Its optimization offers the opportunity to achieve desired results. A logistics technology is possible to describe as a sequence of decision-making processes and procedures, respecting the logistical interaction between the components of the logistics system in given economic environment. Under the term optimization of processes we can understand optimization of raw materials, its storage and release, the smooth flow of production and its semi-finished products. Goal is to ensure the movement of material from point of origin to point of consumption to meet the needs of end customers. Decision making about distribution system design or redesign is based on given database of information. The main goal of distribution system design or redesign is to minimize costs. These costs include costs of purchasing, production costs, inventory costs, costs of individual facilities, transportation costs and costs associated with different level of service requirements. Suppose that the cost of opening distribution center are fixed costs (for example construction costs, rental costs, etc.) and to variable costs belongs transport costs, storage costs, etc.. Requirements on the level of customers service leads to increase of inventory costs, due to increase of safety stocks, increase in opening and operation costs and transportation costs of goods distributing from warehouses to the end customer. Therefore, decisions about distribution system design are important factors significantly affecting the efficiency of the distribution system. In decision making process we predict some elements of system, but we cannot predict them with certainty. The physical form of the distribution system is not static and must be adapted to changes such as changing customer demand, changes in product mix, supply strategies or fluctuations in the cost of equipment, thus changes in the tactical level. In this case even deterministic models contain elements of randomness, therefore their future values can be predicted only with some probability.
2 STOCHASTIC INVENTORY LOCATION MODEL
The aim of our model is to minimize the total costs of setting up, transporting, holding and ordering inventory. Therefore, our model is divided into four main parts. The first part is the sum of the fixed installation costs. Company pays for the construction of DC. The second part is the transportation costs associated with transporting supplies from the manufacturer to DC for a time period of one year. Inventory costs are shown in the third section. The last part represents the cost of safety stock.
Quantitative Methods in Economics | 21 ᡐ〷 ∈ 䙨0,1䙩^ ᡢ 㐄 1,2, … ᠶ (4)
ᡑ〶〷う ∈ 䙨0,1䙩^ ᡡ 㐄 1,2, … ᠵ, ᡢ 㐄 1,2, … ᠶ, ᡱ 㐄 1,2, … ᡅ (5)
The objective function (1) value represents the expected value of the individual-scenario costs. The first term inside the parentheses computes the fixed cost of locating DCs. The second term computes the expected cost to transport goods from the supplier to the DCs as well as the variable shipment cost from the DCs to the retailers. The third term computes the expected cost of holding working inventory at the DCs, assuming that each DC follows an economic order quantity (EOQ) policy, including the fixed costs of shipping from the supplier to the DCs. This
term is similar to the classical expression for the optimal EOQ cost given by 㒕 ⡰ゐ〄〨 〄う and fixed
costs of order ᠩᡓ
ゐ 〘∗. Finally, the fourth term represents the expected cost of holding safety stock at the DCs. This term represents cost of safety inventory hedging against randomness in future customer demands and lead time. Constraints (2) require each retailer to be assigned to exactly one DC in each scenario. Constraints (3) prohibit a retailer from being assigned to a given DC in any scenario unless that DC has been opened. Constraints (4) and (5) are standard integrality constraints.
3 CONCLUSION Facility location model with inventory cost integration is proposed in this paper. Its aim is to minimize costs of operation of distribution system. Stochastic aspect of model is lead time in itself and in demand of customers during the lead time.
References [1] Brezina I, Čičková Z, Gežík P, Pekár J: Modelovanie reverznej logistiky – optimalizácia procesov recyklácie a likvidácie odpadu. Vydavateľstvo EKONÓM, 2009. [2] Fábry J: Optimization of Routes in Pickup and Delivery Problem. In: 28th International Conference on Mathematical Methods in Economics 2010, Pts I and II , 2010, p. 128–
[3] Gežík P; Brezina I; Pekár J: Inventory management model with return In: Conference: 28th International Conference on Mathematical Methods in Economics 2010, 183-187 , [4] Gežík P, Hollá A: Options for return of products to manufacturer In: Proceedings of the 29th International Conference on Mathematical Methods in Economics 2011, 199-204, [5] Pekár J: Umiestňovanie obslužných centier In: AIESA - building of society based on knowledge : proceedings : 14th international scientific conference Bratislava. Vydavateľstvo EKONÓM, 2011. p. 1 - 6. [6] Pekár J: Umiestňovanie obslužných centier In: AIESA - building of society based on knowledge : proceedings : 14th international scientific conference Bratislava. Vydavateľstvo EKONÓM, 2011. p. 1 - 6. [7] Snyder, L. V., Daskin, M. S., Teo, Ch.: The Stochastic Location Model with Risk Pooling. In: European Journal of Operational Research. 179 (2007), 1221 – 1238. [8] Tsiakis, P., Shan, N. a Pantelides, C. C. 2001. Design of multi-echelon supply chain networks under demand uncertainty. In: Industrial and Engineering Chemistry Research , 2001, 3585 - 3604.
Author’s address prof. Ing. Ivan Brezina, CSc., Ing. Anna Hollá, Ing. Marian Reiff, PhD. University of Economics in Bratislava, Faculty of business informatics, Department of Operations research and Econometrics Dolnozemska 1/b, 852 35 Bratislava, Slovak Republic
22 | Multiple Criteria Decision Making XVI
MODELING OF RETURN IN REVERSE LOGISTICS
Brezina Ivan, Gežík Pavel
University of Economics in Bratislava
Abstract Main topic of reverse logistics is return of end-of-life product from the point of final consumption back to the manufacturer. This return can be facilitated by wide range of subjects and in different ways. There are many different approaches how this return can be calculated because there is a number of factors, including the life-cycle stage of a product and the rate of technological change, which influence the quality and quantity of the returns. These characteristics have major impact on demand management, and inventory control. The high level of uncertainty arising from different characteristics of quantity and quality of the returned products. This makes the production planning task more complicated and demands different methods of calculating the return.
Keywords: Recycling, Return, End-of-Life Products, Calculation
JEL Classification: C AMS Classification: 90C
INTRODUCTION
Along with the notion of reverse logistics the questions of extending products' life cycle for next reuse, remanufacturing or recycling of used materials has Has become more important (Kostecki, 1998). New approaches in the field of reverse logistics have been developed (Stock, 1998) and many examples of how to use knowledge of reverse logistics practices have arisen (Rogers and Tibben- Lembke, 1999; Guide, 2000). This paper describes the possibility of obtaining the materials through recycling which can generate additional cost savings associated with the purchase of new materials needed for production. It explains the importance of recycling, not only for environmental and social reasons but also for economic reasons as well. We also describe the ways how the used products return back to the manufacturer in time. The paper is involved in modeling of the scenarios for the return of products depending on time period from which the products are returned back to the manufacturer. Processes associated with the products return and its reuse or remanufacturing are influenced by many factors related to its lifecycle (e.g. service, maintenance, redesign, upgrade, redesign or change the packaging, remanufacturing, reusing, recycling and disposal). The management of these factors is associated with a new kind of uncertainty caused by the nature of the return process
- uncertainty about the number and quality of the returned product. There are seven characteristics of the recoverable manufacturing systems that complicate the management, planning, and control of supply chain functions. They are:^1
- The uncertain timing and quantity of returns,
- The need to balance demands with returns,
(^1) GUIDE, V. D. R. Jr. et al. 2000. Production planning and control for remanufacturing: industry practice and
research needs. In Journal of Operations Management, Vol. 18, Issue 4, 2000. ISSN 0272-
