Optimization of Waste Bank Management using Linear

Programming: Case Study in Medan, North Sumatera

Restu Auliani

, Rulianda Wibowo

and Fikarwin Zuska

Natural Resources and Environmental Management, Universitas Sumatera Utara, Indonesia

Department of Agribisnis, Universitas Sumatera Utara, Indonesia

Department of Social Anthropology, Universitas Sumatera Utara, Indonesia

Keywords: Optimization, Waste Bank, Linear Program

Abstract: The numbers of waste are steadily increasing due to the increase in population and consumption. However,

the management of waste is not effective and efficient which result in environmental, social and health

problem. The waste bank, goverment program to lessen that waste issue, offers a solution that gives benefit

not only for environment cleaness but also economically profitable. The enforcement of waste bank

program is not reaching the society extensively leaving the program with less waste resource and become

unprofitable. This study aims to determine optimization of waste bank of Sicanang to maximize profit with

linear programming method. Waste Bank of Sicanang is the only minucipal main waste bank in Medan that

involves community in waste management while reducing the amount of waste disposed to landfill. Waste

management with waste bank needs to be improved, by optimizing the waste management capacity in this

place, so that the profit earned becomes maximal. The result showed the maximum profit that can obtained

by Sicanang waste bank per month reached Rp. 5.396.162 per month with garbage uptake efficiency reaches

0,52% waste capacity of Medan City per day. This study found the potential increase the percentage of

recycling waste by 11,02% and the profit earned reached Rp. 113.319.408 per month by recycle the garbage

up to 10 tons per day if Medan build 1 unit of waste bank center at each district.

1 INTRODUCTION

Most developing countries in Asia are facing waste

problems (Dhokhikah and Trihadiningrum, 2012).

The problem is caused by the amount of waste

which increases along with the increase of

population and comsumption. Furthermore, it is also

caused by limitation on government funding for

waste management, lack understanding of the

impacts of bad waste management, and poor waste

management in all sectors (Guerrero et al., 2013). It

is therefore necessary to do a sustainable long-term

waste management effort (Kumar et al., 2011). The

sustanaibility of waste management can be enforced

with the waste bank program (Indriati, 2016). The

waste bank collects garbage from the people of

surrounding community for recycling. The people

will receive income accordance to the deposited

garbage (Wulandari et al., 2017). In addition, waste

management through waste bank activities may

reduce the amount of waste disposed to landfill

(Dhokhikah et al.,2015)

Waste Bank of Sicanang is one of the main waste

bank in Medan City. Eventhough, the waste

management for recycling had run for few years,

but the financial gain is still apprehensive. Revenue

gained in 2017 is only sufficient to cover operating

costs without generating profits.

The aim of this study is to determine the

optimization of a waste bank to maximize profits.

This can be solved by using an operational research

approach, using a linear program. The results can be

used by Waste Bank of Sicanang in resource

planning in order to obtain maximum profit. The

optimization result also can be a reference for other

parties who want to establish a waste bank.

Furthermore, optimization of waste banks can

improve the efficiency of waste management of

Medan City.

Auliani, R., Wibowo, R. and Zuska, F.

Optimization of Waste Bank Management using Linear Programming: Case Study in Medan, North Sumatera.

DOI: 10.5220/0009902900002480

In Proceedings of the International Conference on Natural Resources and Sustainable Development (ICNRSD 2018), pages 361-366

ISBN: 978-989-758-543-2

361

2 METHODOLOGY

This study focused on Waste Bank of Sicanang,

Medan, North Sumatera, Indonesia. Household, as

the bank customers, segregate and deliver their an

organic waste to “partner waste bank” and records it

in a log book as saving money. The waste from

partner waste bank is collected and sorted based on

several categories and deliver to Sicanang waste

bank. Furthermore Sicanang waste bank recorded in

the log book. They re - separation of waste into

paper, plastic, glass and metal waste into a more

specific type, then to be packed and sold to waste

buyers. In this case, Sicanang waste bank has

established partnership with several waste buyers.

The data used in this study are labour working

hours, the amount of waste, transportation, and

energy used in operations. Optimization of waste

bank using linear program model. Stages of analysis

are as follows 1) Problem identification; 2)

Formulation of linear program model; 3) Determine

decision variables; 4) Determine the objective

function; 5) Determine the constraints; 6) Solution

of linear program model; 7) Sensitivity Analysis.

3 RESULT AND DISCUSSIONS

3.1 Problem Identification

The initial phase of this research is identifying the

problem. Factors affecting the optimization of the

Sicanang Waste Bank are labour working hours,

transportation, waste supply, and energy. The waste

supply obtained from the community is paper,

plastic glass and metal that have been sorted

according to its type. Prior to the formulation of

linear program model, first calculated the

operational cost of waste bank. The operational cost

of the Sicanang Waste bank will be used to

determine the profit earned by the Sicanang Waste

Bank. The waste that has been managed and sorted

here, then sold to the waste buyer or recycling

industry. The difference between the purchase price

of garbage to the waste bank partner with the

garbage sale to the industry is the profit of Waste

Bank of Sicanang.

The operational cost of the waste bank of

Sicanang is Rp. 20.330.000 every month. The details

are for the payment of salary of 10 employees,

transportation cost, and operational cost and

maintenance of the vehicle. Effective working hours

are 6 days a week Monday - Saturday at 8:00 am -

5:00 pm. So, the daily operational cost is the

operational cost divided by working days, then

obtained Rp.847.083, - per day.

3.2 Formulation of Linear Problem

The formulation of the Linear Program Model

consists of the formulation of decision variables, the

formulation of objective functions, and the

formulation of constraint functions. The constraints

are working hours, transportation, paper supply,

plastic supply, glass supply, metal supply, and

energy.

3.2.1 Variables Function

The quantity of waste managed by Waste Bank of

Sicanang is the decision variable of linear program

model in this research, so in the preparation of

model formed four decision variables that will be

searched combination optimal product as follows:

 x1 = the total waste of paper (in kg)

 x2 = the total waste of plastic (in kg)

 x3 = the total waste of glass (in kg)

 x4 = the total waste of metal (in kg)

3.2.2 Objective Function

The coefficient of objective function is the profit per

kg of each type of waste. The profit per kg of paper,

plastic, glass and metal waste is Rp. 900; Rp. 1,800;

Rp. 400; and Rp. 4,300 obtained by calculating the

difference between the selling price and the purchase

price. The objective function is to maximize the

profit earned by Sicanang Waste Bank by

calculating the profit value of each waste component

minus the operational cost of the Waste Bank of

Sicanang in Rp/day.

The formulation of the purpose function model is

explained as follows:

Max z = [ 900 x1 + 1.800 x2 + 400 x3 +

4.300 x4 ]

–

Rp. 847.083

(1)

3.2.3 Constraints

It is given that Sicanang Waste Bank has a total

working hour a day is 32 hours per day. The ability

of workers to sort 1 kg of paper waste is 0.02 hour.

The ability of workers to sort 1 kg of plastic waste is

0.22 hour. The ability of workers to sort 1 kg of

glass waste is 0.07 hour. The ability of workers to

sort 1 kg of metal waste is 0.08 hour. The ability of

labor to sort in units of kg is expressed in constrains

as stated in Table 1.

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Table 1: Constraints of working hours

Component of waste

Coefficient of working

hours (hour/kg)

Pape

0,02

Plastic 0,22

Glass 0,07

Metal 0,08

Based on table 1 above, our equation becomes :

0,02 x1 + 0,22 x2 + 0,07 x3 + 0,08 x4 ≤ 32 (2)

The next constraints is a limitation for

transporting waste purchasing activities from

community. This activity includes paper, plastic,

glass and metal waste simultaneously in the vehicle

simultaneously. The total payload of 2 units of

vehicle becomes the right-hand side value of the

transportation constraint which is 3000 kg, so the

transport constraint function is as follows:

x1 + x2 + x3 + x4 ≤ 3000 (3)

The third constraint is the total supply of waste is

the limitation of the maximum amount of garbage

that has been processed by Sicanang Waste Bank

during 2017. The function of waste supply

constraints for each type of waste is :

x1 ≤ 294,63 (4)

x2 ≤ 59,5 (5)

x3 ≤ 115,73 (6)

x4 ≤ 72,38 (7)

It is given that Sicanang Waste Bank has a total

energy is 1300 kWh. The assumption of electrical

energy used to operate the water pump, to extract

water from the well is Rp. 200,000 from payment of

electricity is Rp. 700.000 every month. Water is

used only for plastic waste washing. For other types

of waste does not require electrical energy, but only

use human energy to sort things out. The energy

coefficient is obtained from the cost of electricity

paid divided by the price of electricity per kWh.

Then, the coefficient of energy is 0.17 kWh. So our

equation becomes:

0,17 x2 ≤ 1.300 (8)

The values of x will be greater than or equal to 0.

This goes without saying:

x1, x2, x3, x4 ≥0 (9)

3.3 Optimum Solution

Table 2: Answer report target cell

Name Final Value

Profit -Rp. 122.285

Table 3: Answer report adjustable cells

Name Final Value

(

)

294,63

Plastic

(

)

59,50

Glass

(

)

103,24

Metal (x4) 72,38

Table 4: Answer report of constraints

Component of waste Coefficient of working

hours

(

hour/k

Working hou

Binding

Transportation Not Binding

er Su

Bindin

Plastic Su

Bindin

Glass Su

Not Bindin

Metal Suppl

Binding

The model obtained from the previous stage then

solving a linear program using the program solver in

Microsoft Excel software

Based on table 2, the maximum profit value

obtained from the optimization result is -

Rp.122.285, - per day, or equivalent to -Rp

2,934,845 per month. This condition is clearly not

profitable for managers of Sicanang Waste Bank.

In table 3, product combination of optimization

results for paper, plastic, glass and metal waste are

294,63 kg; 59.5 kg; 103.24 kg, and 72.38 kg. With a

combination like this, Sicanang Waste Bank still can

not earn decent profit.

Table 4 shows the constraints of working hours,

paper supply constraints, plastic supply constraints,

metal supply constraints have status ‘binding’ means

slack value of 0 (zero), meaning that the resources

provided have been used up to maximum. The

reverse is true of transport constraints, glass supply

constraints, and energy constraints, having values in

the slack column. It means that there are still

remaining resources on the constrains that have not

been used, so the Sicanang Waste Bank does not

need to make additional transportation, glass supply,

and energy.

3.4 Sensitivity Analysis

Sensitivity analysis is conducted to determine the

sensitivity of the model after the optimization result

Optimization of Waste Bank Management using Linear Programming: Case Study in Medan, North Sumatera

363

is obtained. In the sensitivity analysis, it can be seen

the effect of the sensitivity hose consisting of the

Table 5: Sensitivity report of objective function

Name Allowable

Increase

Allowable

Decrease

(

)

∞ 785,71

Plastic (x2) ∞ 542,86

Glass (x3) 172,727 400

Metal (x4) ∞ 3842,9

minimum limit (allowable decrease) that is the limit

of the constraint decrease that does not affect the

model, and the maximum allowable increase is the

limit of the increase of the constraint that does not

change the model.

Table 5 shows the allowable decrease value or

the allowable allowance limit of Rp.785,71 means

the profit rate per kg of paper waste type should not

be less than Rp. 785,71. Likewise with plastic and

metal waste, the rate of profit per kg of this type of

waste should not be less than Rp. 542.86 and Rp.

3842.9. For an allowable increase in paper, plastic

and metal waste, the profit-increase limit is infinity.

In the type of glass waste, the permitted price

increase limit is Rp. 172 per kg of the starting price,

and the limit of decline is Rp.400 from the initial

profit .Tables must appear inside the designated

margins or they may span the two columns.

In table 6. There is a final value column where

the optimum solution of linear program model, such

as 32 hours working hours with the transportation

used is 529,75 kg, loading paper waste 294,63 kg,

plastic waste 59,5 kg, glass waste 103,24 kg and

metal waste as much as 72.38 kg per day, with

energy used as much as 10.11 kWh. The function of

the working hours constraint has a shadow price of

Rp. 5,714,29 it means that every additional 1 hour

working then it can get additional profit of Rp.

5,714,29. So also with the value of shadow price on

the supply of paper, plastic, and metal, there will be

an additional profit of Rp. 785,71; Rp, 542,85; and

Rp.3.842,86 per additional 1 kg of garbage.

Allowable increase maximum limit of addition

and allowable decrease minimum limit of right side

reduction is specified in the sensitivity analysis to

see the optimum profit limit as long as the constraint

function is still within the permitted range.

Allowable increase the maximum limit of the

addition of transportation, supply of glass and

energy is infinity. This condition indicates that

Sicanang Waste Bank is not yet need to add

transportation, supply of glass and energy. The range

of limits for the sensitivity analysis of each

constraint function is 24.77 ≤ working hours ≤

32.87; 250,92 ≤ paper supply ≤ 655,98;

55,52≤supply plastic≤92,35; 61.45 ≤ metal supply ≤

162,71. Then the sensitivity analysis of the right side

constraint analysis will be made to show the limits

of the profit range.

Figure 1: Sensitivity analysis of working hours

Table 6: Sensitivity report of constrains

Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease

Working hou

32 5714,29 32 0,8741 7,227

Transportation 529,753 0 3000 ∞ 2470,2

er Su

294,63 785,714 294,63 361,35 43,705

Plastic Su

59,5 542,857 59,5 32,85 3,9732

Glass Su

103,243 0 115,73 ∞ 12,487

Metal Suppl

72,38 3842,86 72,38 90,3375 10,926

Energ

10,115 0 1300 ∞ 1289,9

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Figure 2: Sensitivity analysis number of paper

Figure 3: Sensitivity analysis number of plastic

Figure 4: Sensitivity analysis number of metal

Figure 1 shows the most advantageous change of

profits is to combine working hours up to 32.87

hours per day so that the benefits are -Rp. 117.314.

Figure 2 shows the maximum profit is to process

paper waste up to 655.98 kg per day is Rp.161.633

or equivalent to Rp. 3.879.192. Figure 3 shows the

maximum gain that can be achieved with the change

of plastic supply up to 92.35 kg per day is -

Rp.104.452. Figure 4 shows the best gains by

changing the amount of processed metal waste up to

162.71 kg per day for a profit of Rp. 224.840 or

equivalent to Rp. 5.396.162 per month. The

combination of optimum waste that can be processed

of waste bank with maximum profit, the amount of

paper, plastic, glass and metal are 294,63 kg/day,

59,5 kg/day, 0,0085 kg/day, and 162,71 kg/day.

Medan city have generates waste 0,295

kg/person/day. Percentages waste of paper 4,14%,

plastic 5,43%, glass 3,7%, and metal 1,73% (include

aluminium 1,04%) (Khair et al., 2018). Population

of Medan Municipality reach 2.229.408 lifes (BPS

Medan, 2017). Based on that data, the number of

waste in Medan City can calculated upon by

multiply generates waste with percentages of waste

and multiply with the population at each component

of waste.

Table 7 shows the amount of domestic waste in

Medan City, only 0.52% of the waste can be

managed by the Sicanang Waste Bank. The amount

of waste that can be processed the most is the metal

waste that is 1.45% of waste of Medan City, because

the profit of metal selling is the highest. In order for

the amount of waste to be processed evenly for all

types of garbage, it takes the value of profits that are

not much different. Therefore, it is expected that the

goversnment's participation will give subsidy to the

selling price of waste.

Table 8 shows the assumption percentage of

recycling waste in order to improve the efficiency of

waste management of Medan City through recycling

of garbage, one of the ways is to improve the

performance of waste banks and involve community

participation.

Table 7: Percentage of recyclingwaste

Com

onent of waste Percenta

(

)

1,08

Plastic 0,17

Glass 0,00004

Metal 1,45

Total 0,52

Table 8: Assumption percentage of recycling waste

Com

onent of waste Percenta

(

)

Pape

22,72

Plastic 3,50

Glass 0,00074

Metal 30,38

Total 11,02

If it is assumed that there is 1 unit of waste bank

in every sub-district in Medan City, there will be 21

unit of municipal waste bank, with the absorption of

garbage can reach 10 853,82 kg/day or 11,02%

waste of Medan City can be recycled. By

Optimization of Waste Bank Management using Linear Programming: Case Study in Medan, North Sumatera

365

maximizing the participation of the community to

sort the waste at home, and depositing the waste into

the existing waste bank in each sub district, it is

estimated that the profit from this activity reaches

Rp 113.319.408 per month.

4 CONCLUSIONS

Based on the optimization result using linear

program model, it can be concluded that the linear

program model can maximize the profit of Sicanang

Waste Bank with the combination of paper, plastic,

glass and metal waste up to 294,63 kg/day, 59,5

kg/day, 0, 0085 kg/day, and 162,71 kg/day with

profit Rp. 224.840/day or equivalent to Rp.

5.396.162 per month with garbage uptake efficiency

reaches 0.52% of waste of Medan City. This study

found the potential increase the percentage of

recycling waste by 11,02% and the profit earned

reached Rp. 113.319.408 per month by recycle the

garbage up to 10 tons per day if Medan build 1 unit

of waste bank center at each district. We hope you

find the information in this template useful in the

preparation of your submission.

ACKNOWLEDGEMENTS

This research has been supported by Pustanserdik

SDM Kesehatan – Badan Pusat Peningkatan Mutu

Sumber Daya Manusia Kesehatan (BPPSDMK)

Ministry of Health Republic Indonesia.

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