Sewer Maintenance Decision-making Optimisation using the Can-order Policy

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using the Can-order Policy

Master’s Thesis

University of Groningen

Faculty of Economics and Business

MSc Technology & Operations Management

Author:

J.F. (Joost) Koomans van den Dries (S3826570)

Date:

22 June 2020

Supervisors: 1

st

_{N.D. van Foreest}

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Abstract

Present sewer maintenance decision-making process requires a fair amount of experience and expertise. A decision-maker must investigate and assess sewer conditions, define, and implement appropriate maintenance measures while taking multiple decisive factors into consideration. This dissertation explores the opportunity to optimise present sewer maintenance decision-making process by means of implementing the can-order policy. In other words, this dissertation’s goal has been to bring the concept of coordinated sewer maintenance in a network into prominence. Supporting data has been collected with a simulation model that simulates replacement of sewers and all associated costs. The results of this study show promising initial signs of successful implementation of the can-order policy in sewer maintenance. However, sewer maintenance based on the can-can-order policy is observed to be advantageous only when certain requirements are met. Given the novelty of this concept and the simplified implementation, refinement is required to establish support on sewer maintenance based on the can-order policy.

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Preface

Dear Reader,

In front of you lays the thesis titled ‘Sewer Maintenance Decision-making Optimisation Using the Can-order Policy’. This is a product as part of finalizing the Master program Technology and Operations Management (TOM) at the University of Groningen. First, I would like to thank Dr van Foreest for his time, effort, and guidance throughout this project and helping me to develop the model. Further, I would like to thank my friends and family for their support during the last couple of months, especially in these extraordinary times.

Kind regards,

J.F. Koomans van den Dries

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1. Introduction

In general sewers have a relative long theoretical life span, they are practically built to last roughly 60 years (Clemens & Langeveld, 2016). Despite the length of a sewer’s theoretical life span, it often occurs that sewers are written-off in advance of their theoretical lifespan. Since, sewer’s conditions deteriorate, be damaged or even collapse as a result of mechanical processes (e.g. wastage and damage), physical (e.g. water) processes or natural disasters (i.e. flooding and earthquakes) (Li et al., 2016). A recent example of such a failure has been a sewer break in Zwijndrecht (the Netherlands) as a result of the subsidence of the subsoil (Koster, 2020). So, this event has demonstrated how a malfunctioning sewer can result in unsolicited work on the sewer system. Fortunately, events of this scale do not happen often, but could it have been prevented by performing maintenance in time? Since, maintenance alleviates adverse effects of breakdowns, increase availability, increase performance and improve dependability at relative low cost (Simeu-Abazi & Sassine 2001). However, maintenance planning, especially in sewer systems, depends on decision-making. In other words, the ability to use information from a sewer system’s current condition to plan, select and execute an appropriate goal-directed maintenance action or set of actions (Causer & Ford, 2014). As when maintenance is not planned correctly, the costs or economic loss as a result of rehabilitation, replacement, malfunctioning, or non-availability due to structural failure and corrections, may run to several millions of euros a year (Diamantidis et al., 2016; Hillman Willis & Willis, 1995; Romanova et al., 2015). For this reason, there is a growing interest in the development of new technologies and progressive approaches to plan sewer maintenance.

Tsang (2002) emphasizes that the ability to optimize maintenance and maintenance decision-making depends on the availability of qualitative good and timely data. However, Tsang (2002, p. 33) also acknowledges that the use of data is “exacerbated in organisation with operations covering large geographical areas, such as public utilities, transportations and mining operations, building service suppliers”. Research has shown, in order to overcome this deficit, complex and costly online monitoring systems (e.g. usage of sensor networks) in sewers offers a solution to gather data. These systems have been developed in a way that they enable remote detection of events in order to evaluate real-time performance (Stoianov et al., 2007; Thiyagarajan et al., 2017). However, in practice implementation of these online monitoring systems are limited (Whittle et al., 2013).

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concept, i.e. “new technologies that demonstrate the feasibility of each proposed application”(Nair & Boulton, 2008, p. 761),which can be developed further through extensive testing and redesign. Given the nature of this research, this study seeks to obtain data which will help to bring the sewer maintenance based on the can-order policy into prominence. To achieve this, supporting data has been collected with a simulation model programmed with Python programming language. Briefly, the model simulates the deterioration and replacement of sewers in a fictious sewer system according to different scenarios. In other words, predefined experimental factors are randomly generated by the model and produced data is collected for further analysis.

Further, this study set out to investigate the usefulness of inventory control models to plan sewer maintenance. The importance and originality are that it explores less capital-intensive solutions, for example online sewer monitoring, and makes use of the current decision-making taxonomy and data collection methods. In addition, this work will generate fresh insights into how inventory control models can have a different practical usefulness. Finally, this study makes a novel contribution to current research practises on maintenance planning by demonstrating how an optimized and accessible method as the can-order policy can be used to improve current decision-making practises. At last, this dissertation has been organised in the following way. Chapter two begins by laying out the theoretical dimensions of the research and gives a brief overview of the current sewer maintenance decision-making process, the can-order policy, and the similarities between both. The third chapter is concerned with the methodology used for this study. The fourth chapter presents the findings of the research. The remaining chapter of the dissertation addresses the discussion and conclusion.

2. Sewer Maintenance Planning Policy

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In practise, sewers rarely are considered as single commodities. As a matter of fact, decision-makers (e.g. sewer engineers) consider sewers as part of a larger system. Therefore, maintenance is rarely planned for single sewer but for a group of multiple sewers or sewer sections, hereinafter identified as a ‘network’. In consequence, these networks comprise of an assortment of sewer objects (i.e. manholes, sewers, pump stations) each with a unique dimension, for instance length, material, diameter et cetera. As an illustration, Figure 2 shows a schematic overview of a possible network layout. This example entails a network consisting seven sewers and two manholes. However, this is not a reflection of reality, in practise a network might entail a larger number of interconnected sewers and manholes.

To return to the subject, due to the quantity and the varying dimensions in a network, maintenance is hard to plan and depends on the knowledge, skills, and experience of decision-makers. Their objective is to strike a balance between the cost and the gravity of proposed maintenance action. More precisely, strike a balance between the cost to perform maintenance and the technical life of the objects that have been obliged for maintenance. In other words, decision-makers rely on their expertise to optimise maintenance and its associated costs. So, decision-makers repeatedly make comparative assessments between when to perform what type of maintenance measure and against which costs. In practise they assess the coordination of sewer maintenance, that is whether any measures to improve the performance of the sewer system should be taken simultaneously or individually, on Joint fixed costs for preparation of maintenance (management costs) and an item-by-item fixed cost for each sewer to be maintained. More on the decision-making process has been described in section 2.1.

The coordination of sewer maintenance has similarities to ‘the coordinated multi-item inventory problem’, which refers to the problem regarding the coordination of replenishment orders for groups of items in a multi-item inventory system (Atkins & Iyogun, 1988), or better known as the joint replenishment problem. To put it in another way, the coordinated multi-item inventory problem makes a comparative assessment to choose whether items should be replenished individually or in a

Figure 1. Typology Sewer System

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group simultaneously and the costs involved, based on a joint fixed cost for the replenishment order plus an item-by-item fixed cost for each item included in the specified order. Section 2.2 elaborates more upon this phenomenon and how it can be dealt with by using the can-order policy. Eventually in section 2.3 an analogy is drawn with sewer maintenance decision-making process and the design and implementation of the can-order policy in the sewer maintenance has been discussed.

2.1. Sewer Maintenance Decision-making Process

In the Netherlands, municipalities are the organizational authorities which are responsible for managing a sewer system including its objects (i.e. sewers, manholes, pumping stations) located outside buildings in public areas as the performance of the sewer system as a whole. Their day-to-day operational activities comprises four basic activities: 1) carry out investigations, 2) perform assessments, 3) identify maintenance measures, and 4) authorize implementation of the identified maintenance measures. Furthermore, these activities are cyclical in nature, implying that they always recur in the same order.

In addition, the day-to-day operational activities can either be system-focused or object-focused. System-focused intends to change the overall performance of the outside sewer system, for example through modification of the object’s (e.g. sewer diameters) dimensions within the sewer system to assure sufficient drainage capacity. On the other hand, object-focused aims at changing the condition of an outside sewer system’s object. For instance, replace sewers whose service-life have been exceeded, with new identical sewers. However, to implement changes to improve either the system’s performance or the objects’ condition, one must go through a decision-making process (as displayed in Figure 3) in advance. Which have been elaborated upon in the following sections.

Investigations

First stage apprehends organization and realization of investigations. Investigations entail the process of “collecting, indexing, and processing of data to obtain information about the performance of the outside sewer system and the condition of the objects” (NLIngenieurs Sewer System Workgroup, 2009, p. 171). Investigations can either have a generic purpose, for instance to gather information to prepare a long-term strategic or a short-term operational planning, or a specific purpose. For example, as inspection upon completion of construction work to collect data regarding the condition of newly constructed objects. A commonly and often used method to obtain data is by means of periodically scheduled (visual) inspections performed by a crawler-mounted closed-circuit television (CCTV) camera. These visual inspections primarily focus on collecting data about the condition aspects of the various objects making up the sewer system. The results, observations of the condition (i.e. sewer collapses, breaks and blockages), are reported and evaluated according to standard classification

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systems (Carvalho et al., 2018), for example the NEN-EN 13508-2 standard for investigation and assessment of drain and sewer systems outside buildings. As illustration an example has been enclosed in Appendix 1.

Assessments

Second stage is the assessment which entails the determination and evaluation of anomalies between the observed and the required condition. The assessment of the performance and condition of the sewer system pass through five steps as displayed in Figure4. First, the required basic quality of the sewer system must be determined in advance. More precisely, the required basic quality is a specific and measurable description of the quality level of each object’s, in the system, condition according to a standard classification system. In other words, the required basic quality is the basic quality that is deemed as acceptable. However, depending on the determined quality level an object’s quality status might be marked as either ‘warning’ or ‘action’. In case of a warning status, the current condition is open to discussion, and further investigation is required. Whereas an action status states that the current condition does not meet the required quality and maintenance must be performed. Second, inspection data is consulted, if available. Otherwise, instructions are given to perform an inspection. Third, the condition of an outside sewer system is assessed by means of an anomaly analysis, which “provides insight about locations in the sewer system where a sewer’s condition does not meet the required basic quality” (NLIngenieurs Sewer System Workgroup, 2009, p. 184). In other words, the anomaly analysis compares data regarding the required basic quality and the inspection data. Fourth, after the anomaly analysis has been performed the observed anomalies including the local conditions (i.e. geometry of the object, local infrastructure, geohydrological situation, useful loads acting on the object, et cetera) as the nature, cause, severity, and extent of the shortcomings are logged and a provisional choice regarding the nature of the maintenance measure is formulated. Note that the nature of a measure (replacement, repair, renovation, maintenance) depends on the nature the damage and the extent to which the condition deviates from the required quality. At last, a priority is assigned. The priority of a measure is determined by the resulting risks if a measure is not implemented at all, or not implemented in time. Briefly, the purpose of assessment is to determine whether any maintenance measures are required, and if so, which measures. In other words, assessment entails when maintenance measures should be executed and identify the nature of these measures is.

Define Maintenance Measures

Third stage concerns the planning of where, when and what maintenance measure must be applied throughout the entire sewer system. Generally, four main measures are distinguished: 1) regular maintenance (or cleansing), 2) repair, 3) renovation, and 4) replacement. As stated in the previous section, the type of measure depends on the nature and the severity of the observed anomalies. For example, cleansing is required for the removal of undesired obstacles (e.g. roots and debris) and

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settled deposits. Whereas repair involves restoring the object locally to prolong the object’s service life. While renovation involves the extensive repair of an object so that it matches the new structure. At last, replacement involves the “removal or complete decommissioning of an existing object followed by the installation of an object with specifications matching those of the existing object” (NLIngenieurs Sewer System Workgroup, 2009, p.187). In the basics, each measure aims at improving an object’s condition to a certain extent. However, the effect of each measure on the object’s condition varies. As an illustration, Table 1 gives an overview of the qualitative effect per measure.

Activity Object Condition Effect System performance effect Maintenance Leave unchanged Restore original performance Repair Minor condition change Restore original performance Renovation Major condition change (as newly built) Restore original performance Replace Remove existing object, install new object Restore original performance Improve Not applicable Restore original performance

Table 1. Effect per activity on an object’s condition. Source: (NLIngenieurs Sewer System Workgroup, 2009)

Implementation of Maintenance Measures

Fourth stage is the implementation of the maintenance measures. As mentioned before the choice of when to perform what measure (i.e. cleaning, repair, renovation, and replacement) depends on the priority and the period in which the measures must be completed. However, the final choice depends on several other factors, from which the following three factors are most decisive (NLIngenieurs Sewer System Workgroup, 2009): 1) the construction costs relative to the expected technical service life, 2) the local conditions, and 3) whether any measures to improve the performance of the sewer system should be taken at the same time.

Considering the factors above, performing maintenance on single sewer section is from an economic as well as practical perspective unfavourable. As maintenance does not necessarily signify the importance if adjacent sewers in the system are in better condition and not obliged for maintenance. Therefore decision-makers need optimize or in other words strike a balance between relative construction cost and the gravity of maintenance. For example, consider the network in Figure 2, with one sewer obliged to maintenance, two sewers reach a level that maintenance must be performed in upcoming years and four sewers are in good condition. Decision-makers need to make a comparative assessment if maintenance is performed on one sewer only, on the whole sewer system simultaneously or check if it is more favourable to perform maintenance in a network structure (i.e. exclusive group of sewers). This problem appears to be similar to the joint replenishment problem in inventory management, which considers the comparative assessment between when to order a group of products simultaneously or order them individually (Mokhtari, 2018). The following section elaborates upon this subject.

2.2. Inventory Management Perspective

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inventory management engages in describing sets of “decisions, rules, guidelines and/or policies through which the inventory levels to be maintained are determined when stocks are to be replenished and the size by which orders are to be made”(Cevallos-torres & Botto-Tobar, 2019, p.125). In short, inventory management attempts to answer three key questions on an item-by-item basis (Silver, 1981):

1. How often should the inventory status be verified? In other words, what is the review interval? 2. When should a replenishment order be placed?

3. How large should the replenishment order be?

As a matter of fact, there are many ways to cope with managing inventories. For example, by usage of inventory management systems which constantly examine stock levels and product forecasts to decide whether new products should be (re-)ordered. In practise, many inventory management systems appeal on reorder policies (i.e. methods used to determine the way items are ordered) to determine the size of the order and when to place the order. Examples of these policies are the economic order quantity (EOQ), fixed reorder quantity (Q, r) model, or minimum-maximum (s, S) model. However, these models are not suitable for planning sewer maintenance as these policies primarily focus on single item inventory management systems. Since, as argued in section 2.1, sewer maintenance decision making has been contemplated a multi-inventory system problem, a policy that takes multiple items (i.e. items with unique characteristics) into account is required. One policy that has been extensively used in multi-item inventory systems is the can-order policy.

Can-order Policy

In a multi-item ordering process, the can-order policy has been extensively used to optimize ordering processes. Balintfy (1964, p. 292) describes the can-order policy with the following example; “whenever an order for a particular item must be issued, i.e., the stock of any item has dropped to the reorder level, the inventory level of the rest of the items will be checked, and all items which are in their reorder range shall be ordered jointly”. To put is differently, an item 𝑖 triggers a replenishment order when its inventory level is equal to or below a reorder point. As a result, the replenishment order increases inventory of item 𝑖 to the target level. However, the can-order policy states that inventory levels of other items 𝑗 are checked simultaneously and items that reached their can-order level will be included in the order as well, as one can see in Figure 5 (Melchiors, 2002; Ohno & Ishigaki, 2001; Pantumsinchai, 1992).

The previous paragraph implied that the can-order policy comprises of three key parameters: 1) the order-up-to level or target level (𝑆 ), 2) can-order level (𝑐 ), and 3) the reorder level (𝑠 ), which are controlled by the following control rule: 𝑠 ≤ 𝑐 < 𝑆 (Federgruen et al., 1984; Ohno & Ishigaki, 2001; Pantumsinchai, 1992). More precisely, the reorder level is the minimum inventory which triggers a replenishment order. Whereas, the can-order level is the minimum inventory level other products must have to be included in the

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target inventory level after the replenishment order arrived. In addition, from an economic perspective the can-order policy copes with a major joint fixed setup cost associated with the replenishment of the group of items in the order, independent of the order’s size or composition. Moreover, an additional item-by-item specific setup cost for each individual item included in the replenishment order as well (Atkins & Iyogun, 1988; Federgruen et al., 1984).

2.3. Sewer Maintenance planning based on Can-order policy

When comparing the sewer maintenance decision-making process with the three key questions the inventory management attempts to answer, various key similarities can be identified. First, the investigation stage relates to the frequency a sewers’ status (i.e. systems’ performance and object conditions) is checked by means of periodically executed inspections. Second, the assessment stage is strongly related to the second question. As discussed earlier, assessment concerns whether any maintenance measures are required, and if so, which measures and when these measures should take place. At last, definition of the maintenance measure stage relates to the size of the replenishment order. In other words, it concerns which sewer sections in the system requires maintenance. However, there is one major difference, inventories are managed according to so called ‘re-order’ policies and sewer maintenance is managed according to allocation of priorities based on sewer quality. So, the question arises how to align the can-order policy with current sewer maintenance decision-making process. To put is differently, how to design a sewer maintenance decision-making process based on the can-order policy?

Starting with assessing the parameters of both the can-order policy and the maintenance decision making process step-by-step. The first parameter is the deterioration (i.e. process in which the original quality and functionality of the material decreases or is dropped to a point where the sewer is useless) of a sewer’s condition in a network. As described earlier, by performing periodic assessments and investigations a time orientated deterioration process or deterioration rate is established. This process of condition deterioration is commensurable with the process of an inventory that decreases because of product sales over time. At a given point in time the sewer has deteriorated to a condition it is obliged to maintenance, the ‘re-order level’ (in case of an inventory). At this stage in the making process the can-order policy can be applied to optimize maintenance. Normally, a decision-maker fall back on his or her expertise to make a comparative assessment of all neighbouring sewers’ condition in a network. However, when implementing an artifact (e.g. model or algorithm) that incorporates a ‘can-order level’, the comparative assessment is quantified. So, the proposed implication of sewer maintenance based on the can-order policy is, that the decision-maker still decides which sewers in a network are maintained simultaneously or individually, but he or she defines the terms under which maintenance take place. The can-order parameters and the mutual relation have been summarized in Table 2.

Parameters Inventory management Sewer Maintenance (proposed) Decrease per time unit Inventory decrease Condition deterioration

𝑆 Order-up-to-level Maximum inventory level Maximum (or requisite) condition 𝑠 Re-order level Inventory level that triggers

replenishment order

Condition level that triggers maintenance measure

𝑐 Can-order level Check for grouped replenishment Check for grouped maintenance

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To summarize, optimizing decision-making is one of the most frequently stated problems with sewer maintenance. As described in section 2.2 it has been observed that decision-maker are bound by strict guidelines and that they rely on their expertise when planning sewer maintenance in networks. These approaches, however, have failed to address the importance of supportive methodologies as, for instance, the can-order policy. Therefore, the aim of this study is the design an artifact that create a proof of concept of can-order policy’s application in optimisation of sewer maintenance, such that decision-making (when maintenance is performed) can be simplified in order to lower the costs of and improve availability. Chapter three elaborated more about artifact’s implementation and design.

3. Methodology

Considering the nature of this research, the impracticability in a real system and yet to develop a feasible process, a simulation model has been developed. In the first section the model’s content has been described according to the scope, which refers to the breadth of the real sewer system that must be included in the simulation model. In other words, the scope can be thought of as what to model (Robinson, 2014). Next, the model’s components have been described according an input-process-output (IPO) structure. More precisely, it describes the information processing of the simulation model. The last section elaborates upon how the model has been used to produce data for further analysis.

3.1. Model Scope

As discussed earlier, in practise a sewer system consists of numerous interconnected sewers, manholes, pumping stations, et cetera, each with various dimensions dispersed over a large geographical area managed by municipalities. Given the real world’ scale of a sewer system it is difficult to develop a simulation model (i.e. a simplified imitation, on a computer, of the real-world problem) of an equivalent operations system. So, the scope of this research restricts to a simplified network with a layout as have been displayed in Figure 2. So, the simulation model used in this study contains two connected manholes, each with three possible spots (indicated with dotted lines) to branch off. Thus, this model can simulate a sewer system up to seven sewers in total. In addition, the model assumes that when maintenance is simulated, sewers are always connected. However, in practise a presumed sewer system might have a different layout, for example one where sewers are not interconnected but their location is sufficient to be part of the maintenance action (see Figure 6). Considering the novelty of the concept, this has been left out of consideration at this stage.

Further, as depicted earlier a real sewer system contains sewers each with different dimensions. For example, length, material (i.e. concrete, polyvinyl chloride (PVC), or clay ware), diameter et cetera.

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However, regarding the simplicity of the model it is assumed that each sewer in the fictious sewer system has the same dimensions. In this case, a sewer has a fixed length of seventy meters, a diameter of three hundred millimetres and are made of concrete. At last, the simulation only addresses the replacement maintenance measure. Since, at this stage less is known about sewer maintenance based on the can order policy and replacements attempts to be the easiest way to simulate. Because, the effect on a sewer’s condition is taken for granted since the condition improves from a minimum to a maximum. Whereas, in case of the other maintenance measures, the target level is open to question since the effects on the sewer’s condition are considerably less evident. However, this does not dispel that the can-order policy is applicable for the other maintenance measures as well. Basically, in the essence the approach is identical for every measure, a predefined minimum condition level 𝑠 triggers a maintenance measure and after it is performed the condition improves to a target level 𝑆 and the whole sequence repeats.

At last, to validate the effect of sewer replacement based on the can-order policy, two other replacement policies have been incorporated in the simulation as benchmark policies, 1) the single sewer replacement policy and 2) grouped replacement policy. Briefly, the single sewer replacement policy presumes that one sewer at the time is replaced when its condition drops below a predefined threshold. The grouped replacement policy, on the contrary, presumes the opposite. In this case, if one sewer is obliged to maintenance, all other sewers in the network are replaced as well, regardless of their current condition. Given the points discussed above the following sections will elaborate on the model’s components and how they have been designed and implemented in the simulation.

3.2. Model Inputs

This section discusses the model’s input parameters, in other words experimental factors, and how they have been designed and implemented in the simulation. According Robinson (2014) experimental factors are factors to which changes are most likely to yield the desired result. To put it differently, the experimental factors are the quantitative or qualitative model data that can be changed to achieve the modelling objectives (Robinson, 2008). This research intends to optimize sewer maintenance decision-making based on the can-order policy by means of altering the number of sewers in the network 𝑛, the replacement level 𝑠, and the can-replacement level 𝑐. In other words, it is by changing these input values the effects of maintenance based on the can-order policy are brought into prominence. So, it is by experimenting with these factors to get a better understanding of the real system. Therefore, it is useful to determine a range over which the values are to be varied, as Table 3 summarizes for this study. These three factors have been chosen as experimental factors because these are the decisive parameters of the can-order policy. Since, the number of sewers refer to the possible position in the simulated sewer system as described in section 3.1, the replacement level triggers when replacement will take place, and the can-replacement level triggers the assessment of neighbouring sewers.

Experimental Factor Range

Number of sewers in the Network (𝑛) 2, 3, 4, 5, 6, 7 sewers

Replacement level (𝑠) 5, 10, 15 % condition

Can-replacement level (𝑐) 20, 30, 40, 50, 60 % condition

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3.3. Model Process

In order to perform the simulation correctly three additional conditional factors have been designed and implemented in the simulation: 1) repair cost, 2) management cost, and 3) deterioration rates. Initially, repair costs are esteemed the cost related to the replacement of a single sewer. Basically, replacement entails key cost attributes regarding materials, groundwork (equipment included), removal and metalling of road-surfacing (equipment included) and measures regarding safety and accessibility of properties (RIONED, 2015c). It is hard to determine the actual costs for these attributes, so in this research key economic statistics for sewer replacements have been used (see Appendix 2). As an illustration, an example calculation has been given based on the assumptions as mentioned in the scope (see Table 4). Naturally, these figures can be adjusted at any desired moment. Management costs, on the contrary, are presumed the personnel costs regarding preparations (i.e. writing policies), investigations (i.e. perform surveys, inspections, measurements, and calculations), and general and technical support services (i.e. process revisions, issue permits, and handle complaints) for the entire sewer system. Briefly, management cost is cost related to the preparation intended for the realization of sewer replacement. The management cost is extremely hard to calculate because, in practise, it depends on the size of the sewer system a local authority has in administration. However, in order to determine realistic as possible figures, the management cost have been calculated by means of an example as described by the Dutch umbrella organisation for urban water management RIONED (RIONED, 2015a). Based on these figures the cost per sewer has been calculated, as displayed in Table 4. Eventually, with the price per sewer determined, the management cost for the simulated sewer system have been calculated.

Assumed sewer length 70 m1

Replacement Cost

Replacement cost Ø300 sewer 400 €/m1

Replacement manhole 800x800 34 €/m1

Property connection 49 €/m1

Gully connection 28 €/m1

35770 €/sewer

Administration Cost

Personnel required 1.4 Fte*

Labour cost 53.000 €/year

74.200 €/year

Renewal period 60 years

4.452.000 €/period Total Sewer length to manage 121.000 m1

Number of sewers in system 1729 pieces

2575 €/sewer/period *fte = full time equivalent

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Due to the lack of real data, it has been difficult to estimate a sewer’s exact condition and the deterioration rate. Hence, the determination of the condition and the deterioration builds upon two assumptions. First, the sewer’s condition has been expressed in terms of percentages. For example, if the condition of a sewer is equal to hundred percent the sewer is deemed new, whereas a sewer with the condition fifty is deemed to be halfway its theoretical life span. Second, the deterioration rate has been modelled regarding a Poisson distribution. The Poisson distribution is a discrete probability distribution, which applies to stochastic variables that count the occurrence of certain events during a given time interval, distance, area, or volume. In this case, the Poisson distribution has been determined so a sewer is replaced according its theoretical lifespan (i.e. approximately every 60 years). In addition, to simulate the deterioration process two preconditions must be met 1) a simulation horizon must be defined and 2) an initial condition must be determined, otherwise the model will not work appropriately. In the first place, the simulation horizon refers to the time of a simulation is run by the model. Additionally, the length of the simulation horizon depends on the warm-up, this is the “time from the start of a simulation run until the model represents the normal or balanced behaviour of the real system” (Schönemann, 2017, p. 153). To put it in another way, the simulation horizon should be long enough to ensure the model’s output data have settled into a steady state. In other words, it implies when running the simulation, the output generates approximately the same results (Robinson, 2014). For this reason, the model calculates with a simulation horizon of ten thousand years. At last, starting conditions a precondition for the simulation. Since, the simulation has been modelled in a way that the deterioration of a sewer needs an initial condition. The starting conditions for each sewer in the model are determined in advance of the simulation. The simulation, on the other hand, determines the deterioration of each sewer based on the Poisson distribution discussed in one of the sections above.

3.4. Model Outputs

The model’s response parameter is the yearly cost. That is nothing short than the total cost divided by the simulation horizon. The total cost refers to the sum of the repair cost plus the management cost regarding the frequency of replacements over the simulation horizon. However, the total cost is calculated differently for each maintenance policy. For example, the single replacement policy states that whenever a sewer’s condition has deteriorated to the replacement level, only the affected sewer is replaced without taking other sewers into account. So, every single time a sewer is replaced a fixed repair cost and management cost

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spectrum is grouped maintenance policy located. The grouped maintenance policy states that when one sewer’s condition has deteriorated to the replacement level, all sewers in the sewer system are be replaced at once. Thus, when maintenance is performed, the number of sewers in the sewer system are multiplied with their individual replacement cost and the management cost are paid once. At last, in case of the can-order replacement policy the total cost is calculated in the following way. Whenever maintenance is performed, the can-order policy checks how many sewers are obliged to maintenance. Based on the number of sewers included in the network, the replacement cost and the management cost are calculated. As an illustration, Figure 7 displays a schematic representation of the simulation processes for the can-order replacement policy. The schematic representation of the single replacement policy as well as the grouped replacement policy can be found in Appendix 3

To summarize, the model is driven by three experimental factors (input parameters), that are, the number of sewers n, the replacement level s, and the can-replacement level c. By changing the values related to these factors it is most likely to yield the desired results. However, to yield the desired results the model has five conditional factors that are essential to operate the model properly. At last, by determining the experimental factors and conditional factors the model’s response can be calculated.

3.5. Data Collection

Performing one calculation is not enough to determine the effect of sewer maintenance based on the can-order policy, therefore more data is required. Fortunately, the simulation has been developed in a way that it can be used to generate data. To generate data, the concept of Design of Experiments (DoE) have been used. Generally, design of experiments is a highly efficient experimental process that allows the variation of multiple factors simultaneously to support generation of useful and accurate data for future analysis (Lee & Wason, 2019; Murray et al., 2016; Theisens, 2016; Yu et al., 2018). In this case, variation of factors has been achieved by use of randomization. The benefit of randomization is that it is used to execute an experiment in a fully independent way or conduct the ‘run’ in random order. In other words, randomization reduces “the effect of extraneous or uncontrollable conditions that can impact the result of an experiment” (Theisens, 2016, p. 301). Practically, this means that for each run in the simulation a new scenario is generated. A scenario refers to the randomized setup of the simulation’s experimental factors, selected from their given values’ ranges, and conditional factors.

So, to collect data with the simulation model, one must go through three phases. First, determine all experimental and conditional factors required for the model. In case of the experimental factors define feasible ranges. Whereas conditional factors must be determined in advance of the simulation as these values are always identical in each run. Second phase is to run the simulator based on the values determined in phase one. Third phase is to calculate the total cost for each maintenance policy.

4. Results

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4.1. Model Demonstration

For a start, the simulation has been demonstrated according to the three phases as described in chapter 3. First step has been to determine all experimental and conditional factors according the procedures as described in sections 3.2 to 3.4. However, since experimental factors are generated by the simulation, in this case, the values for each experimental factor have been chosen randomly. More precisely, this scenario entails a sewer system that contains four sewers with a replacement level of 10% and a can-replace level of 30%. Furthermore, the values considered for the conditional factors have been summarized Table 5.

Experimental Factors Value(s) Units

Number of sewers in system (𝑛) 4 sewers

Replacement level (𝑠) 10 %

Can-repair level (𝑐) 30 %

Conditional Factors

Deterioration rate (𝑦) 1.5 λ

Simulation horizon (𝑖) 10.000 years

Initial conditions (𝑥) 45, 35, 25, 90 % Replacement cost (𝑅𝐶) Ø300 sewer 35770 €/sewer

Management cost (𝑀𝐶) sewer system 2575 €/sewer/period

Table 5. Sample Settings

Second phase concerns running the simulator based on the values identified in the first phase. The simulation works as follows. First, for each sewer in the simulated sewer system 𝑛 an initial condition 𝑥 has been assigned in advance. So, the simulated sewers’ conditions (𝐶 ) have been determined by the following equation:

(1) 𝐶 = 𝑥

In this example, the condition of 𝐶 = 45, 𝐶 = 35, 𝐶 = 25 and 𝐶 = 90. Second, for each sewer with condition (𝐶 ) the deterioration (𝑦 ) has been computed based on the Poisson distribution with lambda of 1.5. In other words, it generates values based on the fact a sewer is replaced roughly every 60 years. Subsequently, the deterioration of is subtracted from the original condition:

(2) 𝐶 = 𝑥 − 𝑦

Third, in case the condition (𝐶 ) drops below the replacement level (𝑠), replacement according to one of the three replacement policies has been issued and the condition changes to 100% (3a). In case, the condition does not drop below the replacement level, steps one and two are repeated, with an adjusted condition, until a sewers’ condition (𝐶 ) drops below the replacement level (3b).

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The condition deterioration process is iterated over the simulation horizon 𝑖, until the simulation horizon has been exceeded. If that being the case, the simulation stops and the yearly cost for each of the thee maintenance policies are calculated. As an illustration, Figure 8 visualizes deterioration process of the sewer per different replacement policy.

Figure 8. Deterioration process for each replacement policy in the first 100 years.

At last, the yearly costs have been calculated for each of the replacement policies. Since, in each case replacement of a sewer has been simulated differently, the total costs have also been calculated differently as described earlier in section 3.4. In this scenario the mutual differences between the three maintenance policies are not extremely large, as one can see in Table 6. Under such circumstances a decision-maker has the privilege to choose which maintenance policy is best for the upcoming maintenance project.

Maintenance policy Yearly Cost

Single € 3058

Grouped € 2837

Can-order € 2706

Table 6. Output data example scenario

4.2. Aggregated Results

To gain a more general overview of the effects of sewer maintenance based on the can-order policy, data has been collected by simulating randomized scenarios as described in section 3.5. However, since the simulation has been developed in a way that complete randomization of the three experimental factors is not feasible. More precisely, the problem is that the number of sewers in a network cannot be randomly generated. To solve this issue, for each value in its range, 5000 runs with random generated values for the replacement level and can-replace level has been performed. As discussed in section 3.1 the range for the possible number of sewers in a system corresponds to a minimum of two and a maximum of seven. So, this means that for each value for the number of sewers 5000 runs have been performed. In other words, in total 30.000 datapoints have been gathered to perform further analysis. In addition, Appendix 4 gives a summary of the data’s structure by means of randomized samples from the database generated by the simulation.

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system. Afterwards, the cost for the single replacement policy significantly increases compared to the grouped and can-order replacement policies. At last, with successive increases in the number of sewers in a system, it seems that the can-order policy becomes the cheapest maintenance policy.

Second, analysis focuses on the examination of the effect on increasing or decreasing the replacement level and can-replacement level. Starting with the former, as one can see in Figure 10 if the replacement level increases the average cost marginally increases. Which is rather trivial as well, practically what the replacement level simulates is the frequency a sewer is replaced. In other words, when increasing the replacement level, replacements will occur more frequently. By way of contrast, looking at the can-replacement level the behaviour is strikingly different, for both the single replacement policy and the grouped replacement policy the average costs remain practically the same when the can-replacement level is increased. Which can be explained by the fact that both replacement policies do not take the can-replacement level into account. However, what catches the eye is that after a certain can-replacement level, in this case approximately fifty percent, the average cost for the can-order replacement policy becomes equal to the grouped replacement policy. So, there is an indication that there is a limit to the neighbouring sewers’ condition to be replaced simultaneously with a sewer that must be replaced.

Besides determining the effect of both parameters separately, the third analysis concern the effect of the interaction between both the replacement level and the can-replacement level. In other words,

0 2000 4000 6000 8000 2 3 4 5 6 7 Av er ag e Co st [€ ] Number of Pipes

Single Grouped Can-order

Figure 9. Average Cost per Number of sewers in System

2500 2800 3100 3400 3700 4000 20 30 40 50 60 Av er ag e Co st [€ ] Can-replacement level c [%]

2500 2800 3100 3400 3700 4000 5 10 15 Av er ag e Co st Level of s

Figure 10. Average Cost replacement level and can-replacement level 2500 2800 3100 3400 3700 4000 5 10 15 Av er ag e Co st [€ ] Replacement level s [%]

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what happens with the average cost as the difference between both variables increase. As one can see in Figure 11, the behaviour of the average cost is rather equal to the average cost based on the can-replacement level. However, the figure show as the difference between the can-replacement level and the can-replacement level is small, the can-replacement policy is beneficial. However, as the difference increases or in other words the frequency of replacement also increases because of a larger can-replacement level, a grouped can-replacement policy becomes beneficial. This interaction confirms that there is a limit to the can-replacement policy to be beneficial.

4.3. Data Validation

Since randomized scenarios have been used to generate data it is in the study’s interest to check the composition of data to identify if there are disturbing factors and if this has effect on the results. However, as stated before, due to the way the model has been modelled for each value for the number of sewers five thousand random scenarios have been performed. Figure 12 displays the frequency for both the replacement-level as the can-replacement. Both graphs show that that the replacement-level as well as the can-replacement level are reasonably equal distributed, for supporting data see Appendix 5. Overall, the frequency of experimental factors for the replacement level and the can-replacement level give no evidence for significant deviations. Therefore, it has been validated that the results have not been influenced by randomization.

2500 2800 3100 3400 3700 4000 5 10 15 20 25 30 35 40 45 50 55 Av er ag e Co st [€ ] ∆s-c [%]

Figure 11. Average Cost per difference s and c

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5. Discussion and Conclusion

This study set out with the aim of assessing the implementation of the can-order policy in sewer maintenance decision-making process. An initial objective of the project was to create an innovative solution to save on maintenance by means of optimizing sewer maintenance decision-making process. In general, the current study found that the application of the can-order policy shows hopeful signs to increase the effectiveness of sewer maintenance decision-making. Results of this study show that the number of sewers obliged for maintenance in a system is a dominant factor in optimization of the maintenance planning. Since, this is the largest cost centre while planning sewer maintenance. However, the most obvious finding to emerge from the analysis is that the can-order policy is observed to be advantageous only when neighbouring sewers’ conditions are relatively low. In other words, the results indicate that there is a limit to maintenance based on the can-order policy to be advantageous compared to other maintenance policies. Together these results provided important insights into the use of the can-order policy to plan sewer maintenance.

Despite these promising results, these findings may be somewhat limited by the way the model has been developed. In the current situation the simulation model relies excessively on a few key assumptions. Further work is required to establish the viability of maintenance based on the can-order policy. To achieve this, further research should be focused on revision of the model, in which the elimination of key assumptions should be the focus of attention. Initially, it is recommended to consider a larger sewer system compared to the one used in this study, preferably based on real data. Practically, a sewer system of this size will normally be maintained at once. In second place, it is recommended to design a solution, for example a cost penalty, that copes with the adjacency assumption. Since, in practice each time an isolated sewer is maintained a setup cost (i.e. assemble equipment and personnel) must be paid. The current model does not take this into consideration. In the third place, it is recommended to adjust the model in a way that it can deal with various sewer dimensions. In practise, each sewer has a different length or diameter. Changing this in the model, will influence the determination of the overall costs for maintenance in a sewer system. At last, it is recommended to amend the values for both the experimental factors as the conditional factors, throughout this study some values emerged to be overvalued. For example, the values for the replacement level deemed to be impractical. Briefly, despite its limitations, the study certainly adds to bring the understanding of the can-order policy used for sewer maintenance into prominence. Although, a greater focus on the accuracy of data could produce interesting findings that account for the behaviour of the can-order policy in sewer maintenance.

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References

Atkins, D. R., & Iyogun, P. O. (1988). Periodic Versus “Can-Order” Policies for Coordinated Multi-Item Inventory Systems. Management Science, 34(6), 791–796.

https://doi.org/10.1287/mnsc.34.6.791

Balintfy, J. L. (1964). On a Basic Class of Multi-Item Inventory Problems. Management Science, 10(2), 287–297. https://doi.org/10.1287/mnsc.10.2.287

Carvalho, G., Amado, C., Brito, R. S., Coelho, S. T., & Leitão, J. P. (2018). Analysing the importance of variables for sewer failure prediction. Urban Water Journal, 15(4), 338–345.

https://doi.org/10.1080/1573062X.2018.1459748

Causer, J., & Ford, P. R. (2014). “Decisions, decisions, decisions”: Transfer and specificity of decision-making skill between sports. Cognitive Processing, 15(3), 385–389.

https://doi.org/10.1007/s10339-014-0598-0

Cevallos-torres, L., & Botto-Tobar, M. (2019). Problem-Based Learning : A Didactic Strategy in the Teaching of System Simulation. Springer Nature Schwitzerland AG.

Clemens, F., & Langeveld, J. (2016). Toestandsbepaling betonnen riolen.

Diamantidis, D., Holický, M., & Sýkora, M. (2016). Reliability and Risk Acceptance Criteria for Civil Engineering Structures. Civil Engineering Series, 16(2), 1–10. https://doi.org/10.1515/tvsb-2016-0008

Federgruen, A., Groenevelt, H., & Tijms, H. C. (1984). Management Science Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands. Compound Poisson Demands. Management Science, 30(3).

https://doi.org/10.1287/mnsc.30.3.344

Hillman Willis, T., & Willis, W. D. (1995). A quality performance management system for industrial construction engineering projects. International Journal of Quality & Reliability Management, 13(9), 38–48.

Kayiş, E., Bilgiç, T., & Karabulut, D. (2008). A note on the can-order policy for the two-item stochastic joint-replenishment problem. IIE Transactions, 40, 84–92.

https://doi.org/10.1080/07408170701246740

Koster, P. (2020). Gesprongen riool Pieter Zeemanstraat snel vervangen voor drie kwart miljoen euro. AD. https://www.ad.nl/dordrecht/gesprongen-riool-pieter-zeemanstraat-snel-vervangen-voor-drie-kwart-miljoen-euro~a43013d2/?referrer=https://www.google.nl/

Lee, K. M., & Wason, J. (2019). Design of experiments for a confirmatory trial of precision medicine. Journal of Statistical Planning and Inference, 199, 179–187.

https://doi.org/10.1016/j.jspi.2018.06.004

Li, H.-N., Ren, L., Jia, Z.-G., Yi, T.-H., & Li, D.-S. (2016). State-of-the-art in structural health monitoring of large and complex civil infrastructures. Journal of Civil Structural Health Monitoring, 6, 3–16. https://doi.org/10.1007/s13349-015-0108-9

Melchiors, P. (2002). Calculating can-order policies for the joint replenishment problem by the compensation approach. European Journal of Operational Research, 141(3), 587–595. https://doi.org/10.1016/S0377-2217(01)00304-6

(24)

Mathematics and Computers in Simulation, 154, 34–47. https://doi.org/10.1016/j.matcom.2018.06.004

Murray, P. M., Bellany, F., Benhamou, L., Bučar, D. K., Tabor, A. B., & Sheppard, T. D. (2016). The application of design of experiments (DoE) reaction optimisation and solvent selection in the development of new synthetic chemistry. Organic and Biomolecular Chemistry, 14(8), 2373– 2384. https://doi.org/10.1039/c5ob01892g

Nair, A., & Boulton, W. R. (2008). Innovation-oriented operations strategy typology and stage-based model. International Journal of Operations and Production Management, 28(8), 748–771. https://doi.org/10.1108/01443570810888599

NLIngenieurs Sewer System Workgroup. (2009). Sewer Systems Module for Higher Professional Education. https://www.riool.net/evenement-opleiding/hbo/sewer-systems-module-for-hpe Ohno, K., & Ishigaki, T. (2001). A multi-item continuous review inventory system with compound

Poisson demands. Mathematical Methods of Operations Research, 53, 147–165. https://doi.org/10.1007/s001860000101

Pantumsinchai, P. (1992). A Comparison of Three Joint Ordering Inventory Policies. Decision Sciences, 23(1), 111–127. https://doi.org/10.1111/j.1540-5915.1992.tb00379.x

RIONED. (2015a). Personeelskosten. https://www.riool.net/personeelskosten RIONED. (2015b). Riolen, inclusief rioolputten, perceel- en kolkaansluitingen.

https://www.riool.net/riolen-inclusief-rioolputten-perceel-en-kolkaansluitingen RIONED. (2015c). Vervanging. https://www.riool.net/vervanging

Robinson, S. (2008). Conceptual modelling for simulation Part II: A framework for conceptual modelling. Journal of the Operational Research Society, 59(3), 291–304.

https://doi.org/10.1057/palgrave.jors.2602369

Robinson, S. (2014). Simulation: The Practice of Model Development and Use (2nd ed.). Palgrave Macmillan.

Romanova, A., Mahmoodian, M., Chandrasekara, U., & Alani, M. A. (2015). Concrete Sewer Pipe Corrosion Induced by Sulphuric Acid Environment. International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering, 9(4), 467–470.

Schönemann, M. (2017). Multiscale Simulation Approach for Battery Production Systems (C.

Herrmann & S. Kara (eds.)). Springer International Publishing AG. https://doi.org/10.1007/978-3-319-49367-1

Silver, E. A. (1981). Operations Research in Inventory Management : A Review and Critique. Operations Research, 29(4), 628–645.

Simeu-Abazi, Z., & Sassine, C. (2001). Maintenance Integration in Manufacturing Systems: From the Modeling Tool to Evaluation. The International Journal of Flexible Manufacturing Systems, 13, 267–285.

Stoianov, I., Nachman, L., Whittle, A., Madden, S., & Kling, R. (2007). Sensor networks for monitoring water supply and sewer systems: Lessons from Boston. 8th Annual Water Distribution Systems Analysis Symposium 2006. https://doi.org/10.1061/40941(247)100

(25)

Sigma Academy.

Thiyagarajan, K., Kodagoda, S., & Alvarez, J. K. (2017). An instrumentation system for smart monitoring of surface temperature. 2016 14th International Conference on Control, Automation, Robotics and Vision, ICARCV 2016, 2016(November), 13–15.

https://doi.org/10.1109/ICARCV.2016.7838845

Tsang, A. H. c. (2002). Strategic dimensions of maintenance management. Journal of Quality in Maintenance Engineering, 8(1), 7–39. https://doi.org/10.1108/13552510210420577

Whittle, A. J., Allen, M., Preis, A., & Iqbal, M. (2013). Sensor networks for monitoring and control of water distribution systems. Proceedings of the 6th International Conference on Structural Health Monitoring of Intelligent Infrastructure, SHMII 2013, 83–98.

Wieringa, R. J. (2014). Design Science Methodology: for information systems and software engineering. In Design Science Methodology: For Information Systems and Software Engineering. Springer-Verslag. https://doi.org/10.1007/978-3-662-43839-8

Yu, P., Low, M. Y., & Zhou, W. (2018). Design of experiments and regression modelling in food flavour and sensory analysis: A review. Trends in Food Science and Technology, 71, 202–215.

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Appendix 1 – Standard Classification System Example (NEN 3398)

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Appendix 2 – Key Economic Statistics Sewer Replacement

Basic principle Base price sewer 300 mm 400 € / m

Base price sewer 700 mm 800 € / m

Base price sewer drains 2400 € a piece

1 sewer drain per 40 meter

Base price property connection 490 € a piece

1 property connection 10 Meter

Base price cesspit including connection 280 € a piece

1 cesspit including connection per 10 Meter

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Appendix 3 – Simulated Sewer Replacement Policies

Single Replacement Policy

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Appendix 4 – Sample Data

Run 𝒏 𝒔 [%] 𝒄 [%] Single [€] Grouped [€] Can-order [€] ∆s-c

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Appendix 5 – Validation Data

Frequency of 𝒔 Replacement level 𝒔

Number of Sewers 𝒏 5 10 15 Total

2 1657 1662 1681 5000 3 1668 1674 1658 5000 4 1657 1685 1658 5000 5 1682 1626 1692 5000 6 1695 1668 1637 5000 7 1692 1634 1674 5000 Total 10051 9949 10000 30000

Frequency of 𝒄

Can replacement level 𝒄

Number of Sewers 𝒏 20 30 40 50 60 Total