Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty

Accepted Manuscript Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty Vladimir Simić, Svetlana Dabić-Ostojić, Nebojša Bojović PII: DOI: Reference:

S0360-8352(17)30422-9 http://dx.doi.org/10.1016/j.cie.2017.09.013 CAIE 4899

To appear in:

Computers & Industrial Engineering

Received Date: Revised Date: Accepted Date:

23 February 2017 6 September 2017 11 September 2017

Please cite this article as: Simić, V., Dabić-Ostojić, S., Bojović, N., Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty, Computers & Industrial Engineering (2017), doi: http://dx.doi.org/10.1016/j.cie.2017.09.013

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty

Vladimir Simić University of Belgrade, Faculty of Transport and Traffic Engineering Vojvode Stepe 305, 11000 Belgrade, Serbia Phone: +381113091322 Fax: +381113096704 E-mail address: [email protected]

Svetlana Dabić-Ostojić University of Belgrade, Faculty of Transport and Traffic Engineering Vojvode Stepe 305, 11000 Belgrade, Serbia

Nebojša Bojović University of Belgrade, Faculty of Transport and Traffic Engineering Vojvode Stepe 305, 11000 Belgrade, Serbia

1

Abstract: In the European Union, approximately 3.6 million tonnes of used tires are generated annually. Because used tires are not biodegradable, there is strong motivation to successfully manage this fast-growing waste flow. One of the most popular approaches for sustainable environmental stewardship of used tires is retreading. The problem investigated in this paper is to identify optimized purchasing, retreading, and inventory planning schemes of used tires in multiple tire retreading plants as well as allocation patterns of retreaded, reusable, and end-of-life tires that secure maximized profit within a multi-period planning horizon and under multiple uncertainties. This paper proposes an interval-parameter semi-infinite programming model for used tire management and planning. The underlying difference between this model and those developed in previous research is its ability to consider the effects of external impact factors related to complicated economic, environmental, and social activities on used tire management systems. Moreover, it can successfully handle real-life uncertainties of the used tire management systems expressed as functional and crisp intervals. A numerical example is provided to demonstrate the usefulness of the developed model. Flexible long-term purchasing, retreading, inventory, and allocation plans, which are adjustable with variations of external impact factors, are obtained. The presented model has advantages in addressing the dynamic complexity of used tire management systems by introducing the functional interval parameters associated with the price of a new tire as well as electricity and gas prices and labor costs in waste management and transportation sectors. Compared with the available models, the resulting solutions are far more robust because they are able to satisfy all possible levels of external impact factors. The presented model is beneficial for the tire retreading industry, which processes millions of used tires annually. Keywords: Used tires; Functional interval; Semi-infinite programming; Interval-parameter programming; Uncertainty.

2

1. Introduction Management of used tires is globally a crucial environmental problem (Hashemi et al., 2014; Oikonomou and Mavridou, 2009; Li et al., 2016; Labaki and Jeguirim, 2017). Approximately 19.3 million tonnes of used tires are generated annually worldwide (Labaki and Jeguirim, 2017); this figure will rise in the near future along with the expected growth in the world’s motor vehicle fleet. In the European Union, the quantity of used tires exceeded 3.6 million tonnes in 2013 (ETRMA, 2016), which corresponds to 5.92×108 tires (Hita et al., 2016). Because used tires are not biodegradable, there is a strong motivation to successfully manage this fast-growing waste flow, thereby mitigating its negative environmental impact. Unlike waste electrical and electronic equipment (Iakovou et al., 2009; ElSayed et al., 2012; Kuo, 2013), end-of-life (EoL) photovoltaic modules (Fthenakis, 2009), EoL vehicles (Phuc et al., 2017), construction and demolition waste (Dodoo et al., 2009), and other multi-component EoL products, used tires cannot be broken down into separate pieces. Their processing significantly differs from treatments of the aforementioned EoL products. In fact, one of the most popular approaches to sustainable environmental stewardship of used tires is retreading. Retreaded tires are used tires that have undergone a process designed to extend their service life (Boustani et al., 2010). At an acceptable processing cost, tire retreading successfully takes full advantage of the value that remains in the used tires. In this process, used tires are subjected to a sequence of value additive operations and are converted to reusable ones (Mondaln and Mukherjee, 2012). Several benefits associated with the tire retreading process include savings in cost (Subulan et al., 2015; Amin et al., 2017; Machin et al., 2017) and energy (Ferrao et al., 2008; Boustani et al., 2010; Pedram et al., 2017), reduction in environmental pollution (Debo and Van Wassenhove, 2005; Antmann et al., 2013), and non-renewable raw material utilization (Mondaln and Mukherjee, 2012; Uruburu et al., 2013; Bunget et al., 2015; Pedram et al., 2017). Increases in environmental awareness have led to the search for economically attractive and environmentally responsive approaches to managing used tires. Although the relevant literature for our contribution originates from different streams of research, only that regarding used tire management systems is significant for our domain-oriented perspective. Owing to the increased importance of this subject, a considerable number of research papers have been published in the past decade. A detailed analysis of these papers is needed to identify the key directions for further development of this very important and dynamic research area. Lebreton and Tuma (2006) developed a linear programming model to assess the profitability of car and truck tire retreading process in Germany. Pehlken and Müller (2009) analyzed the separation process of recycling EoL tires and concluded that modeling such a process is a challenging task, because there are many uncertainties to identify. They highlighted that more research of this matter is needed. Dehghanian and Mansour (2009) proposed a three-objective linear programming model, which is able to simultaneously maximize economic and social benefits as well as minimize environmental impacts, in order to design a network of recycling plants for used tires in Iran. Kannan et al. (2009) formulated a linear programming model for minimizing the costs of a multi-echelon closed-loop supply chain for a tire manufacturer. Sasikumar et al. (2010) developed a mixed-integer nonlinear programming model for maximizing the profit of a multi-echelon reverse logistics network for truck tire retreading. However, many modeling parameters (e.g. cost parameters) had been identified as deterministic, which limits real-world applicability of this model. Abdul-Kader and Haque (2011) had identified a tire, collection center, recycling plant and retreading plant as “agents” involved in the management of used tires and applied an agent-based simulation approach to tackle the used passenger car tire retreading problem. Mondaln and Mukherjee (2012) used a simulation approach to plan manpower deployment for labor intensive operations of the tire retreading process. Creazza et al. (2012) formulated a mixed integer linear programming model to optimize logistics network of 3

the tire manufacturer Pirelli. Kop et al. (2012) used the fuzzy Analytic hierarchy process to identify the most efficient EoL tire management option in a Turkish context. Vinodh and Jayakrishna (2013) applied the fuzzy Analytic hierarchy process for weighting criteria and VIKOR for selecting the best tire retreading process for an Indian manufacturing organization. De Souza and D’Agosto (2013) proposed a conceptual model of the reverse logistics chain of EoL tires and explored financial benefits of their sending to the cement industry. Pirachicán-Mayorga et al. (2014) analyzed reverse logistics practices in Colombia and proposed a conceptual model of the used tire reverse logistics chain. Dhouib (2014) used the fuzzy MACBETH to assess alternatives in reverse logistics for used tires. Kannan et al. (2014) presented a framework to analyze the motivating factors of EoL tire management in an Indian context and validated it with the assistance of the Interpretive structural modeling. Pehlken et al. (2014) provided a concept for developing a model of EoL tire recycling plant based on Petri nets and neural networks. Dabic-Ostojic et al. (2014) presented a tool based on Bayesian networks for making decisions whether to retread used tires or not. Subulan et al. (2015) proposed a mixed integer linear programming model for tire closed-loop supply chain and suggested that uncertainty analysis related to various modeling parameters definitely deserves future research efforts. Bazan et al. (2015) presented a reverse logistics mixedinteger linear programming model for minimizing the costs of the tire retreading industry in Canada, which captured the costs for greenhouse-gas emissions and energy usage. Vorasayan (2016) used the two-player game theory approach to determine prices of a certified retreaded tire with warrantee and a noncertified retreaded tire under cooperative and non-cooperative schemes. Chang and Gronwald (2016) applied four different multi-criteria decision making methods to rank numerous used tires management alternatives and identified retreading as the best option. Amin et al. (2017) proposed a mixed-integer linear programming model for maximizing the profit of a tire remanufacturing closed-loop supply chain network in Toronto, Canada. They used a simplistic graphical tool to assess decisions under uncertain demand and returns. Pedram et al. (2017) presented a mixed integer linear programming model for maximizing the profit of a multi-echelon closed-loop supply chain of the tire industry in Tehran, Iran. They used a simple scenario-based approach to represent uncertainties in demand, return rate and quality of used tires. Afrinaldi et al. (2017) proposed a two-objective nonlinear programming model for creating an optimal preventive replacement schedule of a bus tire through minimization of its economic and environmental impacts. A review of the literature reveals that numerous system analysis methods have been proposed for solving various problems of used tire management. However, a lack of research exists for uncertainties in used tire management systems. In addition, the literature clearly suggests that no attempt has been made to address used tire management problems through interval-parameter programming, which represents an extension of the classical linear programming problem to an inexact environment (Sengupta et al., 2001; Zhang and Xu, 2014). Interval-parameter programming is an alternative for handling uncertainties in the left- and right-hand sides of constraints and in the objective function, which cannot be expressed as distribution functions owing to the inadequate quality of available information. This approach does not require distribution information because the crisp interval, or the lower- and upper-bounded range of the real number, is acceptable for the uncertain input. On the contrary, the available models for management of used tires cannot address uncertainty related to functional-interval parameters. As an extension of conventional crisp intervals, the concept of functional intervals is proposed for addressing more complicated uncertainty (He et al., 2008) because they include characteristics of intervals and functions. In fact, most of the real-life applications involve highly complex uncertainty. The need for introducing functional intervals in the used tire management problem primarily arises from the effects of external impact factors related to complicated economic, environmental, and social activities on the used tire management systems. In reality, the effects of the external impact factors on the components of the used tire management systems are too significant to be ignored. Thus, another significant limitation of the aforementioned system analysis methods is their inability to reflect the dynamic features of modeling parameters. Therefore, introduction of crisp and functional intervals 4

into the modeling framework can provide a much more realistic representation of used tire management systems. Interval-parameter semi-infinite programming can address uncertainties expressed as crisp intervals and functional intervals with infinite objectives or infinite constraints. As a significant extension of previous efforts in the reviewed research area, an interval-parameter semi-infinite programming model for used tire management and planning is proposed in this paper by allowing the modeling parameters to be functional intervals of multiple independent variables (i.e., impact factors) or crisp intervals. The remaining part of the paper is organized as follows: Section 2 describes the considered problem and presents the interval-parameter semi-infinite programming model for used tire management and planning under uncertainty. Solution approach is provided in Section 3. Section 4 presents results and discussion. Section 5 presents the paper’s main conclusions and summarizes its innovative points. 2. Materials and methods 2.1. Statement of the problem Consider the regional tire retreading management system shown in Fig. 1. Tire retreading plants are responsible for remanufacturing retreadable used tires and for transporting them to dealers of retreaded tires. In addition, they send reusable tires to dealers of used and EoL tires to available destinations for this waste flow (i.e., EoL tires market, waste entities, and application sites). (insert Fig. 1)

Professional, private, and public entities that own used tires, hereafter collectively referred to as used tire owners, are required to deliver them to the nearest collection center. Used tires owners are physically and financially responsible for the transportation of used tires to these collection centers, which include tire dealers, vulcanizing shops, vehicle repair shops, EoL vehicle dismantling companies, drop-off depots, and scrap yards. These centers accept and temporarily accumulate used tires discarded by their last owners and are in fact storage facility providers. Moreover, they can sell used tires to H tire retreading plants located in their region for remanufacturing. Transport to the tire retreading plants is the responsibility of the respective retreading plants. Retreadability (i.e., quality) of used tires available at the collection centers is uncertain and may be determined only in the retreading plants. The transport of retreaded, reusable, and EoL tires between the tire retreading plants and the market dealers, tire recycling plants, waste-to-energy plants, and application sites is controlled and financed by the tire retreading plants (Figs. 12). When shipments of used tires arrive at the tire retreading plants, used tires are unloaded from large trailer trucks and are stored. Every used tire planned for retreading is initially inspected to determine whether it is retreadable, reusable as is, or EoL, in which significant damage or low tread depth is present. The subsequent steps depend mainly on the type of used tire retreading process (Fig. 2). For the retreading type presented in Fig. 2a, after being initially inspected, all retreadable tires are visually analyzed using proper equipment and lighting to identify any damage missed during the initial inspection. Only tires that passed this operation are forwarded to the shearography inspection, which is an advanced non-destructive inspection procedure. This process can determine even the smallest anomalies in the tire structure, including holes, stitches, and porosity in the inner liner, under forced conditions of exploitation. The next retreading operation, buffing, mechanically removes the worn tread, textures the surface, and corrects discrepancies in the circumference of the tire. Then, the buffed retreadable tires are sent to the filling repair operation for cleaning, correcting any remaining imperfections, and eventually restoring the original strength of the casing. Only fully repaired retreadable tires are forwarded to the final preparation station, where a thin layer of 5

adhesive mass is applied around the tire casing. Afterward, a retreadable tire prepared for building is mounted on a building machine that rotates the tire at a particular speed and applies the precured tread rubber around the circumference of its casing consistently and accurately. The next retreading operation is enveloping, in which the retreadable tire with the new tread is first placed inside an outer envelope, and an inner envelope is then fitted inside. Then, the enveloped tires are vacuumed and cured at moderate temperature and pressure to adhere the new treads. In the final inspection, only the labeled retreaded tires meeting rigorous industry quality standards and customer demands are allowed to be forwarded on. (insert Fig. 2)

For the retreading type presented in Fig. 2b, each used tire that passed the initial inspection station is sent to highly qualified operators for sophisticated shearography inspection. Afterward, the retreadable tire is ready for buffing. Residues of old tread are completely eliminated, which leaves the surface clean and ready for the new tread placement. The next destination for the buffed retreadable tire is the filling repair station. Then, the repaired retreadable tire is placed onto a building machine, where the ring of the casing is automatically centered and rolled to maximize adhesion of the new tread. The next operation is monorailing, which uses a double envelope system and prevents any contact with impurities and debris. Then, the curing operation is performed to guarantee a perfect seal between the new tread and the casing. A label must be placed on each retreaded tire before its final inspection. For the retreading type presented in Fig. 2c, the retreadable tire initially inspected by shearography is sent to the buffing station, where high-speed revolving knives and brushes remove the remaining tread and sidewall rubber from the casing. Larger holes in the casing are filled with compound and are then brushed and sprayed with a latex adhesive. The next retreading operation is a computer controlled building process that ensures the proper amount of applied rubber. Then, every retreadable tire with the new tread is placed into a hot, radial matrix within a curing press. The combination of heat, time, and pressure ensures that the new tread is correctly cured, thus resulting in a retreaded tire with a pre-specified pattern and depth. The final inspection procedure involves three steps. The aim of the visual and tactile inspection is to identify any possible imperfections within the tread pattern or sidewall. In the second inspection step, every retreaded tire is rapidly inflated to explore any potential structural defects or weaknesses. The third step uses single-camera shearography to detect even the smallest amount of porosity. Only retreaded tires that successfully pass the complete inspection procedure are labeled. Retreaded tires can be sold at a regional retreaded tire market comprised of m2 dealers of retreaded tires (Fig. 1). On the contrary, reusable tires preserve the basic structure and tread and can be reused with appropriate control. Such tires are resold to m1 dealers of used tires located in the considered region. Finally, EoL tires are used tires that are not of suitable quality for retreading (i.e., marked as unretreadable in one of the retreading operations). Such tires remain in their original shapes for different purposes. Essentially, EoL tires can be resold at a regional EoL tire market (comprised of m3 dealers of EoL tires), 1 tire recycling plants, or 2 waste-to-energy plants located in the considered region. Also, they can be resold to numerous application sites for material recovery (with υg sites employing g-th application option) (Fig. 1). Application options of EoL tires are numerous and usually include: foundation for roads and railways (Siddique and Naik, 2004; Chiu, 2008; Lin et al., 2008; Oikonomou and Mavridou, 2009; Medina Flores et al., 2016; Sengul, 2016; Machin et al., 2017), embankment stabilizers (Debo and Van Wassenhove, 2005; Rowhani and Rainey, 2016), draining material (Shalaby and Khan, 2005; Torreta et al., 2015), erosion barriers (Sunthonpagasit and Duffey, 2003; Edinçliler et al., 2010; Zanetti et al., 2015), artificial reefs (Lin et al., 2008), flooring sports fields and playgrounds (Debo and Van Wassenhove, 2005; Torreta et al., 2015; ETRMA, 2016; Karaağaç et al., 2017; Machin et al., 2017), paving blocks (Zhou et al., 2014; Zanetti et al., 2015; Medina Flores et al., 2016; Karaağaç et al., 2017), roofing materials (Bravo and Brito, 2012; Torreta et al., 2015; Karaağaç et al., 2017), dock fenders (Dhouib, 6

2014; Feriha et al., 2014; Rowhani and Rainey, 2016), wheels for caddies (ETRMA, 2014), gardening (Fıglali et al., 2015), footwear industry (Machin et al., 2017), packing material (Karaağaç et al., 2017) and mats (Machin et al., 2017). Used tire retreading management systems (Fig. 1) are complex waste management systems with many uncertain components. The efficiencies and operational capacities of tire retreading operations vary temporally and cannot be considered as deterministic values. Observing these technical parameters as crisp interval values is purely natural at the scale of a week, month, or year. On the contrary, compound uncertainties exist in economic data. Unit revenues to the tire retreading management system from the sale of retreaded, reusable and EoL tires to selected destinations as well as costs of purchasing used tires from collection centers (Figs. 1 2) are affected by numerous external impact factors that influence modeling parameter values; e.g., the value of a functional interval a  (p)=[a  (p), a  (p)] fluctuates with an impact factor p. However, the price of a new tire has the most significant influence on the unit revenues; i.e., the market price of a retreaded tire is approximately half the market price of a new tire. Moreover, the price of a new tire varies with fluctuations in the interest rate. Considering this external impact factor, the lower and upper bounds of the unit revenues and purchasing cost cannot be represented as constant values. Therefore, these modeling parameters should be presented as functional intervals associated with the price of a new tire. Processing (i.e., retreading) costs of used tires in tire retreading plants should also be presented as functional intervals to provide a much more realistic representation of the used tire management system. Fluctuations in time of processing costs are caused by variations in electricity price and labor cost in the waste management sector (i.e., equipment operator wages). For this reason, adjusting the processing costs with a single independent variable could lead to difficulties in expressing the relationship between these costs and their impact factors through functional intervals. Thus, the processing costs CS  should be presented as functional intervals associated with multiple independent variables; i.e., CS  (μ, σ)=[a0+a1∙μ+a2∙σ, a3+a4∙μ+a5∙σ], where μ[   ,

  ] represents electricity price, which is an independent variable in the range of   and   , and σ[   ,   ] denotes labor costs in the waste management sector, which is an independent variable in the range of   and   . Fluctuation in both factors is affected and conditioned by variation in the interest rate. Even though adding the interest rate as another independent variable in the functional intervals of the processing costs is redundant, its value over a planning horizon should be considered during the process of calculating their coefficients. The costs of transportation of retreaded, reusable, and EoL tires from the tire retreading plants to the secondary tire markets, waste entities, and application sites (Figs. 12) are influenced by various external impact factors. However, gas prices and labor costs in the transportation sector (i.e., truck driver wages) are most important for this economic parameter. Thus, the transportation costs should be presented as functional intervals associated with these two essential external impact factors. The number of objective functions is infinite because each should be satisfied under all possible levels of gas and electricity prices and labor costs in transportation and waste management sectors as well as new tires prices. The interval-parameter semi-infinite programming technique can effectively address the uncertainties expressed as crisp intervals and functional intervals with infinite objectives. Used tire management systems are closely related to the economy, environment, and policy sub-systems (Fig. 3). In fact, any change in these sub-systems could affect used tire management systems. By introducing the functional interval parameters into the modeling framework, the effects of external impact factors related to complicated economic, environmental, and social activities are reflected. However, the conventional approaches can handle problems only in which the coefficients of the objective function or constraints are not affected by external impact factors. If the effects of the external impact factors are significant, the solutions from the conventional approaches become inferior or simply erroneous. The interval-parameter semi-infinite programming approach 7

represents an appropriate solution methodology because it is necessitated by the studied problem itself. As a result, the described problem can be presented as an interval-parameter semi-infinite programming model for used tire management and planning under uncertainty. (insert Fig. 3)

Fig. 4 shows the framework of the proposed model to additionally clarify and justify the methodology selection process. (insert Fig. 4)

2.2. Interval-parameter programming approach A general interval-parameter programming model can be defined as follows (Tong, 1994):

Max f  =C X subject to: A  X  B 

(1b)

X  0

(1c)

(1a)

where  represents the crisp interval number with known upper bound “+” and lower bound “−”, 1n

but unknown distribution information; f  is objective function; C  R    m1

mn

, A  R  

,

 n1

, X   R  ( R  denotes a set of interval numbers). Model (1) can be B  R  decomposed into two sub-models corresponding to the upper and lower bounds of the objective function, f  and f  respectively, and solved by using the best worst case method (Chinneck and Ramadan, 2000; Tong, 1994). 2.3. Interval-parameter semi-infinite programming approach A functional interval represents a type of highly complex uncertainty in real-world systems (Zhu et al., 2011) because it has characteristics of intervals and functions (He and Huang, 2008). It can be identified through regression analysis using historical data. Different from the crisp interval, the functional interval can reflect both internal and external uncertainties of the system by interval parameters themselves or by functional relations to external impact factors, respectively (He et al., 2009b), thus effectively describing uncertainties with more complexity (Zhu et al., 2011). When D  and D  are functions of multiple independent variables, the functional interval D   p  can be defined as (He et al., 2011): D   p    D   p  , D   p   D  p  D   p   D  p   D   p  , p   p  , p   (2)  





where D   p  and D   p  are lower-bound and upper-bound functions respectively, and





p  p1,...,pq is an independent vector consisting of multiple variables. The interval-parameter semi-infinite programming approach can deal with optimization problems where coefficients in either objectives or modeling constraints are linearly related to their independent variables (He et al., 2011). It can tackle uncertainties expressed as crisp and functional intervals with infinite objectives or infinite constraints. A general interval semi-infinite programming model with multiple independent variables can be defined as follows (He et al., 2009a; He et al., 2011): 8

Max f  =C  p  X  ,

p   p  , p   (3a)  

subject to: A  X   B ,

(3b)

X  0

(3c) mn

1n

n1

m1

where C  p   R   , A   R   , B  R   , X  R   ( R  denotes a set of interval numbers or functional intervals. Since, the interval-parameter semi-infinite programming approach represents novel methodology, only a small number of research papers have been carried out. More detailed, it has been used for municipal solid waste management (He and Huang, 2008; He et al., 2009a; He et al., 2011), and agricultural irrigation management (Li et al., 2014). Therefore, there are no existing interval-parameter semi-infinite programming models specially tailored for solving the used tires management and planning problem. In fact, this research presents the first attempt to develop an interval-parameter semi-infinite programming model for supporting the management of some endof-life product thus clearly extending the field of application of this novel methodological approach. 2.4. Modeling formulation Based on interval-parameter programming and semi-infinite programming approaches, an interval-parameter semi-infinite programming model for used tire management and planning under uncertainty can be formulated as follows: T     Μax f        Rhjvt   X hijt  Ft     X hijt t 1  jO hH vVhj ihjv jM 2 iΓ j 1 hH   CPht    Phit   hH

iSh

  CShjt  ,   X hijt 1

hH jh

iΓ j

(4a)

   X hijt  t   Z hit  Whit  vVhj ihjv hH iSh 

    CThjt  ,   jO hH

    ,   ;      ,   ;      ,   ;     ,   ;     ,            

subject to:

Whit  Whit 1  Phit   X hijt , h  H; i  Sh ; t  1,...,T 

(4b)

Whi 0  Пhi 0 , h  H; i  Sh

(4c)

ji

  Whit  Wh min , h  H; t  1,...,T 

iSh

  X hijt  t Chj , h  H; j h ; t  1,...,T  1

(4d) (4e)

i j

 Ehik  X hjit =  X hijt , h  H; i h ; k  K hi ; t  1,...,T  ji1

jIhik

(4f)

9

 X hijt =  X hji' t , h  H; j h ; t  1,...,T 

ij 1

(4g)

i' j

Phit  0, h  H; i  Sh ; t  1,...,T 

(4h)

Whit  0, h  H; i  Sh ; t  0,1,...,T 

(4i)

X hijt  0, h  H; i h ; j i ; t  1,...,T 

(4j)

Detailed nomenclature for the indices and sets, parameters, and variables are provided in the Appendix. In Model (4), the objective (4a) is to maximize the total profit of the system for used tire management over the planning horizon. In the objective function (4a), the first term represents income from the sale of retreaded tires and resale of reusable used and EoL tires. The second term presents the amount of tire retreading fees repaid from the waste tire management fund and is computed on the basis of the quantity of retreaded used tires and the tire retreading fee. The third term defines the purchasing costs of the used tires. The fourth term represents the transportation cost of retreaded, reusable used, and EoL tires from the tire retreading plants to selected destinations (i.e., dealers of retreaded tires, dealers of reusable used tires, dealers of EoL tires, tire recycling plants, waste-to-energy plants, and application sites for various EoL tire material recovery options). The last term of the objective function defines the storage cost of used tires that have not been assigned for processing in the tire retreading plants. Constraints (4b) and (4c) enforce the inventory balances of the tire retreading plants and initialize the inventories of used tires in the tire retreading plants, respectively. Constraints (4d) ensure a safe stock level of used tires in the tire retreading plants. Constraints (4e) represent the operational capacities of retreading entities. Constraints (4f)–(4g) maintain material flow balances of retreading entities installed in the tire retreading plants. Finally, constraints (4h)–(4j) define the value domains (i.e., non-negativity) of decision variables used in the formulated interval-parameter semi-infinite programming model for used tire management and planning under uncertainty. 3. Solution approach To solve Model (4), the best worst case method (Chinneck and Ramadan, 2000; Tong, 1994) can be adopted to convert it into two sub-models corresponding to the lower and upper bounds of the objective function, f  and f  , respectively. The first sub-model, corresponding to f  , is formulated as follows: T     Μax f        Rhjvt   X hijt  Ft     X hijt t 1  jO hH vVhj ihjv jM 2 iΓ j 1 hH   CPht    Phit   hH

iSh

  CShjt   ,   X hijt 1

hH jh

iΓ j

(5a)

   X hijt  t   Z hit  Whit  vVhj ihjv hH iSh 

    CThjt  ,   jO hH

    ,   ;      ,   ;      ,   ;     ,   ;     ,            

subject to:

Whit  Whit 1  Phit   X hijt , h  H; i  Sh ; t  1,...,T  ji

(5b) 10

Whi 0  Пhi 0 , h  H; i  Sh

(5c)

  Whit  Wh min , h  H; t  1,...,T 

(5d)

iSh

  X hijt  t Chj , h  H; j h ; t  1,...,T  1

(5e)

i j

 X hjit

 Ehik 

ji1

 X hijt

  Ehik , h  H; i  h ; k  K hi ; t  1,...,T 

(5f)

jI hik

 X hijt =  X hji' t , h  H; j h ; t  1,...,T 

ij 1

(5g)

i' j

Phit  0, h  H; i  Sh ; t  1,...,T 

(5h)

Whit  0, h  H; i  Sh ; t  0,1,...,T 

(5i)

X hijt  0, h  H; i h ; j i ; t  1,...,T 

(5j)

Μax

Then, the second sub-model, corresponding to f  , can be formulated as follows: T     f        Rhjvt   X hijt  Ft     X hijt t 1  jO hH vVhj ihjv jM 2 iΓ j 1 hH   CPht    Phit   hH

iSh

  CShjt  ,   X hijt 1

hH jh

iΓ j

(6a)

   X hijt  t   Z hit  Whit  vVhj ihjv hH iSh 

    CThjt  ,   jO hH

    ,   ;      ,   ;      ,   ;     ,   ;     ,            

subject to:

Whit  Whit 1  Phit   X hijt , h  H; i  Sh ; t  1,...,T 

(6b)

Whi 0  Пhi 0 , h  H; i  Sh

(6c)

ji

  Whit  Wh min , h  H; t  1,...,T 

iSh

  X hijt  t Chj , h  H; j h ; t  1,...,T  1

(6d) (6e)

i j

 X hjit

 Ehik 

ji1

 X hijt

  Ehik , h  H; i  h ; k  K hi ; t  1,...,T 

(6f)

jI hik

11

 X hijt =  X hji' t , h  H; j h ; t  1,...,T 

ij 1

i' j

(6g)

Phit  0, h  H; i  Sh ; t  1,...,T 

(6h)

Whit  0, h  H; i  Sh ; t  0,1,...,T 

(6i)

X hijt  0, h  H; i h ; j i ; t  1,...,T 

(6j)

The number of objective functions in sub-models (5)(6) is infinite because each of them should be satisfied under all possible levels of gas prices δ (ranging from   to   ), electricity prices μ (ranging from   to   ), labor costs in the transportation sector ρ (ranging from   to

  ), labor costs in the waste management sector σ (ranging from   to   ), and prices of new truck tires  (ranging from   to   ). In order to generate optimal solutions of sub-models (5)(6), the infinite objectives should be converted to a single one (He et al., 2009b). If an equivalent weight is assigned to each of the objectives corresponding to f  , sub-model (5) can be transformed as follows:   T       Μax f        Rhjvt    X hijt  Ft    X hijt 2   t 1  jO hH vVhj ihjv jM 2 iΓ j 1 hH                    CPht  P  CS ,   hit     X hijt hjt  2 2 2   iSh   iΓ 1 hH hH jh j             CThjt  ,  X hijt   2 2  vVhj ihjv jO hH

(7a)

        t   Z hit   Whit  2   hH iSh 

subject to:

Whit  Whit 1  Phit   X hijt , h  H; i  Sh ; t  1,...,T 

(7b)

Whi 0  Пhi 0 , h  H; i  Sh

(7c)

ji

  Whit  Wh min , h  H; t  1,...,T 

iSh

  X hijt  t Chj , h  H; j h ; t  1,...,T  1

(7d) (7e)

i j

 X hjit

 Ehik 

ji1

 X hijt

  Ehik , h  H; i  h ; k  K hi ; t  1,...,T 

(7f)

jI hik

12

 X hijt =  X hji' t , h  H; j h ; t  1,...,T 

ij 1

i' j

(7g)

Phit  0, h  H; i  Sh ; t  1,...,T 

(7h)

Whit  0, h  H; i  Sh ; t  0,1,...,T 

(7i)

X hijt  0, h  H; i h ; j i ; t  1,...,T 

(7j)

Μax

Similarly, sub-model (6) can be transformed as follows:   T       f        Rhjvt    X hijt  Ft    X hijt 2   ihjv t 1  jO hH vVhj jM 2 iΓ j 1 hH        CPht  2  hH

             ,   Phit    CShjt    X hijt 2 2  iSh   iΓ 1 hH jh j

            CThjt ,  X hijt    2 2  vVhj ihjv jO hH

(8a)

        t   Z hit   Whit  2   hH iSh 

subject to:

Whit  Whit 1  Phit   X hijt , h  H; i  Sh ; t  1,...,T 

(8b)

Whi 0  Пhi 0 , h  H; i  Sh

(8c)

ji

  Whit  Wh min , h  H; t  1,...,T 

iSh

  X hijt  t Chj , h  H; j h ; t  1,...,T  1

(8d) (8e)

i j

 X hjit

 Ehik 

ji1

 X hijt

  Ehik , h  H; i  h ; k  K hi ; t  1,...,T 

(8f)

jI hik

 X hijt =  X hji' t , h  H; j h ; t  1,...,T 

ij 1

i' j

(8g)

Phit  0, h  H; i  Sh ; t  1,...,T 

(8h)

Whit  0, h  H; i  Sh ; t  0,1,...,T 

(8i)

X hijt  0, h  H; i h ; j i ; t  1,...,T 

(8j)

13

Through combining the solutions of sub-models (7) and (8), the solutions of Model (4) can be represented as:     (9a) fopt   fopt , fopt ,        h  H; i  Sh ; t 1,...,T  (9b) Phit opt   Phit opt , Phit opt  ,      h  H; i  Sh ; t 1,...,T  (9c) Whit opt  Whit opt , Whit opt  ,      h  H; i h ; j  i ; t 1,...,T  (9d) X hijt opt   X hijt opt , X hijt opt  , To make the procedure for solving the interval-parameter semi-infinite programming model for used tire management and planning under uncertainty more straightforward, a detailed algorithmic procedure is presented in a pseudo-code format: Step 1: Formulate Model (4); Step 2: Use the best worst case method to split Model (4) into two sub-models (5) and (6), where the sub-model corresponding to f  is first desired when the objective is to maximize f  ; Step 3: Convert sub-models (5) and (6) into sub-models (7) and (8), respectively;

Step 4: Solve the optimistic sub-model (7) corresponding to f  and obtain a set of solutions; Step 5: Solve the conservative sub-model (8) corresponding to f  and obtain a set of solutions; Step 6: Form the final solutions of Model (4) by combining those of sub-models (7) and (8); Step 7: Stop. 4. Results and discussion Consider a numerical example in which a regional used tire retreading management system is composed of three tire retreading plants (Figs. 2 and 5). The tire retreading plants can sell retreaded tires on the retreaded tire market, which is composed of three dealers of retreaded tires located in the considered region. EoL tires can be sold on the EoL tire market composed of two dealers of EoL tires or to several waste entities (i.e., three waste-to-energy plants and two tire recycling plants) or even to various application sites for material recovery. Actually, in the considered regional used tire retreading management system, EoL tires can be applied as embankment stabilizers (two sites), dock fenders (one site), and erosion barriers (three sites). The tire retreading plants can allocate reusable used tires to two different dealers of reusable tires located in the analyzed region (Fig. 5). The entire planning horizon is nine years and is divided into three periods of three years. All data used in this numerical example can be found in the Supplementary Material. (insert Fig. 5)

The optimization programs are written and executed in LINGO mathematical modeling language. The number of variables, constraints, and non-zero elements are 1164, 1708, and 6303, respectively, and the computational time is within a few seconds. Fig. 6 presents the calculated profit of the considered regional tire retreading management

 system during the nine-year planning horizon. The solution for the objective function fopt = €[241.05, 516.70]106 provides two boundaries of the expected system profit for the entire nineyear planning horizon. The lower bound value is achieved under demanding conditions (e.g., more expensive purchasing of used tires; greater retreading costs; greater inventory holding costs; greater costs of transportation of retreaded, reusable, and EoL tires; smaller revenue from the sale of retreaded tires as well as the resale of reusable and EoL tires; smaller tire retreading fee; smaller

14

operators and equipment efficiency; smaller capacities of inspection and retreading operations; and retained higher levels of safety inventories), and vice versa. (insert Fig. 6)

To reflect real-life complex uncertainties that exist in the used tire management system, numerous modeling parameters are presented as functional or crisp intervals. The existence of these multiple uncertainties results in a relatively wide interval between the lower and upper bound of the  objective function. In fact, the uncertainty degree of fopt , determined as the ratio of its width to its

difference, is equal to 72.75%; this proves that the considered system is highly uncertain. Essentially, the more distant the period for which the planning is done, the more considerable the uncertainty will be in terms of the values of all modeling parameters. For this particular reason, the obtained interval width of the expected system profit for the third planning period is by far the largest. Accordingly, the uncertainty degree is the greatest in the last planning period. Specifically, the uncertainty degree is equal to 60.71% in the first period, 72.13% in the second period, and 83.92% in the third period. Therefore, the tire retreading manager should be much more cautious when creating and applying long-term plans for the last three-year period. The purchasing cost is the most significant cost parameter because it makes up [50.10, 58.03]% of the total expense of the considered tire retreading management system. For that reason, the optimized allocation scheme for this material flow is valuable for waste managers. Fig. 7 presents the optimal purchasing plan for three different tire retreading plants during the nine-year planning horizon. In the first planning period, the tire retreading plants purchased [40,908.0, 57,172.0] tonnes of used tires from collection centers in total. In the next two planning periods, the purchased quantities of used tires decreased to [39,468.0, 56,160.0] tonnes. (insert Fig. 7)

The capacity of the initial inspection, as the first retreading operation (Fig. 2), directly determines the operational capacity of tire retreading plants and indirectly regulates the quantity of material flows between collection centers and the tire retreading plants (Fig. 1). Under demanding conditions, corresponding to the lower bound of the objective function value, the largest quantity of used tires is purchased by tire retreading plant 2 because it has the largest operational capacity of 2.16 tonnes per hour (Supplementary Table S2 in Online Resource). During the nine-year planning horizon, this tire retreading plant purchased 51,024.0 tonnes of used tires; retreading plants 3 and 1 procured 48,590.0 tonnes and 20,230.0 tonnes, respectively (Fig. 7). Under advantageous conditions, corresponding to the upper bound of the objective function value, tire retreading plant 3 had a significantly larger operational capacity than tire retreading plants 1 and 2 (Supplementary Table S2 in Online Resource). Tire retreading plant 3 purchased the largest quantity of used tires during the planning horizon, followed by tire retreading plants 2 and 1 (Fig. 7). Storage costs comprise [1.10, 2.91]% of the total expenses of the considered tire retreading management system under advantageous and demanding conditions. To avoid unnecessary costs for storing excess quantities, piling of used tires above the safety inventory levels was not detected in any of the considered tire retreading plants or during any of the planning periods. Essentially, during the entire planning horizon, the quantities of used tires that have not been assigned for processing in tire retreading plants 1, 2, and 3 are equal to [170.0, 340.0] tonnes, [432.0, 480.0] tonnes, and [410.0, 620.0] tonnes, respectively. Hence, the levels of inventories piled in the storage areas of the tire retreading plants are always equal to the predetermined safety levels. Usually, safety inventory levels of tire retreading plants are planned in quantities that can secure a month of retreading if the supply of used tires is suddenly interrupted owing to bad weather conditions, disturbances on the secondary market for used tires, or other factors. 15

Table 1 shows the obtained optimized allocation patterns of retreaded, reusable used, and EoL tires from three tire retreading plants to multiple destination entities, including two dealers of reusable used tires, three dealers of retreaded tires, two dealers of EoL tires, two tire recycling plants, three waste-to-energy plants, and six application sites that offer three different options for material recovery of EoL tires, during the nine-year planning horizon. Although various modeling parameters are represented as functional intervals, the obtained solutions are expressed as conventional crisp intervals, thus preventing additional complication and increased complexity in the decision-making process. (insert Table 1)

Resale of reusable used tires on the corresponding secondary market makes up [16.21, 16.45]% of the considered tire retreading management system’s total revenue. The obtained results indicate that dealer 2 of reusable used tires is always favored by all three tire retreading plants in terms of supply (Table 1). The total quantity of tires, first marked as directly reusable by operators during their initial inspection and afterward sold to this dealer, is equal to [13,287.690, 19,010.160] tonnes. The main reason for such an allocation strategy for reusable tires is a significantly better purchase offer by dealer 2. For that reason, although dealer 1 of reusable used tires is located near tire retreading plant 1 (Fig. 5), he is not chosen as the destination entity because he offered only [217.862+10.752∙ , 290.292+11.165∙ ] €/tonne in the first period, [221.807+10.946∙ , 313.529+12.059∙ ] €/tonne in the second period, and [225.823+11.145∙ , 338.626+13.024∙ ] €/tonne in the third period (Supplementary Table S6 in Online Resource). The key revenue category of the investigated waste management system is that associated with the sale of retreaded tires in the corresponding secondary market. The retreading revenue is [80.96, 82.15]% of the total revenue under advantageous and demanding conditions. Therefore, the optimization of the allocation scheme between the tire retreading plants and the dealers of retreaded tires has very high priority when solving the used tire management problem. The results indicate that all retreaded tires are sold to dealer 3 of retreaded tires (Table 1). The creation of such an allocation strategy is dominantly influenced by the corresponding unit revenues (Supplementary Table S6 in Online Resource). In particular, the purchase offer of dealer 3 is [1.38, 1.48]% and [3.79, 4.26]% better than the offers of dealer 1 and dealer 2 of retreaded tires, respectively. All tires identified as EoL by operators of tire retreading plant 1 are resold to site 1 for application as embankment stabilizers. Under demanding conditions, tire retreading plant 2 first allocated 7,376.067 tonnes of EoL tires to site 2 for application as embankment stabilizers, whereas in the last six years, 14,752.133 tonnes of EoL tires have been applied as dock fenders. Under advantageous conditions, only the second material recovery option (i.e., application of EoL tires as dock fenders) is chosen by tire retreading plant 2 owing to its financial attractiveness. Tire retreading plant 3 allocated [27,236.450, 41,186.827] tonnes of EoL tires to the site, where they have been applied as dock fenders. The allocation plan for EoL tires depends on transportation costs and unit revenues because these two economical parameters correspond in value (Supplementary Tables S6 and S8S10 in Online Resource). This differs from the creation of allocation plans for reusable used tires and retreaded tires, in which the buying offers from dealers dominantly influence allocation decisions. To clarify the impacts of considering numerous external impact factors on the studied used tire management problem, the proposed interval-parameter semi-infinite programming model for used tire management and planning is solved through a conventional interval-parameter programming method by fixing all independent variables. Essentially, if the functional intervals of gas prices, electricity prices, cost of new tires, labor costs in the transportation and waste management sectors are substituted with crisp intervals, the used tire management problem can be modeled as an interval-parameter program. The obtained profit during the entire nine-year planning horizon of the considered regional tire retreading management system is €[178.29, 606.58]106. The width of the profit interval obtained through the interval-parameter programming model is 16

significantly larger. In fact, all of the resulting intervals from the interval-parameter model are much larger than those from the interval-parameter semi-infinite programming model for used tire management and planning under uncertainty. This clearly indicates that the solutions from the interval-parameter programming model are much more uncertain than those from the developed model. In addition, the interval-parameter model has another major limitation in that it ignores the effects of external impact factors related to complicated economic, environmental, and social activities on the used tire management systems. In particular, several assumptions must be made for modeling the problem highlighted in this paper as the interval-parameter program: (1) the effect of the prices of new tires on unit revenues, purchasing, and inventory holding costs are insignificant; (2) the effects of electricity price and labor costs in the waste management sector on the processing costs in the tire retreading plants are negligible; and (3) the effects of gas prices and labor costs in the transportation sector on transportation costs of retreaded, reusable, and EoL tires are irrelevant. As a result, compared with the interval-parameter model, the solutions of the formulated model are far more robust to fluctuations of the modeling parameters associated with external impact factors. Therefore, the interval-parameter model is an unrealistic representation of the considered used tire management system. 5. Conclusions In this paper, the interval-parameter semi-infinite programming model is developed for used tire management and planning, in which multiple uncertainties regarded as functional and crisp intervals are effectively reflected. Interval-parameter and semi-infinite programming are coupled within a general optimization framework to solve the used tire management and planning problem under the multiple uncertainties addressed in this paper. The proposed model has been applied to the numerical example. Its merit is manifold. First, the potential and applicability of the proposed model are illustrated. Second, in-depth insights into the effects of complex functional uncertainties on the economic efficiency of used tire management systems are obtained. Third, the influences of conventional interval uncertainties on the model solutions are examined. The innovation and advantages of the presented model are numerous. It is able to: (1) address the dynamic complexity of used tire management systems by introducing the functional interval parameters associated with the price of the new tire, electricity and gas prices, and labor costs in the waste management and transportation sectors; (2) provide an economically optimized waste management system, which helps the tire retreading managers to make additional profit and to significantly reduce the rapidly growing waste flow of used tires; (3) provide the tire retreading managers with flexible long-term purchasing, retreading, inventory, and allocation plans that are adjustable with variations of external impact factors; and (4) generate far more robust solutions compared with the available models for the management of used tires as well as the conventional interval-parameter programming method because they are able to satisfy all of the possible electricity and gas prices, labor costs in the waste management and transportation sectors, and the prices of new tires. The developed model can be utilized for optimal long-term: (1) production planning of multiple tire retreading plants; (2) purchase planning of used tires; (3) inventory management of used tires in the multiple tire retreading plants; (4) allocation planning of retreaded tires to multiple dealers of retreaded tires; (5) allocation planning of reusable tires to multiple dealers of used tires; and (6) allocation planning of EoL tires to multiple destinations for this waste flow (e.g., dealers of EoL tires, recycling plants, waste-to-energy plants, and application sites). Therefore, the interval-parameter semi-infinite programming model for used tire management and planning is beneficial for the tire retreading industry, which processes millions of used tires annually. It should be noted that even though numerous modeling parameters are represented as functional intervals, the obtained solutions do not increase the complexity and do not cause difficulties in the decision-making process. In fact, the solutions are expressed as crisp intervals, 17

thus making the created long-term plans easy to follow. The formulated interval-parameter semiinfinite programming model for used tire management and planning could be successfully applied for solving large-scale real-world problems because its straightforward algorithmic solution procedure does not lead to more complicated intermediate models. In fact, because the developed model can be finally divided into two linear programming problems with a finite number of objective functions, various mathematical solvers can be applied to find their optimal solutions. However, the presented model has room for further improvements. Although decisionmaking based on the lower bound values of the resulting crisp intervals creates a high probability that the created purchasing, retreading, inventory, and allocation plans will be actually fulfilled, it also drastically reduces the value of the system profit. In contrast, the management of used tires based on the upper bound values will lead to high system profit with significantly higher constraints violation risk. As a result, the compound influence of the decision maker’s aspiration level (i.e., readiness to take risk) on the management of used tires requires further exploration. Because human judgment is fuzzy in nature, incorporating the fuzzy programming approach into the proposed model could result in a relationship between decision-making risk and the performances of used tire management systems. Moreover, used tire management can influence the capacity changes of forward and reverse supply chains. Because the mixed integer programming approach is suitable for handling capacity-expansion planning problems, its integration with the developed model presents another direction for further research. In addition, the existing literature lacks documentation of present industry practices in the area of used tires management. The lack of documented practices in this field is a major weakness and drawback of previous papers. Hence, additional research efforts to address these topics are urgently needed. Appendix. Notation Indices and sets: t – index of time period; t  1,,T  H – set of tire retreading plants located in the considered region h – index of tire retreading plant; h  1,…, H 

Sh , h  H – set of storage areas in tire retreading plant h

S

Sh – set of storage areas in all tire retreading plants hH

h , h  H – set of retreading processes (i.e., retreading equipment and manual processes) in tire retreading plant h  h – set of retreading processes in all tire retreading plants hH

h =Sh  h , h  H – set of entities in tire retreading plant h (i.e., storages, manual processes and retreading equipment)   h – set of entities in all tire retreading plants hH

M1 – set of available dealers of reusable used tires (i.e., used tires market) located in the considered region M2 – set of available dealers of retreaded tires (i.e., retreaded tires market) located in the considered region M3 – set of available dealers of EoL tires (i.e., EoL tires market) located in the considered region M=M1  M2  M3 – set of available dealers of reusable used, retreaded or EoL tires (i.e., secondary markets) located in the considered region 1 – set of available tire recycling plants located in the considered region 18

 2 – set of available waste-to-energy plants located in the considered region =1   2 – set of available waste entities (i.e., recycling plants and waste-to-energy plants) located in the considered region g – index of material recovery option for EoL tires; g 1,,G

 g – set of available application sites for g-th EoL tires material recovery option =1    g   G – set of available application sites located in the considered region for all EoL tires material recovery options O  M     – set of available destinations (i.e., secondary markets, waste entities and application sites) in the considered region N    O – set of existing entities (i.e., entities in tire retreading plants and available destinations) A   i, j  i  N, j  N – set of material flows



 j 1  i  i, j   A , j  N – set of entities that precede entity j i  j  i, j   A , i  N – set of entities that follow entity i J – set of materials

gij  J – material on the flow  i, j  (i.e., flow attribute)

Vhj  J, j  – set of materials routed from tire retreading plant h to available destination j





hjv  i i j 1 ,gij  v , h  H, j , v  Vhj – set of entities of tire retreading plant h that route material v to destination j K hi  J, h  H, i h – set of materials processed on entity i of tire retreading plant h





 hik  j j i ,gij  k , h  H, i h , k  K hi – set of entities on which material k is forwarded

from entity i of tire retreading plant h Parameters: f  – expected profit to used tire retreading management system over the planning horizon T – number of analyzed time periods G – number of available material recovery options for EoL tires in the considered region

 – price of a new truck tire (independent variable in the range of  and  )    Rhjvt  , h  H, j  O, v  Vhj ,     ,    – revenue from each unit weight of material v   processed in tire retreading plant h and sold to destination j in period t, which is function of  CPht   , h  H,   ,   – purchasing cost per weight unit of used tires of tire retreading plant   h in period t, which is function of     Zhit  , h  H, i  Sh ,   ,   – inventory holding cost per weight unit and time unit for   used tires piled in storage area i of tire retreading plant h in period t, which is function of 

Ft  – tire retreading fee per weight unit in period t

 – electricity price (independent variable in the range of   and   )

 – labor costs in the waste management sector (independent variable in the range of   and   )  CShjt   ,   , h  H, j h ,      ,    ,     ,    – processing cost per weight unit in the

    case of entity j of tire retreading plant h in period t, which is function of  and 

19

 – gas price (independent variable in the range of   and   )

 – labor costs in the transportation sector (independent variable in the range of   and   )  CThjt  ,   , h  H, j  O,     ,    ,      ,    – transportation cost per weight unit of tires from tire retreading plant h to destination j in period t, which is function of  and  Пhi 0 , h  H, i  Sh – initial inventory weight of used tires piled in storage area i of tire retreading plant h Whmin – safety inventory level in tire retreading plant h  Chj , h  H, j h – capacity of processing entity j of tire retreading plant h

t – duration of planning period t in time units  Ehik , h  H, i h , k  K hi – operational efficiency of material k on entity i of tire retreading plant h

Variables:

Phit , h  H, i  Sh – weight of purchased used tires piled in storage area i of tire retreading plant h in period t Whit , h  H, i  Sh – weight of used tires piled in storage area i of tire retreading plant h at the end of period t X hijt , h  H, i h , j i – weight of material flow routed from entity i of tire retreading plant h to entity j in period t References Abdul-Kader, W., Haque, M.S., 2011. Sustainable tyre remanufacturing: an agent-based simulation modelling approach. International Journal of Sustainable Engineering 4 (4), 330–347. Afrinaldi, F., Taufik, Tasman, A.M., Zhang, H.-C., Hasan, A., 2017. Minimizing economic and environmental impacts through an optimal preventive replacement schedule: model and application. Journal of Cleaner Production 143, 882–893. Amin, S.H., Zhang, G., Akhtar, P., 2017. Effects of uncertainty on a tire closed-loop supply chain network. Expert Systems with Applications 73, 82–91. Antmann, E., Shi, X., Celik, N., Dai, Y., 2013. Continuous-discrete simulation-based decision making framework for solid waste management and recycling programs. Computers & Industrial Engineering 66 (3), 438–454. Bazan, E., Jaber, M.Y., El Saadany, A.M.A., 2015. Carbon emissions and energy effects on manufacturing– remanufacturing inventory models. Computers & Industrial Engineering 88, 307–316. Boustani, A., Sahni, S., Gutowski, T., Graves, S., 2010. Tire remanufacturing and energy savings. Environmentally Benign Manufacturing Laboratory, Sloan School of Management, MIT, Cambridge, MA, USA. (accessed 20.02.17). Bravo, M., Brito, J., 2012. Concrete made with used tyre aggregate: durability-related performance. Journal of Cleaner Production 25 (1), 42–50. Bunget, G., Shen, Q., Gramling, F., Judd, D., Kurfess, T., 2015. Impact-acoustic evaluation method for rubber–steel composites: part I. Relevant diagnostic concepts. Applied Acoustics 90, 74–80. Chang, S.-Y., Gronwald, F., 2016. A multi-criteria evaluation of the methods for recycling scrap tires. The Journal of Solid Waste Technology and Management 42 (2), 145–156. Chinneck, J.W., Ramadan, K., 2000. Linear programming with interval coefficients. Journal of the Operational Research Society 51 (2), 209–220. Chiu, C.-T., 2008. Use of ground tire rubber in asphalt pavements: field trial and evaluation in Taiwan. Resources, Conservation and Recycling 52 (3), 522–532. 20

Creazza, A., Dallari, F., Rossi, T., 2012. Applying an integrated logistics network design and optimisation model: the Pirelli tyre case. International Journal of Production Research 50 (11), 3021–3038. Dabic-Ostojic, S., Miljus, М., Bojovic, N. Glisovic, N., Milenkovic, M., 2014. Applying a mathematical approach to improve the tire retreading process. Resources, Conservation and Recycling 86, 107– 117. De Souza, C.D.R., D’Agosto, M.d.A., 2013. Value chain analysis applied to the scrap tire reverse logistics chain: an applied study of co-processing in the cement industry. Resources, Conservation and Recycling 78, 15–25. Debo, L.G., Van Wassenhove, L.N., 2005. Tire recovery: the RetreadCo case. In: Flapper, S.D.P., Van Nunen, J.A.E.E., Van Wassenhove, L.N. (Eds.): Managing closed-loop supply chains (pp. 119–128). Springer Berlin Heidelberg Dehghanian, F., Mansour, S., 2009. Designing sustainable recovery network of end-of-life products using genetic algorithm. Resources, Conservation and Recycling 53 (10), 559–570. Dhouib, D., 2014. An extension of MACBETH method for a fuzzy environment to analyze alternatives in reverse logistics for automobile tire wastes. Omega 42 (1), 25–32. Dodoo, A., Gustavsson, L., Sathre, R., 2009. Carbon implications of end-of-life management of building materials. Resources, Conservation and Recycling 53 (5), 276–286. Edinçliler, A., Baykal, G., Saygili, A., 2010. Influence of different processing techniques on the mechanical properties of used tires in embankment construction. Waste Management 30 (6), 1073–1080. ElSayed, A., Kongar, E., Gupta, S.M., Sobh, T., 2012. A robotic-driven disassembly sequence generator for end-of-life electronic products. Journal of Intelligent & Robotic Systems 68 (1), 43–52. European Tyre & Rubber Manufacturers’ Association (ETRMA), 2014. Annual report 2013/2014. (accessed 20.02.17). European Tyre & Rubber Manufacturers’ Association (ETRMA), 2016. The 2015 edition of ETRMA's Endof-life Tyres Management report. (accessed 20.02.17). Feriha, K.M., Hussein, R.A., Ismail, G.A., El-Naggar, H.M., El-Sebaie, O.D., 2014. Feasibility study for end-of-life tire recycling in new tire production, Egypt. Journal of Environmental Engineering & Ecological Science 3, 5. Ferrao, P., Ribeiro, P., Silva, P., 2008. A management system for end-of-life tyres: a Portuguese case study. Waste Management 28 (2), 604–614. Fıglali, N., Cihan, A., Esen, H., Fıglali, A., Cesmeci, D., Gullu, M.K, et al., 2015. Image processing-aided working posture analysis: I-OWAS. Computers & Industrial Engineering 85, 384–394. Fthenakis, V.M., 2009. End-of-life management and recycling of PV modules. Energy Policy 28 (14), 1051– 1058. Hashemi, V., Chen, M., Fang, L., 2014. Process planning for closed-loop aerospace manufacturing supply chain and environmental impact reduction. Computers & Industrial Engineering 75, 87–95. He, L., Huang, G.H., 2008. Optimization of regional waste management systems based on inexact semiinfinite programming. Canadian Journal of Civil Engineering 35 (9), 987–998. He, L., Huang, G.H., Lu, H., 2011. Bivariate interval semi-infinite programming with an application to environmental decision-making analysis. European Journal of Operational Research 211 (3), 452– 465. He, L., Huang, G.H., Tan, Q., Liu, Z.F., 2008. An interval full-infinite programming method to supporting environmental decision-making. Engineering Optimization 40 (8), 709–728. He, L., Huang, G.H., Zeng, G., Lu, H., 2009a. An interval mixed-integer semi-infinite programming method for municipal solid waste management. Journal of the Air & Waste Management Association 59 (2), 236–246. He, L., Huang, G.-H., Zeng, G.-M., Lu, H.-W., 2009b. Identifying optimal regional solid waste management strategies through an inexact integer programming model containing infinite objectives and constraints. Waste Management 29 (1), 21–31. Hita, I., Arabiourrutia, M., Olazar, M., Bilbao, J. Arandesand , J.M., Castaño, P., 2016. Opportunities and barriers for producing high quality fuels from the pyrolysis of scrap tires. Renewable and Sustainable Energy Reviews 54, 745–759. Iakovou, E., Moussiopoulos, N., Xanthopoulos, A., Achillas, Ch., Michailidis, N., Chatzipanagioti, M., et al., 2009. A methodological framework for end-of-life management of electronic products. Resources, Conservation and Recycling 53 (6), 329–339. 21

Kannan, D., Diabat, A., Madan Shankar, K., 2014. Analyzing the drivers of end-of-life tire management using interpretive structural modeling (ISM). The International Journal of Advanced Manufacturing Technology 72 (9), 1603–1614. Kannan, G., Haq, A.N., Devika, M., 2009. Analysis of closed loop supply chain using genetic algorithm and particle swarm optimisation. International Journal of Production Research 47 (5), 1175–1200. Karaağaç, B., Kalkan, M.E., Deniz, V., 2017. End of life tyre management: Turkey case. Journal of Material Cycles and Waste Management 19 (1), 577–584. Kop, Y., Genevois, M.E., Ulukan, H.Z., 2012. End-of-life tyres recovery method selection in Turkey by using fuzzy extended AHP. In: Greco, S., Bouchon-Meunier, B., Colleti, G., Fedrizzi, M., Matarazzo, B., et al. (Eds.): Advances in computational intelligence (pp. 413–422). Springer Berlin Heidelberg Kuo, T.C., 2013. Waste electronics and electrical equipment disassembly and recycling using Petri net analysis: considering the economic value and environmental impacts. Computers & Industrial Engineering 65 (1), 54–64. Labaki, M., Jeguirim, M., 2017. Thermochemical conversion of waste tyres—a review. Environmental Science and Pollution Research. http://dx.doi.org/10.1007/s11356-016-7780-0. Lebreton, B., Tuma, A., 2006. A quantitative approach to assessing the profitability of car and truck tire remanufacturing. International Journal of Production Economics 104 (2), 639–652. Li, L., Xiao, H., Ferreira, P., Cui, X., 2016. Study of a small scale tyre-reinforced embankment. Geotextiles and Geomembranes 44 (2), 201–208. Li, X., Lu, H., He, L., Shi, B., 2014. An inexact stochastic optimization model for agricultural irrigation management with a case study in China. Stochastic Environmental Research and Risk Assessment 28 (2), 281–295. Lin, C., Huang, C.-L., Shern, C.-C., 2008. Recycling waste tire powder for the recovery of oil spills. Resources, Conservation and Recycling 52 (10), 1162–1166. Machin, E.B., Pedroso, D.T., de Carvalho, J.A., 2017. Energetic valorization of waste tires. Renewable and Sustainable Energy Reviews. 68 (1), 306–315. Medina Flores, N., Medina-Flores, D., Hernández-Olivares, F., 2016. Influence of fibers partially coated with rubber from tire recycling as aggregate on the acoustical properties of rubberized concrete. Construction and Building Materials 129, 29–36. Mondaln, S., Mukherjee, K., 2012. Simulation of tyre retreading process – an Indian case study. International Journal of Logistics Systems and Management 13 (4), 525–539. Oikonomou, N., Mavridou, S., 2009. Improvement of chloride ion penetration resistance in cement mortars modified with rubber from worn automobile tires. Cement and Concrete Composites 31 (6), 403– 407. Pedram, A., Bin Yusoff, N., Olugu, E.U., Mahat, A.B., Pedram, P., Babalola, A., 2017. Integrated forward and reverse supply chain: a tire case study. Waste Management. http://dx.doi.org/10.1016/j.wasman.2016.06.029. Pehlken, A., Müller, D.H., 2009. Using information of the separation process of recycling scrap tires for process modelling. Resources, Conservation and Recycling 54 (2), 140–148. Pehlken, A., Rolbiecki, M., Decker, A., Thoben, K.-D., 2014. Assessing the future potential of waste flows – case study scrap tire. International Journal of Sustainable Development and Planning 9 (1), 90–105. Phuc, P.N.K., Yu, V.F., Tsao, Y.-C., 2017. Optimizing fuzzy reverse supply chain for end-of-life vehicles. Computers & Industrial Engineering, http://doi.org/10.1016/j.cie.2016.11.007. Pirachicán-Mayorga, C., Montoya-Torres, J.R., Jarrín, J., Halabi Echeverry, A.X., 2014. Modelling reverse logistics practices: a case study of recycled tyres in Colombia. Latin American Journal of Management for Sustainable Development 1 (1), 58–72. Rowhani, A., Rainey, T.J., 2016. Scrap tyre management pathways and their use as a fuel - a review. Energies 9 (11), 888. Sasikumar, P., Kannan, G., Haq, A.N., 2010. A multi-echelon reverse logistics network design for product recovery—a case of truck tire remanufacturing. The International Journal of Advanced Manufacturing Technology 49 (9), 1223–1234. Sengul, O., 2016. Mechanical behavior of concretes containing waste steel fibers recovered from scrap tires. Construction and Building Materials 122, 649–658. Sengupta, A., Kumar Pal, T., Chakraborty, D., 2001. Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets and Systems 119 (1), 129–138. 22

Shalaby, A., Khan, R.A., 2005. Design of unsurfaced roads constructed with large-size shredded rubber tires: a case study. Resources, Conservation and Recycling 44 (4), 318–332. Siddique, R., Naik, T.R., 2004. Properties of concrete containing scrap-tire rubber – an overview. Waste Management 24 (6), 563–569. Subulan, K., Tasan A.S., Baykasoglu, A., 2015. Designing an environmentally conscious tire closed-loop supply chain network with multiple recovery options using interactive fuzzy goal programming. Applied Mathematical Modelling 39 (9), 2661–2702. Sunthonpagasit, N., Duffey, M., 2003. Scrap tires to crumb rubber: feasibility analysis for processing facilities. Resources, Conservation and Recycling 40 (4), 281–299. Tong, S.C., 1994. Interval number, fuzzy number linear programming. Fuzzy Sets and Systems 66 (3), 301– 306. Torreta, V, Rada, E.C., Raggazi, M., Trulli, E., Istrate, I. E., Cioca, L.L., 2015. Treatment and disposal of tyres: two EU approaches. A review. Waste Management 45, 152–160. Uruburu, Á., Ponce-Cueto, E., Cobo-Benita, J.R., Ordieres-Meré, J., 2013. The new challenges of end-of-life tyres management systems: a Spanish case study. Waste Management 33 (3), 679–688. Vinodh, S., Jayakrishna, K., 2013. Application of hybrid MCDM approach for selecting the best tyre recycling process. In: Davim, J.P. (Ed.): Green manufacturing processes and systems (pp. 103–123). Springer Berlin Heidelberg Vorasayan, J., 2016. Price and profitability from two-quality retread tire. KnE Life Sciences, 177–182. Zanetti, M.C., Fiore, S., Ruffino, B., Santagata, E., Dalmazzo, D., Lanotte, M., 2015. Characterization of crumb rubber from end-of-life tyres for paving applications. Waste Management 45, 161–170. Zhang, X., Xu, Z., 2014. Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives. Computers & Industrial Engineering 75, 217– 229. Zhou, H., Holikatti, S., Vacura, P., 2014. Caltrans use of scrap tires in asphalt rubber products: a comprehensive review. Journal of Traffic and Transportation Engineering 1 (1), 39–48. Zhu, Y., Huang, G.H., Li, Y.P., He, L., Zhang, X.X., 2011. An interval full-infinite mixed-integer programming method for planning municipal energy systems – A case study of Beijing. Applied Energy 88 (8), 2846–2862.

23

Collection center

Tire retreading plant

1 ...

1

Used tires

Dealers of used tires ...

Reusable tires m1

...

...

Dealers of retreaded tires 1

...

m2

... ...

Dealers of EoL tires 1

...

Secondary markets

Used tire owner

m3

...

1

...

...

Waste-to-energy plants 1

...

Waste entities

1

...

...

H

υ1

...

Option G 1

...

υG

Applications of EoL tires

... 1

Collection center

Dealer of used tires Dealer of retreaded tires Dealer of EoL tires Recycling plant Waste-to-energy plant

2

Option 1

Used tire owner

Tire retreading plant

Recycling plants h

End-of-life (EoL) tires Retreaded tires

i-th option of EoL tires recovery j-th option of EoL tires recovery

Fig. 1. Material flow network in used tire retreading management systems.

24

Shipments of used tires

RE tires

Shipments of used tires

Shipments of used tires

Storages

Storages

Storages

Used tires

Used tires

Used tires

Initial inspection

EoL tires

RE tires

Retreadable tires

Filling repair

EoL tires

Buffed retreadable tires EoL tires

CC building

Curing in radial matrix

EoL tires

Visual and tactile insp.

Retreadable tires ready for curing EoL tires

Retreadable tires with new treads EoL tires

Retreadable tires prepared for curing EoL tires

Retreaded used tires

RT tires

Inflation test

Retreaded used tires

Tested retreaded tires

Labeling

Single-cam. shearography

Labeled retreaded used tires

Additionally tested retreaded tires

Final inspection

EoL tires

Inspected retreaded used tires EoL tires

Curing

EoL tires

Retreaded used tires EoL tires

Monorailing

EoL tires

Retreadable tires with new treads

Retreadable tires with new treads EoL tires

EoL tires

Buffed retreadable tires EoL tires

Building

Retreadable tires prepared for building

Curing

Buffing

Repaired retreadable tires

Repaired retreadable tires

Enveloping

Retreadable tires ready for buffing

Buffed retreadable tires

Buffing

EoL tires

Shearography EoL inspection tires

EoL tires

Buffing

Retreadable tires ready for buffing

Initial inspection Retreadable tires

Retreadable tires ready for buffing

Shearography EoL inspection tires

Building

RE tires

Shearography EoL inspection tires

EoL tires

Visually inspected retreadable tires

Final preparation

EoL tires

Retreadable tires

Visual inspection

Filling repair

Initial inspection

EoL tires

(b) Tire retreading plant 2

RT tires

EoL tires

EoL tires

Labeling

(c) Tire retreading plant 3

Labeling Labeled retreaded used tires RT tires

Final inspection

EoL tires

(a) Tire retreading plant 1

To dealers of used tires

To recycling plants

To dealers of retreaded tires

To waste-to-energy plants

To dealers of EoL tires

To application sites

Fig. 2. Flow sheets of the tire retreading plants. EoL: end-of-life; RE: reusable; RT: retreaded; CC: computer controlled.

25

Economy ● global

Environment ● natural

● local

● social

Policy ● economical ● environmental ● social

Used tire management system

Fig. 3. Complex relations between a system for management of used tires and external sub-systems.

26

Management of used tires under uncertainty

Technical data

Uncertainties diagnosis: Functional intervals Crisp intervals

Economic data

Intervalparameter programming

Interval semi-infinite programming

Infinite number of objective functions

Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty

Upper bound sub-model

Lower bound sub-model

Solutions of the upper bound sub-model

Solutions of the lower bound sub-model

Final solutions

Fig. 4. Framework of the interval-parameter semi-infinite programming model for used tire management and planning under uncertainty.

27

2

3

3

Tire retreading plant Dealer of used tires

1 2

Dealer of retreaded tires

1

Dealer of EoL tires

3 2

Recycling plant

2

1 1

Waste-to-energy plant

1 2

2 2

1 1 1

2

3

1st option of EoL tires recovery 2nd option of EoL tires recovery 3rd option of EoL tires recovery

Fig. 5. A regional system for management of used tires.

28

Lower bound

Upper bound

200

System profit (€ 106)

190.77 172.01

150 153.92

100

50

82.23

80.83

77.99

t=1

t=2

t=3

Fig. 6. System profit during the planning horizon.

29

24.18

18.72 13.26

6.63

15.99

16.85

18.72 13.26

16.85 6.63

15.99

24.18

24.59 19.15 13.43

15

10

16.61

17.33

20

6.97

Quantity (103 tonnes)

25

5

0

h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3 Lower Upper Lower Upper Lower Upper bound bound bound bound bound bound t=1 t=2 t=3

Fig. 7. Purchasing plan for different tire retreading plants during the planning horizon (10 3 tonnes).

30

Table 1 Allocation patterns of retreaded, reusable used and EoL tires from different tire retreading plants during the planning horizon (103 tonnes). Destination

Entity

Reusable tires Dealer 1 of reusable used tires market Dealer 2 of reusable used tires Retreated tires Dealer 1 of retreated tires market Dealer 2 of retreated tires Dealer 3 of retreated tires EoL tires Dealer 1 of EoL tires market Dealer 2 of EoL tires Recycling Tire recycling plant 1 plants Tire recycling plant 2 Waste-toWtE plant 1 energy WtE plant 2 (WtE) plants WtE plant 3 Application Site 1 for appl. as embankment stabilizers sites Site 2 for appl. as embankment stabilizers for EoL tires Site for application as dock fenders Site 1 for application as erosion barrier Site 2 for application as erosion barrier Site 3 for application as erosion barrier

Tire retreading plant h=1 h=2 – – [2.038, 4.077] [5.181, 5.756] – – – – [7.822, 15.645] [23.235, 25.817] – – – – – – – – – – – – – – [10.029, 20.058] – – [0.0, 7.376] – [14.752, 24.587] – – – – – –

h=3 – [6.068, 9.176] – – [14.665, 22.176] – – – – – – – – – [27.236, 41.187] – – –

31

Supporting information for: Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty This supplement contains the data used in the numerical example presented in the accompanying article. The efficiencies of tire retreading operations are given in Table S1. Table S1 Efficiencies of tire retreading operations in percentages. Operation

Material fraction

Initial inspection

Retreadable tires Reusable tires End-of-life tires Visually inspected retreadable tires End-of-life tires Retreadable tires ready for buffing End-of-life tires Buffed retreadable tires End-of-life tires Repaired retreadable tires End-of-life tires Retreadable tires prepared for building End-of-life tires Retreadable tires with new treads End-of-life tires Retreadable tires with new treads End-of-life tires Retreadable tires prepared for curing End-of-life tires Retreadable tires ready for curing End-of-life tires Retreaded used tires End-of-life tires Retreaded used tires End-of-life tires Inspected retreaded used tires End-of-life tires Tested retreaded tires End-of-life tires Additionally tested retreaded tires End-of-life tires Retreaded tires End-of-life tires

Visual inspection Shearography inspection Buffing Filling repair Final preparation Building Computer controlled building Enveloping Monorailing Curing Curing in radial matrix Visual and tactile inspection Inflation test Single-camera shearography test Final inspection

Tire retreading plant h=1 h=2 [73.50, 76.50] [81.33, 86.50] [9.55, 10.25] [8.20, 10.25] [13.95, 16.25] [5.30, 8.42] [94.0, 95.50]  [4.50, 6.0]  [65.33, 68.10] [68.37, 71.15] [31.90, 34.67] [28.85, 31.63] [82.33, 84.33] [79.24, 83.73] [15.67, 17.67] [16.27, 20.76] [98.0, 99.25] [93.0, 95.78] [0.75, 2.0] [4.22, 7.00] [98.50, 99.50]  [0.50, 1.50]  [97.75, 99.0] [97.50, 99.50] [1.0, 2.25] [0.50, 1.80]     [97.50, 98.50]  [1.50, 2.50]  [98.20, 99.0]  [1.00, 1.80]  [96.73, 98.73] [96.25, 97.50] [1.27, 3.27] [2.50, 3.75]                 [98.50, 99.50] [98.15, 99.33] [0.50, 1.50] [0.67, 1.85]

h=3 [77.36, 82.55] [10.27, 12.65] [7.18, 9.99]   [70.56, 75.88] [24.12, 29.44] [81.46, 86.67] [13.33, 18.54]       [62.67, 67.15] [32.85, 37.33]       [89.62, 93.36] [6.64, 10.38] [98.73, 99.75] [0.25, 1.27] [98.15, 99.33] [0.67, 1.85] [88.67, 93.35] [6.65, 11.33]  

Capacities of tire retreading operations are presented in Table S2, while corresponding tire retreading costs are given in Tables S3S5.

32

Table S2 Capacities of tire retreading operations (tonne/h). Operation Initial inspection Visual inspection Shearography inspection Buffing Filling repair Final preparation Building Computer controlled building Enveloping Monorailing Curing Curing in radial matrix Visual and tactile inspection Inflation test Single-camera shearography test Labeling Final inspection

Tire retreading plant h=1 [0.85, 1.70] [1.15, 2.10] [2.80, 5.0] [1.70, 3.30] [1.15, 2.50] [0.60, 1.25] [1.40, 2.50]  [0.85, 1.65]  [0.80, 1.20]     [0.60, 1.25] [0.60, 1.25]

h=2 [2.16, 2.40]  [2.0, 3.0] [1.38, 1.92] [2.20, 3.30]  [2.40, 3.35]   [2.70, 3.0] [1.10, 1.20]     [1.10, 1.40] [1.10, 1.40]

h=3 [2.05, 3.10]  [2.0, 3.0] [2.40, 3.60]    [1.80, 2.70]    [2.15, 3.05] [0.70, 1.10] [0.82, 1.28] [0.78, 1.12] [0.75, 1.30] 

Table S3 Tire retreading costs in tire retreading plant 1 (€/tonne). Operation Initial inspection Visual inspection Shearography inspection Buffing Filling repair Final preparation Building Enveloping Curing Labeling Final inspection

Planning period t=1 [1.042+23.672∙μ+0.868∙σ, 2.148+44.939∙μ+1.698∙σ] [1.378+46.962∙μ+1.080∙σ, 2.669+83.750∙μ+1.986∙σ] [6.820+1239.984∙μ+1.003∙σ, 12.709+2127.006∙μ+1.773∙σ] [6.165+303.593∙μ+0.403∙σ, 12.747+577.815∙μ+0.791∙σ] [2.365+117.556∙μ+2.275∙σ, 3.312+151.568∙μ+3.023∙σ] [0.785+26.774∙μ+0.546∙σ, 1.804+56.623∙μ+1.190∙σ] [2.175+108.124∙μ+2.092∙σ, 4.031+184.455∙μ+3.679∙σ] [1.042+23.672∙μ+0.868∙σ, 2.148+44.939∙μ+1.698∙σ] [21.032+2867.934∙μ+0.344∙σ, 32.589+4090.639∙μ+0.505∙σ] [0.344+7.827∙μ+0.287∙σ, 1.068+22.333∙μ+0.844∙σ] [0.689+23.481∙μ+0.540∙σ, 1.601+50.250∙μ+1.192∙σ]

t=2 t=3 [1.005+22.841∙μ+0.838∙σ, [0.970+22.045∙μ+0.808∙σ, 2.427+50.774∙μ+1.919∙σ] 2.742+57.354∙μ+2.168∙σ] [1.330+45.324∙μ+1.043∙σ, [1.283+43.739∙μ+1.006∙σ, 3.015+94.613∙μ+2.244∙σ] 3.407+106.899∙μ+2.535∙σ] [6.319+1148.909∙μ+0.929∙σ, [5.870+1067.273∙μ+0.863∙σ, 13.892+2324.937∙μ+1.938∙σ] 15.184+2541.255∙μ+2.119∙σ] [5.712+281.273∙μ+0.373∙σ, [5.294+260.665∙μ+0.346∙σ, 13.934+631.574∙μ+0.864∙σ] 15.230+690.319∙μ+0.944∙σ] [2.282+113.452∙μ+2.195∙σ, [2.202+109.474∙μ+2.118∙σ, 3.742+171.229∙μ+3.415∙σ] 4.227+193.452∙μ+3.859∙σ] [0.758+25.838∙μ+0.527∙σ, [0.731+24.938∙μ+0.509∙σ, 2.038+63.963∙μ+1.345∙σ] 2.303+72.265∙μ+1.519∙σ] [2.099+104.344∙μ+2.019∙σ, [2.025+100.685∙μ+1.948∙σ, 4.554+208.389∙μ+4.156∙σ] 5.144+235.426∙μ+4.696∙σ] [1.005+22.841∙μ+0.838∙σ, [0.970+22.045∙μ+0.808∙σ, 2.427+50.774∙μ+1.919∙σ] 2.742+57.354∙μ+2.168∙σ] [19.487+2657.352∙μ+0.318∙σ,[18.056+2462.216∙μ+0.295∙σ, 35.621+4471.287∙μ+0.552∙σ] 38.936+4887.301∙μ+0.604∙σ] [0.333+7.557∙μ+0.277∙σ, [0.321+7.284∙μ+0.267∙σ, 1.206+25.230∙μ+0.954∙σ] 1.363+28.504∙μ+1.077∙σ] [0.664+22.653∙μ+0.521∙σ, [0.641+21.869∙μ+0.503∙σ, 1.809+56.768∙μ+1.346∙σ] 2.044+64.142∙μ+1.521∙σ]

Note:   €kWh is the electricity price for medium size industrial consumers (Eurostat, 2016a);

  €h is the labor cost in the waste management sector (Eurostat, 2016c).

33

Table S4 Tire retreading costs in tire retreading plant 2 (€/tonne). Operation Initial inspection Shearography inspection Buffing Filling repair Building Monorailing Curing Labeling Final inspection

Planning period t=1 [0.990+22.504∙μ+0.825∙σ, 1.703+35.625∙μ+1.346∙σ] [9.177+1668.492∙μ+1.350∙σ, 15.201+2544.136∙μ+2.121∙σ] [4.864+239.504∙μ+0.318∙σ, 9.472+429.334∙μ+0.587∙σ] [1.044+51.881∙μ+1.004∙σ, 1.481+67.796∙μ+1.352∙σ] [5.167+256.907∙μ+4.971∙σ, 10.260+469.536∙μ+9.365∙σ] [0.798+154.245∙μ+0.078∙σ, 1.824+324.406∙μ+0.170∙σ] [15.042+2051.145∙μ+0.246∙σ, 24.063+3020.413∙μ+0.373∙σ] [0.993+22.571∙μ+0.828∙σ, 1.533+32.073∙μ+1.212∙σ] [0.968+33.015∙μ+0.760∙σ, 1.507+47.292∙μ+1.122∙σ]

t=2 t=3 [0.956+21.717∙μ+0.796∙σ, [0.922+20.957∙μ+0.768∙σ, 1.924+40.246∙μ+1.521∙σ] 2.173+45.468∙μ+1.718∙σ] [8.503+1545.982∙μ+1.250∙σ, [7.879+1432.467∙μ+1.159∙σ, 16.616+2780.856∙μ+2.318∙σ] 18.162+3039.602∙μ+2.534∙σ] [4.507+221.918∙μ+0.295∙σ, [4.176+205.624∙μ+0.273∙σ, 10.353+469.282∙μ+0.642∙σ] 11.316+512.946∙μ+0.702∙σ] [1.007+50.066∙μ+0.969∙σ, [0.972+48.314∙μ+0.935∙σ, 1.674+76.591∙μ+1.528∙σ] 1.891+86.528∙μ+1.726∙σ] [4.987+247.919∙μ+4.797∙σ, [4.812+239.246∙μ+4.629∙σ, 11.591+530.452∙μ+10.580∙σ] 13.095+599.272∙μ+11.953∙σ] [0.740+142.929∙μ+0.073∙σ, [0.685+132.425∙μ+0.067∙σ, 1.994+354.591∙μ+0.185∙σ] 2.180+387.584∙μ+0.203∙σ] [13.937+1900.538∙μ+0.228∙σ, [12.914+1760.990∙μ+0.211∙σ, 26.302+3301.448∙μ+0.408∙σ] 28.749+3608.632∙μ+0.446∙σ] [0.958+21.782∙μ+0.799∙σ, [0.925+21.020∙μ+0.771∙σ, 1.732+36.234∙μ+1.369∙σ] 1.957+40.935∙μ+1.547∙σ] [0.935+31.860∙μ+0.733∙σ, [0.902+30.745∙μ+0.707∙σ, 1.703+53.428∙μ+1.267∙σ] 1.923+60.360∙μ+1.431∙σ]

Note:   €kWh is the electricity price for medium size industrial consumers (Eurostat, 2016a);

  €h is the labor cost in the waste management sector (Eurostat, 2016c).

Table S5 Tire retreading costs in tire retreading plant 3 (€/tonne). Operation

Planning period t=1 Initial inspection [0.692+15.721∙μ+0.576∙σ, 1.266+24.495∙μ+1.001∙σ] Shearography inspection [10.555+1919.002∙μ+1.552∙σ, 17.589+2943.802∙μ+2.454∙σ] Buffing [6.627+326.348∙μ+0.433∙σ, 12.245+555.053∙μ+0.759∙σ] Computer controlled [3.608+804.518∙μ+0.774∙σ, building 6.244+1281.795∙μ+1.271∙σ] Curing in radial matrix [17.460+2380.972∙μ+0.285∙σ, 29.518+3705.160∙μ+0.458∙σ] Visual and tactile inspection [1.984+108.214∙μ+0.214∙σ, 3.384+169.902∙μ+0.346∙σ] Inflation test [2.452+185.741∙μ+3.085∙σ, 3.797+264.787∙μ+4.533∙σ] Single-camera shearography [6.072+1069.529∙μ+1.042∙σ, test 11.307+1833.231∙μ+1.841∙σ] Labeling [0.344+7.827∙μ+0.287∙σ, 1.068+22.333∙μ+0.844∙σ]

t=2 t=3 [0.668+15.171∙μ+0.556∙σ, [0.644+14.641∙μ+0.537∙σ, 1.431+29.932∙μ+1.131∙σ] 1.616+33.816∙μ+1.278∙σ] [9.780+1778.098∙μ+1.438∙σ, [9.061+1647.540∙μ+1.333∙σ, 19.226+3217.709∙μ+2.683∙σ] 21.015+3517.101∙μ+2.932∙σ] [6.141+302.385∙μ+0.401∙σ, [5.690+280.183∙μ+0.372∙σ, 13.385+606.698∙μ+0.830∙σ] 14.630+663.148∙μ+0.907∙σ] [3.343+745.446∙μ+0.717∙σ, [3.097+690.711∙μ+0.664∙σ, 6.825+1401.060∙μ+1.389∙σ] 7.460+1531.422∙μ+1.518∙σ] [16.178+2206.147∙μ+0.264∙σ, [14.990+2044.159∙μ+0.245∙σ, 32.264+4049.908∙μ+0.50∙σ] 35.266+4426.732∙μ+0.547∙σ] [1.838+100.268∙μ+0.198∙σ, [1.703+92.906∙μ+0.184∙σ, 3.699+185.710∙μ+0.378∙σ] 4.043+202.990∙μ+0.414∙σ] [2.272+172.102∙μ+2.858∙σ, [2.105+159.466∙μ+2.648∙σ, 4.150+289.425∙μ+4.955∙σ] 4.537+316.354∙μ+5.416∙σ] [5.626+990.998∙μ+0.965∙σ, [5.213+918.233∙μ+0.894∙σ, 12.359+2003.804∙μ+2.012∙σ] 13.509+2190.249∙μ+2.199∙σ] [0.332+7.553∙μ+0.277∙σ, [0.321+7.289∙μ+0.267∙σ, 1.206+25.231∙μ+0.954∙σ] 1.363+28.504∙μ+1.077∙σ]

Note:   €kWh is the electricity price for medium size industrial consumers (Eurostat, 2016a);

  €h is the labor cost in the waste management sector (Eurostat, 2016c).

The procurement costs of used tires, and selling prices of reusable, retreaded and end-of-life (EoL) tires are given in Table S6.

34

Table S6 Procurement cost and selling prices (€/tonne). Buyer Tire retreading plant Dealer 1 of reusable used tires Dealer 2 of reusable used tires Dealer 1 of retreated tires Dealer 2 of retreated tires Dealer 3 of retreated tires Dealer 1 of end-of-life tires Dealer 2 of end-of-life tires Tire recycling plant 1 Tire recycling plant 2 Cement kiln 1 Cement kiln 2 Cement kiln 3 Site 1 for end-of-life tires application as embankment stabilizers Site 2 for end-of-life tires application as embankment stabilizers Site for end-of-life tires application as dock fenders Site 1 for end-of-life tires application as erosion barriers Site 2 for end-of-life tires application as erosion barriers Site 3 for end-of-life tires application as erosion barriers

Planning period t=1 [96.828+1.006∙, 157.241+1.273∙] [217.862+10.752∙, 290.292+11.165∙] [225.124+11.110∙, 302.388+11.630∙] [326.793+16.127∙, 438.462+16.864∙] [319.531+15.769∙, 426.367+16.399∙] [331.634+16.366∙, 444.510+17.097∙] [2.283+0.088∙, 2.113+0.104∙] [2.206+0.085∙, 2.062+0.102∙] [2.180+0.084∙, 2.037+0.101∙] [2.309+0.089∙, 2.188+0.108∙] [1.565+0.060∙, 1.418+0.070∙] [1.513+0.058∙, 1.398+0.069∙] [1.467+0.056∙, 1.333+0.066∙] [2.822+0.109∙, 2.641+0.130∙] [2.745+0.106∙, 2.515+0.124∙] [3.232+0.124∙, 3.043+0.150∙] [2.437+0.094∙, 2.314+0.114∙] [2.514+0.097∙, 2.414+0.119∙] [2.385+0.092∙, 2.289+0.113∙]

t=2 [98.581+1.024∙, 168.827+1.375∙] [221.807+10.946∙, 313.529+12.059∙] [229.20+11.311∙, 326.593+12.561∙] [332.711+16.419∙, 473.559+18.214∙] [325.317+16.055∙, 460.495+17.711∙] [337.639+16.663∙, 480.091+18.465∙] [2.466+0.095∙, 2.151+0.106∙] [2.382+0.092∙, 2.10+0.104∙] [2.355+0.091∙, 2.074+0.102∙] [2.493+0.096∙, 2.228+0.110∙] [1.690+0.065∙, 1.444+0.071∙] [1.634+0.063∙, 1.424+0.070∙] [1.585+0.061∙, 1.357+0.067∙] [3.047+0.117∙, 2.689+0.133∙] [2.964+0.114∙, 2.561+0.126∙] [3.491+0.134∙, 3.098+0.153∙] [2.632+0.101∙, 2.356+0.116∙] [2.715+0.104∙, 2.458+0.121∙] [2.576+0.099∙, 2.330+0.115∙]

t=3 [100.336+1.043∙, 183.421+1.485∙] [225.823+11.145∙, 338.626+13.024∙] [233.351+11.516∙, 352.735+13.567∙] [338.736+16.717∙, 511.465+19.672∙] [331.208+16.345∙, 497.356+19.129∙] [343.753+16.964∙, 518.521+19.943∙] [2.663+0.102∙, 2.190+0.108∙] [2.573+0.099∙, 2.138+0.105∙] [2.543+0.098∙, 2.112+0.104∙] [2.693+0.104∙, 2.268+0.112∙] [1.825+0.070∙, 1.470+0.073∙] [1.765+0.068∙, 1.449+0.072∙] [1.711+0.066∙, 1.382+0.068∙] [3.291+0.127∙, 2.737+0.135∙] [3.202+0.123∙, 2.607+0.129∙] [3.770+0.145∙, 3.154+0.156∙] [2.842+0.109∙, 2.398+0.118∙] [2.932+0.113∙, 2.503+0.124∙] [2.783+0.107∙, 2.372+0.117∙]

Note:   €tireis the price of a new truck tire.

The inventory holding costs for used tires piled in storages of the tire retreading plants are presented in Table S7. Table S7 Inventory holding costs (€/tonne∙day). Planning period t=1 [0.046+0.0011∙, 0.118+0.0021∙]

t=2 [0.047+0.0011∙, 0.127+0.0023∙]

t=3 [0.048+0.0011∙, 0.138+0.0025∙]

Note:   €tireis the price of a new truck tire.

35

The transportation costs of reusable, retreaded and EoL tires from tire retreading plants 1, 2 and 3 to destination entities are provided in Table S8, Table S9 and Table S10, respectively. Table S8 Transportation costs in the case of tire retreading plant 1 (€/tonne). Destination entity Dealer 1 of used tires Dealer 2 of used tires Dealer 1 of retreated tires Dealer 2 of retreated tires Dealer 3 of retreated tires Dealer 1 of end-of-life tires Dealer 2 of end-of-life tires Tire recycling plant 1 Tire recycling plant 2 Cement kiln 1 Cement kiln 2 Cement kiln 3 Site 1 for end-of-life tires appl. as embankment stabilizers Site 2 for end-of-life tires appl. as embankment stabilizers Site for end-of-life tires appl. as dock fenders Site 1 for end-of-life tires appl. as erosion barriers Site 2 for end-of-life tires appl. as erosion barriers Site 3 for end-of-life tires appl. as erosion barriers

Planning period t=1 [2.541+0.654∙δ+0.024∙ρ, 2.890+1.012∙δ+0.038∙ρ] [15.880+4.079∙δ+0.148∙ρ, 18.057+6.314∙δ+0.237∙ρ] [9.836+2.522∙δ+0.091∙ρ, 11.183+3.904∙δ+0.146∙ρ] [11.768+3.021∙δ+0.109∙ρ, 13.380+4.675∙δ+0.175∙ρ] [22.334+5.730∙δ+0.208∙ρ, 25.395+8.868∙δ+0.332∙ρ] [3.157+0.810∙δ+0.029∙ρ, 3.589+1.253∙δ+0.047∙ρ] [10.573+2.709∙δ+0.098∙ρ, 12.021+4.193∙δ+0.157∙ρ] [5.337+1.370∙δ+0.050∙ρ, 6.069+2.121∙δ+0.079∙ρ] [18.431+4.733∙δ+0.172∙ρ, 20.958+7.326∙δ+0.274∙ρ] [2.745+0.701∙δ+0.025∙ρ, 3.120+1.085∙δ+0.041∙ρ] [14.929+3.830∙δ+0.139∙ρ, 16.975+5.928∙δ+0.222∙ρ] [25.873+6.633∙δ+0.240∙ρ, 29.417+10.266∙δ+0.385∙ρ] [5.835+1.495∙δ+0.054∙ρ, 6.634+2.314∙δ+0.087∙ρ] [14.446+3.706∙δ+0.134∙ρ, 16.425+5.736∙δ+0.215∙ρ] [21.675+5.558∙δ+0.201∙ρ, 24.644+8.603∙δ+0.322∙ρ] [5.337+1.370∙δ+0.050∙ρ, 6.069+2.121∙δ+0.079∙ρ] [13.713+3.519∙δ+0.128∙ρ, 15.593+5.446∙δ+0.204∙ρ] [27.209+6.975∙δ+0.253∙ρ, 30.937+10.797∙δ+0.404∙ρ]

t=2 [2.497+0.647∙δ+0.024∙ρ, 3.006+1.052∙δ+0.040∙ρ] [15.611+4.038∙δ+0.147∙ρ, 18.779+6.567∙δ+0.246∙ρ] [9.674+2.497∙δ+0.090∙ρ, 11.630+4.060∙δ+0.152∙ρ] [11.569+2.991∙δ+0.108∙ρ, 13.915+4.862∙δ+0.182∙ρ] [21.965+5.673∙δ+0.206∙ρ, 26.411+9.223∙δ+0.345∙ρ] [3.094+0.802∙δ+0.029∙ρ, 3.733+1.303∙δ+0.049∙ρ] [10.392+2.682∙δ+0.097∙ρ, 12.502+4.361∙δ+0.163∙ρ] [5.239+1.356∙δ+0.050∙ρ, 6.312+2.206∙δ+0.082∙ρ] [18.144+4.686∙δ+0.170∙ρ, 21.796+7.619∙δ+0.285∙ρ] [2.701+0.694∙δ+0.025∙ρ, 3.245+1.128∙δ+0.043∙ρ] [14.677+3.792∙δ+0.138∙ρ, 17.654+6.165∙δ+0.231∙ρ] [25.451+6.567∙δ+0.238∙ρ, 30.594+10.677∙δ+0.40∙ρ] [5.744+1.480∙δ+0.053∙ρ, 6.899+2.407∙δ+0.090∙ρ] [14.204+3.669∙δ+0.133∙ρ, 17.082+5.965∙δ+0.224∙ρ] [21.315+5.502∙δ+0.199∙ρ, 25.630+8.947∙δ+0.335∙ρ] [5.239+1.356∙δ+0.050∙ρ, 6.312+2.206∙δ+0.082∙ρ] [13.489+3.484∙δ+0.127∙ρ, 16.217+5.664∙δ+0.212∙ρ] [26.768+6.905∙δ+0.250∙ρ, 32.174+11.229∙δ+0.420∙ρ]

t=3 [2.475+0.634∙δ+0.023∙ρ, 3.150+1.103∙δ+0.041∙ρ] [15.409+3.957∙δ+0.144∙ρ, 19.682+6.882∙δ+0.258∙ρ] [9.56+2.446∙δ+0.088∙ρ, 12.189+4.255∙δ+0.159∙ρ] [11.424+2.930∙δ+0.106∙ρ, 14.584+5.096∙δ+0.191∙ρ] [21.688+5.558∙δ+0.202∙ρ, 27.681+9.666∙δ+0.362∙ρ] [3.063+0.786∙δ+0.028∙ρ, 3.912+1.366∙δ+0.051∙ρ] [10.261+2.628∙δ+0.095∙ρ, 13.103+4.570∙δ+0.171∙ρ] [5.178+1.329∙δ+0.049∙ρ, 6.615+2.312∙δ+0.086∙ρ] [17.903+4.591∙δ+0.167∙ρ, 22.844+7.985∙δ+0.299∙ρ] [2.679+0.680∙δ+0.024∙ρ, 3.401+1.183∙δ+0.045∙ρ] [14.492+3.715∙δ+0.135∙ρ, 18.503+6.462∙δ+0.242∙ρ] [25.126+6.434∙δ+0.233∙ρ, 32.065+11.190∙δ+0.420∙ρ] [5.676+1.450∙δ+0.052∙ρ, 7.231+2.522∙δ+0.095∙ρ] [14.026+3.595∙δ+0.130∙ρ, 17.903+6.252∙δ+0.234∙ρ] [21.055+5.391∙δ+0.195∙ρ, 26.862+9.377∙δ+0.351∙ρ] [5.178+1.329∙δ+0.049∙ρ, 6.615+2.312∙δ+0.086∙ρ] [13.319+3.413∙δ+0.124∙ρ, 16.996+5.936∙δ+0.222∙ρ] [26.428+6.766∙δ+0.245∙ρ, 33.721+11.769∙δ+0.440∙ρ]

Note:   €lis the gas price (Europe’s Energy Portal, 2016);   €h is the labor cost in the transportation sector (Eurostat, 2016b).

36

Table S9 Transportation costs in the case of tire retreading plant 2 (€/tonne). Destination entity Dealer 1 of used tires Dealer 2 of used tires Dealer 1 of retreated tires Dealer 2 of retreated tires Dealer 3 of retreated tires Dealer 1 of end-of-life tires Dealer 2 of end-of-life tires Tire recycling plant 1 Tire recycling plant 2 Cement kiln 1 Cement kiln 2 Cement kiln 3 Site 1 for end-of-life tires appl. as embankment stabilizers Site 2 for end-of-life tires appl. as embankment stabilizers Site for end-of-life tires appl. as dock fenders Site 1 for end-of-life tires appl. as erosion barriers Site 2 for end-of-life tires appl. as erosion barriers Site 3 for end-of-life tires appl. as erosion barriers

Planning period t=1 [11.848+3.036∙δ+0.110∙ρ, 13.471+4.699∙δ+0.176∙ρ] [3.039+0.779∙δ+0.028∙ρ, 3.455+1.205∙δ+0.045∙ρ] [10.690+2.740∙δ+0.099∙ρ, 12.154+4.241∙δ+0.159∙ρ] [5.337+1.370∙δ+0.050∙ρ, 6.069+2.121∙δ+0.079∙ρ] [12.515+3.207∙δ+0.116∙ρ, 14.229+4.964∙δ+0.186∙ρ] [16.636+4.266∙δ+0.155∙ρ, 18.916+6.603∙δ+0.247∙ρ] [3.258+0.841∙δ+0.031∙ρ, 3.706+1.301∙δ+0.049∙ρ] [9.240+2.367∙δ+0.086∙ρ, 10.506+3.663∙δ+0.137∙ρ] [8.738+2.242∙δ+0.081∙ρ, 9.935+3.470∙δ+0.130∙ρ] [14.095+3.612∙δ+0.131∙ρ, 16.026+5.591∙δ+0.209∙ρ] [10.328+2.647∙δ+0.096∙ρ, 11.743+4.097∙δ+0.153∙ρ] [12.515+3.207∙δ+0.116∙ρ, 14.229+4.964∙δ+0.186∙ρ] [12.515+3.207∙δ+0.116∙ρ, 14.229+4.964∙δ+0.186∙ρ] [4.128+1.059∙δ+0.038∙ρ, 4.693+1.639∙δ+0.061∙ρ] [8.976+2.304∙δ+0.084∙ρ, 10.207+3.567∙δ+0.134∙ρ] [11.457+2.943∙δ+0.107∙ρ, 13.028+4.555∙δ+0.171∙ρ] [2.424+0.623∙δ+0.023∙ρ, 2.757+0.964∙δ+0.036∙ρ] [16.097+4.126∙δ+0.150∙ρ, 18.303+6.386∙δ+0.239∙ρ]

t=2 [11.650+3.006∙δ+0.109∙ρ, 14.010+4.887∙δ+0.183∙ρ] [2.986+0.771∙δ+0.028∙ρ, 3.593+1.253∙δ+0.047∙ρ] [10.519+2.713∙δ+0.098∙ρ, 12.640+4.411∙δ+0.165∙ρ] [5.239+1.356∙δ+0.050∙ρ, 6.312+2.206∙δ+0.082∙ρ] [12.298+3.175∙δ+0.115∙ρ, 14.798+5.163∙δ+0.193∙ρ] [16.375+4.223∙δ+0.153∙ρ, 19.673+6.867∙δ+0.257∙ρ] [3.204+0.833∙δ+0.031∙ρ, 3.854+1.353∙δ+0.051∙ρ] [9.097+2.343∙δ+0.085∙ρ, 10.926+3.810∙δ+0.142∙ρ] [8.603+2.220∙δ+0.080∙ρ, 10.332+3.609∙δ+0.135∙ρ] [13.862+3.576∙δ+0.130∙ρ, 16.667+5.815∙δ+0.217∙ρ] [10.157+2.621∙δ+0.095∙ρ, 12.213+4.261∙δ+0.159∙ρ] [12.298+3.175∙δ+0.115∙ρ, 14.798+5.163∙δ+0.193∙ρ] [12.298+3.175∙δ+0.115∙ρ, 14.798+5.163∙δ+0.193∙ρ] [4.047+1.048∙δ+0.038∙ρ, 4.881+1.705∙δ+0.063∙ρ] [8.832+2.281∙δ+0.083∙ρ, 10.615+3.710∙δ+0.139∙ρ] [11.268+2.914∙δ+0.106∙ρ, 13.549+4.737∙δ+0.178∙ρ] [2.379+0.617∙δ+0.023∙ρ, 2.867+1.003∙δ+0.037∙ρ] [15.828+4.085∙δ+0.149∙ρ, 19.035+6.641∙δ+0.249∙ρ]

t=3 [11.505+2.945∙δ+0.107∙ρ, 14.683+5.122∙δ+0.192∙ρ] [2.955+0.756∙δ+0.027, 3.766+1.313∙δ+0.049∙ρ] [10.389+2.658∙δ+0.096∙ρ, 13.248+4.623∙δ+0.173∙ρ] [5.178+1.329∙δ+0.049∙ρ, 6.615+2.312∙δ+0.086∙ρ] [12.146+3.111∙δ+0.113∙ρ, 15.510+5.411∙δ+0.203∙ρ] [16.167+4.138∙δ+0.150∙ρ, 20.618+7.197∙δ+0.269∙ρ] [3.165+0.816∙δ+0.030∙ρ, 4.040+1.418∙δ+0.053∙ρ] [8.979+2.296∙δ+0.083∙ρ, 10.829+3.782∙δ+0.142∙ρ] [8.478+2.175∙δ+0.079∙ρ, 10.829+3.782∙δ+0.142∙ρ] [13.692+3.504∙δ+0.127∙ρ, 17.468+6.094∙δ+0.228∙ρ] [10.035+2.568∙δ+0.093∙ρ, 12.80+4.466∙δ+0.167∙ρ] [12.146+3.111∙δ+0.113∙ρ, 15.510+5.411∙δ+0.203∙ρ] [12.146+3.111∙δ+0.113∙ρ, 15.510+5.411∙δ+0.203∙ρ] [4.001+1.027∙δ+0.037∙ρ, 5.115+1.787∙δ+0.066∙ρ] [8.724+2.235∙δ+0.081∙ρ, 11.126+3.888∙δ+0.146∙ρ] [11.121+2.855∙δ+0.104∙ρ, 14.201+4.965∙δ+0.186∙ρ] 2.356+0.604∙δ+0.022∙ρ, 3.005+1.051∙δ+0.039∙ρ] [15.628+4.002∙δ+0.146∙ρ, 19.950+6.961∙δ+0.261∙ρ]

Note:   €lis the gas price (Europe’s Energy Portal, 2016);   €h is the labor cost in the transportation sector (Eurostat, 2016b).

37

Table S10 Transportation costs in the case of tire retreading plant 3 (€/tonne). Destination entity Dealer 1 of used tires Dealer 2 of used tires Dealer 1 of retreated tires Dealer 2 of retreated tires Dealer 3 of retreated tires Dealer 1 of end-of-life tires Dealer 2 of end-of-life tires Tire recycling plant 1 Tire recycling plant 2 Cement kiln 1 Cement kiln 2 Cement kiln 3 Site 1 for end-of-life tires appl. as embankment stabilizers Site 2 for end-of-life tires appl. as embankment stabilizers Site for end-of-life tires appl. as dock fenders Site 1 for end-of-life tires appl. as erosion barriers Site 2 for end-of-life tires appl. as erosion barriers Site 3 for end-of-life tires appl. as erosion barriers

Planning period t=1 [18.558+4.764∙δ+0.173∙ρ, 21.102+7.375∙δ+0.276∙ρ] [6.572+1.682∙δ+0.061∙ρ, 7.472+2.603∙δ+0.098∙ρ] [13.840+3.550∙δ+0.129∙ρ, 15.737+5.494∙δ+0.206∙ρ] [9.367+2.398∙δ+0.087∙ρ, 10.650+3.711∙δ+0.139∙ρ] [3.899+1.090∙δ+0.040∙ρ, 4.447+1.687∙δ+0.063∙ρ] [23.931+6.134∙δ+0.222∙ρ, 27.209+9.495∙δ+0.356∙ρ] [11.172+2.865∙δ+0.104∙ρ, 12.703+4.434∙δ+0.166∙ρ] [17.978+4.609∙δ+0.167∙ρ, 20.441+7.133∙δ+0.267∙ρ] [3.873+0.997∙δ+0.036∙ρ, 4.404+1.542∙δ+0.058∙ρ] [22.461+5.761∙δ+0.209∙ρ, 25.539+8.917∙δ+0.334∙ρ] [9.240+2.367∙δ+0.086∙ρ, 10.506+3.663∙δ+0.137∙ρ] [6.913+1.775∙δ+0.064∙ρ, 7.860+2.747∙δ+0.103∙ρ] [17.470+4.484∙δ+0.163∙ρ, 19.865+6.941∙δ+0.260∙ρ] [6.925+1.650∙δ+0.060∙ρ, 7.856+2.554∙δ+0.096∙ρ] [2.923+0.747∙δ+0.027∙ρ, 3.323+1.157∙δ+0.043∙ρ] [20.459+5.247∙δ+0.190∙ρ, 23.262+8.121∙δ+0.304∙ρ] [11.339+2.912∙δ+0.106∙ρ, 12.894+4.507∙δ+0.169∙ρ] [7.031+2.912∙δ+0.106∙ρ, 7.994+2.796∙δ+0.105∙ρ]

t=2 [18.262+4.716∙δ+0.171∙ρ, 21.946+7.670∙δ+0.287∙ρ] [6.462+1.665∙δ+0.060∙ρ, 7.771+2.707∙δ+0.102∙ρ] [13.607+3.515∙δ+0.128∙ρ, 16.366+5.714∙δ+0.214∙ρ] [9.214+2.374∙δ+0.086∙ρ, 11.076+3.859∙δ+0.145∙ρ] [3.828+1.079∙δ+0.040∙ρ, 4.625+1.754∙δ+0.066∙ρ] [23.536+6.073∙δ+0.220∙ρ, 28.297+9.875∙δ+0.370∙ρ] [10.993+2.836∙δ+0.103∙ρ, 13.211+4.611∙δ+0.173∙ρ] [17.690+4.563∙δ+0.165∙ρ, 21.259+7.418∙δ+0.278∙ρ] [3.802+0.987∙δ+0.036∙ρ, 4.580+1.604∙δ+0.060∙ρ] [22.093+5.703∙δ+0.207∙ρ, 26.561+9.274∙δ+0.347∙ρ] [9.097+2.343∙δ+0.085∙ρ, 10.926+3.810∙δ+0.142∙ρ] [6.805+1.757∙δ+0.063∙ρ, 8.174+2.857∙δ+0.107∙ρ] [17.191+4.439∙δ+0.161∙ρ, 20.660+7.219∙δ+0.270∙ρ] [6.825+1.634∙δ+0.059∙ρ, 8.170+2.656∙δ+0.10∙ρ] [2.869+0.740∙δ+0.027∙ρ, 3.456+1.203∙δ+0.045∙ρ] [20.126+5.195∙δ+0.188∙ρ, 24.192+8.446∙δ+0.316∙ρ] [11.150+2.883∙δ+0.105∙ρ, 13.410+4.687∙δ+0.176∙ρ] [6.922+1.788∙δ+0.064∙ρ, 8.314+2.908∙δ+0.109∙ρ]

t=3 [18.022+4.621∙δ+0.168∙ρ, 23.001+8.039∙δ+0.301∙ρ] [6.387+1.632∙δ+0.059∙ρ, 8.144+2.837∙δ+0.107∙ρ] [13.446+3.444∙δ+0.125∙ρ, 17.153+5.988∙δ+0.225∙ρ] [9.108+2.326∙δ+0.084∙ρ, 11.609+4.045∙δ+0.152∙ρ] [3.783+1.057∙δ+0.039∙ρ, 4.847+1.839∙δ+0.069∙ρ] [23.252+5.950∙δ+0.215∙ρ, 29.658+10.350∙δ+0.388∙ρ] [10.854+2.779∙δ+0.101∙ρ, 13.846+4.833∙δ+0.181∙ρ] [17.467+4.471∙δ+0.162∙ρ, 22.281+7.775∙δ+0.291∙ρ] [3.765+0.967∙δ+0.035∙ρ, 4.80+1.681∙δ+0.063∙ρ] [21.817+5.588∙δ+0.203∙ρ, 27.838+9.720∙δ+0.364∙ρ] [8.979+2.296∙δ+0.083∙ρ, 11.452+3.993∙δ+0.149∙ρ] [6.711+1.722∙δ+0.062∙ρ, 8.567+2.994∙δ+0.112∙ρ] [16.976+4.349∙δ+0.158∙ρ, 21.653+7.566∙δ+0.283∙ρ] [6.730+1.601∙δ+0.058∙ρ, 8.563+2.784∙δ+0.105∙ρ] [2.838+0.725∙δ+0.026∙ρ, 3.622+1.261∙δ+0.047∙ρ] [19.881+5.090∙δ+0.184∙ρ, 25.356+8.852∙δ+0.331∙ρ] [11.012+2.825∙δ+0.103∙ρ, 14.054+4.913∙δ+0.184∙ρ] [6.829+1.752∙δ+0.063∙ρ, 8.713+3.048∙δ+0.114∙ρ]

Note:   €lis the gas price (Europe’s Energy Portal, 2016);   €h is the labor cost in the transportation sector (Eurostat, 2016b).

Other modeling parameters are provided in Table S11. Table S11 Other modelling parameters. Description Planning horizon Working time of the tire retreading plants in the planning horizon Tire retreading fee in the first planning period Tire retreading fee in the second planning period Tire retreading fee in the third planning period Initial inventory weight Safety inventory level in tire retreading plant 1 Safety inventory level in tire retreading plant 2 Safety inventory level in tire retreading plant 3

Unit 3,285 daysa 23,400 hb [74.04, 169.29] €/tonne [75.38, 182.84] €/tonne [76.75, 197.48] €/tonne 0 [170.0, 340.0] tonnesc [432.0, 480.0] tonnesd [410.0, 620.0] tonnese

a

Nine-year planning horizon with three three-year plan periods. 10 hours per day, 5 days per week, 52 weeks per year. c The monthly processing capacity of tire retreading plant 1. b

38

d e

The monthly processing capacity of tire retreading plant 2. The monthly processing capacity of tire retreading plant 3.

References Europe’s Energy Portal, 2016. Historical energy price data. (accessed 20.02.17). Eurostat, 2016a. Electricity prices by type of user - industrial consumers (code: ten00117) (last update: 30th of May, 2016). (accessed 20.02.17). Eurostat, 2016b. Labour costs annual data – Nace rev. 2 (Transportation and storage; Total labour costs) (code: tps00173) (last update: 25th of January, 2016). (accessed 20.02.17). Eurostat, 2016c. Labour costs annual data – Nace rev. 2 (Water supply, sewerage, waste management and remediation activities; Total labour costs) (code: tps00173) (last update: 15th of April, 2016). (accessed 20.02.17).

39

Highlights

> IPSIP model for used tire management and planning under uncertainty is developed. > Flexible long-term purchasing, retreading, inventory and allocation plans are provided. > The model can handle real-life uncertainties expressed as functional and crisp intervals. > The model can address the dynamic complexity of the used tires management systems. > The model could be applicable across the tire retreading industry.

40