Development of a Financing Optimization Framework Based on Risk Simulation in BOT Projects: A Case Study of the Waste-to-Energy Project

Infrastructure projects that are mostly characterized by high uncertainty usually face various risks at all stages as timing risks, cost risks, and disruption in the executive processes (by the reason of unpredictable obstacles in fnancing risks, technology production, and so on). Owing to the complex nature of infrastructure projects, the build-operate-transfer (BOT) contract is usually concluded between the private and public sectors. Considering that the public sector transfers all or part of its fnancial risk to the private sector (contractors), in this type of contract, the distribution of risks is diferent from that of traditional contracts. Besides, project implementation methods and the lack of risk management might lead to the failure of the project. As the implementation of such projects, along with the risks of the projects that require a large amount of investment, it would be necessary to develop a proper fnancing schedule with consideration of the efect of repayment of various loans in the project to ensure the feasibility of the project. So, in this project, considering the efects of risks in a waste-to-energy infrastructure project, an optimal project fnancing framework is developed. In the current research, using Monte Carlo simulation, the impact of risks on the project is investigated during the construction period and the operation period. Te results have shown that consideration of the impact of the risks on projects might have a signifcant efect on the increase of time and cost; nevertheless, the cost of optimal fnancing might reduce the project proft by 23%. Te results indicate that choosing the appropriate fnancing solution guarantees the project’s fnal proft. Besides, it can help project managers to make the best fnancing decisions based on realistic situations.


Introduction
Hundreds of contractors go bust annually for diferent reasons, certainly one of which would be high uncertainty in the construction industry. Although many diferent factors could lead to failure in the labor market, fnancing and budgeting factors are among the most important and common reasons [1]. Beyond 60% of contractors' failures stem from fnancing issues, the lack of fnancing leads to the failure of 77-95% of contractors [2]. Failure to establish a connection between the fnancing plan and the project schedule afects cash fow and produces an unrealistic schedule, and probably it would lead to the contractors' failure on the way of implementing their projects. Te existence of fnancing problems not only afects the cash fow of the project but also causes high tension and disagreement among the project members; consequently, the conficts among them [3] and contractors' claims [4] are increased, and thus contract terminations get presumable [2]. Incorporating both fnancing and scheduling aspects is crucial for the successful management of construction projects, and minimizing fnancing costs emerges as a signifcant factor in achieving this goal.
Contractors often experience imbalanced cash infows and outfows throughout the project, leading to negative balances during certain periods. Consequently, they may need to utilize their own capital or seek external borrowing to address these fnancial fuctuations. In this case, the repayment of this amount necessitates paying an interest rate in addition to the principal amount. Tis issue, which is known as the cost of fnancing, shall be calculated in the projects' costs and proft calculation; otherwise, the calculations would be distant from reality.
Because of the diferent nature of BOT projects, these projects are implemented in a way that the contractor generally fnances the project either with his capital or by borrowing from a third party and earns his proft during a certain period of project operation. So, the importance of fnancing, as well as the cost of fnancing in such projects, is more important than that in other projects.
Additionally, BOT projects are always characterized by high uncertainty. A BOT project faces diferent risks at all stages, such as timing risks, cost risks, and disruption in implementation processes because of fnancing risks and technological risks. Considering that in this type of contract, the public sector transfers all or part of its fnancial burden to the private sector (contractor); thus, risk management in these projects requires a more detailed investigation. Tough the current complex situation cannot be addressed by the conventional risk evaluation method, fnding a new approach is extremely important from a practical standpoint [5]. So, the identifcation of these risks and uncertainties from the outset and the consideration of their probability and impact through correct planning could help the success of these projects [6]. Examining diferent fnancing ways for such projects, and taking into account the impact of their risks, is vital for reducing project management costs and guaranteeing the contractor's fnal proft. Te innovation and contribution of this study are as follows: (i) Performing qualitative and quantitative risk analysis to evaluate the project risk probability and its impact on objectives (time and cost) (ii) Using a more realistic duration and cost for project activities (considering risk impacts) (iii) Developing a fnancing optimization to investigate the reduction of project proft (iv) Applying as a framework to waste-to-energy BOT projects which is more complicated than common construction projects (v) Finding optimized time, cost, and proft of a real BOT project (WTE) with more realistic inputs Terefore, this study is structured as follows. In the literature review section, a review is conducted on the previous studies of risk management, cash fow, and fnancing. Te gap in the research is suggested at the end of this section. Te "Problem Statement" section demonstrates the framework steps and the mathematical approach in detail. Te case study, results, and sensitivity analysis are explained in the "Results and Discussion" section. In the "Managerial Insights and Practical Implications" section, practical aspects of the results and framework are introduced. Eventually, in the "Conclusions" section, the study outcomes are summarized and concluded.

Literature Review
In this part of the article, the research and studies performed in the risk management of build-operate-transfer (BOT) contracts, their cash fow, and fnancing are discussed.

Risk Management.
Risk management is a scientifc approach for identifying, minimizing, and predicting the adverse efects of infrastructure projects [7]. Without effective management and decision-making, some conficts might arise among stakeholders which could have serious consequences including rising disposal costs, fnancial loss, project cancellation, or project postponement [8]. So, to maintain the proper performance of risk management, the stakeholders are to continuously improve their knowledge of risks. According to Davies et al. [9], the necessity for efective risk management in projects is undeniable. Teir research revealed that a substantial 37% of projects in Egypt experienced cost overruns, while an overwhelming 98% of Egyptian contractors delivered their projects with signifcant delays to clients. Numerous other studies in the literature mirror these fndings, emphasizing the critical role of risk management, particularly in large-scale and infrastructure projects (Altoryman [10]; Taroun et al. [11]); besides, infrastructure projects are generally recognized as projects having high costs and long performance durations. Based on society's needs, the importance of succeeding in these projects is very important. So, to improve the risk management of these projects, the use of quantitative risk analysis techniques has been recommended in the literature; nevertheless, in infrastructure projects, lack of knowledge and implementation in terms of risk analysis is noticeable, empathetically in Iran.
Te success of public-private partnerships (PPPs) depends on efectively managing risk, where one of the key problems would be estimating the likelihood of a risk and its impact on project goals [12]. Bing et al. [13] used a questionnaire to investigate risk allocation in UK construction projects. Tey suggested that project-specifc risks are better to be left to the private sector. Burke and Demirag [14] reviewed and analyzed risk transfer and stakeholder relationships in public-private partnership contracts. Song et al. [15], using the fuzzy model and system dynamics, presented a model for estimating the operational time in an energy conversion project under a BOT contract. By using their model, they chose the most feasible option among eight alternatives. In their research, they stated that the developed model helps the public sector in better decision-making and choosing feasible options. However, there have been many limiting assumptions (such as merely focusing on the public sector, not considering risks, and responding to them during the project) that have not been considered in their research. Ma et al. [16] proposed a time and cost estimation model for the grant period of public-private partnership projects. By using the real-option analysis and risk allocation, they produced a decision-making model for the operational period; besides, they implemented their proposed model on a water treatment plant project in China. Digiesi et al. [17] proposed a model for reducing the exposure risk for employees performing repetitive manual tasks. Recently, Aladag and IsiK [18] evaluated design and construction risks in megatransportation projects with BOT contracts in their research.
Diferent approaches have been presented in quantitative risk analysis by diferent researchers. Sato et al. [19] delved into the risks associated with road projects in Japan, conducting a quantitative analysis using empirical data. Teir research aimed to introduce risk management and implement quantitative risk analysis based on real project data. On a similar note, Platon and Constantinescu [20] explored the risks of investment projects utilizing Monte Carlo simulation. Teir study emphasized the signifcance of risk assessment in investment projects to examine the probability of achieving favorable performance thresholds for metrics such as the internal rate of return (IRR) or net present value (NPV). In 2015, Leo conducted a study focusing on the variables that could substantially impact the success of quantitative risk analysis in large projects.

Cash Flow and Financing.
Cash fow is considered one of the most important parameters and fnancial infuencing factors during the life of a project. During the project period, the complete history of all payments (cash outfows) and incomes (cash infows) caused by the implementation of the project [21] is shown by that. Te net diference between cash fow inputs and outputs represents the proft of the project [22]. Au and Hendrickson [23], modeling the liquidity of contractor income and expenses, presented a graph based on which the amount of expenses and incomes has been displayed in specifc periods (weekly or monthly). Contractors need to evaluate and build their cash fow model based on the credit line of their accounts [24]. Elazouni and Metwally [25] presented a cash fow model that included various project revenues and costs (inputs and outputs) during the project period. Liu and Wang [26] presented a resource-constrained project planning model integrated with cash fow. Ahmed [27], using the Monte Carlo simulation technique, evaluated the sensitivity of activities to cash fow parameters.
Te distinctive feature of liquidity is that it is used as a resource for proceeding with construction activities, and simultaneously the completed activities in the project produce this same resource (liquidity) and use that to fnance the remaining activities. Terefore, by integrating the critical path method and the cash fow model, some researchers conducted in this feld introduced the fnance-based planning method.
Until 2004, the use of fnancing costs in scientifc research was practically denied; Elazouni and Gab-Allah [28] introduced the fnance-based scheduling method in their research.
Tis method involves integrating the scheduling and fnancing functions of a construction project, where the scheduling of construction activities is determined by considering both precedence relations and fnancing constraints. Te goal of fnance-based scheduling is to calculate a feasible schedule minimizing project delays while minimizing the cost of fnancing based on liquidity constraints. In case, the cumulative negative balance including fnancing costs surpassed the threshold, the start time of the activity is changed in the fnance-based scheduling method based on the foat of the entire activity, and if necessary, the project duration increases without exceeding the fnancial limit. Te research of Elazouni [29] and Fathi and Afshar [30] is based on this method. Recently, Alavipour and Arditi [31] have presented a model that takes into account various fnancing options and a work schedule with typical activity durations to minimize fnancing costs. In another study, Alavipour and Arditi [32] have proposed a comprehensive model that analyses time-cost trade-ofs and optimize fnancing; besides, Elghaish et al. [33] created a BIM-based methodology for integrated project delivery (IPD) cash fow analysis across all of its stages. Although the mentioned studies introduced an applied fnancing optimization model, their focus has been on projects with a small number of activities and a fxed duration, on which the efects of risk have not been observed.

Research Gap.
Te survey of the related works is presented in Table 1. As can be seen, the research studies carried out in the mentioned felds are very extensive. However, these studies have shortcomings that are briefy mentioned as follows.
Despite the review of the project scope, the mentioned models have not considered the simultaneous efects of project risks and their fnancing. Te risk research related to the construction of waste-to-energy power plants (in the feld of renewable and new energies) has been rarely carried out and has often been examined qualitatively. Te efect of risk management processes and fnancial and quantitative analyses has been rarely seen in these studies. Generally, in international investigations, so far, no research has been performed in the feld of developing fnancial optimization models based on the quantitative simulation of risks in the BOT contracts to examine all the existing situations that stem from risks, unlimited fnancing options, grant periods, the efects of the infation rate, and responses to secondary risks and such issues.
Considering the novelty of the feld of renewable energy and the mentioned cases, the research gap in this feld is noticeable. Besides, the development of an optimization model that encompasses all the mentioned complex conditions and brings the simulation as close to reality as possible is recommended. Tis model, among varied options with appropriate precision, helps in fnding the best solution for the private sector (contractor) and is useful for enabling project success in high-risk renewable and new energy projects. Considering the existing gap in this feld, this article aims to investigate the efect of project fnancing on the fnal proft of the contractor and to develop a fnancing schedule based on the simulation of project risks via diferent fnancing options in a BOT project. In this research, the efects of project risks of the construction and operation period have been considered on the time, cost, and income of a waste-toenergy power plant construction project, and based on that, the best project fnancing option is calculated. Te main innovation of the current research is addressing an unexplored issue that has not been previously discussed in existing studies. Tis topic helps the project planners to familiarize themselves with the conditions that cause the occurrence of the project risks and their time and cost impact, as well as the fnancing conditions of the project and its cash fow during diferent periods. Also, considering the length of the operation period, the planners could take the necessary arrangements to fnance and ensure proft.

Problem Statement
In this section, the methodology of the current research is introduced and discussed. Te foundation of the fnancebased optimization model of this research is to identify diferent fnancing conditions of the project at diferent times based on schedule, to minimize the repayment costs of these fnancing options, and as a result to increase the proft of the project. Furthermore, by identifying and ranking risks, the efect of their occurrence on the project and project goals could be checked. Considering that project fnancing is very important and common in BOTprojects, the optimization of project fnancing to minimize the costs of project fnancing (such as the cost of repaying various types of loans, credit lines, and renting or depreciation of purchased machinery) would be very important. To better understand the methodology and purpose of this research, Figure 1 displays the concept of the framework and Figure 2 shows the implementation steps and the workfow of the research methodology. In the rest of this section, the concepts specifed in Figure 2 are examined and introduced.

Project Risk.
To achieve the main goal of this part of the research, the process introduced in this part is presented. In general, the project risk stages of this research include the three main stages of risk identifcation, qualitative analysis, and quantitative analysis of risks.

Risk Identifcation.
Te main purpose of this section is to identify and rank the risks of waste-to-energy projects that are implemented using BOT contracts. To successfully implement this process, it has been tried to involve stakeholders as much as possible in carrying out and verifying the steps and results of this stage. Te process of identifying risks includes the following: (i) Determining the project risk exposure (ii) Identifying risks related to the project (iii) Prioritizing project goals (including time, cost, and quality)

Qualitative Risk Analysis.
Tis process aims to analyze risks qualitatively and prioritize them because it allows spending resources to increase opportunities and reduce threats to the most possible extent. Tis process is repetitive, and if new risks appear, they will be identifed and analyzed.
As qualitative analysis is dependent on descriptive and linguistic perceptions, and as the perceptions of diferent people difer with regard to the importance of risks, it would be only suitable for the initial stages of the project, when accurate information is not enough for a detailed evaluation. In this section, the occurrence probability and the impact of risk on the project goals are the main factors of the identifed risks, and their ranking is represented in Tables 2  and 3.

Risk Ranking Based on Optimistic and Pessimistic
Approach. After identifying the probability and efect of risks, it would be possible to rank them based on the optimistic and pessimistic approaches. Te approach of the Project Management Institute (PMI), by which the risk factor is equal to the product of its probability and its impact, is an optimistic view of risk analysis; that is, in the interval between zero and one, the risk factor will always be lower than its probability and impact. In this approach, the calculation of the risk factor is shown in equation (1). Tis approach means that the organization has chosen a riskseeking strategy and has a greater desire for accepting risk.
According to this equation, the total amount of risk factor is always smaller than the smallest value of P and I or equal to that. It could be concluded that in this case, the smallest value of P and I determines the severity of the risk.
Cooper et al. [34] introduced a pessimistic approach to risk analysis, which means in the range of zero and one, the risk factor is always greater than the probability of its occurrence and impact. In this approach, the risk factor calculation is shown in equation (2). Tis approach means that the organization has chosen a risk-averse strategy and is less willing to accept risk.
3.2. Qualitative Risk Analysis. Te Monte Carlo method, which can negatively infuence a project and support scheduling or budgeting reserves, is suggested by the Project Management Institute (PMI) as a way to evaluate risks. Te application of Monte Carlo in quantitative risk analysis ofers several advantages. Its utilization in cost and time management primarily involves quantifying the risk level Complexity associated with budgetary or completion periods [35]. Te Monte Carlo method proves valuable in assessing the certainty of meeting a target completion date during schedule development. Modeling project schedules using Monte Carlo simulations is a fundamental aspect of quantitative risk analysis. In real-world scenarios, Monte Carlo simulations have proven to be efective tools for evaluating scheduling risk [36]. Project managers can employ the Monte Carlo method to incorporate uncertainty into their schedules and networks, thereby ensuring reasonable duration and cost expectations. Subsequently, contingency decisions can be confdently made based on the results of Monte Carlo simulations. With a given level of confdence, Monte Carlo simulations can aid in revealing the chance of meeting a scheduled completion date or pointing to the predicted results in terms of time and cost. Te Monte Carlo simulation technique examines the impact of the project's challenges and risks; besides, it predicts the project's schedule and budget based on that. So, based on the possible output of various scenarios, the decision-making power is increased. Hence, this research employs the Monte Carlo simulation technique to explore the impact of risk on project activities.
Subsequently, the upcoming sections will thoroughly examine the development of the project schedule and cost model, along with a comprehensive analysis of associated risks.

Schedule Activities.
To avoid the high complexity of modeling and due to the scope of the project, the project schedule includes the two parts of construction and operation. Table 4 shows the title of the items related to the list of scheduling activities, which includes the activity level in the WBS, the WBS code of the activity, the name of the activity, and the activity code.
Tis section encompasses the probability distribution of project activity durations, which are considered at a higher level, leading to relatively long durations. For each activity, a triangular distribution is utilized, incorporating optimistic, most likely (original schedule), and pessimistic values. Te project controlling department has provided the calculated optimistic and pessimistic values as percentages of the probable time. Table 5 presents the titles of these items in the model, with the "simulation value" column defning the distribution assumptions for the Monte Carlo simulation of the model. Table 6 presents the key elements of the risk modeling section and their infuence on the project schedule. Te "Risk1" entry on the left comprises the risk rating obtained from qualitative analysis, the assumption of uniform probability distributions, and the probability of risk occurrence. On the other side, the "risk impact" item includes the optimistic, most likely, and pessimistic percentage values representing the time efect of the risk, based on inputs from experts and project planners. Tese values are incorporated using triangular distribution assumptions. Te last column contains the conditional formula (equation (3)) used to assess the occurrence and impact of the risk. It should be noted that certain items account for two potential risk occurrences and their corresponding impacts, which are treated independently and combined accordingly.

Probability Modeling of Risk Occurrence and Its Impact on Project Schedule.
Considering the occurrence probability of the defned risks and also the extent of their impact on the time of each activity, the duration of each activity is obtained from the following equation:

Analysis of the Construction Period CPM Network.
Te schedule network analysis during the construction phase is conducted using the critical path method (CPM). Table 7 presents the titles of the items analyzed in this section. Starting from the left, the columns represent the earliest start time, earliest fnish time, latest start time, latest fnish time, total foat, and critical path index for each activity. To streamline the model, all precedence relations are defned as fnish-to-start with corresponding lead or lag values. Te calculation method can be observed from the following equation:  Complexity provided the necessary information for the values in the probable, optimistic, and pessimistic columns. Table 9 presents the daily overhead costs, which typically encompass indirect costs arising from factors like the project's unique characteristics and expenses related to the central ofce. Tese indirect costs can have a signifcant impact on the fnal project cost, particularly as the project duration increases, potentially leading to losses. Additionally, the project's scale infuences the rise in overhead costs.
Similar to the probability and risk impacts on the project time, the probability and impact of risks on the direct costs of the project are calculated. One key distinction is that not all risks afecting the project timeline necessarily impact project costs. For instance, delays in the delivery of drawings during the design phase may not directly afect the project's direct costs. However, with the increase of the total project time, the overhead costs increase either and consequently result in a rise in the project total cost. In defning the risk impact on direct costs, the efect of some risks on cost is correlated with the corresponding efect of that risk on time.
As an example, the cost impact of a risk on a particular activity may exhibit either a direct or inverse correlation with the time efect of that risk on the same activity. Tis aspect has been incorporated into the modeling process based on insights from experts in the PMO cost control unit. Consequently, the fnal costs of each activity are determined by considering the direct cost along with the probability and efect of the associated risks, as shown in the following equation: In line with the research by Song et al. [15], the operating period costs in public-private partnership projects encompass salaries, maintenance, energy, and raw materials. Given the long time horizon of these projects (at least 10 years), accurately estimating the fnal cost for the period requires        annual consideration of existing risks' impact. Terefore, the risks' efect on the operation period is calculated on an annual basis, and the base cost for the following year is adjusted accordingly for the aforementioned four cost categories. Additionally, infation risk is separately accounted for at the end of each year, with its impact on all four costs calculated using the triangular distribution function. Te fnal cost of each of the four main operation period costs is computed according to equation (7). Notably, the main costs for year zero are determined based on the input from experts at the cost control unit of the PMO.
With the completion of the construction period and getting into the operation period of the project, the income of the project would be entered into the cash fow via the sale of the product resulting from the project. As the risks of the operation period afect the costs, the occurrence of these risks could afect the project's income and bring the calculations closer to reality. As the focus of this research is on the waste-to-energy project, the monthly sale of this energy considers the contractor's income during the operation period. According to the opinions of experts in this feld, the sale of power from burning biomass is considered income. Depending on the type of devices used in the construction period, the amount of power generated is calculated, and the amount of power sale is obtained as an average. In this way, the contractor's income is calculated during the operation period based on the amount of power sold. By being added to the project's infows, it completes the cash fows of the entire project from the very beginning of the construction period to the end of the operation period. In that way, the calculation of the fnal proft of the project would be possible.

Development of Quantitative Risk Analysis Model.
Te primary objective of this research, as stated at the outset, is to analyze the quantitative impact of project risks on the project's time and fnal cost. Te outcomes of this analysis encompass the construction period's completion time, construction period cost, operation period cost, total cost, income, and fnal project proft. Te calculations for each output are presented in the following equations:

Financing Optimization Model.
In BOT projects, the contractor generally implements the construction period at his own expense and gains proft from the operation phase of the project over several years through the sale of a specifc product (or service). Terefore, the cumulative cash fow of the contractor is negative at the beginning of the project and will gradually become positive near the end of the operation period when the fnal proft of the project is gained. Taking into account this issue, the contractor should keep in mind that in case no proper planning is devised for fnancing the project during the construction period, it could cause irreparable damages to the project and ultimately to the contractor and eventually cause the project failure or cessation. Terefore, making detailed fnancial planning prior to the start of the project is necessary for considering the efect of diferent fnancing options and the costs of using them in the project. Tis causes the following: (1) Te contractor could make the necessary planning for using his various fnancing options (necessary measures to receive various loans and create credits from various institutions) before the start of the project and at the time of contracting. (2) Te efect of loan repayment with diferent interest rates is observed according to the existing risks on the cash fow, and the best fnancing option is chosen based on that. (3) Considering the long period of construction and operation, the economic conditions of the country, failure to consider the efect of loan repayments, and various credits might ultimately lead to the loss of the contractor and cause the project failure. Terefore, by choosing the correct fnancing option and considering its efect during the project, the contractor might identify and guarantee his proft and plan before the contract.
In this section, diferent project fnancing options are introduced, and their efects on the cash fow have been investigated.

Diferent Project Financing
Options. Tis research incorporates three distinct fnancing options into the cash fow model, drawing inspiration from Alavipour and Arditi's [31] study. Tese fnancing categories comprise short-term loans, a single long-term loan, and lines of credit, covering a comprehensive range of lending methods. Te model considers various repayment schedules for these loans. Long-term loans entail monthly repayments throughout the project construction period, while short-term loans are repaid over 3, 6, 9, or 12 months, with options for monthly or quarterly repayments. Additionally, the repayment structure difers between short-term and long-term loans, whereas long-term loans involve fxed monthly repayments of both principal and interest and short-term loans entail principal payment after a specifed period followed by monthly interest payments.

Complexity 9
In contrast to short-term loans, the amount of credit that a credit account receives can be used until the contractor pays of his debt. Every month, the contractor can borrow an amount based on his needs and repay a portion of that along with its interest. However, the longer the repayment period, the higher the compound interest rate. So, it seems quite wise and logical to repay the credit account in the shortest possible time.
Generally, the interest rate is annually expressed. An annual rate that simultaneously considers borrowing and compounding costs results in an annual efective interest rate [37]. In this research, for calculating the monthly interest rate, it is assumed that a lender announces the annual efective interest rate to the contractor, and the contractor calculates the monthly interest rate based on the annual efective interest rate.
It shall be noted that for bringing the introduced fnancing model closer to reality, each of the proposed options has limitations. In reality, lenders might have limitations on the amount of a loan or credit account per project period. However, in this research, it is assumed that this amount has no limit.
Apart from the user-input cash fow parameters, the model also takes into account specifc fnancing details such as fnancing options, annual interest rates, interest payment schedules, and the contractor's credit amount for each period. Te model grants the contractor the fexibility to select the minimum cumulative cash fow balance, even allowing for negative values. Tis implies that the contractor can defer certain costs without incurring interest charges, leading to negative cumulative cash fow. However, if the contractor cannot postpone costs without interest, the minimum cumulative balance is set to zero.

Creating the Model and the Objective Function.
Te primary objective of this section is to determine the total cost of fnancing by analyzing the project's cash fows. Contractors typically receive a signifcant portion of their profts towards the project's completion. It is at this stage where the combination of positive cash infows and outfows results in variable proft fgures.
As mentioned in the previous section, the total time of the project is equal to the end of the operation period. Equation (13) shows the total time of the project. To fnalize the cash fow model, fnancing fows are added to the input and output fows of the project (mentioned in the previous section). Financing fows include the borrowed amount (fnancing infow), repaid amount (fnancing outfow), and fnancing cost (fnancing outfow), which are shown in the following equations: RE y � RE ST,y + RE LT,y + RE LC,y , FI y � FI ST,y + FI LT,y + FI LC,y .
Also, the calculation of the net outfow of fnancing at the end of the period y and the net fow of fnancing at the end of the period y is shown in the following equations: Te net cumulative balance of fnancing cost is calculated using the following equation: So, the objective function of the introduced fnancing model could be expressed with the following equation: As there are many limitations on the way of the introduced objective function, fnancing limits and cash fow limits are introduced in the next two sections.

Financing Limitations of the Objective Function.
In this section, equations (21)-(25) of fnancing restrictions related to the objective function are introduced.
Te total amount of the borrowed loan related to each short-term loan shall not exceed the limit already set for each short-term loan option: At the end of each period, the borrowed amount for short-term loans and long-term loans should not exceed the respective limits specifed for each type of loan, respectively: Te credit required at the end of each period should not surpass the total credit line limit: Te credit drawn from the credit line at the end of each period should not exceed the credit limit specifed for that period:

Cash Flow Limitations of the Objective Function.
Te net cumulative balance of cash fow (including fnancing fows) in each period is calculated through the following equation: 10 Complexity N y ′ � P in y − P out y + NFC y ; y � 0, N y−1 ′ + P in y − P out y + NFC y ; y ≠ 0.

⎧ ⎪ ⎨ ⎪ ⎩ (26)
Te constraint applied to the minimum cumulative balance of cash fow (including fnancing fows) in each period is shown in the following equation: As in BOT projects, fnancing is generally considered as the responsibility of the private sector, and a fnancing schedule should be developed that refects the diferent fnancing methods and the efect of loans and credits' repayments on the fnal proft of the project. Such a problem, owing to the wide range of fnancing modes that it has, cannot be solved normally. Solving such a difcult problem requires a strong and efcient model, so that in addition to high accuracy in reaching the optimal solution, it might be able to do this work in a reasonable time. For this particular purpose, this research leans towards using metaheuristic algorithms. Tese algorithms have diferent positive and negative aspects that sometimes cause them to reach nonoptimal or near-optimal solutions in a time-consuming process. To solve this problem, the combined algorithm introduced in the research conducted by Tavakolan and Nikoukar [38] has been used. Tis algorithm is a combination of the shufe frog algorithm as the basic algorithm and the improved genetic algorithm as the auxiliary algorithm. By eliminating nonoptimal solutions in the previous generations, the mutation operator of the genetic algorithm, while avoiding getting trapped in the local optima, reduces the search space. Tis improvement in the mutation operator of the genetic algorithm increases the accuracy of the answers, reduces the volume of computations, and thus signifcantly reduces the time of the program's execution.

Results
In this section, the obtained results are discussed based on the previous section. At frst, the data collection procedure and real project information are described as a case study; then, the quantitative analysis result and also the optimization of fnancing result are presented. After that, for checking the efect of the input variable change on the fnal results, a sensitivity analysis is performed, and eventually, the results are discussed.

Data Collection and Project Inputs.
Te data required for the current research were collected during the process and according to the following procedure: (i) Using a questionnaire flled up by the project members, the risk exposure of the project is calculated (ii) Risks related to the project have been identifed using feld and library studies, as well as interviews with project stakeholders (iii) To identify the possibility of contamination and the efect of the identifed risks on the main objectives of the project, a questionnaire was compiled and flled up by experts in the feld related to the project (iv) Te schedule and cost estimation of the project activities were compiled by the contractor planning members and were used in this research (v) Te required information and assumptions of the project, including the specifcations and scope of the project, the cost and revenues of the exploitation period, assumptions related to fnancing, and others are prepared by the contractor's planning team and are used in the research In the frst part, which is the frst step in the risk identifcation process, the risk exposure of the project is checked. As mentioned, to ensure consistent results, two simple questionnaires were used, one of which was expected to be flled up by the authors and the other by a member of the private sector. In both methods, the project is placed in the high-risk group and shows that the risk study will be necessary for the project; therefore, according to the decision made in terms of the necessity of project risk management, the research process can be continued.
In the next step, project risks are identifed. Considering the four main goals of time, cost, quality, and scope for the project and using the AHP method prioritization among the project goals have been performed to identify the risks and their probability and impact. Te results are shown in Table 10.
As it is evident from Table 10, based on the collective opinion, the order of the project objectives is in the sequence of time, cost, quality, and scope. Te weights of time and cost are higher than the others, and in the comparison between the weights of time and cost, the time objective has a higher priority. So, in the risk assessment, the time factor shall be given more attention than the rest of the factors. Also, the two factors of time and cost are considered for modeling.
To collect information about the importance of the identifed risks, their probability, and their impact on the selected time and cost goals, a questionnaire was prepared and distributed among experts. Figure 3 shows the severity of each of the optimistic and pessimistic approaches in a descending order. As can be seen, the downward trend of both approaches is almost constant, and it should be noted that high-ranked risks have signifcant numbers in terms of probability and impact.

Case Study.
To model the introduced framework, a real case study is introduced in the feld of renewable and new energies that focuses on the conversion of waste to energy through incineration. In this project, several assumptions have been considered for developing a schedule. Tese assumptions are mentioned as follows: (i) Te schedule is in the construction period and is divided into four categories: engineering, procurement, construction, and precommissioning.

Complexity
(ii) Te design phases of this project, which are carried out in Iran, include the design of structures and buildings, mechanical facilities, electrical facilities, precision instruments, and landscaping. Each of these phases is divided into two subsets of engineering phases 1 (initial design) and 2 (shop drawings). (iii) In the procurement phase, the disciplines of structure and architecture, mechanical and electrical instrumentation, and landscaping are mentioned in the activity order, with merely this diference that some of the main mechanical and electrical equipment, owing to the nature of the project, are procured from outside of Iran. So, this section is considered a separate activity. (iv) As the process of importing externally procured equipment into the workshop entails the continuous and long process of ordering, manufacturing, sending, and installing, the external procurement activity is thus considered a one-year activity. (v) For each of the defned items in the procurement section, one activity in the construction phase is considered. (vi) Considering that the import and installation of the main external procured equipment must be done continuously, the project structure and building must be completed before the equipment is entered the workshop. (vii) Te approximate initial duration of the project, regardless of the impact of risks, is three years.
Te schedule of the construction period is shown in Figure 4.
Te Monte Carlo simulation model for the construction and operation periods can be observed in Figures 5 and 6, considering the mentioned scenarios.
To implement the model, the Crystal Ball software is used as an Excel add-in. Using the Monte Carlo method, distributions are sampled and the number of simulation runs is considered 10,000; besides, the confdence level of 95% is considered as the stop criteria for the simulation.

Quantitative Analysis
Results. Te subsequent part of this section presents the outcomes derived from the Monte Carlo simulation concerning the primary objectives, which encompass the construction period's duration, the construction period's cost, the operation period's cost, the total cost, and the overall proft. Figure 7 shows the obtained cumulative and the density distribution functions for the time of the construction phase. Te average duration is about 1446 days (48 months), and its standard deviation is about 76 days (2.5 months). Te ftted distribution for this Figure 7 is the beta distribution with an A-D value of 0.4348; besides, the average duration is 1446 days which is compared to the initially estimated duration of 1095 days (three years) which shows a 32% increase. According to the probability of the obtained risks and their impact on project duration, the probability of project implementation in the estimated duration is almost equal to zero, which indicates the prominence of the identifed risks. Figure 8 shows the obtained cumulative and density distribution functions for the cost of the construction phase. Te average cost is about 582 billion tomans, and its standard deviation is about 19 billion tomans. Te ftted distribution for the fgure is the beta distribution with an A-D value of 0.8719. Moreover, the average cost of 582 billion tomans, compared to the initially estimated cost of 510 billion tomans, shows an increase of 14%, according to the probability of the obtained risks and their impact on the project cost, and the probability of the project implementation in the estimated cost is almost equal to zero, which indicates the primacy of the identifed risks. Figure 9 shows the obtained cumulative and the density distribution functions for the cost of the operation phase. Te average cost obtained is about 1,945 billion tomans, and its standard deviation is about 757 billion tomans. Te average cost obtained is 1,945 billion tomans which compared to the initial estimated cost of 1,700 billion tomans shows an increase of 11%. Considering the probability and the risk impact on the cost of operation, the probability of implementing the project with the estimated cost is almost zero, which indicates the importance of the identifed risks. Figure 10 shows the obtained cumulative and density distribution functions for the total cost of the construction and operation phases (the total cost of the BOT contract implementation). Te average cost obtained is about 2,525 billion tomans, and its standard deviation is about 758 billion tomans. Te average cost obtained, being compared to the initial estimated cost of 2210 billion tomans, shows an increase of 14%.

Complexity
It should be noted that the mentioned numbers are calculated based on a 50% confdence level and do not have a high reliability. Terefore, to increase the reliability of the mentioned numbers, it would be necessary to check higher confdence levels. Table 11 shows the project time and cost at diferent confdence levels.
Considering that through the conversion of waste to energy via burning, the contractor's income is obtained during the operation period; therefore, through the calculation of the power plant capacity, the estimated amount of required electricity, the minimum guarantee of electricity purchase by the government, and also the basic rate of electricity purchase the fnal income of the project during the operation could be calculated. Considering the current net value of money, the optimal operational period and the fnal proft of the contractor could be calculated. According to the mentioned topics, the following assumptions are considered for calculating the income of the operation period:

Complexity 13
(iv) Te minimum purchase price of basic power is 777 tomans per kilowatt-hour (v) Incomes in diferent years are calculated based on the estimated infation in the previous year (vi) Te annual discount rate is considered 15% Figure 11 shows the probabilistic diagram of the optimized time of the operation period. As could be seen, an average of 18 years is needed for the operation period with the mentioned conditions, so that the contractor does not incur any losses but based on the initial estimate, a 15-year operation period is needed. Also, with confdence levels of 70% and 90%, 19 and 21 years are entailed for ensuring the contractor's proft. Te obtained results indicate that in case the risks of the project are taken into account and an operation of 15 years period is selected, at the time of the contract, the contractor would sufer irreparable losses. Figure 12 shows the probability distribution diagram of the obtained optimal proft that corresponds to the obtained optimal period in the operation phase. With confdence levels of 50%, 70%, and 90%, the predicted proft of the contractor (net present value of money) would be equal to 20, 34, and 51 billion tomans, respectively.

Financing Results.
To ensure the correct performance of the introduced method, the results obtained from the algorithm on a numerical example of their research have been compared with the results obtained on that by Alavipour and Arditi [31]. Table 12 represents the comparative results, and as can be seen, the obtained results are similar and valid. Table 13 shows the basic information that is necessary for the hybrid optimization algorithm. Using a form created in the VISUAL STUDIO software, this information is entered by the user.
Te initial information has three parts: hybrid algorithm specifcations, fnancing specifcations, and general project specifcations. As can be seen in the table, the initial population size of the algorithm is considered 100 chromosomes, which is divided into 10 groups. Te generations' improvement is carried out during 100 iterations with a single-point crossover and a mutation rate of 25%.
Te necessary specifcations for fnancing are considered based on the current condition of the project and its risks. As can be seen, the annual percentage rate for long-term loans is 8%, the annual percentage rate for short-term loans (3 to 12 months) is 23% to 8%, and the annual percentage rate for credits is 15%; besides, the time of receiving a long-term loan is at the beginning of the project (month 0), and its repayment would be until the end of the construction period. Te limit for receiving long-term loans is 300 billion tomans.

Complexity
For short-term loans, the amount is 2 billion tomans, and there is no limit for receiving credit. Te minimum negative cumulative balance of the contractor's cash fow is considered zero.
It should be mentioned that for investigating the efect of fnancing on the project, the considered confdence level of time, based on the simulation results, is 90%. And the operation period is 20 years. Te information on cash   Figure 11: Te distribution obtained from the simulation to calculate the optimal exploitation period. 16 Complexity infows and outfows of the project during the period of construction and operation is given in Table 14.
To implement the fnancing optimization, the project information is read from an excel sheet the address of which is given by the user. Te algorithm is written in VB.Net language. After the start of the program, cash infows and outfows are calculated for each period of the project. Tese fows would be used in calculating the fnancing fow of the project. Ten, the hybrid algorithm, based on the given information and limitations, applies diferent fnancing options to the cash fow of the project, calculates the optimal option, and prints the results in an Excel sheet. Te obtained results show all the incoming and outgoing liquidity fows for the project, long-term loans, short-term loans, and credits received in each period (monthly) from the beginning of construction to the end of the operation. Tables 15   and 16 show the summary of the results obtained from the project fnancing optimization.
As can be seen, the cumulative balance of cash fow with fnancing, compared to the cumulative balance of cash fow without fnancing, is quite 23% diferent. Tis indicates the importance of proper fnancing, as well as its impact and also the signifcance of the cost of repaying long-term and shortterm loans and credits. Considering the impact of fnancing in the estimation of operation periods can determine the project's failure or success.

Sensitivity Analysis.
To examine the efects of the changes on the total cost of the project fnancing, a sensitivity analysis is performed in the negative credit limit of the contractor's cumulative cash fow (fnal proft of the project). As shown in Table 17, the analysis is based on fve stages of change in the negative credit limit. Figure 13 shows that in the initial state of the project, a change in the negative cumulative balance of the contractor's cash fow has had the greatest impact on the reduction of fnancing costs compared to the initial state (credit limit � zero). As the negative credit limit increases, its efect intensity is reduced, so the increase of the negative credit limit of the contractor, compared to 300,000 million tomans, does not have much efect on the reduction of fnancing costs.
As expected, the worst case occurs when the contractor cannot accept a negative credit limit (the credit limit is zero). Hence, in order to prevent the contractor from surpassing the credit limits, a considerable fnancing cost is necessary. Tis aspect clearly demonstrates how the negative credit limit of the contractor's cash fow contributes to reducing fnancing costs.   Besides, the results show that the amount of credit used is much higher than the amount of short-term and longterm loans. Tus, to investigate the efect of changes in the repayment percentage on the fnal cost of fnancing, another sensitivity analysis is performed on the repayment percentage of the fnancing options (credit line, short-term loan, and long-term loan). Figure 14 demonstrates the change in the fnancing cost arising from the change in the repayment percentage of the credit line. As predicted, a drastic change is observed in the  18 Complexity cost of fnancing due to the change in the repayment percentage. In this way, if a credit line with a lower repayment percentage is used, fnancing costs would be signifcantly reduced. At the same time, no signifcant efect is observed on account of the change in the repayment percentage of long-term and short-term loans.

Discussion
In this section, the obtained results and their superiority are examined compared to other research. It shall be noted that the obtained results have been seen and approved by the project contractor. Based on the results obtained from this research, the implementation and operation planning of the project have been revised.
(i) Te results obtained from the questionnaire indicate that risks such as infation, currency supply, and contractors' claims are among the risks which are most likely to occur and have an impact on the time and cost of the project. Moreover, the risks of delay in the delivery of imported goods and equipment, changes in the vendor list, and changes in technical maps shall be placed in the planning priority.
(ii) Te results of the quantitative risk analysis show that according to the project conditions and in case the current conditions continue, with 90% confdence, in the construction period, the implementation of waste-to-energy power plant construction projects can face a 32% increase in time and a 20% increase in cost. Being aware of these issues, and planning to face them before project implementation, or including these risks in the contract clauses can create a guarantee for the proftability and success of the project. (iii) According to the conditions of the project risks, with 90% confdence, the impact of the risks of the operation period on costs, including salaries and wages, maintenance, raw materials, and energy, can lead to an increase of 40%. If these risks and their impact on the costs of the operation period are not taken into account, the operation period would increase, which causes contractual and legal conficts between the contractor and the client. (iv) Using the developed model of this research can help the managers and planners of the contractor. So, in the case of developing the project as a BOT, due to   the risks of this period and at the time of signing the contract, they can predict the increase in the operation duration. In the investigated case study, an increase of 33% (5 years) in the duration of the operation period is predicted compared to when no risks are considered in the project. Terefore, it would be necessary to modify the operation period at the beginning of the project by considering the risks of the project and its efect on the construction and operation period.

Managerial Insights and Practical Implications
Te proposed model can be applied to solve fnancing optimization problems with a variety of fnancing options. In practice, the results of the model can help contractors and investors to plan the project considering risk impact and fnancial issues. Furthermore, the proposed model can help contractors to determine and promote an appropriate fnance scheduling to guarantee the project proft. Also, correct estimation of the operation period can reduce conficts between the project stakeholders. Presently, the impact of project risks on project schedules and costs cannot be calculated using planning software (such as Primavera P6 and MS Project). Tese programs cannot produce optimized fnancing fows based on project schedules; therefore, almost any schedule that does not take into account the project's constraints and risks would be impractical. As mentioned throughout the study, the study's practical contribution is focused on a workable fnancial schedule for a real project that takes into consideration the uncertainties of the project activities and the efects that they have on project objectives (time and cost).
Tis, when calculating real time and cost, could enable project managers to take advantage of cutting-edge planning tools that refect the project's existing features and uncertainties and produce an optimized fnancing schedule.
While taking risks into account, to provide a workable fnance schedule, the proposed framework might be added to software like MS Project as a plugin. Additionally, the proposed method is used on the mentioned actual project and will be applied to additional contractor projects upon request.

Conclusion
In this article, a fnancing optimization model has been developed that considers the impact of the risks on the BOT contract and focuses on a waste-to-energy power plant construction project. Tis study presents a fnance-based scheduling model that might handle a variety of constraints. Compared with previous research, there are some signifcant results and improvements in the proposed model:  20 Complexity been calculated as 21 years, which shows a 40% increase compared to the initial operation period of 15 years. Tis issue shows that not considering the efect of risks can lead to a signifcant loss for the contractor and increase the conficts between the client and the contractor. (iii) Te fnancing optimization model introduced in this research might check the cash fows of the project in all time frames of the project. (iv) According to the analysis of the fows during the life of the project and according to the constraints of the contractor, a fnancing plan is carried out, based on which the contractor can prevent the occurrence of negative liquidity during the project and also can calculate the efect of loans and credits' repayments on the fnal proft of the project. (v) Te results of the application of this optimization model to the case study of the waste-to-energy project have shown that the consideration of fnancing from the beginning of the construction period, the repayment of loans and credits along with their interest rates, can lead to a decrease of 23% in the project's proft. (vi) Tis issue shall also be considered by the contractor at the time of signing the contract. Besides, if the contractor can increase the negative credit limit of his cumulative cash fow during the project, he can prevent the reduction of the fnal proft of the project to an acceptable extent. Te result of the frst sensitivity analysis shows that if the contractor can bear a negative cash fow of up to 300 billion, the reduction of the project's proft due to the payment of fnancing costs can be reduced from 23% to 5%. Tis issue causes more signifcant proft for the contractor.
(vii) In addition, the results of the second sensitivity analysis show that the change in the interest rate for the credit line option can have a signifcant efect on the change in the fnancing cost of the project. Tis is while the change of interest rate in both longterm and short-term loans does not have much efect on the cost of fnancing.
Te fnancing optimization model, along with the quantitative risk analysis model other than helping planners and managers to make strategic decisions, allows them to get aware of the project conditions prior to implementation. At the same time, this model is designed as an Excel add-in, which is easy to work with; besides, it ofers an acceptable calculation and processing speed due to the large scale of the project.
Similar to all other research, this research also has had its limitations, one of which has been the examination of risks and their impact on other areas of renewable and new energy, i.e., wind and solar energy projects.
Since the quantitative risk analysis model is written in an Excel fle via the Crystal Ball plugin, the automatic analysis of the schedule would not be probable. Te schedule must be written in an Excel fle, and the problem inputs must be determined manually. On the other hand, as the types of projects and contracts can be diferent, the cash fow information of the incoming and outgoing activities in the fnancing optimization model is to be written manually in Excel. In terms of calculations, it is assumed that these fows are divided equally over the entire duration of the activity.
According to the mentioned limitations, the following items are suggested to improve future research: (i) Considering the basic need for risk management in projects, especially infrastructural projects, preformation of the studies on diferent areas is suggested (such as other renewable energies); besides, it is suggested that the process of risk identifcation and management is performed and compiled in a documented manner. (ii) Te development of an automatic and comprehensive platform for risk management that has a suitable user interface, as well as various capabilities compatible with other areas of construction projects, is introduced as another suggestion for future studies.

Notations
Indices k: Index of identifed risk k ∈ 1, 2, ..., K { } R k : Set of identifed risks (risk k) i: Index of project activity i ∈ N t: Index of operation year t ∈ 1, 2, ..., T { } u: Index of operation cost u ∈ 1, 2, 3, 4 { } ⊂ U y: Index of cash fows period y ∈ 0, 1, ..., Y { }. Parameters n: Number of identifed risks P R k : Probability of risk R k occurrence I R k : Impact of the risk R k occurrence Con t i,R k : Conditional impact of risk R k on activity i duration UR k : Random value drawn from a uniform distribution (related to risk R k ) FD i : Final duration of activity i considering its risk impacts SV ND i : Random value drawn from a normal distribution for activity i EST i : Earliest start time of successor activity i EFT j : Earliest fnish time of predecessor activity j Lag i,j : Required time interval between the start time of successor activity i and the completion time of predecessor activity j LST: Latest start time of an activity LFT: Latest fnish time of an activity Con t i,R k : Conditional impact of risk R k on activity i cost FC i : Final cost of activity i considering its risk impacts FOC t,u : Final cost of operation cost u at operation year t considering its risk impacts Con c u,t,R k : Conditional impact of risk R k on operation cost u at operation year t TD C : Total construction duration Total project cost TI t : Total income at operation year t V t,ND : Amount of power sales at operation year t drawn from a normal distribution S t : Price of one unit of power sale at operation year t TD O : Total operation duration TD: Total project duration B y : Total amount borrowed at the end of period y RE y : Total amount repaid at the end of period y FI y : Total fnancing cost at the end of period y TR y : Total outfow of fnancing at the end of the period y NF y : Net fow of fnancing at the end of the period y NFC y : Net cumulative balance of fnancing cost at the end of the period y TFC: Total fnancing cost N y ′ : Net cumulative balance of cash fows (project and fnance) at the end of period y P in y : Total project infow at the end of period y P out y : Total project outfow at the end of period y. Decision Variables B ST,y : Te cumulative lent short-term loan amount at the end of period y B LT,y : Te cumulative lent long-term loan amount at the end of period y B LC,y : Te cumulative lent line of credit amount at the end of period y RE ST,y : Te cumulative repaid short-term loan amount at the end of period y RE LT,y : Te cumulative repaid long-term loan amount at the end of period y RE LC,y : Te cumulative repaid line of credit amount at the end of period y FI ST,y : Te cumulative fnancing cost of short-term loan at the end of period y FI LT,y : Te cumulative fnancing cost of long-term loan at the end of period y FI LC,y : Te cumulative fnancing cost of line of credit at the end of period y CL ST : Total limit set for short-term loan options CL ST ′ : Te limit set for short-term loan options at the end of each period CL LT ′ : Te limit set for long-term loan options at the end of each period C LC,y : Required credit at the end of period y CL LC : Total limit of the line of credit CL LC ′ : Te credit limit in each period MN: Minimum cumulative balance of cash fow in each period.

Data Availability
Data generated or analyzed during this study are available from the corresponding author upon reasonable request.

Conflicts of Interest
Te authors declare that there are no conficts of interest.