SIMULATION OF MODELS LEADS TO A STRATEGY FOR WASTE MANAGING

Oanijel Markovic University of Nis

Faculty of Mechanical Engineering

Vojislav Tomic University of Nls

Faculty of Mechanical Engineering

Miomir Jovanovic University of Nls

Faculty of Mechanical Engineering

SummaJY: Waste has a special kind of importance in the lives of modern cities. A trend of modern waste managing is based on the minimizing ol waste, which is delivered to landfills by using different recycling technologies. The glass waste recycling can be peljormed on 95% of the total waste. Theoretically, glass can be recycled repeatedly. That is why the basic question is: To calculate economic profitability of the distance between recycling centres and points where the glass waste is collected. There are important ecological collection analyses and the glass waste analyses based on a model of medium sized cities in Serbia. In order to evaluate the profitability of the transport of ecological and economic system, a vehicle routing method is applied as well as optimal evaluation of the glass transportation expense. For vehicle routing and optimal expense calculation, Clarke-Wright algorithm of economy was used. Keywords: glass, recyclillg, trallsport, Clarke- Wright

1. INTRODUCTION

Waste has a special significant role in the lives of modern cities. Total increment of waste materials quantity and rapid depletion of natural power and raw material resources demand a change of a traditional industrial waste treatment model. Waste managing requires new law legislations, measures and special rules of behaviour in accordance with the demands of ISO 14001 standards. Measures are applied right from the start of waste accumulation until it is put aside (dislocation , recycling). The above mentioned measures depend on the fact whether the waste is hazardous or not. In this integrated industrial ecosystem, consumption of energy and raw materials has to be optimized and waste accumulation minimized. Only 16% of glass containers that are annually put into traffic are being recycled in Serbia. Just to compare, 95 ,7% of glass containers are recycled in Switzerland [1]. In contrast with other kinds of containers, glass containers do not have to change their prime purpose before being used again. So, glass is a kind of material that can be completely recycled, which actually means that from It of glass litter with the addition of energy you can get 1 t of new glass products of equal quality (the circular course of production is closed). Therefore the importance of the question: Evaluate economic arrangement model of the waste and the distance of the recycling centre so that it represents a maintainable ecological system of the society.

Correspondence to: M.Sc. Danijel Markovic Faculty of Mechanical Engineering, A. Medvedeva 14, 1800 N is, Serbia E-mail: danijel@masfak.ni .ac.rs

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2. LOGISTIC MODEL OF ACCUMULATION AND GLASS RECYCLING

Today's waste managing model includes: forming, accumulation, storing, processing, transport, recycling, in other words, putting hazardous and not hazardous waste aside. Places for the glass accumulation are usually near commercial centres, restaurants or some local waste dumps. The glass waste is specific in its separate accumulation. It accelerates the recycling process and consequently makes secondary raw materials cheaper. On the other side, it requires special glass banks (containers) positioning and high er ecological population awareness. Glass accumulation as a kind of secondary raw material accumulation demands separation of the glass according to its colour: white glass (transparent) and coloured glass (green and brown). That is why most of the glass containers for glass accumulation have separate compartments for transparent, green and brown (dark) glass. Different glass colours have different chemical composition. Technologies of glass gathering are different in many aspects in cities. In figure 1 some types of glass banks (containers) are shown.

Figure 1. Types of containers

'? • Proc. XIX International Conference MHCL'09 - 223

Technical characteristics of different glass containers are given in table l.

Table 1. Technical characteristics of containers

Vo~ 1,1 m3 1,6 m3 3,2 m3 5,0 m3

Width [mm] 1000 1500 1500 1850

Lenght[mm] 1000 900 1500 1850 High [mm] 1240 1513 1665 1665

Opening for glass 0 200 0 200 0 200 0 200

Glass containers are complex constructions that absorb noise, allow admittance to different coloured glass and protect workers from injuries as well as vehicles from damaging. The latest technologies facilitate informative connection between containers and logistic bases and send a sms message about a position and condition of the waste container occupation. In industrially developed countries because of demands for huge storage space and manual manipulation, returnable transport and high hygienic conditions, a production system of nonreturnable bottles is being developed. This system is followed by separate glass accumulation that involves population. The term "recycling" includes an organized collection of things made from the same material with no usable values, which can be made reusable by further processing. The need for treatment or waste storing is reduced with recycling and energy as well as resources is saved. If we use It of the waste glass, we will save 700 kg of sand, 200 kg of limestone, 200 kg of soda and energy (transport and treatment in a recycling factory) . The main advantages of the glass recycling are [2]:

• reduction of energy needed for new glass production up to 25%,

• glass recycling technologies pollute air minimally,

• reduction of capacity needed for the final waste storing. The second best option and the best ecological solution is the usage of returnable bottles,

• while producing I kg of glass we will need 20 litres of water less, as well as 1,5 kg of raw materials less, 1.4KWh of energy and the gas emission is 25% smaller.

To evaluate the profitability of transport in an ecological and economic system, a method of vehicle routing is applied as well as optimal calculation of glass transport expenses. A typical region of developed cities is observed with a number of people wanted (about 300000), which is mostly aimed at in the world today. Table 2 shows a statistically quantified value of the glass waste in Nis [5], as one of the representative cities.

Table 2. The quantity of waste in the city of Nis

Tipeof Quantity per Quantity per

Quantity per year [x 103] waste

day/ people day / year

Plastics 0.036 13.14 3942 Paper 0.028 10.22 3066 Glass 0.016 5.84 1752

-

224 - Proc. XIX International Conference MHCL'09

3. CLARKE-WRIGHT ALGORITHM

The primary idea of Clarke-Wright's algorithm (CW) is based on the economy (savings) of a used route; time spent on the route, fuel consumption, and total transportation expenses, which is possible by choosing the shortest routes for transportation vehicles. Optimization of the transportation system, from the aspect of a logistic approach to a transportation management, is initially made possible by optimizing transportation routes of the goods. Logistic processes of the waste glass treatment are represented with graphs . Points represent conditions and branches represent processes. While maintaining the area, if the B (the base) point is a point from which the transportation vehicle starts and returns to at the end of its service, then any pair of points (i,j) can maintain that same transportation vehicle in two ways: to start from the base, service the point i, return to the base, service the point j , and return to the base again (figure 2a) or to leave the base, service the point i, then the point j , and after that return to the base (figure 2b). The value d(i ,j) represents the shortest way between the points i and j or the shortest transportation time between the points i and j or the smallest fuel amount consumed on the route from the point i to the point j and so on, which depends on the essence of the concrete problem[3J.

B (a)

d(i,j)

B (b)

Figure 2. Graph as a basis of the logistic model of choice rout

If the value d(i ,j) represents a total expense from the point i to the point j , then, regarding the figure 2a case, the total transportation expenses are:

T(i,j) = d(B,i) + d(i ,B) + d(B,j) + dU,B) (I)

and regarding figure 2b:

T(i ,j) = d(B,i) + d(i ,j) + dU ,B) (2)

Total transportation expenses in the second case (variation b) are smaller for the value:

T'(i ,j) = d(i ,B) + d(B,j) - d(i,j) (3)

Based on this (CW algorithm) it is concluded that the saving T(iJ ) is greater if we unite the points i and j. The only limitation factor is the transportation vehicle capacity. To make the one route union of the points i and j possible, the transportation vehicle capacity has to be greater than the total amount of service demands that appear in those two points. Clarke-Wright's algorithm of saving while

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projecting transportation vehicle routes consists of several algorithm steps: Step I: to calculate the saving T(i,j) = d(8 ,i) + d(8,j) -d(i,j), for every pair of points (i,j) that has to be serviced . Step 2: to rang al l the savings and classify them according to their value. Make a list of savings values that starts with the greater one; Step 3: while consideri ng the saving T(i ,j) include an adequate branch (i ,j) in a partial route if operative limitations are not broken: a) if neither point i nor point j were included into any partial route; b) if one of the points i and j is already in cluded in some existing partial route and if that point is not the internal poi nt in the route; c) if both points i and j are included in two different partial routes and none of them is internal in these routes, so, it is possible to uni te partial routes into one; Step 4: when the savings list is completed after classification, the algori thm shou ld be finished to its end.

4. TH E GLASS TRANSPORTATION EXPENSE CALCULATION ACCORDING TO CLARKE­WRIGHT MODEL

For one logistic model, it is necessary to set the location of a recycling centre considering both economy and ecology. To determine the location, information about the quantity of the waste glass is needed (for example, tbe region ofN is, 1752t for recycling per year) [5]. The model basic parts are: an accumulation point, a storage point and a recycling point. As an example, Nis region was observed. Nis city center, as a representative area, is tbe part where the waste glass managing is rather specific . In the narrowest city centre part, there are II containers for the glass waste materials,

I, I m' capacity. Locations of the containers are set according to the quantity of waste generated in celtain places (restaurants, markets, malls , nightclubs). When choosing a location, one has to be careful about the space needed for manipulation of the transportation vehic le that coll ects the waste.

Model [ (figure 3a) represents the transportation of the waste glass from the base point "8" (picture 4) to the recycling centre that is on a hypothetical distance of a= 17 km. The transportation vehicle is the same as the one that collects tbe waste, 5t carrying capacity. The transportation vehicle, after coll ecting the waste, goes to the recyc ling centre where the glass is stored. Then it returns and collects the waste again. Model JI (figure 3b) represents the waste glass transportation fi'om the base point "8" (figure 4) to the hypotheticall y assumed reloading station where, with the other transportation vehicle goes to the recycling centre. At the reloading stations, there are containers with the carrying capacity of 25t. The transportation vehicle that collects the glass waste an'ives at the reloading station where it is emptied and returns to the collecting process. From the reloading station to the recycling centre, a special transpoltation vehicle performs the container transportation. The aim is to calculate, considering different variation solutions, the economic profitability in the form of a mathematical formula:

minLCij . xij . X BRC (4)

where: Cu - is the price a/transportation, Xii - is the distance between the points, XBD - is the distance from the base point to the recycling centre.

D ) ~~

.----- J ---~''''- ------......... .-(~ \ _.-

e.,.. -"' \ ---- ( /~ B; T,i

~~ I -I \ ~. \ ,~ (.0-.. ~ fn:\ '. ~~--"0~) I

. ~~:.::; -------., \..~y . j -----~ '~-'--

Figure 3a and 3b. Two different models of recycling point position

According to Clarke-Wright's a lgorithm, during the first step one should calculate the savings for each pair of points that should be serviced. For example, for a pair of point ( 1,3) it should be:

T(2,3) = d(0,2) + d(0,3) - d(2,3) = 490 + I 140 - 730 = 900 dinars.

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Applying the same methodology, savings for each pair of points (i ,j) are calcul ated. During the second step, savings ranging according to their values is completed as shown in table 5. The third step includes route projecting where the greatest saving belongs to the branch (10, II ).According to tabl~ 5 results, demands for service in points 10 and 11 are Vl0+ VII = 432 + 2 16 = 648 < 5 000 = V (unit is kg) .

Proc. XIX International Conference MHCL'09 - 225

(

Figure 4. Location (nodes) of containers in the city of Nis with the selected routes of movement of vehicles

Since one transportation vehicle can maintain both points due to its capacity, the first partial route is being formed 0 -10 - 11- O. Considering its value, the next saving is on the branch (8,1 1). Since the point II is an external point in the existing partial route (the opposite point to the base point 1), it is possible to include point 8 into the route directly through the point 11 , and the capacity of the transportation vehicle can satisfy the total demand for service on this formed route (route 0 - 8 - 10 -II -0, demand: V8 + V 10 +

Tabl . ~--- -- -- . - ---- _. _._ .. - _._-_. __ .

V II = 576 + 432 + 2 16 = I 224 < 5 000 = V). The next saving happens on the branch (9, 11). The procedure continues until the vehicle's capacity is satisfied. In the end, when all the savings have been taken into consideration, an optimal route schedule is made:

Rout I 0 - 3 - 4 - 5 - 9 - 8 - 10 - 11 - 0 Rout II 0 - 1 - 2 - 6 - 7 - 0

Transport costs of node pairs

0 1 2 3 4 5 6 7 8 9 10 11 0 / 890 490 1140 1800 1400 990 370 11 30 1360 1230 2360

1 890 / 660 1030 2200 2270 1850 1180 2000 2130 2080 3250

2 490 660 / 730 2220 1850 1340 820 1570 1820 1680 2780

3 11 40 1030 730 / 1030 1760 1370 1480 2270 1725 2330 3400

4 1800 2230 2290 1030 / 1420 1640 2140 2880 2000 2560 3150

5 1400 2290 1890 1760 1420 / 840 1710 2490 1040 1610 2250

6 990 1880 1480 1370 1640 840 / 940 1675 1230 1800 2950

7 370 1260 860 1510 2170 1770 940 / 760 1300 860 1990

8 11 30 2020 1620 2270 2930 2530 1675 760 / 1200 800 1230

9 1360 2250 1850 1725 2000 1040 1230 1300 1200 / 870 1490

10 1230 2120 1720 2370 2560 1610 1800 860 800 870 / 1130

1\ 2360 3250 2850 1670 3150 2250 2950 1990 1230 1490 11 30 /

Table 4. Requirements for serving in nodes

oints

226 - Proc. XIX International Conference MHCL'09 © FME, Belgrade. All rights reserved

Table 5. Value of savings in nodes

Value of savings

T(I 0, I I ) 2460 T(I ,3) 1000 T(8 , 1 I) 2260 T(2,3) 900

T(9, 1 I) 2230 T(3 ,5) 780

T(3 ,4) 1910 T(3 ,9) 775

T(4,5) 1780 T(3,6) 760

T(5 ,9) 1720 T(7 ,8) 740

T(9, I 0) 1720 T(7, I 0) 740

T(8 , I 0) 1560 T(7, II) 740

T(5 ,6) 1550 T(I ,2) 720

T(5 , II) 1510 T(I ,4) 490

T(8 ,9) 1290 T(4 , I 0) 470

T(4,9) 11 60 T(6,8) 445

T(4,6) 1150 T(7,9) 430

T(6,9) 1120 T(6,7) 420

T(5 , I 0) 1020 T(6, I 0) 420

T(4, II) 1010 T(6 , 1I) 400

The total transportation expenses, for routes I and II are Cb = 1800 dinars. These transportation expenses include the expenses up to the base point only. Savings algorithm CW applied in this way regards the projection of transpol1ation vehicle routes (vehicles are from a homogenous fleet). Considering the fact that this algorithm enlarges the transportation veh icle route up to the maxill1ull1 capacity of the vehicles, in case of heterogeneous fleet the 1l10st frequently used transportation vehicle would be the one with the highest capacity. [n this case, fixed fleet expenses are not taken into consideration because the price per kiloll1eter is defined as a service charge.

Modell e.xpenses

Model I represents a transport of the glass waste from the base point B to the recycling centre that is on a hypothetical distance XOD = 17 kll1 (XOD - the distance from the base point to the recycling centre). This distance ill1plies that the recycling center is in the city. The sall1e 5t capacity transportation vehicle that collects the glass waste performs transportation. Transportation expenses of XOD = 17 km are added to those expenses calculated according to CW algorithll1 . The transportation vehicle collects and transports the glass waste every fifth day. Model I expenses are calculated according to the following formula:

Cso = Xso' c, (5)

where: c, - is the transportation price per kilometre [dinlkm], XOD - is the distance between the base point and the recycling centre. Total transportation expenses for model I are:

Cso = xso' c,=1 7· 140=2380 dinars

Monthly transportation expenses are:

Correspondence to: M.Sc. Danijel Markovic Faculty of Mechanical Engineering, A. Medvedeva 14, 1800Nis, Serbia E-mail: danijel@masfak.ni.ac .rs

© FME, Belgrade. All rights reserved

T(2,6) 140 T(2,9) 30 T(I ,9) 120 T(3,7) 30

T(3, I I) 100 T(4,7) 30

T(I ,7) 80 T(I ,5) 20

T(2,4) 70 T(I ,8) 20

T(2, II) 70 T( I, II ) 0

T(5 ,7) 60 T(3,8) 0

T(2,8) 50 T(4,8) 50

T(I , IO) 40

T(2,5) 40

T(2,7) 40

T(2, I 0) 40

T(3 , I 0) 40

T(5 ,8) 40

T(I ,6) 30

emes = CSD '1l1lU!s+Cb . limes =

Cmes = 2380 ·6 + 1800 ·6 = 25080 dinars where: Cb - represents expenses up to the base point, I1.mes - represents nUll1ber of routes per month.

Model II expenses

Model [I represents a model with a reloading station that is on a hypothetical distance XO,c = 3 kll1 frOIl1 the base point, that is, froll1 the very city. A reloading station actually ll1eans that the glass waste is reloaded into containers with 25t of carrying capacity. These containers, after they are fi lled, are taken over by a transpol1ation vehicle and delivered to a recycling centre which is on a distance X,cD = 70 km. This model advantage is the fact that the transportation vehicle that collects the glass waste does not go to the recyc ling centre, which reduces its total working hours. Model II expenses are calculated according to the formula:

CSO = Xs tc • C, + X'cO . c, (6) where: XO,c - is the distance from the base point to reloading station, c, - is the price of transpol1ation per km [dinlkll1], X,cD - is the distance between the reloading station and the recycling centre. The total transportation expenses for the model [I are :

CBD = 3 ·140 + 70 · 140 = 10220 dinars

Monthly transpol1ation expenses are:

C",es = XBrc . c,' 11/lIIcs + C b . nmcs + XrcD . C,· 1l2mes

Cmes = 3 ·140 · 6 + 1800 . 6 + 70 ·140· Cm" =23 120 dinara

where: I1. lmes - is a number of tours (per month) froll1 the base point to the reloading station, Cb represents expenses up to the base point, n2mes - is a number of tours (per month) from the reloading station to the recycling centre. Model II shows that the variation II is preferable and for the tr~trnent inside the state circles (Serbia), regional recycling ce~tres should be built.

Proc. XIX International Conference MHCL'09 - 227

4. CONCLUSION

To solve the waste problem does not mean to put it aside but to work preventively on the minimization of its fOlming. Based on what has been said above, the following conclusions can be drawn:

• accumulation of the glass waste has ecological and economic advantage,

applying Clark-Wright's algorithm minimal transportation expenses can be calculated, • glass accumulation technology is greatly developed in the world and shows certain advantages regarding other material considering a recycling degree, • simulating the models represented in this paper, we come to limit distances where profitability of recycling is certain. This is actually the case in which the best economic models are those models where the distance between recycling centers and city composition points is up to 100 km. Therefore, it can be concluded that this way calculated distances determine both regional and state approach - strategy for the glass waste managing.

228 - Proc. XIX International Conference MHCL'09

Note: Paper is done within the research project " Development of the Model and Tehnologies of Logistics of the Comunal Waste Transport" from the Progralll of Technological Developillent, No. 14068, financed by the Ministry of Science of the Republic of Serbia.

REFERENCES

[I] ReplIblicki zavod za statistikll, ReplIblika Srbija 2007.

[2] Baric M.: Recikliranje stakla ekono111ska i ekoloska isplativost, Zagreb, 2004.

[3] 80rdevic B.: Optimizacija realizacije lransportnih problema rllling-modelo111, VTA Beograd, 2005.

[4] Nacionalna strategija upravljanja otpadolll sa program om priblizavanja EU, Vlada Republike Srbije, Beograd, 2003.

[5] Stefanovic G. , Cojbasic Lj., Stosic P. , Nikolic M., Markovic D.: Ispitivanje kolicine i sastava cvrstog otpada, Soko Banja, 2005 .

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