Waste Management 69 (2017) 518–534

Contents lists available at ScienceDirect

Waste Management

journal homepage: www.elsevier .com/ locate/wasman

An optimization model for collection, haul, transfer, treatment anddisposal of infectious medical waste: Application to a Greek region

http://dx.doi.org/10.1016/j.wasman.2017.08.0370956-053X/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: voudrias@env.duth.gr (E.A. Voudrias).

Gerasimos Mantzaras, Evangelos A. Voudrias ⇑Department of Environmental Engineering, Democritus University of Thrace, GR-67100 Xanthi, Greece

a r t i c l e i n f o

Article history:Received 20 March 2017Revised 31 July 2017Accepted 21 August 2017Available online 6 September 2017

Keywords:Infectious medical waste managementOptimization modelCost minimizationTransfer stationsInfectious medical waste treatment

a b s t r a c t

The objective of this work was to develop an optimization model to minimize the cost of a collection,haul, transfer, treatment and disposal system for infectious medical waste (IMW). The model calculatesthe optimum locations of the treatment facilities and transfer stations, their design capacities (t/d), thenumber and capacities of all waste collection, transport and transfer vehicles and their optimum trans-port path and the minimum IMW management system cost. Waste production nodes (hospitals, health-care centers, peripheral health offices, private clinics and physicians in private practice) and their IMWproduction rates were specified and used as model inputs. The candidate locations of the treatment facil-ities, transfer stations and sanitary landfills were designated, using a GIS-based methodology.Specifically, Mapinfo software with exclusion criteria for non-appropriate areas was used for siting can-didate locations for the construction of the treatment plant and calculating the distance and travel time ofall possible vehicle routes. The objective function was a non-linear equation, which minimized the totalcollection, transport, treatment and disposal cost. Total cost comprised capital and operation costs for: (1)treatment plant, (2) waste transfer stations, (3) waste transport and transfer vehicles and (4) waste col-lection bins and hospital boxes. Binary variables were used to decide whether a treatment plant and/or atransfer station should be constructed and whether a collection route between two or more nodes shouldbe followed. Microsoft excel software was used as installation platform of the optimization model. For theexecution of the optimization routine, two completely different software were used and the results werecompared, thus, resulting in higher reliability and validity of the results. The first software was Evolver,which is based on the use of genetic algorithms. The second one was Crystal Ball, which is based onMonte Carlo simulation. The model was applied to the Region of East Macedonia – Thrace in Greece.The optimum solution resulted in one treatment plant located in the sanitary landfill area ofChrysoupolis, required no transfer stations and had a total management cost of 38,800 €/month or 809€/t. If a treatment plant is sited in the most eastern part of the Region, i.e., the industrial area ofAlexandroupolis, the optimum solution would result in a transfer station of 23 m3, located near KavalaGeneral Hospital, and a total cost of 39,800 €/month or 831 €/t. A sensitivity analysis was conductedand two alternative scenarios were optimized. In the first scenario, a 15% rise in fuel cost and in the sec-ond scenario a 25% rise in IMW production were considered. At the end, a cost calculation in €/t/km forevery type of vehicle used for haul and transfer was conducted. Also, the cost of the whole system wasitemized and calculated in €/t/km and €/t. The results showed that the higher percentage of the total costwas due to the construction of the treatment plant.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Mathematical programming has been used to optimize munic-ipal solid waste (MSW) management systems, including haul andtransfer (Abdelli et al., 2016; Laureri et al., 2016; Son and Luati,2016; Das and Bhattacharyya, 2015; Sanjeevi and Shahabudeen,

2016; Hemmelmayr et al., 2013a, 2013b; Zsigraiova et al., 2013;Chatzouridis and Komilis, 2012; Apaydin and Gonullu, 2011;Faccio et al., 2011; Kuo and Wang, 2011; Gupta and Sharma,2011; Arribas et al., 2010). Such techniques have also been usedfor healthcare waste, but the applications are very limited (Budakand Ustundag, 2013; Almeida, 2011; Shih and Lin, 2003; Shi et al.,2009). For example, Shih and Lin (2003) used dynamic program-ming and integer linear programming methods with multicriteriaoptimization for planning of infectious medical waste (IMW)

Table 1Exclusion criteria of inappropriate areas for the construction of IMW treatmentfacilities.

Criteria Exclusion Buffer Zone

Anthropogenic areasResidential areas (CMD, 2002) 1000 mMajor road network 500 mEnvironmentally sensitive areasSurface water and coast line 1000 mNatura 2000 areas 1000 mForest areas 1000 mLand use All sites excludedAreas of permanent irrigationPasture landsCultivated areasOther exclusions All sites excludedPurely rocky areas

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 519

collection systems. Shi et al. (2009) presented a mixed integer lin-ear programming model with cost minimization for medical wastereverse logistics networks and used a genetic algorithm method tosolve the proposed model. Budak and Ustundag (2013) developed amixed integer linear programming model to determine the optimalnumber and location of the facilities, by minimizing total cost.Other authors used GIS tools to optimize health care waste man-agement systems (Shanmugasundaram et al., 2012; Alagoz andKocasoy, 2008). Chaerul et al. (2008) used a goal programmingapproach for resolving complexities in healthcare wastemanagement.

Voudrias and Graikos (2014) presented a preliminary design ofan IMW management system for the Region of East Macedonia-Thrace (ΕΜΤR) in Greece. Steam sterilization was used as the treat-ment technology, but the siting of the treatment plant was notoptimized and was placed in the geographic center of the region.Although a collection and transport plan was proposed, the authorsindicated that there are several potential such plans, which couldbe evaluated for selection of the optimum one. Siting of formaltransfer stations (TSs) was not considered, instead IMW storagerooms in public hospitals would be used as collection points ineach prefecture. However, siting of TSs for IMW hauling is a signif-icant issue regarding management cost minimization, but onlysparingly has been addressed (Budak and Ustundag, 2013;Almeida, 2011). Although it is customary to collect and treatIMW from a few large producers, it is difficult and expensive to col-lect IMW from many widely spread small producers and this is thesituation in which use of TSs may be necessary.

TSs for medical waste are operated in the United States, forexample in the states of California, Florida, Texas, New York, etc.The medical waste management program of the Public HealthDepartment of the State of California presents tables with medicalwaste TSs and treatment facilities (CDPH, 2017). The operation ofsuch TSs for medical waste only recently (2012) was introducedin Greece (CMD, 2012). It is apparent that optimization of the sys-tem components is necessary to achieve management costminimization.

The objective of this work was to develop an optimizationmodel to design a collection, haul, transfer, treatment and disposalsystem for IMW. The model output includes the exact locations ofthe treatment facilities and TSs, their design capacities (t/d), thenumber and capacities of all waste collection, transport and trans-fer vehicles and their optimum transport path, as well as the min-imum total management cost. The model was applied to the EMTRin Greece, for which IMW data were available (Voudrias andGraikos, 2014; Graikos et al., 2010; Kizlary et al., 2005;Mandalidis, 2011).

The paper has the following elements of novelty. It extendedprevious work by Chatzouridis and Komilis (2012) on MSW, byincluding treatment facilities in the model. In addition, there aresignificant differences between MSW and medical waste. Forexample, quantities of IMW are significantly smaller than thoseof MSW for the same population, with production nodes widelyspread. Because IMW is a hazardous waste, special precautionsand measures are necessary. For example, there are limits on stor-age temperature and time and the characteristics of the waste col-lection vehicles (Voudrias and Graikos, 2014). The novelty in themethodology is that IMW collection is not conducted on the sameday for all producers, but varies, depending on the amounts pro-duced. For example, collection frequency for a peripheral healthoffice could be once a month, for a healthcare center once a week,whereas for a hospital every day. This differs from the approachapplied in many MSW collection and transport models, but it isnecessary to reduce collection and haul cost. However, this intro-duces significant complexity to the mathematical model, whichwas developed in this paper. Thus, our objective function is much

different from the published for MSW models with constant dailycollection patterns. Finally, operation of TSs in IMW managementsystems along with economic data for TSs and special collectionvehicles and bins originating from primary sources are provided.The model can be applied to IMWmanagement problems, in whichonly candidate locations for the treatment plants and TSs are pre-viously defined and the model determines their numbers, exactlocations and capacities.

2. Methodology

The proposed methodology consisted of the following fourparts: (1) Exclusion of inappropriate areas for the construction oftreatment facilities, (2) siting of all candidate IMW TSs and possi-ble positions of treatment facilities for IMW, (3) model develop-ment in a user-friendly environment, such as an Excel

�

spreadsheet, to minimize total system cost and (4) modelapplication.

2.1. Exclusion of inappropriate areas

Greek legislation (CMD, 2006, 2002) requires that the operationof hazardous waste treatment plants should not cause any damageto the environment and human health. Table 1 summarizes the cri-teria used in this work, to exclude unsuitable areas for constructionof IMW treatment facilities, using the appropriate GIS software(Mapinfo Professional 10.5 of Pitney Bowes Software, Stamford,Connecticut USA).

2.2. Siting of treatment facilities and waste transfer stations

Once the inappropriate areas were excluded, all remainingareas in the region were considered suitable for siting IMW treat-ment plants. One candidate area for each municipality of the regionwas selected, based on the following steps: (1) If one or moreindustrial areas existed within the borders of the municipalitythe candidate area was sited within the most accessible industrialarea and the nearest to most region’s hospitals, following the prox-imity principle. Facilities for management of MSW are consideredin industrial areas. (2) If no industrial area existed within themunicipality, then among the appropriate areas the nearest tomost region’s hospitals and most accessible was selected, followingthe proximity principle.

Concerning the positions of IMW TSs, two siting scenarios wereconsidered, if legal requirements are fulfilled. In the first, scenarioA, candidate positions were in a small distance from the regionalgeneral hospitals. In the second, scenario B, positions were locatednearby the regional facilities for MSW TSs (Chatzouridis and

520 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

Komilis, 2012). From the operation point of view, these were themost convenient places for TS siting.

2.3. Optimization model

The optimization model included the objective function, thedecision variables and the constraints. Therefore, all possible traveldistances (km) and times (min) among IMW producers, wastetreatment plants and sanitary landfills were calculated and wereused as the main input data in the optimization model.

2.3.1. Objective functionThe objective function (OBF) developed in this paper was simi-

lar in principle, but more complicated than the OBF presented byChatzouridis and Komilis (2012) and was used to minimize thetotal system cost, which consists of the fixed and the variable cost.The fixed cost comprised the capital cost of the waste collectionvehicles of all sizes, the construction cost for the treatment facili-ties and waste TSs and the purchase cost of temporary storagefacilities (refrigerated chambers, waste bins and hospital boxes).The variable cost comprised the haul cost of all types of waste col-lection vehicles (fuel consumption and maintenance), the laborcost, the operating cost of waste transfer stations and treatmentfacilities and the sanitary landfill tipping (gate) fee. The cost forthe sanitary landfill construction was not included.

The proposed OBF is a non-linear equation and is presented ingeneral terms in Eq. (1). The detailed mathematical form of theOBF is presented in Appendix A. The OBF was based on the ideathat each production node has to transfer all IMW to only one TSor directly to the treatment plant. Special waste collection vehicles(WCV) with refrigerated chambers must be utilized (CMD, 2012).From TSs, larger refrigerated WCVs transfer the collected IMWdirectly to treatment plant only. Finally, all treated IMW are trans-ported via ordinaryWCV (with no refrigeration) to the nearest san-itary landfill. Fig. 1 presents a conceptual flow chart for acollection, haul, transfer, treatment and disposal system for IMW.

Fig. 1. Conceptual flow chart for a collection, haul, transfer, tre

Greek regulations (CMD, 2012) require that storage time forIMW must be limited to �5 d at temperature �5 sC. For quantities<500 L, temporary storage can be extended up to 30 d at tempera-tures �0 sC. Since most of the IMW producers in a Greek regionhave a production of <500 L/month, it was decided to include inthe OBF infectious waste production nodes formed by groups of,rather than individual waste producers. Thus, for the case studyof EMTR, a total of 17 producer groups were formed and dis-tributed in 3 categories. In addition, to avoid considering unneces-sary collection routes, it was decided to compute cost not on adaily basis but on a 4-week (28 days) period, taking advantage ofthe maximum storage time allowed for small producers.

Two types of refrigerated WCVs were considered: Larger sizevehicles collecting from producer groups including hospitals andsmaller size vehicles collecting from the other two smaller pro-ducer group categories. Because of the large number of possiblecollection routes, it was assumed that a vehicle starts collectionfrom a production node and returns to the same departure point.At the end of one collection route, the same vehicle can continuecollection in the same production node, if not already finished, orgo to another production node, provided that the total collectionand transport time does not exceed the maximum daily work time.Simultaneous collection in a production node by two vehicles orig-inating from different departure points is not allowed. Model opti-mization will determine the combination of collection routesresulting in cost minimization.

The possible WCV routes used in the model and described in theOBF are summarized in Fig. 2, using the concept of the TravellingSalesman Problem (Das and Bhattacharyya, 2015; Dumitrescuet al., 2009; Son and Louati, 2016): (1) WCVs depart from the treat-ment facilities, move to a producers group for IMW collection viathe shortest route and return to the treatment facilities for unload-ing and treatment. (2) WCVs depart from a TS, move to a producersgroup for IMW collection via the shortest route and return to theTS for unloading and temporary storage. (3) WCVs depart from aTS, move to a producers group for IMW collection via the shortestroute, transport the load to the treatment facility and return to the

atment and disposal system for infectious medical waste.

Fig. 2. Possible WCV routes used in the model and described in the OBF.

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 521

TS. (4) Larger size loaded WCVs depart from a TS, transport theload to a treatment facility and return to the TS. (5) WCVs departfrom a treatment facility, transport the treated waste to a sanitarylandfill and return to the treatment facility. Because of shreddingand removal of excess water following steam sterilization, a 40%weight reduction and 50% volume reduction was assumed andincorporated in model equations.

In the developed OBF, critical input parameters include IMWquantity produced by each production node, total transporttransfer times (which consist of travel time, IMW pickup timeand queue time) and travel distances for every route followedby each type of WCV. All variable cost parameters were calcu-lated directly from critical input parameters and fixed costparameters.

MinCost ¼ WCVAInvCost þWCVBInvCost þWCVTSInvCost þWCVLFInvCost þ TotalWCVATransCost þ TotalWCVBTransCost

þ TotalWCVTSTransCost þ TotalWCVLFTransCost þ TotalWCVAMaintenanceCost þ TotalWCVBMaintenanceCost

þ TotalWCVTSMaintenanceCost þ TotalWCVLFMaintenanceCost þ TotalWCVALaborCost þ TotalWCVBLaborCost

þ TotalWCVTSLaborCost þ TotalWCVLFLaborCost þWTSUnitCost þ TotalWTSTipFeeþ TotalTPWasteCost

þ TotalLFTipFeeþ FixedCost ð1Þ

522 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

where

MinCost: the total minimizable system cost (dependent vari-able) for the period examined (€/month, here a month=28days)WCVΑ: WCV for hospitalsWCVΒ: WCV for the rest of producersWCVTS: WCV used for transferring IMW from TSs to treatmentfacilitiesWCVLF:WCV used for transporting treated IMW from treatmentfacilities to landfillInvCost: WCV investment cost for the type of vehicle that isreferred to (€/month)TotalTransCost: WCV operation cost for the type of vehicle thatis referred to (€/month)TotalMaintenanceCost: WCV maintenance cost for the type ofvehicle that is referred to (€/month)TotalLaborCost: WCV labor cost for the type of vehicle that isreferred to (€/month)WTSUnitCost: investment cost for construction of a TS (€/month)TotalWTSTipFee: gate fee for storing IMW to a TS (€/month)TotalTPWasteCost: treatment facilities operating and IMW treat-ment cost (€/month)TotalLFTipFee: gate fee for landfill (€/month)FixedCost: The rest of fixed costs (€/month)

The detailed mathematical form of OBF with its constraints ispresented in Appendix A.

2.3.2. Solution of the modelIn order to increase reliability in optimization, two different

software programs, were used for model solution and the resultswere compared. The first software was Evolver 5.5 (Palisade Corpo-ration, Ithaca NY USA), which is based on the use of genetic algo-rithms. The second software was Crystal Ball 11.1.1.1.00 ofOracle�, which operates on the Monte Carlo method. The platformfor both software was an Excel� spreadsheet, so the user can easilyadjust the problem parameters and input variables. Both softwareutilize meta-heuristic methods, as they search for an optimal solu-tion, contrary to most classical optimization software, which uti-lize mathematical differentiation. Meta-heuristic methods rely onthe exploration of the field of possible values for the variables ofthe examined problem and on some degree of serendipity. Thus,the utilization of two completely different software resulted inhigher reliability and validity of the results. Classical mathematicalprogramming tools resulted in convergence and local minimaproblems and, therefore, were excluded from optimization.

Model solution results include the optimum locations of thetreatment facilities and TSs, their design capacities (t/d), the num-ber and capacities of all waste collection, transport and transfervehicles and their optimum transport routes and the optimalIMW management system cost.

Due to the complexity of the OBF, a six-step process describedbelow was applied with both software, for reaching the optimalsolution:

1. In the first step, the optimal location of the treatment facilitywas found, after searching the candidate locations of treatmentfacilities with the lower impact on the total system cost. Thecapacity of the treatment facility was based on the daily IMWproduction.

2. In the second step, the target was to find the location of one ormore of the most ‘‘influential” TSs, which result in the most sig-nificant reduction of total cost. The results of this step mightproduce various combinations of TSs, which are all examinedin steps 3 to 5. For this step only, initial capacities of TSs wereassumed to be the 2/3 of the maximum IMW production to bestored in the TSs.

3. In the third step, capacities of TSs designated in the second stepwere varied, in order to find the optimal capacities for TS,through total cost minimization. In all trials, TS capacity wasconsidered equal to the capacity of the WCV transporting theIMW from the TS to the treatment facility.

4. In the fourth step, the capacities of WCVs transporting IMWfrom TSs to treatment facilities were varied to find the optimalWCV capacities and optimal capacities of TSs were readjusted, ifnecessary.

5. In the fifth step, capacities of WCVs transporting the treatedIMW to the sanitary landfill, for all combinations of WCVs andTSs of the previous steps, were varied, in order to optimizethe combination of WCVs and TSs.

6. In the sixth and final step, it was assumed that no TSs were nec-essary and, thus, the optimization model became simpler withfewer variables. By adjusting capacities of WCVs transportingthe treated IMW, the optimal solution with no TSs was found.

The optimal solution resulting from steps 1–5 was compared tothat resulting from step 6 and the solution minimizing the totalsystem cost was selected. This solution provides the number andtype of necessary WCVs and TSs and their capacities, along withthe capacity of the treatment facility and the locations of the TSs,the treatment facility and the sanitary landfill. Optimal collectionroutes were, also, specified.

3. Model application to East Macedonia-Thrace region of Greece

3.1. IMW sources

EMTR occupies a total area of 14,157 km2, which is the 10.7% ofthe area of Greece. Its population is 606,170 residents (based onthe 2011 census), which is approximately the 5.6% of the popula-tion of Greece. EMTR is divided in 5 prefectures (Drama, Kavala,Xanthi, Rodopi and Evros). Two islands, Thasos and Samothraki,belong to the Prefectures of Kavala and Evros, respectively. Thereare two public hospitals located in the Prefecture of Evros andone major public hospital in the capital city of each prefecture.

IMW producers in EMTR include: (1) Public hospitals, (2) socialsecurity infirmaries, (3) healthcare centers, (4) peripheral healthoffices, (5) private clinics, (6) diagnostic laboratories and (7)physicians in private practice. The last producer included dentists,artificial kidney units, medical microbiology laboratories, axial

Table 2List of IMW producers in EMTR (4th Health Regional Administration of Greece, 2013, www.4ype.gr).

IMW Producer Drama Kavala Xanthi Rodopi Evros Total

Public hospitals 1 1 1 1 2 6Social security infirmaries 1 1 1 1 1 5Healthcare centers 3 3 3 2 4 15Peripheral health offices 20 26 17 21 31 115Private clinics 1 3 1 1 1 7Diagnostic laboratories 2 – 1 2 1 6Physicians in private practice 152 213 149 163 219 896

Fig. 3. IMW producers in the EMTR.

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 523

tomography units and magnetic resonance imaging units amongothers. A list of IMW producers in EMTR is presented in Table 2and their location is shown in Fig. 3.

3.2. Siting of treatment facilities and waste transfer stations

The first step for siting candidate areas for installation of thetreatment facility was to apply GIS-based software for exclusionof inappropriate areas, using the criteria of Table 1. The unsuitableareas are being displayed in Fig. 4 in brown color and the suitablefor treatment facility areas in green. The procedure for siting treat-ment facilities and TSs, described in Section 2.2, was applied. InFig. 5, the candidate TS positions for the two scenarios (Section 2.2)are depicted. The islands of Thasos and Samothraki and the mostremote from major hospitals municipalities were not consideredin the siting process.

3.3. IMW production

It was impossible and out of the scope of this paper to measureproduction by all sources; such data are never readily available.

Nevertheless, IMW production rates in EMTR were not arbitrary,but were directly obtained, estimated, or extrapolated fromVoudrias and Graikos (2014), Mandalidis (2011) and Komiliset al. (2011). Production rates by the 896 physicians in privatepractice are very scarce or non-existing. The authors used datafrom a small producer in Greece (Graikos et al., 2010), from dentalpractices (Kizlary et al., 2005) and from the literature (Pruss et al.,1999). Based on the principles of Section 2.3.1, individual wasteproducers were divided in a total of 17 waste producer groupsand distributed in the 3 categories: (1) The major public hospitalsand the physicians in private practice of the respective prefectureof the region, with the total IMW stored in the hospital (6 groups).(2) The social security health office and the private health services(private clinics, diagnostic centers) of the respective prefecture ofthe region, with the IMW stored in the individual producer (5groups). (3) The healthcare centers and the associated peripheralhealth offices of the respective prefecture of the region, with theIMW stored in the individual producer (6 groups). Average dailyproduction by each production source (Table 2) is presented inTable 3. Thus, the total average weekday production of 2136 kg/dof IMW for EMTR was estimated.

Fig. 4. Unsuitable and candidate areas for installation of the treatment facility in EMTR. The optimal location of the treatment facility in the wider sanitary landfill area ofChrysoupolis is, also, shown.

Fig. 5. Candidate TS positions for the two siting scenarios.

524 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

3.4. Collection plan

Since most producers were peripheral health offices with pro-ductions of less than 500 L/month, it was decided to use the rele-vant provisions of the Greek legislation (CMD, 2012) referring tocases of temporary storage of one month, for computing the OBF.However, to have a period that would allow a weekly plan ofIMW collection, which would serve the major producers, it was

decided that the period (reference time) to use in the OBF wouldbe equal to 28 days (Section 2.3.1). Additionally, the maximumtime that IMW could remain in TSs was decided equal to 4 days,which is the larger number of possible days that its quotient with28 is an integer. Greek legislation allows a maximum of 5 days’storage.

Based on the definition of the 17 producer groups and the OBFreference time of 28 d, IMW productions were calculated for

Table 3IMW production by each source in EMTR.

Daily IMW production onregular weekdays (kg/d)

Daily IMW productionon Saturdays (kg/d)

Daily IMW productionon Sundays (kg/d)

Weekly IMW production(kg/w)

Public hospitals 1569 521 521 8885Social security infirmaries 54.0 0 0 270Healthcare centers 52.6 52.6 52.6 368Peripheral health offices 14.4 14.4 14.4 101Private clinics 53.3 53.3 53.3 373Diagnostic laboratories 24 24 0 144Physicians in private practice 369 0 0 1846Total 2136 665 641 11,987

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 525

various periods of time smaller than the OBF reference time (e.g., 1weekend, 2 days, 1 week, etc.). The results of these calculationswere used to define the less frequent possible collection routesfor each IMW producer or producer groups (Section 2.3.1) and alsocomply with the legal restrictions. Thus, a collection plan for the28-d period was designed, aiming to minimize the number of dailypossible collection routes. Producers within a producer group mayhave different collection frequencies, depending on the amountproduced. For example, collection frequency for peripheral healthoffices was once/month, whereas for a healthcare center could beonce a week. The collection plan defined the days of collection,to minimize the total distance traveled. WCVs did not visit everyphysician in private practice, but each one of the 6 producer groupsthey formed with the major public hospitals.

3.5. System sizing and cost data

Based on production rates and collection frequencies, collectionWCV capacities were decided to be 5 m3 for WCVs which collectfrom hospitals and 2 m3 for WCVs which collect from the otherproducers. Concerning the sizing of TSs and the related WCVs, aninitial assumption of the 2/3 of the maximum produced quantityof IMW for every 4-day period was made. This quantity corre-sponds to 45 m3. Likewise, a first assumption for the capacity ofWCVs, which transport sterilized IMW was made, based on theaverage weekday IMW production. Considering the mass reductionafter sterilization, a WCV capacity of 9 m3 was calculated. Theabove capacities were varied during model runs, to achieve costminimization. All costs for WCVs and TSs were calculated frommarket current prices. Daily treatment quantity of IMW and costof treatment facility were obtained from the work of Voudriasand Graikos (2014). All costs were expressed into 28 day equalcosts corrected for inflation at a horizon of 10 years. This time per-iod pertains to the permit of operation time, issued according toGreek regulations. Fixed and variable costs for WCVs, TSs andtreatment facility are presented in Tables S1 to S7 in the electronic

Table 4Optimization results listed with decreasing total management cost.

Siting of treatment facility Siting of TS/sitingscenario

Amount of IMWtransferred toTS (t/month)

(1) BASE CASE Chrysoupolissanitary landfill

No TS –

(2) Xanthi industrial area No TS –(3) Xanthi industrial area Next to MSW TS of Sappes/B 9.6(4) Xanthi industrial area Next to Alexandroupolis

general hospital/A15.9

(5) Alexandroupolis industrial area Next to Kavala generalhospital/A

16.1

(6) Alexandroupolis industrial area Next to MSW TS of Kavala/B 16(7) Alexandroupolis industrial area No TS –

supplement. Labor costs were estimated using current daily (8 h/d)pays of 40 €/d and 30 €/d for a WCV driver and a worker, respec-tively. It was assumed that each WCV transferring IMW from aTS to the treatment facility (WCVTS) employed one driver andone worker. All other WCVs employed only one driver.

4. Results and discussion

4.1. Optimization results

Taking into account all candidate areas of Fig. 4, the applicationof the optimization model showed directly that the optimal loca-tion of the treatment facility in EMTR was in the wider sanitarylandfill area of Chrysoupolis. According to Table 4, the optimalsolution (38,800 €/month or 809 €/t) with the treatment facilitylocated in the wider sanitary landfill area of Chrysoupolis (35 kmfrom the industrial area of Xanthi) required no TSs. All WCVsdepart from the treatment facility and oneWCV with 7 m3 capacitywas used for transport of the treated waste to the sanitary landfill.Because of their daily variation, a total of 28 figures would berequired to show all collection-transport paths (WCV routes).Fig. 6 presents day 1 of collection from hospitals and rest of pro-ducers as an example of optimal routing. Specifically, Fig. 6-topshows the optimal path with departure from the treatment unit(start), routing to major hospitals for collection and return to thetreatment unit. Fig. 6-bottom shows in red color the optimal pathwith departure from the treatment unit (#1), routing to healthcarecenters and peripheral health offices of the Prefecture of Xanthi. Italso shows in blue color the optimal path for collection-transportfrom social security, private clinics and diagnostic laboratories ofthe Prefecture of Rodopi. Numbers show the sequential routingstops with departure from and return to the treatment unit.

The optimal solution was used as the base case in this study. Inaddition to the optimal solution, other scenarios were investigated,in case the optimal solution could not be implemented, e.g., forpolitical reasons. A total of two additional positions (industrial

Amount of IMWtransferred directlyto facility (t/month)

Total haulcost(€/month)

Totalhaul cost(€/t)

Totalmanagementcost (€/month)

Totalmanagementcost (€/t)

47.9 8660 181 38,800 809

47.9 8880 185 39,000 81438.3 8460 177 39,300 82032 8340 174 39,600 827

31.8 8700 182 39,800 831

31.9 8850 185 39,950 83447.9 9880 206 40,000 835

Fig. 6. Top: Optimal path for collection on day 1 frommajor hospitals with departure from and return to the treatment facility. Bottom: Optimal path with departure from thetreatment facility (#1), routing to healthcare centers and peripheral health offices of the Prefecture of Xanthi (red line). Optimal path for collection-transport from socialsecurity, private clinics and diagnostic laboratories of the Prefecture of Rodopi (blue line). (For interpretation of the references to color in this figure legend, the reader isreferred to the web version of this article.)

526 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

areas of Xanthi and Alexandoupolis) are presented in this paper(Table 4), as the remainders were much more expensive options.For these two positions, one scenario with no TSs and the two sit-ing scenarios for TSs (Fig. 4 and Section 2.2) were considered.

Alexandroupolis industrial area was investigated, because it wasthe most remote candidate position for the treatment unit. There-fore, construction of TS could be necessary, to reduce total treat-ment cost.

izationru

ns. TS ca

pacity

(m3)

Max

imum

stored

amou

nt

(m3)

Numbe

rof

WCVs

from

TSto

facility

Cap

acity

ofW

CVs

from

TSto

facility

(m3)

Numbe

rof

WCVsfrom

hos

pitals

Cap

acityof

WCV

sfrom

hos

pitals

(m3)

Numbe

rof

WCVsfrom

other

sources

Cap

acityof

WCVsfrom

other

sources

(m3)

Cap

acityof

WCVsto

sanitary

landfi

ll(m

3)

Dep

arture

points

ofW

CVs

––

––

35

22

7AllW

CVsfrom

trea

tmen

tfacilities

––

––

35

22

7AllW

CVsfrom

trea

tmen

tfacilities

1914

.51

152

52

27

2W

CVsfrom

trea

tmen

tfacilities

and2W

CVsfrom

TSroupo

lis

l/A

2319

.81

202

52

29

2W

CVsfrom

trea

tmen

tfacilities

and2W

CVsfrom

TS

l/A

2319

.91

202

52

29

2W

CVsfrom

trea

tmen

tfacilities

and2W

CVsfrom

TSS

2319

.51

202

52

29

2W

CVsfrom

trea

tmen

tfacilities

and2W

CVsfrom

TS–

––

–3

52

27

AllW

CVsfrom

trea

tmen

tfacilities

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 527

In the second-best solution (39,000 €/month or 814 €/t) ofTable 4, the treatment plant was located in the industrial area ofXanthi and required no use of TSs. A total of 4 WCVs were needed,with departure points in the treatment facility. A vehicle of 7 m3

capacity was used for the transportation of treated IMW to thelandfill.

In the third best solution (39,300 €/month or 820 €/t) ofTable 4, the treatment plant was located in the industrial areaof Xanthi and required a 19 m3 TS next to MSW facility ofSappes (Fig. 5). A total of 4 WCVs were needed, with 2 depart-ing from the TS and 2 from the treatment facility. A vehicle of7 m3 capacity was used for the transportation of treated IMWto the landfill.

In the fourth best solution (39,600 €/month or 827 €/t) ofTable 4, the treatment plant was located in the industrial area ofXanthi and required a 23 m3 TS next to the main hospital ofAlexandroupolis (Fig. 5). A total of 4 WCVs were needed, with 2departing from the TS and 2 from the treatment facility. A vehicleof 9 m3 capacity was used for the transportation of treated IMW tothe landfill.

In the fifth best solution (39,800 €/month or 831 €/t) of Table 4,the treatment plant was located in the industrial area of Alexan-droupolis and required a 23 m3 TS next to the general hospital ofKavala (Fig. 5). A total of 4 WCVs were needed, with 2 departingfrom the TS and 2 from the treatment facility. A vehicle of 9 m3

capacity was used for the transportation of treated IMW to thelandfill.

In the sixth best solution (39,950 €/month or 834 €/t) ofTable 4, the treatment plant was located in the industrial areaof Alexandroupolis and required a 23 m3 TS next to MSW facilityof Kavala (Fig. 5). A total of 4 WCVs were needed, with 2 depart-ing from the TS and 2 from the treatment facility. A vehicle of 9m3 capacity was used for the transportation of treated IMW tothe landfill.

In the seventh best solution (40,000 €/month or 835 €/t) ofTable 4, the treatment facility was located in the industrial areaof Alexandroupolis and required no use of TSs. ThreeWCVs for hos-pitals and 2 from the other type of producers were needed, withdeparture points located in the treatment facility. A vehicle of 7m3 capacity was used for the transportation of treated IMW tothe landfill.

The results showed that if the treatment plant was located inthe most remote industrial area of Alexandroupolis, a TS next tothe general hospital of Kavala was necessary to minimize cost. Inaddition to total cost, other parameters were also investigatedand are compared in Tables 4 and 5.

According to Table 4, the haul cost ranges from 174 to 206 €/t,depending on location of the treatment facility. For comparison,Chatzouridis and Komilis (2012) reported optimum MSW collec-tion cost for the same Greek Region equal to 42.4 €/t with use ofTSs. If TSs were not present, the MSW collection cost wouldincrease to 52.5 €/t.

Table5

Characteristicsof

TSsan

dW

CVsfrom

theop

tim

Sitingof

trea

tmen

tfacility

Sitingof

TS/siting

scen

ario

BASE

CASE

Chryso

upo

lis

sanitarylandfi

llNoTS

Xan

thiindu

strial

area

NoTS

Xan

thiindu

strial

area

Nex

tto

MSW

TSof

Sapp

es/B

Xan

thiindu

strial

area

Nex

tto

Alexa

nd

general

hos

pita

Alexa

ndrou

polis

indu

strial

area

Nex

tto

Kav

ala

general

hos

pita

Alexa

ndrou

polis

indu

strial

area

Nex

tto

MSW

Tof

Kav

ala/B

Alexa

ndrou

polis

indu

strial

area

NoTS

4.2. Comparison between the two-optimization software

Several scenarios were simulated using the Crystal Ball soft-ware and compared to the results of Evolver software. Bothsoftware resulted in the same optimal locations for the treat-ment unit and TSs. According to Table 6, the results were iden-tical, suggesting increased confidence and reliability of theoptimization methodology. Identical were, also, the results forthe numbers of collection vehicles and capacities of collectionvehicles and TSs. However, Evolver was faster in most optimiza-tion steps, whereas Crystal Ball required smaller userintervention.

Table 6Comparison of optimal cost solutions between the two different software programs on the scenario of siting the TSs next to hospitals.

Initial Run

Model Solution Steps

Evolver Crystal BallMost Influential Treatment Plant Locations Chrysoupolis Landfill Area and Xanthi Industrial Area Chrysoupolis Landfill Area and Xanthi Industrial Area

Comparison of SpecificTreatment Plant Locations

Chrysoupolis Landfill Area Xanthi Industrial Area Alexandroupolis IndustrialArea*

Evolver Crystal Ball Evolver Crystal Ball Evolver Crystal Ball

Most Influential TSLocations

next toAlexandroupolisHospital

next to Alexandroupolis Hospital andnext to Komotini** General Hospital

next toAlexandroupolisHospital

next toAlexandroupolisHospital

next toKavala’sHospital

next toKavala’sHospital

Selected TS for next Step next toAlexandroupolisHospital

next to Alexandroupolis Hospital** next toAlexandroupolisHospital

next toAlexandroupolisHospital

next toKavala’sHospital

next toKavala’sHospital

Optimal System Cost withthe Use of Selected TS

39233.62€/month

39230.43 €/month 39606.78€/month

39606.78€/month

39810.70€/month

39809.17€/month

Optimal System Costwithout the Use of TS

38806.20€/month

38806.20 €/month 39027.67€/month

39027.67€/month

40015.49€/month

40015.49€/month

* Case study for a remote treatment plant location.** Results for Komotini General Hospital are not shown, because it was a more expensive option than using the TS next to Alexandroupolis General Hospital.

528 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

4.3. Sensitivity analysis

For a more in-depth examination of IMW collection, transportand treatment in EMTR, a sensitivity analysis was performed withrespect to fuel cost and IMW production rate. The analysis used the1st siting approach for TSs.

A 15% increase on fuel cost was chosen, which resulted in anincrease of the haul cost for all types of vehicles. The optimal solu-tion under these conditions required again no TSs and the treat-ment facility located in the sanitary landfill area of Chrysoupolis,with a cost of 39,150 €/month (Table 7). Also, the number ofneeded vehicles and their departure points was the same withthe base case. That is, 3 WCVs of 5 m3 capacity from hospitals, 2WCVs of 2 m3 capacity from other producers and 1 WCV of 7 m3

capacity from the treatment unit to the sanitary landfill were used.Such an increase in fuel cost raised the optimal solution total man-agement cost by 350 €/month, which was not sufficient to justifyconstruction of a TS for minimizing the system cost.

In the second case, a 25% increase on IMW production rate waschosen. Since storage conditions depend on the IMW amount pro-duced, a new collection plan had to be developed for the Region. Inthis new plan, capacities of WCVs from hospitals had to be changedto 7 m3 (from 5 m3 in the base case. Thus, 3 WCVs of 7 m3 capacity

Table 7Comparison of optimal transport cost for base case and Xanthi case and sensitivity analysXanthi case.

WCVs fromhospitals(€/t/km)

WCVs fromother producers(€/t/km)

WCVs owaste tlandfill

Base Case 0.0079 0.0477 3.57Sensitivity Analysis on Fuel

Cost increase by 15%0.0084 (6.3%") 0.0498 (4.4%") 3.57 (0%

Sensitivity Analysis on IMWproduction rate increase by 25%

0.0071 (10.1%;) 0.0371 (22.2%;) 3.33 (6.

Treatment Plant Located inIndustrial Area of Xanthi

0.0081 0.0478 0.0265

Sensitivity Analysis on FuelCost increase by 15%

0.0085 (4.9%") 0.0499 (4.4%") 0.0272

Sensitivity Analysis on IMWproduction rate increase by 25%

0.0072 (11.1%;) 0.0378 (20.9%;) 0.0242

Calculation of the transport cost (€/t/km) required the calculation of total costs for everyWcost and transport cost by ship from the two islands), the amount (t) of transported woptimal solutions included no transfer stations.

from hospitals, 2 WCVs of 2 m3 capacity from other producers and1 WCV of 11 m3 capacity from the treatment unit to the sanitarylandfill were used. Again, the optimal solution resulted in no TSsand the treatment facility in the landfill area of Chrysoupolis, witha total management cost of 41,000 €/month (Table 7). The samenumbers of needed vehicles with the same departure points as inthe base case were also calculated. Such an increase in IMW pro-duction did not affect the system in a way to make necessary theinstallation of a TS in EMTR. The increase by 2200 €/month com-pared to the optimal cost of the base case examined, was attributedto increased treatment and landfill costs.

Table 7 compares, also, transport cost for the base case and thecase of treatment plant located in industrial area of Xanthi with thetwo respective cases of the sensitivity analysis described above.Calculation of the transport cost (€/t/km) required the calculationof total costs for every WCV type (capital and insurance cost, main-tenance cost, fuel consumption cost, labor cost and transport costby ship from the two islands), the amount (t) of transported wasteand the total transport distances. Transfer cost was not included,because the optimal solutions included no TSs.

According to Table 7, the transport cost (€/t/km) for WCVs fromhospitals is the lowest, because these vehicles transport the largestamount of the produced IMW on a daily basis, thus traveling the

is. Numbers in parenthesis correspond to % difference with respect to base case and

f treatedo MSW(€/t/km)

Totaltransportcost (€/t/km)

Totaltransportcost (€/t)

Totalmanagementcost (€/t)

Totalmanagementcost (€/month)

0.0073 181 809 38,800) 0.0076 (4.1%") 188 (4.1%") 816 (0,9%") 39,150 (0.89%")

7%;) 0.0061 (16.4%;) 158 (12.7%;) 683 (15.5%;) 41,000 (5.6%")

0.0072 185 813 39,000

(2.6%") 0.0075 (4.1%") 193 (4.1%") 821 (0.95%") 39,400 (0.93%")

(8.7%;) 0.0061 (15.3%;) 163 (12.2%;) 694 (14.7%;) 41,300 (5.7%")

CV type (capital and insurance cost, maintenance cost, fuel consumption cost, laboraste and the total transport distances. Transfer cost was not included, because the

Table 8Allocation of optimal system cost for base case and Xanthi case and sensitivity analysis. Numbers in parenthesis correspond to % difference with respect to base case and Xanthicase.

VehicleInvestmentCost

VehicleHaulCost

VehicleLaborCost

Investment + operationcost for treatmentplant

Landfill Cost IMWTreatmentCost

Total

Base Case 6.3% 6.1% 8.7% 64.7% 1.8% 12.4% 100%Sensitivity Analysis on Fuel Cost increase by 15% 6.2% 7% 8.6% 64.1% 1.8% 12.3% 100%Sensitivity Analysis on IMW production increase by 25% 6.2% 6.7% 8.9% 61.2% 2.3% 14.7% 100%Treatment Plant Located to Industrial Area of Xanthi 7.6% 8.8 6.3% 63.2% 1.8% 12.3% 100%Sensitivity Analysis on Fuel Cost increase by 15% 8.5% 8.7% 6.2% 62.6% 1.8% 12.2% 100%Sensitivity Analysis on IMW production increase by 25% 9% 9.2% 6.2% 59% 2.2% 14.4% 100%

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 529

largest distances. In contrast, WCVs from other producers trans-port smaller amounts and travel smaller distances. The data alsoshow that transport cost is most sensitive to the 25% increase inIMW production. More specifically, the 15% fuel cost increaseresulted in 4.1% increase in the €/t/km transport cost and 4.1%increase in the €/t transport cost. In contrast, increase in IMW pro-duction rate by 25% resulted in 16.4% decrease in the €/t/km costand 12.7% decrease in the €/t cost, thus realizing scale economy.

Similar results were obtained for the case the treatment plantwas located in the industrial area of Xanthi. Thus, the 15% fuel costincrease resulted in 4.1% increase in the €/t/km transport cost and4.1% increase in the €/t transport cost. In contrast, increase in IMWproduction rate by 25% resulted in 15.3% decrease in the €/t/kmcost and 12.2% decrease in the €/t cost, thus realizing scaleeconomy.

Table 8 presents the allocation of total cost in different cost cat-egories for the cases presented in Table 7. The treatment unitinvestment cost corresponds to the necessary costs to constructand install the treatment facility expressed at a horizon of 10 years,as explained in Section 3. The treatment unit operation costincluded the needed cost for the operation of the facility (i.e.needed electric energy consumption). It is obvious that the largestcost component corresponds to the investment and operation costof the treatment facility, for all cases presented in Table 8.

5. Conclusions

In this work, a conceptual model was developed to optimize thedesign of a collection, haul, transfer, treatment and disposal systemfor infectious medical waste. The system consists of IMW produc-tion nodes (groups of IMW producers), the intermediate nodes ofTSs, the obligatory intermediate nodes of treatment facilities andfinally the terminal nodes (landfills). The model calculates the opti-mum locations of the treatment facilities and TSs, their design

capacities (t/d), the number and capacities of all waste collection,transport and transfer vehicles and their optimum transport pathand the optimal IMW management system cost. The conclusionsfrom model application to the East Macedonia – Thrace Region inGreece can be summarized as follows:

� The optimal position for the treatment facility was in the sani-tary landfill area of Chrysoupolis and required no TSs.

� The optimal solution included 3 collection WCVs from hospitalsand 2 from other producers, with respective capacities 5 and 2m3/WCV, and all of them had as departure point the treatmentfacility. Also, a vehicle of 7 m3 capacity was used for transport oftreated IMW to the landfill. Optimal cost was 38,800 €/month or809 €/t.

� The same results were produced from two different optimiza-tion software, Evolver and Crystal Ball. Evolver was faster inmost stages of the solution, but needed a frequent user inter-vention, while Crystal Ball was more automated.

� Sensitivity analysis with respect to 15% increase in fuel cost and25% increase in IMW production resulted in the same positionfor the treatment facility, as in the base case and required nouse for TSs.

� Total system cost was more sensitive to increase in IMW pro-duction than to increase in fuel cost.

� The major cost component was the installation and operation ofthe treatment facility (64.7% of total management cost), whilecollection and transport cost was significantly lower (21.1% oftotal management cost).

Acknowledgement

The authors wish to thank Mr. I. Papaspyros for his assistance inusing the Crystal Ball and Evolver software.

Appendix A

Before computing the OBF (Eq. (1)), it was necessary to compute the following: (1) The number of WCVs of all categories, usingEqs. (1)–(A4) below. (2) The number of transfer vehicles, using Eq. (A5) below. (3) The number of vehicles transporting the treated wasteto the sanitary landfill, using Eqs. (A6)–(A8) below. Then, the OBF was computed, using Eq. (A9).

nWCVAj;k ¼ maxXgu¼1

½Ru;d � ðtu;j;d þ QueueWCVAu;dÞ þ CTmu;d� � yu;j;dþ½tu;j;k;d þ Rku;d � ðtu;k;d þ QueueWCVAu;dÞ þ QueueWCVAu;d þ CTmu;d � yu;j;k;d�

( )

AllowTime

ðA1Þ

where

u �N and u = {1,2,. . .,g}j �N and j = {1,2,. . .,t}k �N and k = {1,2,. . .,h}d �N and d = {1,2,. . .,m}

530 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

nWCVBj;k ¼ maxXv

u¼gþ1

½Ru;d � ðtu;j;d þ QueueWCVBu;dÞ þ CTmu;d� � yu;j;dþ½tu;j;k;d þ Ru;k;d � ðtu;k;d þ QueueWCVBu;dÞ þ QueueWCVBu;d þ CTmu;d� � yu;j;k;d

( )

AllowTimeðA2Þ

where

u �N and u = {g + 1,g+2,. . .,v}j �N and j = {1,2,. . .,t}k �N and k = {1,2,. . .,h}d �N and d = {1,2,. . .,m}

nWCVAk ¼ maxXgu¼1

½Ru;d � ðtu;k;d þ QueueWCVAu;dÞ þ CTmu;d� � yu;k;dAllowTime

ðA3Þ

where

u �N and u = {1,2,. . .,g}k �N and k = {1,2,. . .,h}d �N and d = {1,2,. . .,m}

nWCVBk ¼ maxXv

u¼gþ1

½Ru;d � ðtu;k;d þ QueueWCVBu;dÞ þ CTmu;d� � yu;k;dAllowTime

ðA4Þ

where

u �N and u = {g+1,g+2,. . .,v}k �N and k = {1,2,. . .,h}d �N and d = {1,2,. . .,m}

nWCVTSj;k ¼ max

Xvu¼1

X1j¼1

Xqd¼1

IMWu;d�yu;j;dWCVTSMass

� �� ðtj;k þ CTmjþ QueueWCVTSÞ

AllowTime

24

35

;Xvu¼1

X1j¼1

X2qd¼qþ1

IMWu;d�yu;j;dWCVTSMass

� �� ðtj;k þ CTmjþ QueueWCVTSÞ

AllowTime

24

35

; . . . ;

Xvu¼1

X1j¼1

Xmd¼m�ðq�1Þ

ðIMWu;d�yu;j;dWCVTSMass Þ � ðtj;k þ CTmjþ QueueWCVTSÞ

AllowTime

24

35

66666666666666666664

77777777777777777775

ðA5Þ

where

u �N and u = {1,2,. . .,v}j �N and j = {1,2,. . .,t}d �N and d = {1,2,. . .,m}q�N and m/q �N and q 6 5

WCVLFusualk ¼Xvu¼1

IMWu;d�Pv

u¼1

Pt

j¼1ðIMWu;d�yu;j;dÞ

WCVLFMass

� �� 0;6 � ðtlfk þ CTmkþ QueueWCVLFÞAllowTime

8<:

9=; ðA6Þ

where

u �N and u = {1,2,. . .,v}k �N and k = {1,2,. . .,h}d �N and d = {1,2,. . .,m} and d/q = decimalq�N and m/q �N and q 6 5

WCVLFtransk ¼Xvu¼1

IMWu;d þPv

u

Ptj ðIMWu;d � yu;j;d�ðq�1ÞÞ þ ðIMWu;d � yu;j;d�ðq�2ÞÞ þ . . .þ ðIMWu;d � yu;j;d�½q�ðq�1Þ�Þh i

WCVLFMass

24

35�

0;6 � ðtlfk þ CTmkþ QueueWCVLFÞAllowTime

8>>>><>>>>:

9>>>>=>>>>;

ðA7Þ

where

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 531

u �N and u = {1,2,. . .,v}k �N and k = {1,2,. . .,h}d �N and d = {1,2,. . .,m} and d/q �Nq �N and m/q �N and q 6 5

nWCVLFk ¼ maxWCVLFusualk; WCVLFtransk ðA8Þ

MinCost ¼Xtj¼1

Xhk¼1

ðnWCVAj;kÞ þXhk¼1

nWCVAk

!�WCVAInvCostþ

Xtj¼1

Xhk¼1

ðnWCVBj;kÞ þXhk¼1

nWCVBk

!�WCVBInvCost þ

Xtj¼1

Xhk¼1

ðnWCVTSj;kÞ �WCVTSInvCostþ

Xhk¼1

nWCVLFk �WCVLFInvCost þXgu¼1

Xtj¼1

Xmd¼1

ðRu;d � du;j;dÞ �WCVAHaulCost � yu;j;d" #

þ

Xgu¼1

Xtj¼1

Xhk¼1

Xmd¼1

du;j;k;d þ ðRu;k;d � du;k;dÞ� � �WCVAHaulCost � yu;j;k;d

( )þ

Xgu¼1

Xhk¼1

Xmd¼1

ðRu;d � du;k;dÞ �WCVAHaulCost � yu;k;d" #

þXv

u¼gþ1

Xtj¼1

Xmd¼1

ðRu;d � du;j;dÞ �WCVBHaulCost � yu;j;d" #

þ

Xvu¼gþ1

Xtj¼1

Xhk¼1

Xmd¼1

du;j;k;d þ ðRu;k;d � du;k;dÞ� � �WCVBHaulCost � yu;j;k;d

( )þ

Xvu¼gþ1

Xhk¼1

Xmd¼1

ðRu;d � du;k;dÞ �WCVBHaulCost � yu;k;d" #

þ

Xvu¼1

Xtj¼1

Xhk¼1

Xqd¼1

IMWu;d � yu;j;dWCVTSMass

� � dj;k � yu;j;d

� ��WCVTSHaulCost

( )þ

Xvu¼1

Xtj¼1

Xhk¼1

X2qd¼qþ1

IMWu;d � yu;j;dWCVTSMass

� � dj;k � yu;j;d

� ��WCVTSHaulCost

( )þ

þ . . .þXvu¼1

Xtj¼1

Xhk¼1

Xmd¼m�ðqþ1Þ

IMWu;d � yu;j;dWCVTSMass

� � dj;k � yu;j;d

� ��WCVTSHaulCost

8<:

9=;þ

Xvu¼1

Xhk¼1

Xq�1

d¼1

IMWu;d �Pv

u¼1

Ptj¼1

Pq�1d¼1 ðIMWu;d � yu;j;dÞ

h iWCVLFMass

� dlfk � 0;624

35 �WCVLFHaulCost

8<:

9=;

8<:

9=;þ

Xvu¼1

Xhk¼1

Xqd¼q

IMWu;d þPv

u¼1

Ptj¼1

Pqd¼1ðIMWu;d � yu;j;dÞ

h iWCVLFMass

� dlfk � 0;624

35 �WCVLFHaulCost

8<:

9=;

8<:

9=;þ

þ . . .þXvu¼1

Xhk¼1

Xm�1

d¼ðm�qþ1Þ

IMWu;d �Pv

u¼1

Ptj¼1

Pm�1d¼ðm�qþ1ÞðIMWu;d � yu;j;dÞ

h iWCVLFMass

� dlfk � 0;624

35 �WCVLFHaulCost

8<:

9=;

8<:

9=;þ

Xvu¼1

Xhk¼1

Xmd¼m

IMWu;d þPv

u¼1

Ptj¼1

Pmd¼ðm�qþ1ÞðIMWu;d � yu;j;dÞ

h iWCVLFMass

� dlfk � 0;624

35 �WCVLFHaulCost

8<:

9=;

8<:

9=;þ

Xgu¼1

Xtj¼1

Xmd¼1

Ru;d � ðtu;j;d þ QueueWCVAu;dÞ þ CTmu;d

� � � Dhr � yu;j;d( )

þ

Xgu¼1

Xtj¼1

Xhk¼1

Xmd¼1

tu;j;k;d þ Rku;d � ðtu;k;d þ QueueWCVAu;dÞ þ QueueWCVAu;d þ CTmu;d

� � � Dhr � yu;j;k;d( )

þ

Xgu¼1

Xtj¼1

Xhk¼1

Xmd¼1

Ru;d � ðtu;k;d þ QueueWCVAu;dÞ þ CTmu;d� � � Dhr � yu;k;d

( )þ

Xvu¼gþ1

Xtj¼1

Xmd¼1

Ru;d � ðtu;j;d þ QueueWCVBu;dÞ þ CTmu;d� � � Dhr � yu;j;d

( )þ

532 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

Xvu¼gþ1

Xtj¼1

Xhk¼1

Xmd¼1

tu;j;k;d þ Rku;d � ðtu;k;d þ QueueWCVBu;dÞ þ QueueWCVBu;d þ CTmu;d

� � � Dhr � yu;j;k;d( )

þ

Xmu¼gþ1

Xtj¼1

Xhk¼1

Xvd¼1

Ru;d � ðtu;k;d þ QueueWCVBu;dÞ þ CTmu;d

� � � Dhr � yu;k;d( )

þ

Xvu¼1

Xtj¼1

Xhk¼1

Xqd¼1

IMWu;d � yu;j;dWCVTSMass

� � ðtj;k þ CTmjþ QueueWCVTSÞ

� �� Dhr

( )þ

Xvu¼1

Xtj¼1

Xhk¼1

X2qd¼qþ1

IMWu;d � yu;j;dWCVTSMass

� � ðtj;k þ CTmjþ QueueWCVTSÞ

� �� Dhr

( )þ

þ . . .þXvu¼1

Xtj¼1

Xhk¼1

Xmd¼m�ðqþ1Þ

IMWu;d � yu;j;dWCVTSMass

� � ðtj;k þ CTmjþ QueueWCVTSÞ

� �� Dhr

8<:

9=;þ

Xvu¼1

Xhk¼1

Xq�1

d¼1

IMWu;d �Pv

u¼1

Ptj¼1

Pq�1d¼1 ðIMWu;d � yu;j;dÞ

WCVLFMass� 0;6 � ðtlfk þ CTmkþ QueueWCVLFÞ

" #� Dhr

( )þ

Xvu¼1

Xhk¼1

Xqd¼q

IMWu;d þPv

u¼1

Ptj¼1

Pqd¼1ðIMWu;d � yu;j;dÞ

WCVLFMass� 0;6 � ðtlfk þ CTmkþ QueueWCVLFÞ

" #� Dhr

( )þ

þ . . .þXvu¼1

Xhk¼1

Xm�1

d¼ðm�qþ1Þ

IMWu;d �Pv

u¼1

Ptj¼1

Pm�1d¼ðm�qþ1ÞðIMWu;d � yu;j;dÞ

WCVLFMass� 0;6 � ðtlfk þ CTmkþ QueueWCVLFÞ

" #� Dhr

8<:

9=;

þXvu¼1

Xhk¼1

Xmd¼m

IMWu;d þPv

u¼1

Ptj¼1

Pmd¼ðm�qþ1ÞðIMWu;d � yu;j;dÞ

WCVLFMass� 0;6 � ðtlfk þ CTmkþ QueueWCVLFÞ

" #� Dhr

( )þ

Xtj¼1

yj �WTSUnitCost

!þ

Xvu¼1

Xtj¼1

Xmd¼1

ðIMWu;d � yu;j;dÞ �WTSTipFee

" #þ

þXvu¼1

Xmd¼1

ðIMWu;dÞ � TPWasteCost

" #þ

Xvu¼1

Xmd¼1

ðIMWu;dÞ � 0;6 � LFTipFee" #

þ FixedCost ðA9Þ

whereIndices:

u – integers referring to IMW production nodes, u є {1,. . ., g,. . ., v}

When u є {1,. . ., g}, production nodes refer to hospitalsWhen u є {g+1, . . ., v}, production nodes refer to the otherproducers

j – integers referring to the candidate TS positions, j є {1,. . ., t}k – integers referring to the candidate treatment facilities posi-tions, k є {1,. . ., h}d – integers referring to the days of the period of the examinedcase, d є {1,. . ., m}q – integers referring to the days of the period chosen for thetransportation of IMW from a TS to a treatment facility (restric-tions: v /q �N and q<5)

Variables:

MinCost – the total minimizable system cost (dependent vari-able) for the period examined (€/month, here a month=28 days)yu,j,d – binary (adjustable) variable that indicates an invalid (0)or valid (1) route, starting from a TS j, moving to a group of pro-ducers u and back to j, on day d of the examined periodyu,j,k,d – binary (adjustable) variable that indicates an invalid (0)or valid (1) route starting from a TS j, heading to a group of pro-ducers u and moving to treatment facilities k for IMW treat-ment and back to j, on day d of the examined periodyu,k,d – binary (adjustable) variable that indicates an invalid (0)or valid (1) route starting from treatment facilities k moving to

a group of producers u and back to k, on day d of the examinedperiodyj – binary variable that indicates whether a TS j should be con-structed (1) or not (0). Its value represents the number of con-structed TSs and is calculated via the OBF.

Parameters:

IMWu,d – IMW production by producers’ group u until collectionday d (kg)WCVMass – weight that can be carried by each type of vehicleduring a trip (kg)tu,j,d – travel time of a collection WCV from TS j to producers’group u and back to j on day d (minutes)tu,j,k,d – travel time of a collection WCV from TS j, heading to agroup of producers u and moving to treatment facilities k forIMW treatment and back to j, on day d (minutes)tu,k,d – travel time of a collectionWCV from treatment facilities kto producers’ group u and back to k on day d (minutes)tj,k – travel time of a WCV that transfers IMW from a transferstation j to treatment facilities k and back to j on day d(minutes)tlfk – travel time of a WCV that transfers sterilized IMW fromtreatment facilities k to landfill and back to k on day d (minutes)du,j,d – traveled distance of a collectionWCV from TS j to produc-ers’ group u and back to j on day d (km)du,j,k,d – traveled distance of a collection WCV from TS j headingto a group of producers u and moving to treatment facilities kfor IMW treatment and back to j, on day d (km)

G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534 533

du,k,d – traveled distance of a collection WCV from treatmentfacilities k to producers’ group u and back to k on day d (km)dj,k – traveled distance of a WCV that transfers IMW from a TS jto treatment facilities k and back to j on day d (km)dlfk – traveled distance of a WCV that transfers sterilized IMWfrom treatment facilities k to landfill and back to k on day d (km)HMWu,d – produced and stored IMW on production node u oncollection day dRu,d – number which indicates the necessary collection routesthat aWCV will have to complete from a TS or treatment facilityto a group of producers u on day d and back to starting point, forcollecting the total IMW quantity. (Ru,d = the rounded to thenext integer quotient of HMWu,d/WCVMass)Rku,d – number of necessary collection routes that a WCV willhave to complete, departing from a TS to a group of producersu to treatment facilities k and back to u on day d, to collectthe total produced IMW by the group u. (Rku,d = Ru,d – 1)QueueWCVu,d – queue time of a collection WCV in TSs or treat-ment facilities which refers to collected IMW quantity fromgroup u on day d (min/kg)QueueWCVTS – queue time of a WCV which transfers IMW fromTSs to treatment facilities (min/trip)QueueWCVLF – queue time of a WCV which transfers sterilizedIMW to landfill (min/trip)CTmu,d – loading time of IMW collection for group u and day d(min)CTmj – loading time of IMW from a TS (min)CTmk – loading time of sterilized IMW from treatment facilities(min)AllowTime – the maximum allowable time that a WCV can oper-ate per day (min/d)HaulCost – total cost for using the type of WCV which is referredto (€/day)Dhr – labor cost per minute for a WCV (€/minute)WTSTipFee – IMW tipping fee for storing into a TS (€/kg)TPWasteCost – IMW treatment cost (€/kg)LFTipFee – sterilized IMW tipping fee in landfill (€/kg)nWCVj,k – needed number of the type of WCV that it refers to,which depart from TS j and go to treatment facilities knWCVk – needed number of the type WCV that it refers to,which depart from treatment facilities knWCVTSj,k – needed number of WCVs that transfer IMW, depart-ing from TS j to treatment facilities kWCVLFusualk – needed number of WCVs that transport steril-ized IMW from treatment facilities k, on days that IMW is nottransferred from TSsWCVLFtrans k – needed number of WCVs that transport steril-ized IMW from treatment facilities k, on days that IMW is trans-ferred from TSsnWCVLFk – needed number of WCVs that transport sterilizedIMW from treatment facilities k.

Model constraints:The OBF on Eq. (A9), is subject to the constraints that are

described on Eqs. (A10)–(A14).Xtj¼1

Xhk¼1

ðyu;j;d þ yu;j;k;dÞ þXhk¼1

yu;k;d ¼ 1 for every u ¼ 1 to v and d ¼ 1 to m

ðA10Þ

If yu;j;d–0 for any u and d for a j variable; then yj ¼ 1 for this j

ðA11ÞXhk¼1

ðyu;j;k;dÞ 6 1 for for every u ¼ 1 to v; j ¼ 1 to t and d ¼ 1 to m

ðA12Þ

Xhk¼1

ðyu;k;dÞ 6 1 for for every u ¼ 1 to v and d ¼ 1 to m ðA13Þ

Xvu¼1

Xmd¼1

IMWu;d ¼Xvu¼1

Xtj¼1

Xmd¼1

ðIMWu;d � yu;j;dÞ

þXvu¼1

Xtj¼1

Xhk¼1

Xmd¼1

ðIMWu;d � yu;j;k;dÞ

þXvu¼1

Xhk¼1

Xmd¼1

ðIMWu;d � yu;k;dÞ ðA14Þ

Eq. (A10) expresses that only one of all likely collection routeson day d between a group of IMW producers u is valid. A groupof producers should haul its IMW on only one TS or directly totreatment facilities. Eq. (A11) expresses that if at least one ofIMW producers on any day transfers its waste on a TS j, then sta-tion j is operating in the OBF with the related cost. Additionally,Eqs. (A12) and (A13) express that only one of the candidate loca-tions for treatment facilities is acceptable during each run of themodel. Finally, Eq. (A14) describes the system mass balance andindicates that the total IMW produced is either hauled to a TSand then directed to treatment plant or hauled directly to thetreatment plant from WCVs departing from the TSs or the treat-ment plant.

Appendix B. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.wasman.2017.08.037.

References

Abdelli, I.S., Abdelmalek, F., Djelloul, A., Mesghouni, K., Addou, A., 2016. GIS-basedapproach for optimized collection of household waste in Mostaganem city(Western Algeria). Waste Manage. Res. 34 (5), 417–426.

Alagoz, A.Z., Kocasoy, G., 2008. Improvement and modification of the routingsystem for the healthcare waste collection and transportation in Istanbul.Waste Manage. 28, 1461–1471.

Almeida, J., 2011. A cost optimization model for hazardous medical wastemanagement in Portugal. Universidade Tecnica de Lisboa. Thesis for theDegree of Civil Engineer.

Apaydin, O., Gonullu, M.T., 2011. Route time estimation of solid waste collectionvehicles based on population density. Global Nest J. 13 (2), 162–169.

Arribas, C., Blazquez, C., Lamas, A., 2010. Urban solid waste collection systems usingmathematical modeling and tools of geographic information systems. WasteManage. Res. 28, 355–363.

Budak, A., Ustundag, A., 2013. A risk analysis of waste collection and disposal inhealth institutions of Turkey. In: Kahraman, Cengiz (Ed.), Proceedings of the 4thInternational Conference on Risk Analysis and Crisis Response. CRC Press, printISBN 978-1-138-00019-3.

CDPH – California Department of Public Health, 2017. Registered medical wastetransfer stations and treatment facilities. http://www.cdph.ca.gov/certlic/medicalwaste/Pages/default.aspx.

Chaerul, M., Tanaka, M., Shekdar, A.V., 2008. Resolving complexities in healthcarewaste management: a goal programming approach. Waste Manage. Res. 26,217–232.

Chatzouridis, C., Komilis, D., 2012. A methodology to optimally site and designmunicipal solid waste transfer stations using binary programming. Resour.Conserv. Recycl. 60, 89–98.

CMD – Common ministerial decision, 2002. ‘‘Classification of public and privateworks and activities into categories, in accordance with Article 3 of Law 1650/1986” (in Greek). Official Government Gazette, FEK 1022B’/15393/2332.

CMD – Common ministerial decision, 2006. ‘‘Measures, terms and limitations forthe management of hazardous waste, in compliance with the provisions ofDirective 91/689/EC” (in Greek). Official Government Gazette, FEK 383B’/13588/725.

CMD – Common ministerial decision, 2012. ‘‘Measures and terms for managementof waste from health-care facilities” (in Greek). Official Government Gazette,FEK 1537B’/146163.

Das, S., Bhattacharyya, B., 2015. Optimization of municipal solid waste collectionand transportation routes. Waste Manage. 43, 9–18.

Dumitrescu, I., Ropke, S., Cordeau, J.F., Laporte, G., 2009. The travelling salesmanproblem with pickup and delivery: polyhedral results and a branch and cutalgorithm. Math. Program. 121 (2), 269–305.

534 G. Mantzaras, E.A. Voudrias /Waste Management 69 (2017) 518–534

Faccio, M., Persona, A., Zanin, G., 2011. Waste collection multi objective model withreal time traceability data. Waste Manage. 31 (12), 2391–2405.

Graikos, A., Voudrias, E., Papazachariou, A., Iosifidis, N., Kalpakidou, M., 2010.Composition and production rate of medical waste from a small producer inGreece. Waste Manage. 30, 1683–1689.

Gupta, A., Sharma, D.C., 2011. Integer programming model for integrated planningof solid waste management in Jaipur. Int. J. Sci. Eng. Res. 2 (3), 1–10. ISSN 2229-5518.

Hemmelmayr, V.C., Doerner, K.F., Hartl, R.F., Vigo, D., 2013a. Models and algorithmsfor the integrated planning of bin allocation and vehicle routing in solid wastemanagement. Transport. Sci. 48 (1), 103–120.

Hemmelmayr, V., Doerner, K.F., Hartl, R.F., Rath, S., 2013b. A heuristic solutionmethod for node routing based solid waste collection problems. J. Heuristics 19(2), 129–156.

Kizlary, E., Iosifidis, N., Voudrias, E.A., Panagiotakopoulos, D., 2005. Composition andproduction rate of dental solid waste in Xanthi, Greece. Waste Manage. 25 (6),582–591.

Komilis, D., Katsafaros, N., Vassilopoulos, P., 2011. Hazardous medical wastegeneration in Greece: case studies from medical facilities in Attica and from asmall insular hospital. Waste Manage. Res. 29 (8), 807–814.

Kuo, Y., Wang, C.-C., 2011. Optimizing the VRP by minimizing fuel consumption.Manage. Environ. Qual.: Int. J. 22 (4), 440–450.

Laureri, F., Minciardi, R., Robba, M., 2016. An algorithm for the optimal collection ofwet waste. Waste Manage. 48, 56–63.

Mandalidis, A., 2011. Composition and production rate of hazardous medical wastefrom the healthcare centers of Stavroupolis, Avdira and Ehinos in the Prefectureof Xanthi, Greece Undergraduate Thesis. Department of EnvironmentalEngineering, Democritus University of Thrace, Xanthi, Greece.

Pruss, A., Giroult, E., Rushbrook, P., 1999. Safe Management of Wastes fromHealthcare Activities. WHO. available from www.who.int.

Sanjeevi, V., Shahabudeen, P., 2016. Optimal routing for efficient municipal solidwaste transportation by using ArcGIS application in Chennai, India. WasteManage. Res. 34 (1), 11–21.

Shanmugasundaram, J., Soulalay, V., Chettiyappan, V., 2012. Geographicinformation system-based healthcare waste management planning fortreatment site location and optimal transportation routing. Waste Manage.Res. 30 (6), 587–595.

Shi, L., Fan, H., Gao, P., Zhang, H., 2009. Network Model and Optimization of MedicalWaste Reverse Logistics by Improved Genetic Algorithm. Chapter in Advances inComputation and Intelligence, Volume 5821 of the series Lecture Notes inComputer Science, Springer, pp. 40–52.

Shih, L., Lin, Y., 2003. Multicriteria optimization for infectious medical wastecollection system planning. Pract. Period. Hazard. Toxic Radioact. WasteManage., 78–85 http://dx.doi.org/10.1061/(ASCE)1090-025X(2003)7:2(78).

Son, L.H., Louati, A., 2016. Modeling municipal solid waste collection: a generalizedvehicle routing model with multiple transfer stations, gather sites andinhomogeneous vehicles in time windows. Waste Manage. 52, 34–49.

Voudrias, E., Graikos, A., 2014. Infectious medical waste management at theregional level. J. Hazard. Toxic Radioact. Waste, ASCE. ISSN 2153-5493/04014020(9).

Zsigraiova, Z., Semiao, V., Beijoco, F., 2013. Operation costs and pollutant emissionsreduction by definition of new collection scheduling and optimization of MSWcollection routes using GIS. The case study of Barreiro, Portugal. Waste Manage.33, 793–806.