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ciples of socially responsible investing. Expert method was used. Experiments have shown that the use of mathematical models to assess the competence of experts gives good results. This technique allows you to get more accurate results for the determination of the project category.
References
1. Barsola, J., Kosmynskaya, E., 2013. Responsible investment. Journal KPMG. Vol. 3, pp.3-7.
2. Bayura, D.O., 2011. Social investment as a higher level of corporate social responsibility. Theoretical and applied problems of economy. Vol. 24, pp. 212-218.
3. Blagonravov A.A. 2000. Risk Management: Sustainable development. Synergetics. A series of "Science: unlimited possibilities and potential limitations". Science. 431 p.
4. Donets, L.I. 2012. Justification economic decisions and assessing risks. Centre textbooks. 467 p.
5. Gorbulin, V.P., Kaczynski, A.B. 2007. Systematic Strategy of National Security of Ukraine. GC "SPC" "Yevroatlantykinform". 592 p.
6. http://www.bcg.com/expertise_impact/capabilities/risk_management /impactstorydetail.aspx?id=tcm:12-88755&practicearea= risk+management, Boston Consulting Group
7. http://www.equator-principles.com/, Official site of the Equator Principles
8. http://www.ftse.com/index.jsp, FTSE Group (Financial Times Stock Exchange)
9. http://www1 .ifc.org/wps/wcm/connect/Topics_Ext_Content/IFC_Exte rnal_Corporate_Site/IFC+Sustainability/Risk+Management/, Banking on Sustainability. Financing Environmental and Social Opportunities in Emerging Markets. IFC, Washington. p. 11.
10. http://zakon2. http rada.gov.ua/laws/show/964-15, Law of Ukraine "On National Security".
11. http://zakon4.rada.gov.ua/laws/show/254K/96-Bp, Constitution of Ukraine.
12. Investment projects on modernization of the district heating systems of cities of Donetsk, Kremenchug, Zaporizhia, 2010.
13. Kaczynski, A.B, Egorov, Y., 2009. Environmental Security of Ukraine: system principles and methods of formalization. National Security: Ukrainian dimension. Vol. 4, pp.71-79.
14. Libanova Ye., 2010. The social market economy orientation as a precondition for the consolidation of society. Visnuk NAN of Ukraine, Vol.8, pp. 3-14.
15. Slushaienko N., 2008. Expert-regression estimation of investment projects. Journal of State and Regions, Vol. 5, p.179-182.
16. Slushaienko N., 2012. Formation of investment strategy in financial industrial groups using system analysis. Economics. Vol. 91(4), p.125-135.
17. Zelenko, A., Natalenko, M. 2012. The role of social investment in the socialization of economic relations between the entities and the public. Journal of Economic reform. Vol. 3(7), pp.106-111.
18. Mossfeldt, Marcus and Osterholm, Par, 2011. The persistent labour-market effects of the financial crisis. Applied Economics Letters, Vol. 18, Issue 7, pp. 637-642.
19. Nakanishi, Yasuo, 2001. Dynamic labour demand using error correction model. Applied Economics, Vol.33, Issue 6, pp. 783-790.
Надійшла до редколегії 23.04.14
О. Черняк, д-р екон. наук, проф.,
Н. Слушаєнко, канд. фіз.-мат. наук, доц. КНУ імені Тараса Шевченка, Київ
СИСТЕМНІ ПРИНЦИПИ СОЦІАЛЬНО-ВІДПОВІДАЛЬНОГО ІНВЕСТУВАННЯ ЕНЕРГЕТИЧНИХ ПРОЕКТІВ УКРАЇНИ
Досліджується новий напрямок інвестування сучасних проектів - соціально відповідальне інвестування (СВІ). Розглядаються системні принципи соціального інвестування, включаючи вибір оптимальних варіантів аналізу ризиків, їх оцінки та мінімізації. Розглядається методика оцінки соціальних проектів в енергетиці України за кожним видом ризику СВІ. Проведено експертну оцінку трьох енергетичних проектів. Побудовано регресійну модель оцінки компетентності кожного експерта і встановлено категорію проектів відповідно до екологічних і соціальних принципів аналізу.
Ключові слова: соціально-відповідальні інвестиції, інвестиційний ризик, принципи соціального інвестування, стратегія модернізації, регресійний аналіз.
А. Черняк, д-р экон. наук, проф.,
Н. Слушаеко, канд. физ.-мат. наук, доц. КНУ имени Тараса Шевченко, Киев
СИСТЕМНЫЕ ПРИНЦИПЫ СОЦИАЛЬНО-ОТВЕТСТВЕННОГО ИНВЕСТИРОВАНИЯ ЭНЕРГЕТИЧЕСКИХ ПРОЭКТОВ УКРАИНЫ
Исследуется актуальное направление инвестирования современных проектов - социально-ответственное инвестирование (СОИ). Рассмотрены принципы построения целостной системы обеспечения, включающие выбор оптимальных вариантов анализа рисков, их оценки и минимизации. Рассматривается методика оценки социальных проектов в энергетике Украины по каждому виду риска СОИ. Проведена экспертная оценка трех энергетических проектов. Построена регрессионная модель оценки компетентности каждого эксперта и установлена категория проектов, соответствующая экологическим и социальным принципам анализа.
Ключевые слова: социально-ответственное инвестирование, инвестиционный риск, принципы социального инвестирлования, стратегия модернизации, регрессионный анализ.
Bulletin of Taras Shevchenko National University of Kyiv. Economics, 2014, 6(159): 16-21 UDC 519.85 JEL: C 610
E. Ivokhin, Doctor of Sciences, Associate Professor, Almodars Barraq. Subhi Kaml, PhD student, Taras Shevchenko National University of Kyiv, Kyiv
CASE STUDY IN OPTIMAL TELEVISION ADVERTS SELECTION AS KNAPSACK PROBLEM
Abstract : In this research paper, we shall consider the application of classical 0-1 knapsack problem with a single constraint to selection of television advertisements at critical periods such as prime time news, news adjacencies, break in news and peak times using the WINQSB software. In the end of this paper we shall formulate the task of investigation of the post optimality solution of optimal Television Adverts Selection with respect to time allocated for every group adverts.
Keywords: advertisements, integer programming, knapsack problem, fuzzy linear programming, sensitivity analysis.
Introduction. The Knapsack Problems are among the simplest integer problems. The problems in this class are typically concerned with selecting from a set of given items, each with a specified weight and value. Sum of weights a subset of items does not exceed a prescribed capacity and sum of selected items values is maximum.
Knapsack problems have been intensively studies since the pioneering work of Dantzig [1] in the late 50's,
both because of their immediate applications in industry and financial management, but more pronounced for theoretical reasons, as Knapsack problems frequently occur by relaxation of various integer programming problems. In such applications, we need to solve a Knapsack problems each time a bounding function is derived demanding extremely fast solution techniques. The family of Knapsack problems all require a subset of some given items to cho-
© Ivokhin E., Almodars Barraq. Subhi Kaml, 2014
sen such that the corresponding profit sum is maximizing without exceeding the capacity of the knapsack(s). In the 01 Knapsack problems each item may be chosen at most once, while. The multi-choice Knapsack problems occur when the items should be chosen from disjoint classes. Sinha and Zoltners [2] proposed to use multi-choice Knapsack problems to select which components should be linked in series in order to maximizing fault tolerance.
Moreover Nauss [3] proposed to transform nonlinear knapsack problems to multi-choice Knapsack problems. In the second category we should mention that the 0-1 Knapsack problem appears as sub problem when solving generalized assignment problem, which again is heavily used when solving Vehicle Routing Problem (G.Laport [4]).
Knapsack problems and analysis data. Suppose the producer of a Tv program wants to select among numerous adverts for the prime time (news at 19:00 h GMT), which is interspersed with five or six spots of adverts of not more than three minutes each. It is self-evident that the optimal solution of the knapsack problem above will indicate the best possible choice of investment.
The objects to be considered will generally be called items and their number by n. The value and size associated with the j -th item will be called profit (cost of advert) and weight (duration of advert), respectively.
The traditional 0-1 Knapsack Problem (KP) for this case can be mathematically formulated through the following integer linear programming n
£ VjX, ® max
j=1 (1)
subject to
£ WjXj < W, Xj e{0,1}, j = 1,n , (2)
j=1
where Vj is value (cost of advert) and Wj is the weight
(duration of advert) of the j-th item respectively, j = 1, n , and W is the maximum time allocated for adverts.
If we know quantity of different adverts categories, costs and weights in each category, the model above can be rewrite as
m ni .
£ £ v'jxji ® max
i=1 j=1 (3)
£ wjxji < W1, Xj, e {0,1}, j = 1, ni , i = 1, m , (4)
j=1
where m represented the quantity of categories n(-,
i = 1, m , - quantities of advertise in every category.
There are two basic methods for solving the 0-1 knapsack problems: the first, the ideas ofbranch-and-bound techniques have frequently been applied to Knapsack problems since Kolesar [5] and, the second, dynamic programming methods. However we uses the first method in software WINQSB [6] to have been used to solve large scale problems. This study was undertaken using data collected from S.K.Amponsah [7].
TV is a public broadcaster which depends to the greater extent on government subvention. Broadcasting Corporation is however mandated to generate revenue to supplement the government subvention. To this end TV has various ways of generating additional income. These include sponsorship of programs, social and funeral announcements, advertisements among others. However, this research focused on advertisements, which are slotted in the programs schedules prepared quarterly to generate additional income to sustain the operations of the TV station. TV uses an arbitrary method in the selection. In this process an advert is accepted if there is an available time without regard to optimizing revenue. The category of adverts selection studied included:
• prime time news (19.00 h GMT);
• news adjacencies (five minutes before and after news at 12.00, 14.00, 19.00 and 22.30 h GMT);
• other news time (12.00, 14.00, 19.00, 22.30 h GMT);
• break in programs (peak and off peak).
Table 1 shows the various rates for the different categories of adverts at TV. For example Prime time News adverts for 15 sec costs $215 while for 60 sec, the rate is $750. The rates are high for Prime time News and news adjacencies. These are periods where most customers want their adverts televised to reach a larger TV audience. The off peak rates are low compared with the peak periods. Customers usually request for a number of spots for their adverts. Table 2 shows request received by TV for Prime time News (19 h GMT). Customer 1 requested for two spots of adverts for fifteen seconds each at prime time news. The cost of the two adverts is $ 430 (i.e., 215+215) as indicated in the value column. The weight of this advert is 30 sec.
Table 1. TV adverts rates
Category (i = 1,4) Rates in $
16 second 30 second 46 second 60 second
Prime times news (19h GMT) 215 376 662 760
News adjacencies 130 260 376 600
Break in news 136 244 362 626
Break in program 91 16o 220 360
Table 2. Prime time news adverts-19:00 h GMT
Advertise No. j Time in sec. No. of spots requested Category (weight), wj Cost $ (value), vj-
1 16 2 30 430
2 30 3 90 1125
3 46 1 45 562
4 16 1 15 214
6 30 3 90 1125
б 46 2 90 1124
7 60 1 60 750
S 30 2 60 750
9 46 2 90 1124
10 16 1 15 215
11 16 1 15 215
12 30 1 30 375
13 46 2 90 1124
Закінчення табл. 2
Advertise No. j Time in sec. No. of spots requested Category (weight), w} Cost $ (value), v1
14 16 2 30 430
16 30 2 60 1125
16 46 2 90 1124
17 30 3 90 1125
1S 30 3 90 1125
19 46 2 90 1124
20 60 1 60 750
21 46 1 45 562
22 16 1 15 215
23 16 1 15 215
24 16 1 15 215
26 30 2 60 750
26 30 3 90 1125
27 16 2 30 430
2S 60 1 60 750
29 30 3 90 1125
30 16 2 30 430
Additionally, customer number 5 requested three spots of 30 sec each, i.e. 90 sec (weight) with a cost of $1125 (value). The total time available for adverts at the prime time news is 20 min (i.e., 1200 sec) but the total time requested is 1710 sec. Other customers opt for the News Adjacencies. This is 5 min before and after the prime time news at 19.00 h
GMT. As shown in Table 3, the total time available is 10 min (600 sec) but the customers requested a total of 810 sec. Tables 4 and 5 depicts the weights and the values for the adverts requested for the 22:30 news time and for peak time on week days, respectively. The total time available is 600 sec but the customers requested 720 sec.
Table 3. Adverts for news adjacencies -18:55 -19:00 and 20:00-20:05
Advertise No. j Time requested (weight), w2 Cost $ (value), vj
1 30 260
2 45 375
3 15 130
4 90 750
6 60 500
б 60 250
7 90 750
S 15 130
9 15 130
10 30 250
11 30 260
12 60 500
13 45 375
14 15 130
16 15 130
16 15 130
17 60 250
1S 30 260
19 60 500
20 30 260
Table 4. Adverts for Break in News at 22:30 Hours GMT
Advertise No. j Time requested (weight), w? Cost $ (value), vj
1 30 150
2 45 200
3 15 75
4 90 400
6 60 290
б 60 270
7 90 400
S 15 75
9 15 75
10 30 150
11 30 150
12 60 290
13 45 200
14 15 75
16 15 75
16 15 75
17 60 270
1S 30 150
19 60 290
20 30 150
Table 5. Break in program adverts for peak time on week days
Advertise No. j Time requested (weight), w y Cost $ (value), v‘j
1 15 91
2 15 91
3 30 160
4 90 440
6 30 182
б 90 480
7 90 440
S 90 480
g 60 320
10 15 91
11 15 91
12 15 91
13 60 320
14 90 480
16 30 182
16 60 360
17 90 480
1S 30 182
Finally the mathematical problem is formulate as knapsack optimization problem :
430x11 + 1125X2! + 562x31 + 214x41 + 1125x5! + 1124x6! + 750x71 + 750x8! + 1124x9! + 215 x^ + 215x!!! + 375x!21 + +1124x13! + 430x! 4! + !!25x! 51 +! 24x! 6! +!! 25 X! 71 +!! 25 X! 8! +!! 24 X! 91 + 750x20! + 562x2!! + 2! 5x22! +
+2! 5X23! + 2! 5X24! + 750x25! + !!25x26 ! + 430X27! + 750x28! +!! 25x29! + 430x30! + 260X! 2 + 37 5x2 2 +! 30X3 2 +
+750X4 2 + 500X5 2 + 260X6 2 + 750X7 2 + !30X8 2 + ! 30X9 2 + 250X! 02 + 260X!! 2 + 500X! 22 + 375X! 32 + ! 30X! 42 +
+ !30X!5 2 + !30X!6 2 + 250X17 2 + 260X18 2 + 500X19 2 + 260X20 2 + !50X!3 + 200X2 3 + 75X33 + 400X43 + 290X53 +
+270x6 3 + 400X7 3 + 75x8 3 + 75x9 3 + !50x! 03 +! 50 X! 13 + 290x! 23 + 200x! 33 + 75 X! 43 + 75 X! 53 + 75 X! 63 + 270x! 73 + +150X18 3 + 290x19 3 + 150X20 3 + 9^4 + 91x2 4 + 160X34 + 440x44 + 182X54 + 480X64 + 440X74 + 480x84 + 320x9 4 +
+9!x!0 4 + 9!x!! 4 + 91X12 4 + 320X13 4 + 480X14 4 + !82x! 54 + 360X16 4 + 480x! 7 4 + !82x!8 4 —— max
subject to
30x11 + 90x21 + 45x31 + 15x41 + 90x51 + 90x61 + 60x71 + 60x81 + 90x91 + 15x101 + 15X1U + 30x121 +
+90X131 + 30X141 + 60X151 + 90X161 + 90X171 + 90X181 + 90X191 + 60X20 1 + 45X211 + 15X22 1 +
+15X231 + 15x241 + 60X251 + 90x261 + 30x271 + 60x281 + 90x291 + 30x301 < 1200 ;
30X1 2 + 45X2 2 +1 5X3 2 + 90X4 2 + 60X5 2 + 60X6 2 + 90X7 2 + 15X8 2 + 15X9 2 + 30X10 2 +
+30X112 + 60 X122 + 45X132 +1 5X142 +15 X152 +15 X162 + 60X17 2 + 30X18 2 + 60X19 2 + 30X20 2 < 600 ,
30x1,3 + 45x2,3 +1 5x3,3 + 90x4,3 + 60x5,3 + 60x6,3 + 90x7,3 + 15x8,3 + 15x9,3 + 30x10,3 +
+30X113 + 60X123 + 45X133 + 15X143 +1 5X153 +1 5X163 + 60X173 + 30X183 + 60X193 + 30X20 3 < 600 ;
15X1 4 + 15X2 4 + 30X3 4 + 90X4 4 + 30X5 4 + 90X6 4 + 90X7 4 + 90X8 4 + 60X9 4 +
+1 5X10 4 + 15X114 + 15X12 4 + 60X13 4 + 90X144 + 30X154 + 60X164 + 90X174 + 30X18 4 < 600
where
1, if j-th advertise of i-th category is selected, j = 1,ni, i = 1,m, m = 4,n1 = 30, n2 = 20, n3 = 20, n4 = 18,
The optimal selection these adverts yielded $26659. From the Table 6, nineteen adverts were selected from the 30 requested to give an optimal value of $15503. The selection for news adjacencies, the break in news, break in program and a peak period yielded $5070, $2860, $3350, respectively.
Xji ,
10, otherwise
Results of the analysis. By using software WINQSB we obtained the results for the analysis of data from the Table 1 to 5 (Prime Time News, news adjacencies, break in News and break in program) are shown below.
Table 6. (Provide self-explanatory caption)
Advert Category No. of adverts requested No. of adverts selected Time availability, sec Optimal value, $
Prime times news (19h GMT) 30 23 1200 16379
News adjacencies 20 16 600 6070
Break in news 20 17 600 2S60
Break in program 1S 13 600 3360
Total 26669
Adverts numbers which selected in categories:
- prime times news: {1,2,4,5,8,10,11,12,14,15,17,18,19,20,22,23,24,25,27,28,29,30}
- ews adjacencies: {1,2,3,4,7,8,9,11,12,13,14,15,16,18,19,20};
- break in news: {1,2,3,5,6,8,9,11,12,13,14,15,16,17,18,19,20};
- break in program: {1,2,3,5,6,8,10,11,14,15,17,18}.
The resulting solution can be examined for sensitivity.
Sensitivity analysis is usually performed by using principles of shadow prices and reduce costs [6]. But in this case we have nonconventional linear programming task. So sensitivity problem can be formulated as the fuzzy mathematical programming problem with fuzzy time values allocated for every group adverts [8]:
m ni i
E E vijXji ® max i=1 j=1
subject to
E wjxjj < Wi, Xjj є {0,1}, j = 1, n¡ , i = 1, m,
j=1
(6)
(б)
where W1, i = 1, m, - fuzzy defined time values allocated
for every group adverts. Fuzzy values Wi, i = 1, m, can be considered as the right triangular fuzzy numbers (TFN) W = (Wi ,Wi ,Wi + AW'), i = 1m with tolerances
AW' > 0 , i = 1, m . These tolerances determine the values of the boundary changes necessary time resources.
Using the max-min operator (as Zimmermann [9]) crisp linear programming problems for (5), (6) is formulated as follows:
l — max, (7)
m ni ■.
£ £ vjxji -1(U - L) > L , (8)
i=1 j =1
£ w'jxjj +1aw' < w' +AW' , i = tm , (9)
j=1
Xjj e {0,1}, j = 1,ni, i = 1, m , 1 e [0,1], i = 0,m ,
m ni
,i' о
where U = E E VjX'ji i=1 j =1
m ni i 1 L= E E vX i=1 j=1
X0. X1
j *ji ’
j = 1, ni
i = 1, m , - optimal solutions of optimization tasks (5), (9) for l = 0 and l = 1, i = 1, m , respectively.
Solving this task as a fuzzy linear programming problem with the several parameters l, i = 1, m , we obtain values that determine possible changes in the right-hand
sides of constraints that achieves the optimum value of the objective function.
Conclusion. This publication examines the application of the classical 0-1 knapsack problem with one constraint to the television broadcast adverts selection during critical periods. It is defined the task of obtaining the maximum profit from the advertising, broadcast in four categories of events. The solution of the real example is obtained by using WINQSB software. The problem of the sensitivity analysis study of the television advertising adverts choice solutions depending on the time periods allocated for every group adverts. It is considered fuzzy linear programming problem with multiple parameters, the solution of which allows to get the best choice of broadcasts for the changes in time limits allocated to each of the categories. The proposed approach yields optimal choice adverts and ensures the highest profit in the process of broadcasting. Availability limits and possible changes in the time bands provide the choice variability and allow the obtaining of the optimum value of the objective function subject to the ambiguity of time requests. This approach can be seen as the process of predicting the impact of changes in the input data on the solution obtained.
References
1. Dantzig, G.B., 1957. Discrete Variable Extreme Problems. Operations research, 5, pp.266-277.
2. Sinha, A. and Zoltners, A.A., 1979. The multi-choice knapsack problem. Operations Research, 27, pp.503-515.
3. Nauss, R.M., 1978. The 0-1 knapsack problem with multi-choice constraint. European journal of Operations Research, 2, pp.125-131.
4. Laport, G., 1992. The Vehicle Routing problem: An overview of exact and approximate algorithms. European journal of Operations Research, 59, pp.345-358.
5. Kolesar, P.J., 1967. A branch and bound algorithm for knapsack problem. Management science,13, pp.723-735.
6. James, K.H., 2000. Computing True Shadow Prices in Linear programming. INFORMATICA, V.11, No.4, pp.421-434.
7. Amposah, S.K., Oppong, E.O., and Agyeman, E., 2011. Optimal television adverts selection case study: Ghana television. Research journal of information technology, 3(1), pp. 49-54.
8. Ivokhin E.V., Almodars Barraq Subhi Kaml, 2013. Single-Objective Linear Programming Problems With Fuzzy Coefficients and Resources. Computational and Applied Math., N2, pp. 117-125.
9. Zimmermann H.J., 1978. Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, pp.45-55.
Надійшла до редколегії 13.03.14
Є. Івохін, д-р фіз.-мат. наук, доц.,
Aлмодарс Баррак Субхі №мл, асп.
КНУ імені Тараса Шевченка, Київ
ПРИКЛАД ОПТИМАЛЬНОГО ВИБОРУ ТЕЛЕВІЗІЙНОЇ РЕКЛАМИ НА ОСНОВІ ЗАДАЧІ ПРО РЮКЗАК
У цьому дослідженні розглянуто застосування классической задачи 0-1 ранце с одним ограничением для розв'язання задачі вибору пакетів телевізійної реклами у критичні періоди трансляцій, таких як прайм-тайм новини, новини між продовженнями, у перервах новин та у години пик за допомогою програмного забезпечення ШШОЭВ. Сформульовано проблему постоптимального дослідження розв'язків задачі оптимального вибору телевізійної реклами за обсягом часу, відведеному кожній групі об'яв.
Ключові слова: реклама, цілочисельне програмування, задача про рюкзак, нечітке лінійне програмування, аналіз чутливості.
Е. Ивохин, д-р физ.-мат. наук, доц.,
Aлмодарс Баррак Субхи №мл, асп.
КНУ имени Тараса Шевченко, Киев
ПРИМЕР ОПТИМАЛЬНОГО ВЫБОРА ТЕЛЕВИЗИОННОМ РЕКЛАМЫ НА ОСНОВЕ ЗАДАЧИ О РЮКЗАКЕ
В этом исследовании рассмотрено применение классической задачи 0-1 ранце с одним ограничением для решения задачи выбора пакетов телевизионной рекламы в критические периоды трансляций, таких как прайм-тайм новости, новости между продолжениями, в перерывах новостей и в часы пик с помощью программного обеспечения ШМОЭБ. Сформулирована проблема постоптимального исследования решений задачи оптимального выбора телевизионной рекламы по времени, отведенному каждой группе объявлений.
Ключевые слова: реклама, целочисленное программирование, задача о рюкзаке, нечеткая линейное программирование, анализ чувствительности.
