Sustainable multi-trip periodic redesign-routing model for municipal solid waste collection network: the case study of Tehran

Daily transportation of wastes due to its environmental, financial, and social aspects has been considered a challenging issue in developing countries’ municipal solid waste management systems. The location of transfer stations as intermediate nodes in municipal solid waste management network affects optimal collection frequency. A sustainable multi-period and multi-trip vehicle routing problem integrated with relocation models was developed to redesign the intermediate transfer stations and find optimal vehicle routes and the best collection frequency for each municipal solid waste generation point. Regarding the social aspects of a sustainable solid waste management system, an extended social life cycle assessment methodology for redesign and routing operations was developed based on the UNEP guidelines. The social life cycle assessment methodology evaluated the probable social effects of the system throughout the entire life cycle using an iterative policy. In this study, selected impact subcategories and inventory indicators for the routing and redesign system were utilized to quantify the system social score. Besides, the developed model was solved for different problem instances. The results indicated that system social score was affected by collection frequencies decisions, redesign policy, and the number of demand nodes. Furthermore, the model was applied to a real-world case study resulting in a total cost reduction of 66% that occurred by a 86% reduction in weekly traveled distance and a 12% decrease in routing social score.


Introduction
Currently, atmospheric CO 2 is about 412 ppm, increasing by 2 ppm per year (Hannan et al. 2018). Transportation, residential and commercial buildings, commercial and public services, agricultural and fishing sectors are considered among expanding sources of CO 2 generation during 1990-2017 (Rüstemoğlu 2021). Also, power generation and transport together accounted for over two-thirds of total CO 2 emissions in 2019. After electricity and heat emissions allocation to target sectors, transport sector emissions equal 27% of the global CO 2 emissions in 2019 (IEA 2021). Besides, 5% of the global GHG emissions refereed to the perishable part of solid waste (Edalatpour et al. 2018). Daily transportation for collecting MSW is one of the major parts of developing countries' MSWMS. As there are many limitations in these countries, including inadequate financial resources, any stages of the MSW management process should be done as efficiently as possible. From the increasing atmospheric CO 2 viewpoint and optimizing the MSW collection process in these countries, investigation on the transportation section is critical. Investigation of MSW management systems centers on the study of isolated impacts, considering social and environmental impacts could present an inclusive framework for waste management systems (Medina-Mijangos et al. 2021). In the Brundtland Report, sustainability is defined as the capability to know the requirements of today without bargaining the capability of future generations to know their requirements. To refer to the sustainable systems, three aspects of sustainability-economic, environmental, and social-need to be studied (Ameli et al. 2019).
MSWM involves several strategic, tactical, and operational decisions. Simultaneously addressing two or three groups of them will increase the accuracy of resultant decisions. Making an efficient MSWM policy may raise many challenging questions: What is the best policy for redesigning an existing ITrS in MSWMS? What is the optimum allocation pattern for waste generation points to the ITrSs? What is the best collection frequency for generation points in a certain period? What is the best route for each vehicle? How to minimize costs for the presented structure? How to attain a sustainable MSWMS? A sustainable MSWM network has been introduced to address the questions. Besides, to achieve an optimal solution concerning three dimensions of sustainability, a MILP problem was presented.

Literature review
This section provides brief literature on relocation, sustainability, and variants of VRP, LRP, multi-trip, and multiperiod vehicle routing problems, which are essential for making MSWMS' routing decisions. Decisions are categorized into two leading groups: strategic/tactical and operational decisions. Redesign/relocation optimization literature in MSWM is devoid of any in-depth research. Regarding redesign/relocation in other logistic networks, restructuring a warehouse network could result in an annual saving of 5-10% of total logistics costs (Ballou 2007). The consolidation of strategic and tactical decision levels could arrange LRP (Prodhon 2011) for MSW (Asefi and Lim 2017;Asefi et al. 2015;Asefi et al. 2019;Erfani et al. 2017;Farrokhi-Asl et al. 2017;Rabbani et al. 2017).
Location-inventory-routing problem is utilized to formulate automotive industry supply chains considering strategic and operational decisions and environmental issues (Tavana et al. 2021). The redesign of the distribution network of an actual electronics company was examined by formulating a MILP for three-echelon multi-commodity of LRP (Sanghatawatana et al. 2019).
MSWM model with the capability of detecting the optimal locations of MSWMS facilities consisting of ITrSs, treatment, recycling, and disposal centers and determining the optimum routing strategy was organized (Asefi et al. 2015). Bin location problem and CVRP using GIS were solved for a real case to reduce daily collection tours and reached a suboptimal solution (Erfani et al. 2017). The location of depots and disposal centers from possible points was decided for the waste collection problem by solving with metaheuristic algorithms . Choice of treatment facility potential locations and designing routes with multi-compartment vehicles assumption are reached by developing an NSGA-II metaheuristic (Rabbani et al. 2017).
In an uncertain environment, the total cost of chains and lost demands of production and distribution of perishable products in a green reverse supply chain network are minimized. The problem is designed for a green reverse supply chain network by considering the location-inventory-routing problem (Parast et al. 2021).
In many developing countries, there is a problem in collecting wastes where trucks are fully utilized only on certain days when demand is at its maximum level. At the same period, they are partially loaded on other days and would generate additional costs for operational collection stages (Ghiani et al. 2014).
In waste management papers, some research works examine the PVRP, extending the classical VRP that customers are serviced with different frequencies over a time horizon (Beltrami and Bodin 1974). A mathematical model for the infectious hospital waste collection problem was proposed through a two-phase PVRP (Shih and Chang 2001). The gathering of recycling paper strongboxes in the context of the period vehicle routing system was studied with a real case in Portugal (Baptista et al. 2002). An algorithm for a waste collection organization containing different sites in Viseu, Portugal, was developed (Matos and Oliveira 2004).
Recently, a MILP model for urban waste collection considering multi-trip VRP with time windows and SA algorithm for solving the model in small and medium sizes was developed (Babaee Tirkolaee et al. 2019).
The summary of the literature in Table 1 demonstrates that various kinds of optimization models in strategic, tactical, and operational issues have been developed in the field of MSWM. The reviewed studies did not concurrently reflect three dimensions of sustainability with strategic, tactical, and operational decisions in MSWM. It seems that there is a gap in MSWM literature about the absence of an optimization model for considering three dimensions of sustainability aggregated with three aspects of strategic, tactical, and operational issues in MSWM literature.
Here, a mathematical MILP model is developed to optimize the collection operations and network structures through solving an SMTP-reLRP for MSWMS.
The SMTP-reLRP minimizes economic and environmental costs subject to social and other adapted constraints. The proposed SMTP-reLRP simultaneously decides the customers, vehicles, and the trips of a vehicle that should be serviced each day of a specific time horizon with considering redesign decisions of ITrSs.
The significant research contributions are: • Introduction of a MILP optimization model to consider the strategic, tactical, and operational issues of MSWMSs simultaneously integrated with the sustainability concept • Extension of an S-LCA approach to focus on the social impact of the collection operation and network redesign • Using Tehran metropolitan city to validate the developed model • Developing a solution to the stated problems related to waste collection in Tehran

Problem definition and mathematical model
Graphical representation for MSW collection VRP is provided in Fig. 1a. The MSW collection process starts from ITrSs, vehicles' depots, and refuse collection (from customers) starts until the vehicle's capacity is full. The vehicles' destination will be its starting point (ITrS), referred to as a "trip." In classic VRP, it is assumed that each vehicle only makes one trip, but this is not possible due to the shortage of vehicles. For this reason, a sequence of trips must be performed by each vehicle called a "journey." The network consists of two echelons with two different main fleets, small and lightweight vehicles for the first part and heavyweight semitrailers for the second part. The lightweight vehicles and heavyweight semitrailers are called vehicles and semitrailers, respectively. In the first echelon, "transportation" costs for waste collection are considered. In contrast, only waste "transferring" costs are addressed in the second echelon. An example of the SMTP-reLRP solution is given in Fig. 1b. Cooperating municipal solid waste collection demonstrated in Fig. 1c is considered the next generation of the MSW collection networks. The IMC concept is introduced to gain the advantages of economies in scale-related costs and service-related transaction cost in MSWMS, which incorporate small and large municipalities, including private segment businesses or higher-level government (Sarra et al. 2020). The authors explored the IMC concept in the service provision sector for different purposes, namely discovering the optimal element for IMC for the case of waste collection services (Sarra et al. 2020), effects of IMC on costs (Bel and Sebő 2021), drivers of cooperation and effect of IMC on public service cost or spending (Bel and Warner 2016), and efficiency gains of IMC (Allers and De Greef 2018). The presented network demonstrates the possible joint operations between local governments, municipalities, or other relevant agencies in the MSWM network. Several empirical studies investigated the characteristics of a joint operation in MSWM in various countries to exploit the economy of scale and minimize service transaction costs (Ferraresi et al. 2018;Soukopová et al. 2017). The IMC concept in the SMTP-reLRP model can be considered the next generation of MSWM network design.

Routing and redesign social scores
Social life cycle assessment frameworks evaluate the probable social effects of products and services throughout their entire life cycle. It is an iterative methodology, which signifies the enhancement of the assessment through valuation loops. Typically, the methodology contains six steps as follows: 1. Identify the question(s) to be replied to by the S-LCA. The answers identify the goals, stakeholders, processes, system boundaries, and type of impact assessment method. 2. Collect inventory data 3. Turn gathered information into social effects 4. Interpret findings and suggest hotspots and areas for improvement 5. Communicate results 6. Consider limitations and future research The S-LCA framework could monitor possible impacts on different categories of stakeholders. Social impacts are Fig. 1 a) Graphical representation for the current MSW collection problem, b) an illustration of the SMTP-reLRP solution in a week, c) the proposed inter-municipal cooperation categorized by stakeholder types to ensure the framework's comprehensiveness. The socially significant characteristics of the stakeholders are addressed in terms of impact subcategories. These subcategories are evaluated via impact indicators. Several indicators may be utilized to evaluate each subcategory (UNEP 2020).
For social impact assessment of redesign and routing operations in the proposed model, guidelines for social life cycle assessment of products and organizations of UNEP (UNEP 2020) are adopted with some modifications. The proposed S-LCA approach description is shown in Fig. 2. The developed S-LCA approach contains four key stages: Clear goal and scope, Study and investigation of life cycle inventory, Evaluation of life cycle impact, and Interpretation of life cycle.
The first step is to assess the social scores of the routing and redesign system. The scope is MSW collection network processes from demand nodes to ITrSs and the ITrSs to treatment, recycling, and disposal facilities.
Inventory indicators of all system flows are defined to reach the goal stated in the first step, and its target is data collection for all unit processes. The second step contains: 1. Detecting the information to be ranked for collection 2. Gathering information for hotspot valuation for processes included in goal and scope section 3. Gathering information for the nominated stakeholders and subcategories 4. Gathering corresponding information for the impact assessment 5. Gathering prime and general information for unit procedures and activity variables 6. Gathering information for scoring Information gathering about the activity variable is vital, should be ranged via the output of every related process, and exposes the portion of a particular activity related with an element of the process. Worker-hours and added value are the most commonly used activity variables. Worker-hours indicate the total time required accomplishing a unit process, and value-added refers to the total added value produced in every process. It should be noted that social hotspots are unit processes that could reflect a problem, a hazard, or a chance where a situation occurs (UNEP 2020).
The third step calculates the routing and redesign section's social score using a characterization model based on a scoring system. The guidelines for social life cycle assessment of products and organizations of UNEP (UNEP 2020) include five stakeholder groups and further 31 assessment subcategories introduced through international consensus and presented to the experts, including managers, engineers, workers, consumers, and local communities. The goal and scope are clarified according to their attitudes and impact subcategories selected by stakeholders and experts who have more influence on stakeholders. Table 2 presents the routing and redesign section, respectively. Twenty-one and 16 inventory indicators are developed for the routing and redesign section, respectively, to obtain the facilities' scores (see Table 2).
There are inventory indicators and measurement guidelines for each subcategory to assess life cycle impacts. The scoring system assigns a value of {1, 2. …, m i } for inventory indicator i for fulfillment degree of the social criteria, respectively, lowest to highest. Response provided by the stakeholder questioned concerning fulfillment will be changed into these quantities. The number of all the interviewed stakeholders is n. By considering that s ij is the Fig. 2 Developed S-LCA process for calculating the routing and redesign system social score selected score of stakeholder j to indicator i indicators average scores can be determined by Eq. (1): The social score for indicator i ( s i ) will be a decimal number between 0 and 1. For calculating the final social score of routing, it is necessary to normalize all average scores of 21 indicators as presented in Eq. (2): The α i coefficients show the importance weight of indicator i, and their summation equals one. In addition, the selected impact subcategories and 16 developed inventory indicators for the redesigned system are presented in Table 2. Similarly, redesign social score is calculated. Social inventory indicators are defined as variables that provide the (1) status of a specific process and are true representations of the social condition of routing and redesign system boundaries. The methodological sheets are the tools providing a comprehensive overview of such indicators. These sheets are meant to inspire S-LCA case studies based on the guidelines rather than to present a complete set of indicators. In addition, the S-LCA databases are a helpful source of indicators for which general information is obtainable. Here, the GaBi LCWE database has been used. Besides, in this study, in order to identify relevant indicators, core groupings through a collection of different players were used.
Life cycle interpretation is the last step and indicates that the routing system has higher positive social impacts than the redesigned system.

Problem assumptions and formulation
Problem assumptions are as follows: Customer's demand for waste collection is deterministic and known. A potential location for establishing new ITrS or aggregation with Cost minimization (COST) as the objective function is demonstrated in Eq. (4) and consists of two parts to tackle two dimensions of sustainability.
TPCOST or the routing cost is calculated based on the distance matrix, as Eq. (6).
TFCOST is waste transferring costs between ITrSs and treatment, recycling, and disposal facilities, as shown in Eq. (7). The coefficient is referred to as returning cost from treatment, recycling disposal facilities to ITrSs when the semitrailers are empty.
RCOST is specified by Eq. (8). The equation denotes the cost for relocating an existing ITrS to a new or another existing ITrS.
MCOST is fixed maintenance costs of a new or an existing ITrS, including insurance, taxes, and rent costs, as described in Eq. (9).
SCOST is cost savings resulting from the closure of existing ITrSs, or merging surplus ITrSs as Eq.
(10). The ITrSs closure policy usually causes a significant saving for firms. For the waste collection companies, the total costs which could be saved by ITrSs closure are classified into two main categories: • Fixed cost • Variable cost: capacity cost and the revenue from the sale of assets raised per unit of capacity, for example, conveyor line equipment.
FVCOST is the fixed cost of vehicles paid to the contractors, as shown in Eq. (11).
(4) Minimize COST = ECOCOST + ENVCOST Environmental costs produced by waste transportation by vehicles and waste transferring by semitrailers are considered in the ENVCOST equation. As shown in Eq. (12), it consists of three parts. Transportation and transferring wastes could result in GHG emissions. GHG emissions related to the collection routes and the second echelon of the network produced by semitrailers are measured through ENVCOST. The environmental cost of emission m through the collection phase is calculated by the first term in Eq. (12). Moreover, the second term calculates the environmental cost of emission m from waste transportation by semitrailers when traveling FTL. The last term is the environmental cost of emission m when the semitrailers are empty during their trip back to the ITrSs.

Constraints
The constraints are divided into four main components: generation nodes, vehicles, tours, and ITrSs. In the following, the connection among the components is provided:

Generation node's constraints
Constraints (13) ensure that every generation node is served at least once in a given period.
In contrast, Constraints (14) emphasize that every generation node must be served at most once each day of a specific period.
Constraints (15) consider the relation between x krt ij and y krt j variables.
Constraints (16) ensure the flow conservation for the generation node and ITrS.
Constraints (17) indicate that the demands are met during the planned period.

ITrSs constraints
Constraints (20) and (21) ensure that the inlet flow to each ITrS (total daily waste collected) and the outlet flow to the ITrSs (to processing plants) must be equal.
Constraints (22) Constraints (26) and (27) denote that it must be preestablished before allocating the vehicles to any ITrSs.
Constraints (28) and (29) indicate the number of vehicles allocated to ITrSs and the total number of existing vehicles.

Tours constraints
Constraints (30) are sub tour elimination constraints.

The connection among vehicles and generation nodes constraints
After leaving the ITrS, each vehicle could only visit a generation node on its trip, and the return trip to the ITrS should be from a generation node addressed in Constraints (31) and (32).

The connection among vehicles, generation nodes, and ITrSs constraints
Similarly, Constraints (33) and (34) emphasize that before the collection operation commences, the origin of these flows must be established. Constraints (35) indicate that if the vehicle wishes to have a trip that serves more than one customer in the network, there is an edge connecting these two customers.
Finally, Constraints (36) considers network social sustainability in collection operation and network redesigning process. The lower bound of the network social score is calculated based on the sensitivity analysis method and consultant with the local governments and the responsible organizations for MSWMSs.
The value of the minimum acceptable social score of the network (∆) is the lower bound of the network social score and calculated based on the sensitivity analysis method with a consultant with the local governments and the responsible organizations for MSWMSs. The procedure estimation of ∆ parameter is as follows: Assume all participants choose the maximum value for all indicators in determining the social score of the routing and redesign sections. For different ∆ values, the problems were solved, and feasible solutions were recorded. The above mentioned procedure was repeated with a minimum value of routing and redesign sections. List the value of ∆ and determine the acceptable range ∆. Here, the list was called the technical list ∆ and was presented to the experts to select the system social score extreme point.

Constraints (37)-(44) include the binary and non-negative requirements for the variables.
In Constraints (18), (20), and Objective function, q jt is the demand of customer j on day t, which depends on whether or not the vehicles have been served to customer i in previous days. Every day that the customer is not served, the demand for the day will be aggregated, and the same customer's Then, the model will be nonlinear and must be linearized: Note Constraints (47) and ϕ jt ∈ N will be added to the main constraints. Constraints (30) is a classic sub tour elimination constraint for VRPs and greatly influence solving time. Here, a replaced formulation to overcome the limitations (Miller et al. 1960) is derived, and Equations (48), (49), and μ j ≥ 0 are added to the model.
It can be seen that Objective function and Constraints (18), (49), and (20) will be nonlinear. The following constraints must be considered in the model for the linearization.

Problem dimensional analysis
The presented formulation is the SMTP-reLRP model for waste management systems as a MILP formulation that contains continuous, binary, positive integer variables (45) and constraints. Table 3 compares solving time with input dimension for different problem instances.

Case study description
A real case study with Tehran, the capital of Iran, was used to represent the applicability of the SMTP-reLRP model. Tehran is located in the north of the country, has a 664 km 2 land area, and its population was estimated at 8.6 million, being the main cultured metropolitan area in the country (Khoshand et al. 2019). TWMO is responsible for collecting, separating, and processing MSW of all 22 districts, but the collection operation is outsourced to 58 contractors (TWMO 2019). The case is related to the contractor who collects the MSW of district 8, region 2, Haft Howz neighborhood, which discharges the collected MSW in Beyhaghi ITrS. Currently, the MSW collection of this area is carried out by two vehicles during the day. The main version of TMWO, approximate location of MSW containers, and the current collection route of the vehicles are shown in Fig. 3a, b, and c. Each vehicle performs some trips every day, and the patterns of routes in all trips are similar for each vehicle. The drivers repeat their trips at least twice in 24 h. The MSW container numbers in Fig. 3b indicate the order of visits, and Fig. 3c, d demonstrates current vehicle 1 and 2 route patterns implemented by the contractor, respectively. The number of MSW containers in the considered region was 69, with a maximum capacity of 55 kg. About the daily demand parameter in the SMTP-reLRP model, the data was derived from the weighing system located in Beyhaghi ITrS. By examining daily generated MSW in 2018, the average daily demands for the route of vehicles 1 and 2 were 664 kg and 456 kg, respectively.
As the containers were located in a region with the same geographical, historical, cultural, and economic characteristics, it was realistic to assume the daily route demands were equal. Therefore, the daily demands of MSW containers in the route of vehicles 1 and 2 were 40 kg and 41 kg, respectively. Both vehicles were similar and had 6 tons of capacity. Weekly fixed and variable costs were 148.79 UC or Unit Cost (Because contractors' costs were confidential, the exact unit was not provided) and 4.6* 10e-7 UC per meter and per kg, respectively (TWMO 2019). The maximum daily working time for them is 300 min.
NEOS solver for optimization was used (Czyzyk et al. 1998). Within the NEOS server, IBM ILOG CPLEX Optimizer was applied. For MILPs, CPLEX uses a branch and cut algorithm to solve a series of LP subproblems and obtain the exact solution for the problem (Rosenthal 2016).
For addressing the case into the network concepts and solve the problem, it is vital to define the nodes and arc of the MSWM network. Consider a network that constitutes nodes and arcs; if you define some nodes along the arcs, the network contains redundant nodes. Here, nodes along the arcs were considered as non-key nodes. For determining the key nodes, square adjacency matrix A [| customers| ] was utilized. In other word, the square adjacency matrix helps to detect the non-key nodes. As a result, the key nodes of the network could be found by deleting the non-key nodes from the network. It is a zero-one matrix with zeros on its diagonal since edges from a customer node to itself are not allowed. Other elements of A ij are one when there is just one choice for continuing the trip, which is an edge from customer node i to customer node j. It is usual to have just one choice for servicing other MSW containers from a fixed container in the streets. The adjacency matrix could help omit the MSW container nodes that do not determine the optimal route. For example, for the route of vehicle 1, as the container nodes, 1 to 12 are located in a one-way street; if node one is selected, then there is no other choice for completing the trip unless reaching node 12. The region's 26 key MSW container nodes are shown in Fig. 3e. Therefore, the daily demand for key MSW containers was achieved by aggregating the daily demand of non-key MSW containers to the nearest key MSW container.
Semitrailer capacities for transferring MSWs from ITrSs to the processing plants are 22 tons with 5.6*10e−7 UC variable cost per kilogram and meter. The candidate ITrS for considering the redesigning options is Banihashem ITrS. The saving cost of Beyhaghi ITrS closure was considered 7474 UC.
Aradkooh waste processing plant, the biggest one in Tehran, was considered a processing plant in the model and had For solving the problem presented in a real case study, some main parameters of the SMTP-reLRP model should be set. The case study's environmental and social parameters setting process is provided in the following sections, respectively.

Environmental parameters
Four major types of emissions, namely: CO 2 , SO 2 , NO x , and VOC, are the primarily related emissions that cause environmental costs. Transportation and transferring processes unit environmental cost and the emissions volume were considered based on recent researches (Hoang et al. 2019). As the MSW is transported and transferred by diesel-fueled trucks named vehicles and semitrailers, GHG emissions (kg/kg of MSW) are equal.

Social parameters
At first, the inventory indicators for the social score of routing and redesign operations were scored by 43 people, including employees of TWMO and contractors in charge of waste collection. Secondly, for routing and redesign operation, the summation of normalized weight is 0.6 and 0.4, respectively. Thirdly, the network minimum acceptable social score was chosen via sensitivity analysis. Considering   Fig. 3 a) MSW container's location map of Haft Howz neighborhood (TWMO 2019). b) Current approximate MSW container location. c, d) Daily route pattern by vehicles. e) 26 key MSW container nodes that all participants choose the worst and the best score for each indicator, the social score of the routing section will be equal to 0.25 and 1, respectively. It is the same for the social score of the redesigning. Considering economic and environmental function, Fig. 4a indicates the network minimum acceptable social score was between 0.0001 and 0.4; as for the other values, the solver has an infeasible solution. Here, ∆ parameter was considered 0.004 according to the questionnaire provided for the experts of TWMO and contractors in charge of the waste collection company.
Finally, regarding the social score for routing and relocation, Fig. 4a indicates that the diagram related to S scr , S scl = 1 has the most feasible solutions. In other words, the higher the scores provided by experts, the higher probability of finding the optimal solution. These values are S scr = 0.63 and S scl = 0.62 by considering the scores of employees of TWMO and contractors in charge of waste collection. Furthermore, estimation methods for the defined parameters of the model are presented in Table 4.

Results
The results of the solving model for the case study and generated experiments are provided in this section. For the above mentioned case study, Fig. 4b shows the graphical results of solving the SMTP-reLRP model. As the actual distances between ITrSs and demand nodes are long, the location of ITrSs was considered symbolically.
Daily trips of vehicles and tour duration for the optimal solution are provided in Table 5. The optimal solution indicates that vehicles should begin their trips from Beyhaghi, and vehicles 1 and 2 can cover all weekly requirements for waste collection with 3 and 2 trips, respectively.
The results show that there is no need to relocate Beyhaghi ITrS for the case of the first research question. For the Tehran case, TWMO is responsible for collecting, separating, and processing MSW of all 22 districts, but the collection operation is outsourced to 58 contractors. The results of solving the case are related to one of these contractors, and for this contractor, Beyhaghi is the best choice of being ITrS.
It seems that by considering some/all of these contractors or changing system boundaries and solving the problem from a general perspective, the relocation/redesign of Beyhaghi ITrS will not be unexpected. Moreover, in the current Tehran ITrSs' structure, there is no cooperative perspective between ITrSs as value chain actors. Cooperating municipal solid waste collection scheme demonstrated in Fig. 1c could change ITrSs' structure. In other words, if the ITrSs as value chain actors work with cooperation, the result of the relocation of them is expected. It could be considered as a direction for future researches.
Besides, the comparison of the annual capacity of the ITrSs and the average annual amount of Tehran MSW generation rate indicates that the redesign of ITrSs will be more probable. The average daily amount of Tehran MSW generation rate is about 9000 tons, which equals 328*e10+4 tons in a year (TWMO 2019). According to the annual capacity of an ITrS, which is 175*e10+4 tons, having 11 ITrSs is not cost-effective, and revision in Fig. 4 a) Acceptable range of ∆ parameter via economic and environmental function consideration. b) Optimal routing and redesign for the case study It should be noted the solution of the model is obtained with this assumption that only the revenues from the equipment sale were included in the saving cost from the closure of Beyhaghi ITrS (7474 UC). However, if the profit from the ITrS's estate sale was taken into account, this number will increase to 1257474 UC.
The second research question is about the allocation rule of waste generation points to the Beyhaghi ITrS. Compared to the existing MSW collection operation, the routing pattern switched from two dimensions for each vehicle. The first dimension is the number of generation nodes visited in a trip for the vehicles. The second dimension will be the number of trips assigned to each vehicle in a day.
The third research question was about the collection frequencies for the generation points. The results indicated that the optimum solution for any generation node was visiting and servicing them just once a week. For the other research questions about the best routes, Fig. 4b was shown, and as a result, cost minimization representation was investigated through solving the model with scenarios in which social and environmental considerations were ignored. In other words, to evaluate the impact of sustainability, the SMTP-reLRP model was compared with various models with different assumptions of sustainability concept in Table 6: I) only economic aspect of sustainability was considered, II) the economic and environmental aspects of sustainability were considered, III) the economic and social dimensions of sustainability were considered. Table 6 shows the evaluation between  -(22-21-20-19-18-17-16-15-14)(green)-12-11-10-9-8-7-6-5-4-3-2-1-23-22-21-20-19-18-17-16-15-14-  the primary outcomes of the SMTP-reLRP model and all customized models. In addition, the economic dimension of sustainability was considered in various considered models. The SMTP-reLRP and model (I) comparison implied that model (I) represented less COST and more minor social gains and implied that omitting the social limitations might decrease costs from the collection network. Model (I) and model (II) had the same solution for collecting MSW networks. As the environmental costs were considered in the model (II), its calculated cost was more than model (I).
Similarly, the SMTP-reLRP model and model (III) show that they provided the same solutions. For this case, the sustainability concept resulted in a sustainable solution with a higher social score and higher costs than the model's solution without considering the sustainability factors. Table 6 was presented to compare the result with the existing situation. The weekly cost function had decreased 2,348,916 UC, which equals 122,143,679 UC in a year. Cost saving of 66% was obtained via finding optimal weekly collection frequency and finding the best redesign. The objective function, the total traveled distance of the current status, and the weekly numbers of vehicles' trips were calculated with the current minimum collection frequency in 24 h. The maximum daily working hour was reduced from 24 to 5 h. Moreover, the number of working days was decreased from 7 days to 1 day. Table 6 indicated that the current collection operation suffers from inefficiencies in terms of cost objectives. Generally, it should be noted that Tehran municipality outsourced the collection operation to the contractors. There are many inefficient rules for controlling the contractors, which led to inefficient collection operations.

Computational results
To investigate the performance and the efficiency of the proposed SMTP-reLRP model, it was tested for several experiments with different customer sizes. The presented MILP was implemented and solved by GAMS (24.8.5). The experiments were run on a personal computer with Intel(R) Core(TM) i7-7500U, CPU @ 2.70GHz, 8G of RAM, and Windows 10.

Experimental data design
In this problem, several parameters were given as input data. The closure cost of the existing ITrS was considered 9474 UC. Fixed storage costs of the existing and candidate ITrSs were considered 7937 and 8030 UC, respectively. A waste processing plant was considered as the destination of the MSWs. The test problems included two vehicles and one semitrailer with a maximum capacity of 6 and 22 tons in the first and second echelon. Unit costs, fixed cost of overhead, and maximum daily working time of vehicles were similar to the real case. It was assumed that the maximum daily number of trips that a vehicle could travel is ten. The demands of the customer nodes were randomly generated in U (20,200). The traveling times between nodes were randomly generated in U(1, 7).
Similarly, the traveling times between ITrSs and the customers were randomly generated in U(15, 32). The customer nodes' demands and traveling times utilized in this study could be found in the Supplementary Information. The model was tested on three categories, small, medium, and large problems. These test problems were designed based on real-world conditions. For this reason, it was supposed that for each waste generation node (bins), a population of 100 people was applied. This assumption seems to be true as, on average, the population of the alleys or the section using the bins was 100 people. Therefore, a population of 100 people was considered for MSW generation nodes. The problems were solved first to investigate the feasibility of the solutions and then represent the computational applicability of the SMTP-reLRP model. In Table 7, the solutions, including the economic, environmental value of the objective function, social score, computational time and problem size, were reported. It should be noted that a run time limitation of 10,000 s was considered.
As shown in Table 7 and Fig. 5, the run time value increased significantly for increasing population and problem size because of the high complexity of the problem.

Sensitivity analysis
Intuitively, the system will visit more economical costs at the high value of relocation costs. The instance problem with 14 customers introduced in the previous section was conducted considering the change intervals of +30%, +40%, and +50% to investigate the sensitivity of the solution to different values of relocation cost parameter. Fig. 6a plots the total economical cost of the instance for different relocation costs. Besides, Fig. 6b represents the total environmental cost of the instance for different values of the total amount for CO 2 emission (considering the change intervals of +30%, +40%, and +50%) from MSW transportation by vehicles. This plot determines that the environmental cost function seems an increasing function of the CO 2 emission as input.

Discussion
The SMTP-reLRP model was solved for different problem instances with different demand nodes, and the results were represented in Fig. 7. The economic and environmental costs were an increasing function of the number of the demand nodes. The solution indicates that for 1, 2, 3, 4, and 5th problem instances, the vehicles tried to do collection operation using one day (as the objective function is to minimize the economic and environmental costs). The solution of the 6, 7, and 8th problem instances indicated that collection operation was carried out in multiple days. So the increasing rate of the social score was smoother than the previous days. On the other hand, the 9th instance problem's solution represents that both ITrSs were opened, and the redesign strategy improved the social score value. As a result, and for answering the paper's first and third key questions, the redesigning policy and collection frequencies were affected by the number of demand nodes.
For future research, various directions could be considered. At first, studying the environmental factors in different collection frequencies is suggested, e.g. the effect of collection frequency on attracting pests and leachate leakage. Secondly, limited data for testing the model resulted in challenging observations of potential model features, such as facility relocation. Solving the model for investigating the  Plot of the total environmental cost vs the total amount for CO 2 emission reduction possibility of ITrSs numbers in Tehran city is a direction for future research.
The cooperative perspective between ITrSs as value chain actors or IMC concept involved in the proposed model will be another direction for future researches. Moreover, an extension of the model in stochastic form to accommodate the demand uncertainty is suggested.

Conclusion
This research introduces the SMTP-reLRP model to consider three sustainability dimensions simultaneously with strategic, tactical, and operational issues in MSWMSs. Given the literature, this is the first study that considers economic, environmental, and social concerns for two main parts of MSWMSs named MSW collection and ITrSs redesign. The SMTP-reLRP develops multi-trip PVRP by considering redesign strategies for ITrSs regarding sustainability. Regarding the social aspect of sustainability, an extended social life cycle assessment methodology was developed for impact assessment of redesign and routing operations. A real case study was investigated to represent the SMTP-reLRP model applicability. For obtaining the exact solution of the problem, CPLEX optimizer was used. It has been described that for the real case, the proposed model can result in total cost reduction by 66% that occurred by 86% reduction in weekly traveled distance and a 12% decrease in routing social score.
Author contribution LM used a relatively broad conceptualization of municipal solid waste process effects on the environment and social segment. LM also developed the methodology of the research. LM and SM analyzed and interpreted the waste collection process data regarding collection nodes' locations, collection frequencies, and collected waste. SM also utilized data curation to ensure data quality and accuracy. LM wrote down the original draft document. MSS carried on effective research investigation, and all levels were performed under close supervision of SM. LM used the GAMS as a solution provider for the real problem and performed the validation process for the obtained results. SM and MSS reviewed the manuscript, and LM edited it according to their comments. All authors read and approved the final manuscript.
Availability of data and materials All data generated or analyzed during this study are included in this published article and its supplementary information files.

Declarations
Ethics approval and consent to participate Not applicable.

Consent for publication Not applicable.
Competing interests The authors declare no competing interests. Fig. 7 Comparison of the results of solving the problem instances in terms of environmental and economic costs and social score