multi-objective reverse logistics model for integrated computer waste management

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DOI: 10.1177/0734242X06067252

2006 24: 514Waste Manag ResPoonam Khanijo Ahluwalia and Arvind K. Nema

Multi-objective reverse logistics model for integrated computer waste management

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514 Waste Management & Research

Waste Manage Res 2006: 24: 514–527Printed in UK – all right reserved

Copyright © ISWA 2006Waste Management & Research

ISSN 0734–242X


This study aimed to address the issues involved in the plan-ning and design of a computer waste management system inan integrated manner. A decision-support tool is presentedfor selecting an optimum configuration of computer waste man-agement facilities (segregation, storage, treatment/processing,reuse/recycle and disposal) and allocation of waste to thesefacilities. The model is based on an integer linear program-ming method with the objectives of minimizing environmen-tal risk as well as cost. The issue of uncertainty in the estimatedwaste quantities from multiple sources is addressed using theMonte Carlo simulation technique. An illustrated example ofcomputer waste management in Delhi, India is presented todemonstrate the usefulness of the proposed model and tostudy tradeoffs between cost and risk. The results of the exam-ple problem show that it is possible to reduce the environ-mental risk significantly by a marginal increase in the availa-ble cost. The proposed model can serve as a powerful tool toaddress the environmental problems associated with expo-nentially growing quantities of computer waste which arepresently being managed using rudimentary methods of reuse,recovery and disposal by various small-scale vendors.

Poonam Khanijo AhluwaliaArvind K. NemaDepartment of Civil Engineering, I.I.T. Delhi, India

Keywords: Computer waste, integrated waste management, multi-objective optimization, reverse logistics model, Monte Carlo simulation, wmr 904–1

Corresponding author: Arvind K. Nema, Department of CivilEngineering, I.I.T. Delhi, New Delhi-110016, India.Fax: ++91 11 26581117 e-mail: [email protected]

DOI: 10.1177/0734242X06067252

Received 5 September 2005; accepted in revised form 25 April2006

Figures 1–4 appear in color online: http://wmr.sagepub.com

Introduction

Solid waste management, which is already a mammoth taskin India, has become more complicated by the arrival of com-puter waste, particularly personal computers, printers andother computer peripherals. It has been estimated that thetotal number of obsolete personal computers emanating frombusiness and individual households in India would be around1.38 million in 2003 (Toxics Link 2003). A recent publica-tion estimated obsolete personal computers to be around2.25 million units in India in 2005, and projected it to toucha figure of 8 million obsolete units by the year 2010, at anaverage annual growth rate of approximately 51% (Boralkar2005). Considering an average weight of 27.18 kg (ToxicsLink 2003) for a desktop/personal computer then approxi-

mately 61 155 tonnes of obsolete computer waste would havebeen generated in India in 2005 and, at the projected growthrate, this would increase to about 217 440 tonnes by the year2010. An effective waste management system should includewaste collection and transportation, resource recovery throughsorting and recycling, resource recovery through waste process-ing, waste transformation and disposal (CPHEEO 2000). Thesemanagement steps are aptly applicable even for computer-waste. A comprehensive model should not only incorporatethe above-mentioned management steps but should also beable to suggest the location of such facilities, transportationroutes and allocation of different wastes to the facilities. Fur-thermore, for hazardous waste streams such as that of compu-

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Waste Management & Research 515

ter waste, in which recovery and reuse are important concernsand the need exists to minimize both environmental andhealth risks and maximize returns, reverse logistics can be usedas a powerful tool to integrate all of the above aspects into acomplete systems framework.

The objectives of this paper are to: (1) review existingoptimization models/techniques for solid hazardous waste man-agement; (2) to present a decision-support tool using reverselogistics for computer waste management, which would helpselect optimum configuration of transportation routes andfacilities considering environmental risk as well as cost; and(3) to address uncertainty in the estimated waste quantitieswith respect to different time steps.

Review of existing models for hazardous waste management

In the past many researchers and environmental engineershave attempted to address the problem of solid waste manage-ment with the aid of various mathematical models. Althoughthe focus of this paper is the management of computer wasteusing the systems approach, very scanty literature is availableon the relevant subject. Hence, we cover literature pertainingto hazardous waste management and computer waste.

Peirce & Davidson (1982) applied a linear programmingtechnique to identify a cost-effective configuration of trans-portation routes, transfer stations, processing facilities andsecure long-term storage impoundments. Jennings & Sholar(1984) formulated the regional hazardous waste managementsystem as a transportation routing problem with sources gen-erating multiple types of wastes. Zografos & Davis (1989)suggested a multi-objective formulation of hazardous wasterouting problem using a goal programming approach toaddress population at risk; risk imposed on special populationcategories, travel time and property damages. Zografos &Samara (1990) proposed a combined location-routing modelexamining trade-offs between hazardous waste transportationand disposal risks, routing risk and travel time. The modeldetermined the location of hazardous waste disposal facilitiesand the routes from given hazardous waste generation sites tothe selected disposal facilities.

Lund (1990) proposed a linear programming method thatboth evaluates and schedules adoption of each of several pos-sible recycling efforts, minimizing total present value costand considering the effect of recycling on landfill exhaustionand future costs. The method also suggested a least-cost life-time for the landfill, considering the recycling costs of defer-ring landfill closure and the benefits of deferring landfill clo-sure and future replacement costs.

List et al. (1991) surveyed methodological research onhazardous materials transportation in the areas of risk analy-

sis, routing/scheduling and facility location. The review tracedthe evolution of models from single-criterion optimizationsto multi-objective analyses. ReVelle et al. (1991) suggesteda model based on the method of shortest path, a zero-onemathematical programme for sighting and the weightingmethod of multi-objective programming for simultaneous sit-ing and routing the disposal of hazardous waste. Stowers &Palekar (1993) proposed a model that simultaneously consid-ered the risk posed by location and transportation risks whilesearching for an optimal location of a single obnoxious facil-ity on a network.

Jacobs & Warmerdam (1994) presented a linear program-ming model to aid decision-makers in the simultaneous rout-ing and siting of hazardous waste transport, storage and dis-posal operations. Boffey and Karkazis (1995) addressed theproblem of safe transport of hazardous waste with the aid of alinear and a non-linear model. They further derived a condi-tion, which, if satisfied, ensures that the linear model andthe non-linear model generate the same optimal solutionpath, and, if not satisfied, provides a strategy for obtainingthe optimal solution to the non-linear problem.

Mirchandani et al. (1995) described a model based onheuristics for optimally locating a number of inspection sta-tions along a road network plying trucks carrying hazardouswaste, with the objective of intercepting the maximum numberof trucks to prevent hazardous material (HAZMAT) viola-tions.

Ferrer (1997) addressed the complexity of personal com-puter (PC) manufacturing and the difficulties in developingan adequate recovery process. He also proposed and evalu-ated a recovery process. Fleischmann et al. (1997) did a sys-tematic overview of the issues arising in context of reverselogistics. They discussed the implications of the emergingreuse efforts and reviewed the mathematical models pro-posed in the literature. Giannikos (1998) presented a multi-objective model for locating disposal or treatment facilitiesand transporting hazardous waste along the links of a trans-portation network. Four objectives were considered: (1) min-imization of total operating cost; (2) minimization of totalperceived risk; (3) equitable distribution of risk among popu-lation centres; and (4) equitable distribution of the disutilitycaused by the operation of the treatment facilities. A goal-programming model was proposed to solve the problem.Nema & Gupta (1999) proposed a model based on a multi-objective integer programming approach to suggest the opti-mal configuration of facilities for transportation, treatmentand disposal with minimum cost and minimum risk to theenvironment. Hu et al. (2002) presented a cost-minimizationmodel for multi-time-step, multiple-type hazardous wastereverse logistics system. The model addressed the classicalhazardous waste treatment problem with a systematic man-



P.K. Ahluwalia and A.K. Nema


agement strategy rather than with waste treatment technolo-gies as conventionally employed.

Shih & Lin (2003) presented a multiple criteria optimiza-tion approach that considered minimization of the cost, riskand workload for collection system planning for infectiousmedical waste. A compromise programming method was usedto integrate the three objectives, and an example of a collec-tion of infectious waste in Taiwan City was presented. Thelocation of medical institutions, an actual road map and pop-ulation density were provided, using a geographic informa-tion system.

Nema & Gupta (2003) improved upon their suggestedmodel based on a utility function approach by basing the modelon integer goal programming technique. The model was ableto address practical issues such as multiple objectives, com-patibility between waste types, compatibility between wasteand waste technologies and the waste residue generation asso-ciated with treatment technologies.

White et al. (2003), with the help of a case study, describedthe recovery of computers as a step-by-step process and alsoframed an environmental research agenda for recovery man-agement.

As can be seen, none of the above mathematical formulationsaddress all components of a complete solid waste managementsystem, and most of them do not address the reverse flow ofwaste, which is necessary for addressing special waste streamssuch as computer waste. As is demonstrated in the present study,recovered cost is substantial in developing countries such asIndia (Toxics Link 2003). In addition, the generation of wasteat any source node varies with time and so it is advisable to havea multi-time step model that takes into account such variations.Moreover, the above models do not also take into account theuncertainty associated with the data related to waste genera-tion. Furthermore, risk, as addressed in most of the models, isonly considered for the transportation of hazardous waste. Itneeds to be accounted for at every stage, namely storage, seg-regation, treatment and disposal facilities. Integration of allthe above components would make a complete system ofcomputer waste management that can serve as a tool for theconcerned managers.

Proposed model formulation

Any regional network of waste management consists of sourcenodes, a set of transportation routes, and facilities, such assegregation facilities, storage facilities, treatment/processingfacilities, reuse/recycle facilities and disposal options. Moreo-ver, the generation of waste at any source node varies withtime and therefore a multi-time step model that takes intoaccount time variations in the generation of waste is pro-posed. Each activity, whether it is transportation of waste,

processing, storage or disposal, has a certain cost and risk fac-tor associated with it. Thus, the main objective of any solidwaste management programme is to select each activity suchthat the cost and risk factors are minimized.

The following two objectives are addressed in the presentmathematical formulation.

1. Minimization of total cost, which includes transportationcost, segregation cost, storage cost, treatment/processing cost,disposal cost and cost recovered from the reuse and recy-cle of waste. For each facility operating costs, as well ascapital costs are included.

2. Minimization of total risk, which includes transportationrisk, as well as site risk.

Each of these objectives can be minimized individually to obtaincost and risk for the minimum cost and minimum risk scenar-ios. However, because the two objectives have different units,combining both of them poses a problem. This has beenaddressed by Nema & Gupta (1999) by proposing a compositecost–risk utility function.

Objective = Minimize (U)U = Weighting to risk × (risk/minimum achievable risk) +

Weighting to cost × (cost/minimum achievable cost).

The decision-maker can assign the different weightings to costand risk and the model can then be used to analyse differentscenarios involving various combinations of the two.

The decision variables in this mathematical formulation are:

i. waste quantities travelling on a set of transportationroutes;

ii. decision variables for the location of a set of facilities; andiii.the quantities being processed/stored/disposed at various

facilities.

The problem is subject to the following constraints:

i. mass balance at source nodes, segregation facilities andprocessing or treatment facilities;

ii. capacity constraints at processing, reuse/recycle and dis-posal facilities; and

iii.logical constraints at various facilities.

The mathematical formulation of the model is given inAppendix I [equations (1) to (28)].

Formulation of objective functionThe model has two sets of equations one for cost and theother for risk. Total cost is the sum of cost of segregation and





storage at source nodes, cost of transportation of waste fromsource nodes to processing facilities, cost of processing wasteat processing facilities, transportation cost of reusable wastetypes to reuse facilities, transportation cost of the non-reusable,non-processable portion of waste from source nodes to disposalfacilities, capital cost for locating facilities (processing anddisposal), cost of disposal, cost recovered from the sale of recy-clable portion of generated waste and cost recovered fromthe sale of reusable portion of generated waste. The cost ofsegregation at source nodes [Appendix I, equation (1)] wasderived by multiplying the quantity of waste arriving at sourcenode minus waste directly going for reuse and disposal, withthe cost of segregation per unit weight of waste. The cost ofstorage at source nodes [Appendix I, equation (2)] is the quan-tity of waste arriving at the source node multiplied by thecost of storage per unit weight of waste and ratio of storedwaste to incoming waste. The cost of transportation of wastefrom one node to other [Appendix I, equations (3), (6) &(7)] is the quantity of waste travelling from origin node todestination node at a particular time step multiplied by theunit cost of transportation per unit weight per unit distancefor the waste type and the distance between the origin nodeand destination node. The cost of processing or disposal atany facility [Appendix I, equations (4) & (9)] is the quantityof waste reaching the facility at any time step multiplied bythe cost of processing/disposal per unit weight at the facility.The capital cost for locating facilities [Appendix I, equations(5) & (8)] is the equitable capital cost of waste processing/disposal facility per time step multiplied by a binary variablewith value1 or 0 depending on whether the facility is sited bythe model or not. The cost recovered from the sale of therecyclable portion of waste [Appendix I, equation (10)] isthe quantity of a waste type reaching the processing facilityat any time step, multiplied by the cost recovered by sale ofprocessed waste per unit weight at any time step and theratio of processed/recycled waste to incoming waste comingfor processing/recycling. As this cost is recovered, it is sub-tracted from the total cost spent. The cost recovered fromthe sale of the reusable portion of generated waste [AppendixI, equation (11)] is the quantity of a waste type reaching thereuse facility at any time step, multiplied by the cost recov-ered by the sale of reusable waste per unit weight at that timestep. As this cost is recovered, it is subtracted from the totalcost spent.

The risk being addressed in this formulation is relative risk.It is being assumed that the minimization of relative risk leadsto the minimization of actual risk. Total risk can be expressedas a summation of transportation risk and risk at various facili-ties due to segregation, processing, reuse, storage and disposalof waste. Transportation risk for a route [Appendix I, equa-tions (13)–(16)] is a function of waste quantity being trans-

ported on that route, hazard potential of the waste, probabil-ity of accident and population impacted on that route (Nema& Gupta 1999). Site risk [Appendix I, equations (17)–(21)]is a function of waste quantity arriving at the site, hazardpotential of the waste, probability of accident and populationimpacted at that site. The hazard potential of the waste hasbeen derived by gathering information on the relative impor-tance of various waste types and their attributes related toboth chronic and acute risk (direct skin contact hazard, flam-mability, toxicity, abatement potential, release to air, water,etc.) using the Delphi technique. The hazard potential of thewaste was then determined using a combination of the deci-sion alternative ratio evaluation (DARE) technique (Klee1976) and the Analytical Hierarchy Process (Saaty 1980).

Formulation of constraintsThe mass balance at various nodes ensures that the wastequantity arriving at a node (source node/facility) is equal tothe waste present at the node and waste leaving the node[Appendix I, equations (22) & (23)]. The capacity constraintat various facilities ensures that the waste quantity reaching afacility at any time step is less than the designated capacity ofthe facility for that time step [Appendix I, equations (24), (26)and (28)]. Logical constraint at facilities [Appendix I, equa-tions (25) and (27)] to be selected will ensure that if no wasteis arriving at a facility over all the time steps, the binary vari-able associated with a facility is assigned a value 0 (i.e. thefacility is not sited). The logical constraint will be satisfied whenthe binary value associated with the facility is forced to be oneby the capacity constraint equation when waste arriving atthat facility is greater than zero. To force the value of thebinary variable to be one even for small quantities of wastearriving at that facility, the waste quantity is multiplied by alarge number.

Example problem

The case study undertaken is that of computer waste generationin Delhi based on a study undertaken by Toxics Link (ToxicsLink 2003). Delhi is the National Capital Region of India.Currently the recycling and recovery of precious metals andother useful parts of computer waste is being done mostly byunskilled labour in small centres located in the heart of Delhi.The methods employed are very rudimentary and pose graveenvironmental and health hazards (Toxics Link 2003). Hence,it is important to plan computer waste management in citiessuch as Delhi using the systems approach.

The proposed waste types considered in the example prob-lem, their description, unit cost of transportation and hazardpotential arrived at are given in Table 1. The map giving loca-tion details of the various nodes is shown in Figure 1. The net-





work consists of 16 nodes, the details of which are given inTable 2. The sources cum segregation nodes are nodes wherecomputer waste collected from around the city/region arrivesand is segregated. Storage facility is available at these nodesand it is assumed that 20% of the waste arriving at each facil-ity is being stored for future action. Two nodes representpotential options for disposal sites. Two potential processingfacilities for segregated plastic and two potential processingfacilities for segregated metal scrap were also included in thestudy. The case study is analysed for a total of four time steps;each of which spans 3 months. The waste generation varies ateach source node with each time step and the waste genera-

tion rates at various source nodes are given in Table 3. Recov-ered cost from various waste types and their weight-wise frac-tions are given in Table 4. The distances between variousnodes required by the model are given in Table 5. The linksare grouped into four groups (Table 5) on the basis of theregion they are passing through and various risk attributes areassigned. The details of various source nodes such as the prob-ability of an accident, population impacted, segregation andstorage costs are given in Table 6. Further details of variousfacilities such as the probability of an accident, populationimpacted, capacity, capital and operating costs are given inTable 7.

Fig. 1: Map of Delhi showing location of various source nodes and facility nodes.

Table 1: Proposed waste types of the example problem, their description and unit cost of transportation.

Waste type DescriptionUnit cost of

transportation(US $ tonne–1 km–1)

Hazard potential of

waste*

Primary waste types

WA Computer/PC 2 0.04

WB Dot matrix printers 2 0.04

WC Desk-jet printers 2 0.04

Sub-waste types of primary wastes

W1 Cathode ray tube (CRT) 3 0.15

W2 Processor chip, Reusable floppy drive, Hard disk 3 0.08

W3 Printer motor 3 0.07

W4 Printer cartridge 3 0.10

W5 Brominated or ABS (acrylonitrile–butadiene styrene) plastic 2 0.11

W6 Circuit boards, Damaged CRTs, Defective IC, Mother boards, CPU, Condensers, Capacitors, PVC wires, Non-reusable hard disk, Floppy drive, Non-reusable printer motor and cartridge

3 0.26

W7 Metal casings and scrap metal 2 0.13

*Hazard potential of the waste arrived at after analysis of feedback by experts using Analytical Hierarchy Process (Saaty 1980).





Table 2: Description of various nodes in the case study.

Node no. Name of place Node type

1 Maya Puri2 Kirti Nagar3 Turkman Gate4 Lajpat Nagar Source cum segregation sites5 Mustafabad6 Mandoli7 Shastri Park8 Old Seelampur9 Okhla Landfill Proposed secured landfill units10 Ghazipur11 Wazirpur Industrial Area Proposed site for plastic pelletization plant12 Timarpur Proposed site for processing metal scrap13 Uday Vihar Proposed site for plastic pelletization plant14 Mangolpuri Industrial Area Proposed site for processing metal scrap15 Dr. Lohia Industrial Area Reuse facility for old intact CRTs16 Nehru Place Reuse facility for old working PCs, Dot matrix and desk-jet printers, Intact floppy

drives, Processor chip, Hard disk, Speeder motor and CartridgeSource: Data collected through personal survey during the period April to July, 2005 from various computer vendors in Delhi.

Table 3: Waste generation rates at various source nodes (tonnes per 3-month time step).

S. no. Node no. Type of waste

Time step

T1 (Jan–Mar)(tonnes)

T2 (Apr–June)(tonnes)

T3 (Jul–Sept)(tonnes)

T4 (Oct-Dec)(tonnes)

1 1 WA 35 38 35 302 2 WA 35 38 35 303 3 WB 6 8 4 24 4 WC 4 5 4 35 5 WA 35 38 35 306 6 WB 6 8 4 27 7 WC 4 5 4 38 8 WC 4 5 4 3Source: Data collected through personal survey during the period April to July, 2005 from various computer vendors in Delhi.

Table 4: Recovered cost from various waste types and their weight-wise fractions.

Waste typeRecovered cost (US $ tonne–1)#

Weight-wise fractions of primary waste#

T1 T2 T3 T4

Re-usable primary waste WA 88 83 86 88 = 0.1 WAa

WB 13 10 10 12 = 0.5 WB a

WC 38 33 33 38 = 0.3 WC a

Sub-waste typesW1 30.0 27.0 33.0 32.0 = 0.04 WAW2 25.0 22.5 27.5 26.0 = 0.10 WAW3 20.0 18.0 22.0 21.0 = 0.01 WCW4 15.0 13.5 16.5 16.0 = 0.001 WCW5 10.0 9.0 11.0 10.5 = 0.25 WA + 0.35 WB + 0.35 WCW6 0.0* 0.0* 0.0* 0.0* = 0.36 WA + 0.24 WC + 0.05 WB + 0.05(W5 + W7)W7 5.0 4.5 5.5 5.0 = 0.15 WA + 0.1 WC + 0.1 WB# Source: data collected through personal survey during the period April to July, 2005 from various computer vendors in Delhi.a It implies 10% of the waste type WA, 50% of the waste type WB and 30% of the waste type WC arriving at the respective source nodes is in working condition and is reusable.* W6 waste type cannot be recycled or reused, hence the recovered cost = 0.





Table 5: Distance between source nodes and various facilities and grouping of various links for risk attributes (probability of accident and population impacted).

Node no. 1 2 3 4 5 6 7 8 9 10

9 22.8 19.6 12.7 5.4 22.3 23.6 16.2 17.2 0.0 12.0

(C) (B) (B) (A) (C) (C) (B) (B) (B)

10 43.0 16.3 7.6 12.4 11.6 11.2 7.6 7.1 12.0 0.0

(D) (B) (A) (B) (B) (B) (A) (A) (B)

11 9.7 12.9 10.1 2.5 14.6 15.9 10.6 11.6 28.9 16.5

(A) (B) (B) (A) (B) (B) (B) (B) (C) (B)

12 12.5 16.2 8.9 21.2 6.3 10.1 8.9 9.9 19.2 12.1

(B) (B) (A) (C) (A) (B) (A) (A) (B) (B)

13 5.9 7.0 22.4 18.0 18.6 23.6 16.2 17.2 29.1 30.1

(A) (A) (C) (B) (B) (C) (B) (B) (C) (D)

14 7.0 7.1 16.6 21.3 16.1 21.1 16.5 17.5 29.1 30.1

(A) (A) (B) (C) (B) (C) (B) (B) (C) (D)

15 6.2 5.4 10.1 16.2 15.9 17.9 13.2 14.3 27.5 27.5

(A) (A) (B) (B) (B) (B) (B) (B) (C) (C)

16 15.0 14.0 11.1 4.1 21.3 21.3 15.6 16.6 5.0 14.4

(B) (B) (B) (A) (C) (C) (B) (B) (A) (B)

NoteDistances (in km) are indicated in the upper portion and grouping in parenthesis in the lower portion of the cell.Risk attributes (probability of accident & population impacted) for various grouping of links are as follows:

Group Probability of accident (× 10–6) Population impacted (× 1000)

A 1 0.25

B 2 0.50

C 3 0.75

D 4 1.00

Table 6: Risk attributes (probability of accident & population impacted), segregation and storage costs at various source nodes.

Node no.Probability of accident

(× 10–6)Population impacted

(× 1000)Segregation cost(US $ tonne–1)

Storage cost(US $ tonne–1)

1, 2, 5 2 0.50 22 6

3, 4, 6, 7, 8 1 0.25 22 6

Table 7: Risk attributes (probability of accident and population impacted), capacities and running costs for various facility options.

Node no.Probability of

accident(× 10–6)

Population impacted(× 1000)

Capacity(tonnes time-step–1)

Capital cost for locating facility (US $ time-step–1)

Running/processing cost ($ tonne–1)

Disposal facilities

9 2 0.50 100 15000 32

10 1 0.25 95 13500 30

Plastic processing facilities

11 1 0.25 40 25000 20

13 2 0.50 35 23500 20

Metal processing facilities

12 1 0.25 22 25000 18

14 2 0.50 25 23500 18

Reuse facilities

15 2 0.50 8 0* 2

16 1 0.25 45 0* 2

*Reuse facilities are already existing at node no. 15 and 16, hence capital cost for locating the facility = 0.





Proposed framework of waste management

Presently in India, computer scrap is managed through variouslow-end management alternatives such as product reuse, openburning, backyard recycling and disposal in sanitary landfills.These methods of disposal are very rudimentary and posegrave environmental and health hazards (Toxics Link 2003).As computer waste is a conglomeration of highly toxic ele-ments, a framework based on maximum reuse/recycle for per-sonal computers (PCs) and printers is proposed.

The cathode ray tubes (CRTs) (W1) of waste computers(WA) are proposed to be regunned and used in the manufactureof televisions of local brands and screens for video games. Theintact integrated processor chip (IC), reusable floppy drivesand hard disks (W2) would be used in the manufacture of chil-drens’ laptops, toys and in the assembling of cheaper comput-ers. The brominated or acrylonitrile butadiene styrene (ABS)plastic casings or disassembled plastic portions of PCs andprinters (W5) would be sold to a plastic scrap dealer. Circuitboards, damaged CRTs, defective IC, mother boards, centralprocessing unit (CPU), condensers, capacitors, polyvinyl chlo-ride (PVC) wires, non-reusable hard disk, floppy drive, non-reusable printer motor, cartridge and other non-reusable resi-due of both printers and PCs (W6) is proposed to be dumpedin a secured landfill. Metal casings and scrap metal (W7) dis-assembled from computers and printers would be sold to ametal scrap dealer. It is proposed to reuse the working dot matrixprinter (WB) in the secondary market. Plastic (W5) and metal(W7) would be recovered from the non-reusable dot matrixprinter and would be sold to plastic and metal scrap dealersrespectively. The non-recyclable portion (W6) of the non-reusable dot matrix printer would be sent to a secured landfill.The deskjet printer (WC) would be disassembled and thespeeder motor (W3) would be reused for the manufacture oftoys. It is assumed that the speeder motor can be recycled fora maximum number of two times after which the metallic partof the non-reusable motor would be broken down using a ham-mer and the metal components (W7) would be sent for process-ing at the metal scrap processing facility. The cartridges (W4)would be refilled and resold as long as the cartridge writer isintact (assumed for up to three cycles). The plastic part of thenon-reusable cartridge would be broken down using a ham-mer and the plastic (W5) would be sent for processing at theplastic processing facility. The non-recyclable residue afterprocessing of plastic and metal scrap is proposed to be land-filled in a secured landfill.

Results and discussion

The proposed model was solved using a trial version ofLINGO 9.0 (an internationally acclaimed integer linear pro-gramming solution package), but it can also be solved using

any other integer linear programming solution package. Theexample problem has been solved for the following sets of jointfunctions of cost and risk: (i) minimization of cost (cost weight-ing = 1 and risk weighting = 0); (ii) equal weightings to cost andrisk (cost weighting = 0.5 and risk weighting = 0.5); (iii) min-imization of risk (risk weighting = 1 and cost weighting = 0).The constraints are checked for each time step and the resultsare summarized over all the time steps to give the total cost andtotal risk over all four time steps. The minimum cost achievedis US $ 193 848.00 (cost weighting = 1 and risk weighting= 0) and the maximum cost incurred is US $ 340 991.00 (riskweighting = 1 and cost weighting = 0). The management costper tonne of waste ranges from US $ 386.15 (cost weighting = 1and risk weighting = 0) to US $ 679.26 (risk weighting = 1 andcost weighting = 0). Similarly the minimum risk achieved is173.5164 × 10–3 (risk weighting = 1 and cost weighting = 0)and the maximum risk is 5446.0130 × 10–3 (cost weighting = 1and risk weighting = 0). The risk per tonne of waste ranges from3.4565 × 10–4 (risk weighting = 1 and cost weighting = 0) to108.4863 × 10–4 (cost weighting = 1 and risk weighting = 0).Cost and risk achieved in the compromise solution (costweighting = 0.5 and risk weighting = 0.5) are US $ 194 452.00and 182.2420 × 10–3, respectively. Selected facilities andpaths of transportation for various scenarios are depicted inFigures 2–4. It should also be noted that the risk valuesreported are relative risk values.

As evident from the results, cost and risk have an inverserelationship, namely as the cost or the available budgetincreases the risk involved can be reduced. The ratio of max-imum cost (cost weighting = 0) to minimum cost achieved (costweighting = 1) was approximately 1.8. The ratio of maximumrisk (cost weighting = 1) to minimum risk (cost weighting = 0)observed was approximately 31. Analysis of results indicatethat this is largely due to transportation paths (Figure 2), withmore probability of accident and more population beingimpacted (Table 5) being chosen in the minimum cost sce-nario. However, we would like to emphasize that theseresults are specific to the example problem chosen. Hence, inthe present case study an 80% compromise in the cost leadsto a risk value approximately 31 times lower.

In the case of developing countries such as India, theavailable budget for activities such as that of solid waste man-agement is usually restricted (CPHEEO 2000) and, at the sametime, it is also desirable to minimize the risk involved. Thiscan be achieved by making a compromise between the costand the risk as demonstrated by the scenario of 50% weightingto each cost and risk. A decision-maker or a group of decision-makers can assign the weightings based on the available budget.As is evident from the results, it is possible that a marginalincrease in the cost may significantly lower the risk. It wasalso observed that maximum capacity utilization is achieved





Fig. 2: Facilities and paths selected for the minimum cost scenario.

Fig. 3: Facilities and paths selected for the equal weightings to cost and risk.





in the scenario of equal weightings to cost and risk, whereas,maximum under-utilization of the capacities (of various facili-ties) is seen in the minimum risk scenario. Hence, in the caseof the minimum risk scenario more buffer is available to absorbfluctuations in the generation of waste.

In a real life situation, the generation of waste at any nodeis not constant, even within the same time frame. It fluctuatesaround a certain mean value. To study the effect of such fluc-tuations on each solution, a sensitivity analysis was requiredon the waste quantities generated. Sensitivity analysis can beaccomplished in part with the aid of the solution packageLINGO, which reports the dual price (increase or decrease inthe value of the objective function from a unit change in thequantity) of the waste generation quantities. From this anal-ysis, it is evident that the waste type WC affects the value ofthe objective function the most and, hence, is most critical.Minimization of waste type WC would minimize both costand risk values to a greater extent than any other waste type.This analysis however does not indicate the implication of thechange in waste generation quantities on the decisions (facil-ities sited) by the model. Hence, a rigorous analysis was doneusing a Monte Carlo simulation. Ten scenarios, each for ran-dom 5 and10% variation in the waste quantities for each timestep were considered to evaluate their sensitivity on the deci-

sions (regarding selection of facilities) reported by the model.Two of the scenarios considered for each case were for extrememinimum and maximum variation. The waste generation inthe remaining time steps was subjected to a similar randomvariation. The above reported decisions had 100% reliabilityfor a 5% variation in the waste quantities for all three scenar-ios (minimum cost, equal weightings to cost and risk and min-imum risk). This implies that, for up to ± 5% variations in thequantities, the reported decisions (sited facilities) would remainthe same for all three scenarios of different weightings to costand risk. The reported decisions remained the same for fourout of the total of ten cases studied for 10% variation in thewaste quantities for minimum cost. The reported decisionsremained the same for six out of the total of ten cases studiedfor 10% variation in the waste quantities for equal weightingsto cost and risk. The reported decisions remained the same forall ten minimum risk scenarios. Hence, it is evident that thereis a tradeoff between precision in data collection and cost ofselected facilities. If the precision in the collected data is less,the model may select more expensive/non-optimum facilities.

Although in this case study the minimum site risk and min-imum transportation risk were being achieved in the mini-mum risk scenario, if the decision-maker elected to minimizetotal risk, the model may not individually minimize site risk

Fig. 4: Facilities and paths selected for the minimum risk scenario.





or transportation risk. However, if the decision-maker desiresto individually minimize transportation risk or site risk, thesame can be achieved using only the equations pertaining tothe corresponding risks in the objective function.

Summary and conclusions

A multi-objective, multi-time-step reverse logistics formulationfor integrated solid waste management for computer wastemanagement has been presented here. A case study of Delhi ispresented to illustrate the usefulness of the model. The pro-posed model may be used to guide managers working in thefield of solid waste management in the following ways.

• To select the optimum configuration of waste manage-ment facilities and transportation routes. The model canbe used as a decision-support tool for selecting overall con-figuration of waste reuse, recycle, treatment and disposalfacilities, and transportation routes based on the respec-tive capital cost, operation and maintenance costs andenvironmental risk parameters. The objective of the plan-ning could be minimization of cost, minimization of riskor a compromise between cost and risk. The model canguide managers in the planning of new facilities at appro-priate locations and select the routes depending on theirpriority of objectives.

• To allocate waste to the waste management facilities. Theproposed model can help the decision-makers in decidingthe allocation of waste quantities to the various waste man-agement facilities (existing as well as newly sited) so as toachieve the desired objective.

• To minimize risk for a given budget. This feature of themodel may be useful to the authorities to enable them to

minimize risk for a given budget. In order to minimize riskfor a given budget, the objective function should be to min-imize risk and the model should be subjected to a con-straint such that the total cost is equal to or less than thegiven budget. Care should be taken to ensure that the budgetcost specified is more than or equal to the minimum feasiblecost; otherwise, the model will give an infeasible solution.

• To achieve equitable distribution of risk. This feature of themodel may be used by the civic authorities to arrive at uni-form distribution of risk over the concerned area. Equitabledistribution of risk in the scenario of choice may be achievedpartially by subjecting the risk at a site or in a transportationlink to a constraint such that the risk at that particularnode or link does not exceed an acceptable level. How-ever, this feature will increase the number of equations,one equation corresponding to each of the transport links aswell as for the facilities. Therefore it is suggested that onlythose links that have sensitive receptors are selected.

It should be noted that the efficacy of the model results isdependent on the accuracy of data collection. If the range ofuncertainty is larger the model results would be less reliable.The model assumes that all costs (capital/operating/processing/disposal) remain constant within the same time step; how-ever, they may vary with different time steps. Common practi-cal constraints such as shortage of power supply, availablelabour, etc., may limit the actual capacity available at certainfacilities and hence the decision-maker may suitably inter-pret the results given by the model. The risk addressed isonly relative risk and further improvement may be obtainedby correlating the risk values associated with various wastemanagement operations to activities that are easily identifia-ble, such as transport and handling of fuels.

References

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Appendix I

Equations of the proposed mathematical model

(A) Total cost = the total cost can be summarized under the headings (a) to (k).

(a) Cost of segregation at source nodes

(1)

(b) Cost of storage at source nodes

(2)

(c) Cost of transportation of waste from source nodes toprocessing facilities

(3)

(d) Cost of processing waste at processing facilities

(4)

(e) Capital cost for locating processing facilities

(5)

(f) Transportation cost of reusable waste types to reuse facili-ties

(6)

(g) Transportation cost of non-reusable, non-processableportion of waste from source nodes to disposal facilities

(7)

(h)Capital cost for locating disposal facilities

(8)

(i) Cost of disposal

(9)

(j) Cost recovered from the sale of recyclable portion of gen-erated waste

(10)

(k) Cost recovered from the sale of reusable portion of gener-ated waste

(11)

(B) Total risk (TOR)

TOR = Rt + Rs (12)

where Rt is the risk due to transportation [headings (l) to (o)]and Rs is the site risk [headings (p) to (s)].

(l) Risk due to transportation of waste from generationnodes to processing facilities

Ask g( )As∗k g d ′–( ) Ask g d ′–( )+

d ′ 1=

Td ′

∑–s 1=

w

∑g 1=

n

∑k 1=

e

∑=

As″k g g′–( )g′ 1=

n′

∑

+ Bsg×

Ask g( ) Bst Rst××s 1=

w

∑g 1=

n

∑k 1=

e

∑=

As′k g sr ′–( ) Ts′ D g sr ′–( )××Sr ′ 1=

rssr

∑s ′ 1=

w′

∑g 1=

n

∑k 1=

e

∑=

Bsr′ × As′k g sr ′–( )Sr ′ 1=

rssr

∑s ′ 1=

w′

∑g 1=

n

∑k 1=

e

∑=

CPsr′ Ysr′×[ ]Sr ′ 1=

rssr

∑=

As″k g g′–( ) Ts″ D g g′–( )××g 1=

n

∑g ′ 1=

n′

∑s″ 1=

w″

∑k 1=

e

∑=

As∗k g d ′–( ) Ts∗ D g d ′–( )××g 1=

n

∑d ′ 1=

Td ′

∑s∗ 1=

w∗

∑k 1=

e

∑=

CPd′ Yd′×[ ]d ′ 1=

Td ′

∑=

As∗k g d ′–( ) Ask g d ′–( )s 1=

w

∑+s∗ 1=

w∗

∑⟨ ⟩g 1=

n

∑

d ′ 1=

Td ′

∑k 1=

e

∑=

As′k sr ′ d ′–( )s ′ 1=

w ′

∑Sr ′ 1=

rssr

∑⟨ ⟩+

Bd′×

–( ) As′k g sr ′–( ) Bs′k Rs′k××Sr ′ 1=

rssr

∑g 1=

n

∑s ′ 1=

w ′

∑k 1=

e

∑=

–( ) As″k g g ′–( ) Bs″k×g ′ 1=

n′

∑g 1=

n

∑s″ 1=

w″

∑k 1=

e

∑=





(13)

(m)Risk due to transportation of reusable portion of waste toreuse facilities

(14)

(n)Transportation cost of non-reusable waste from sourcenodes to disposal facilities

(15)

(o) Transportation cost of waste directly going to disposalwithout segregation

(16)

(p) Site risk at source nodes due to segregation

(17)

(q) Site risk at source nodes due to storage

(18)

(r) Site risk at disposal facilities

(19)

(s) Site risk at processing facilities

(20)

(s) Site risk at reuse facilities

(21)

Constraints(t) Mass balance at source nodes

(22)

(u) Mass balance at processing facilities

(23)

(v) Capacity constraint at processing facilities

(24)

(w)Logical constraint at processing facilities

(25)

(x) Capacity constraint at disposal facilities

(26)

(y) Logical constraint at disposal facilities

(27)

As′k g sr ′–( ) HPs′×Sr ′ 1=

rssr

∑g 1=

n

∑s ′ 1=

w′

∑k 1=

e

∑=

PAD g sr ′–( ) PD g sr ′–( )×( )×

As″k g g′–( ) HPs″×g 1=

n

∑s″ 1=

w″

∑g′ 1=

n′

∑k 1=

e

∑=

PAD g g′–( ) PD g g′–( )×( )×

As∗k g d ′–( ) HPs∗×g 1=

n

∑d ′ 1=

Td ′

∑s∗ 1=

w∗

∑k 1=

e

∑=

PAD g d ′–( ) PD g d ′–( )×( )×

Ask g d ′–( ) HPs×g 1=

n

∑d ′ 1=

Td ′

∑s 1=

w

∑k 1=

e

∑=

PAD g d ′–( ) PD g d ′–( )×( )×

Ask g( ) As ∗k g d ′–( )d ′ 1=

Td ′

∑ As″k g g′–( )g ′ 1=

n′

∑+

–

s 1=

w

∑g 1=

n

∑k 1=

e

∑=

Ask g d ′–( )d ′ 1=

Td ′

∑+

HPs PAD g( ) PD g( )×( )××

Ask g( ) Rst× HPs PAD g( ) PD g( )×( )××[ ]s 1=

w

∑g 1=

n

∑k 1=

e

∑=

As∗k g d ′–( ) HPs∗×s∗ 1=

w∗

∑

g 1=

n

∑d ′ 1=

Td ′

∑k 1=

e

∑=

Ask g d ′–( )s 1=

w

∑ HPs×+

PAD d ′( ) PD d ′( )×( )×

As ′k sr ′ d ′–( )s ′ 1=

w′

∑sr ′ 1=

rssr

∑ HPs′ PAD d ′( ) PD d ′( )×( )××+

As′k g sr ′–( ) HPs′×Sr ′ 1=

rssr

∑s ′ 1=

w′

∑g 1=

n

∑k 1=

e

∑=

PAD sr ′( ) PD sr ′( )×( )×

As″k g g′–( ) HPs″×s″ 1=

w″

∑g 1=

n

∑g′ 1=

n ′

∑k 1=

e

∑=

PAD g′( ) PD g′( )×( )×

Ask g( )[ ]s 1=

w

∑ As∗k g d ′–( )s∗ 1=

w∗

∑

d ′ 1=

Td ′

∑=

Ask g d ′–( )s 1=

w

∑

As″k g g′–( )s″ 1=

w″

∑g′ 1=

n ′

∑+ +

As′k g sr ′–( )s ′ 1=

w′

∑sr ′ 1=

rssr

∑+ g k,∀

As′k g sr ′–( ) 1 Rs′k–( )×{ }s ′ 1=

w′

∑g 1=

n

∑

As′k sr ′ d ′–( ){ } Sr′ k,∀s ′ 1=

w′

∑d ′ 1=

Td ′

∑=

As′k g sr ′–( ){ } Cap.sr′.k Ysr′×≤s ′ 1=

w ′

∑g 1=

n

∑ Sr′ k,∀

Ysr′ 104 As′k g sr ′–( )×{ } s ′ 1=

w′

∑g 1=

n

∑k 1=

e

∑≤ Sr′∀

As′k sr ′ d ′–( ) Ask g d ′–( )s 1=

w

∑g 1=

n

∑+s ′ 1=

w ′

∑Sr ′ 1=

rssr

∑

As∗k g d ′–( )s∗ 1=

w∗

∑ Cap.d′.k Yd′×≤+ d′ k,∀

Yd′ As′k sr ′ d ′–( )s ′ 1=

w′

∑sr ′ 1=

rssr

∑

k 1=

e

∑≤

Ask g d ′–( )s 1=

w

∑ As∗k g d ′–( )s∗ 1=

w∗

∑+

g 1=

n

∑+

104× d′∀





(v) Capacity constraint at reuse facilities

(28)

Objective function = minimize (Total cost, Total risk)

Ysr′ = either 1 or 0Yd′ = either 1 or 0Yg′ = 1 (as the facility is already existing).

NotationAsk(g) Amount of waste s arriving at source node g in

time step ‘k’.As′′k(g–g′) Amount of reusable waste type s′′ going to reuse

facility from source node g in time step ‘k’.As*k(g–d′) Amount of non reusable, non processable waste

type s* going to disposal facility from sourcenode g in time step ‘k’.

Ask(g–d′) Amount of waste type s directly going for dis-posal from source node g in time step ‘k’.

As′k(g–sr′) Amount of processable waste type s′ travellingfrom source node g to suitable processing facilitysr′ at time step ‘k’.

As′k(sr′–d′) Amount of residue of waste type s′ travellingfrom segregation facility sr′ to disposal facility d′at time step ‘k’.

Bsg Unit cost of segregation for waste type s.Bsr′ Unit cost of processing at facility sr′.Bst Unit cost of storage for waste type s.Bd′ Unit cost of disposal at facility d′.Bs′k Cost recovered by sale of waste s′ per unit

weight at time step k.Bs′′k Cost recovered by sale of waste s′′ per unit

weight at time step k.Cap.sr′.k Capacity of processing facility sr′ at time step k.Cap. d′.k Capacity of disposal facility d′ at time step k.Cap. g′.k Capacity of reuse facility g′ at time step k.CPsr′ Equitable capital cost of waste processing facil-

ity sr′ per time step.CPd′ Equitable capital cost of waste disposal facility d′

per time step.d′ Disposal facility (total Td′ available options for

disposal facilities).D(g–d′) Distance of waste source node g to disposal facil-

ity d′.D(g–sr′) Distance of waste source node g to processing

facility sr′.D(g–g′) Distance of source node g to reuse facility g′.D(sr′–d′) Distance of waste processing facility sr′ to dis-

posal facility d′.

g Waste generation node (total ‘n’ waste genera-tion nodes).

g′ Reuse facilities (total n′ reuse facilities).HPs Hazard potential of waste s.HPs* Hazard potential of waste s*.HPs′ Hazard potential of waste s′.HPs′′ Hazard potential of waste s′′.K Number of time steps.PAD(g–d′) Probability of accident on route g to d′.PAD(g–sr′) Probability of accident on route g to sr′.PAD(g–g′) Probability of accident on route g to g′.PAD(sr′–d′) Probability of accident on route sr′ to d′.PD(g–d′) Population impacted on route g to d′.PD(g–sr′) Population impacted on route g to sr′.PD(g–g′) Population impacted on route g to g′.PD(sr′–d′) Population impacted on route sr′ to d′.PAD(sr′) Probability of accident on processing facility sr′.PD(sr′) Population impacted on processing facility sr′.PAD(g′) Probability of accident on reuse facility g′.PD(g′) Population impacted on reuse facility g′.PAD(d′) Probability of accident on disposal facility d′.PD(d′) Population impacted on disposal facility d′.Rs′k Ratio of processed/recycled waste to incoming

waste s′ coming for processing/recycling.Rst Ratio of stored waste to incoming waste.rssr Total number of processing facilities.s Waste types (total w waste types).s′ Waste type which can be processed and recycled

(total w′ processable waste types.s′′ Waste types which can be reused (total w′′ reus-

able waste types).s* Waste types which can not be processed or

reused (total w* waste types).sr′ Processing facility.Time step k e years (time step k < 1 year and exact divider of

1 year).Ts′ Unit cost of transportation per unit weight per

unit distance for waste type s′.Ts′′ Unit cost of transportation per unit weight per

unit distance for waste type s′′.Ts* Unit cost of transportation per unit weight per

unit distance for waste type s*.Ysr′ Binary variable with value 1 or 0 depending on

whether processing facility sr′ is sited by themodel or not.

Yg′ Binary variable with value 1 as the reuse facilityg′ is assumed to exist.

Yd′ Binary variable with value 1 or 0 depending onwhether the disposal facility d′ is sited by themodel or not.

As″k g g ′–( ){ } Cap.g′.k Yg′×≤s″ 1=

w″

∑g 1=

n

∑ g′ k,∀



multi-objective reverse logistics model for integrated computer waste management

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