^{2}PProfessor, Dept of Building and Real Estate (BRE), the Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
^{3}PDepartment of Civil and Architectural Engineering College of Engineering, Sultan Qaboos University. P.O. Box 33, Al khoud 123 Muscat, Oman
Keywords: Cash flow forecasting mode; Activities’ criticality; CPM; Simulation;
Cashflow parameters, including the maximum value of the cumulative negative balance, financing cost, project profit and project duration, vary according to the specified values of the stochastic activities’ start times. In this paper, the CPM networks are linked to the cashflow models such that the delays in the activities start times are reflected directly in the calculation of the cashflow parameters. Discrete uniform probability distributions can reasonably be assumed to sample start times within the ranges between activities’ early and late start times. Discrete uniform distributions assign equal probability to the start times within the specified range.
The Monte Carlo simulation technique is used to generate schedules by sampling from the discrete uniform distributions of the activities start times while maintaining activities’ relationships and calculates the associated cash flow parameters. Accordingly, the activities’ criticality can reliably be assessed using the correlation and quantitatively evaluated using the correlation coefficient. Likewise, the activities’ criticality related to the cash flow parameters describes the sensitivity of the individual cashflow parameters to the delays in their start times. Currently, there is a lack of a tool in the literature that practitioners can use to assess an activity’s criticality to cash flow parameters.
Cash flow forecasting models should be developed before submitting tenders, as a means to preview the distribution of cash flow and the amount of equity required. Cash flow forecasting models are used to preview fundrelated requirements and they can be used to manage the fluctuation of the project cash balance. (Cheng C, et al. [3])
Many researchers have studied cash flow forecasting. Au and Hendrickson (1986) developed a cash flow forecasting model. Their model determines the cumulative cash flow at the end of a set period, the net balance (defined as net cash flow at the end of a set period and after receiving a payment), the total financing cost, the accumulated financing cost, the cumulative negative balance at end of a period and the net cumulative cash flow or the project’s profit. Navon, [14] developed a cash flow management model for the organizational level, using a detailed computer program which can be used at both the company and the project level to compute the expected capital cost and determine the loans needed. Navon’s model incorporates a time lag, so it is considered to be a tool for forecasting cash flow, thanks to its flexibility. However, this model does not consider the uncertainty environment.
Hwee and Tiong, [8] developed a model that has a cash flow forecasting ability. The model uses a program to predict the trend of cash flows in a project, and accounts for a degree of uncertainty. The Internal Rate of Return (IRR) is presented as the performance of the project’s profit, due to the lost cost of interest. Kaka and Lewis, [10] presented a dynamic cash flow forecasting model that would assist contractors to effectively plan and manage the cash flow of individual projects at a company level. Park, et al. [17] proposed a model to forecast cash flow during construction based on the planned earned value. This study introduced moving weights of cost categories, dependent upon the progress of a project. Their model can be used as a simple tool to forecast cash flow at the jobsite; however, it has some shortcomings as it depends on managing the cost and earned value each month, and it ignores the inherent difficulties involved in obtaining reliable variables at the jobsite. Elazouni A, [5] developed mathematical equations to calculate cash flow parameters from the contractors’ perspective as Contractors normally deposit the payments into the creditline accounts to continually reduce the outstanding debit (cumulative negative balance). Other Contractors use loans to borrow money and reduce the negative cash flow (Alavipour and Arditi, 2018). Cheng, et al. [3] developed a cash flow forecasting model. Their model uses the average values of construction scheduling predictions to decrease variation, reduce costs and increase earnings, but this use of averaged figures can be considered one of its shortcomings. Zayed and Liu, [20] developed a cash flow mathematical model that considers uncertainty. Their model can be used as an automated tool to forecast cash flow.
Scheduling activities should be done so that cash inflow occurs early and cash outflow occurs later. (Padman and Zhu, [16]; Kimms, [11]; Vanhoucke, et al. [19]). The Resource Investment Problem (RIP) is defined as the problem of minimizing renewable resource costs subject to a project due date. The objective is to obtain a schedule aligned with the resource requirements (Najafi and Azimi, [13]).
The cost–schedule integration technique assumes that cash flows for a project are a function of the project schedule makes extensive use of the project estimate and schedule data. The integration between scheduling and cash flow requires detailed information such as the bill(s) of quantities and detailed schedules, including activity descriptions and activity durations with all the resources needed for these activities (Chen, et al, [4]; Navon, [14]).
Many researchers have focused on the domain of Resource Constrained Scheduling Problems (RCSP) with cash flow. Zhu and Padman, [21] applied tabu search Meta heuristics procedures to produce the best schedules in over 85% of the projects. Waligora, [7] elaborates the properties of an optimal schedule and formulates a mathematical programming problem for optimal resource allocation. Padman and Zhu, [16] presented a problem space computational model to solve the scheduling problem with cash flow. Najafi and Azimi, [13] defined the project scheduling problem as the combination of precedence constraints and resource constraints, such as project duration, project total cost and optimization of net present value. Navon, [14] developed automatic cost/schedule integration, which allows the cost of each resource to associate automatically with its appropriate activity. Chen, et al. [4] presented a methodology to assess the accuracy of Cost Schedule Integration (CSI) models and their components. Chen and Weng, (2009) proposed GA model that considered the problems of time cost trade off and resource constrains scheduling problems. The main purpose of their model is to generate schedules. Maravas and pantouvakis (2012) developed a method for project managers to incorporate the source of uncertainty. Their developed method can assist managers with working capital requirements; it can be used for earned value. However, authors did not incorporate factors impacting cash in and out flow. Han, et al. (2014) proposed a method to predict project profit, evaluate projects and determine the negative balance. The authors examined risk variables and its impact on project cost. However, the example application did not describe the cost increase at the activity level. A detailed schedule is recommended for a better forecasting of project cash flow. Han, et al. (2014) recommended the future work, they advised that different factors should be defined and incorporated with the cash flow to address the cost increase. Lu, et al. (2016) developed a methodology frame work to analyze cash flow and support decision making. The framework helped contractors to accurately define alternatives. However, the proposed framework did not consider uncertainty. It neglected sub contractor’s factor cost. ElAbbasy, et al. (2017) proposed multi objective scheduling optimization model for multiple construction projects. The model included project scheduling, resource allocation and cash flow forecasting. Alavipour and Arditi, (2018) developed a model to minimize financing, the model generated cash flow based on a CPM network.
The CPM model, which is built in an Excel environment, takes the activity data as inputs and calculates the early start, early finish, late start, late finish and the total float of the activities based on the activities’ durations and on the dependencies between activities. Activities C, F, G, J, M and O exhibited total float values of zero and thus were considered the critical activities. Figure 2 shows the CPM network of the project activities’ durations with all the CPM calculations. The start times of activities are defined in specific ranges. These specific ranges are determined based on the extension scheme. Different schedules are generated by assigning different activity start times, within their respective ranges. The start time of each activity can be shifted within a range defined by an early to a late start, plus an extension increment, while maintaining the dependencies between activities.
The total direct cost of each day was calculated as the sum of the direct costs of all the activities ongoing that day. The total direct cost of each week was calculated as the sum of the total direct cost of the five days comprising that week. Cash outflow is the total direct cost of each week plus the overhead. Cash inflow is the cash outflow of each week plus the mark up. To stochastically incorporate the impact of the quantitative factors on the cash inflow and outflow transactions, the probability distribution of the weight and the effect of each factor defined by Zayed and Liu, [20] were used. The cash outflow of each week is calculated based on the total direct cost plus the overhead, incorporating the combined impact of all the weights and effects of all the cash outflow qualitative factors. The cash inflow is calculated as the cash outflow plus the mark up, thereby incorporating the impact of all the qualitative factors that affect the cash inflow. Equations 1 and 2, developed by Zayed and Liu, [20], are used to adjust cash inflow and outflow in order to incorporate the impact of the factors that affect the cash inflow and cash outflow transactions, using stochastic analysis.
$$Cash\text{}inflow\text{}model\text{}=(1{\displaystyle {\sum}_{l=1}^{n}{W}_{l}*{E}_{l}*P})*Cashi{n}_{m}\text{}Eq.\text{}1$$
Where ${W}_{l}$ is the weight of factor l; ${E}_{l}$ is the effect of factor l; P is the percent of cash that represents the factors’ effect, and ${C}_{inm}$ is the owner payment at specific time period m.
$$Cash\text{}outflow=(1+{\displaystyle {\sum}_{k=1}^{n}{W}_{k}*{E}_{k}*P)*\left(1+i\right)*Cashou{t}_{m}}\text{}Eq.\text{}2$$
Where ${W}_{k}$ is the weight of factor k, and ${E}_{k}$ is the effect of factor k. out ${C}_{outm}$ is the estimated cash outflow of the project at a specific time m. P is the range of percentage of cash that is affected by the qualitative factors; it represents the cash involved in the calculations. In order to get the accurate value of the p percent, which is the percentage of cash that is affected by the qualitative factors’ effect a special questionnaire was designed as part of the current study and sent to thirty companies in North America. Companies are selected based on their experience and based on data availability of their contact information. Eleven companies responded which constitutes 37% of the total distributed. The results showed that P percent follow a triangle probability distribution, with a minimum value of 4%, a maximum value of 60%, and a mean value of 35%. Table 2 shows that the impact of the qualitative factors that affect the cash inflow decreases the cash inflow by 9%. In Table 3, the impact of the factors that affect the cash outflow is calculated to be 10.6 %, which means that the cash outflow transactions will be increased by this percent.
Category 
Factors 

Financial 
F1Change of progress payment duration (I) 
F7Loan repayment (O) 
Subcontractor 
Sub1Decisions to subcontract (O) 
Sub3Failure of subcontractor (I&O) 
Suppliers 
Sup1Delay of making payments (O) 
Sup3Delay in delivery (I&O) 
Prior to 
P1Poor design (O) 
P4Cash flow forecasting (O) 
P3Estimating strategies (O) 


During 
D1Mistakes in executing the work (I&O) 
D5Small project’s duration increase/decrease (I&O) 
Communication 
C1Disputes between contractor and owner (I&O) 
C3Relations with owner (I&O) 
Others 
O1Weather condition (I&O) 
O3 Negative change order (I&O) 
Factors 
Weight (W) 
Effect (E) 
P 
W*E*P 
F1 
0.02617 
0.819 
0.3 
0.00643 
F2 
0.018995 
0.713 
0.3 
0.004063 
F3 
0.019968 
0.758 
0.3 
0.004541 
F4 
0.018021 
0.704 
0.3 
0.003806 
F5 
0.013871 
0.626 
0.3 
0.002605 
F9 
0.015617 
0.666 
0.3 
0.00312 
F10 
0.014745 
0.664 
0.3 
0.002937 
P2 
0.011678 
0.572 
0.3 
0.002004 
P5 
0.011448 
0.613 
0.3 
0.002105 
D1 
0.017889 
0.708 
0.3 
0.0038 
D3 
0.01139 
0.525 
0.3 
0.001794 
D4 
0.018397 
0.715 
0.3 
0.003946 
D5 
0.012533 
0.635 
0.3 
0.002388 
D6 
0.022081 
0.813 
0.3 
0.005386 
D9 
0.02268 
0.856 
0.3 
0.005824 
C1 
0.016145 
0.689 
0.3 
0.003337 
C2 
0.013209 
0.645 
0.3 
0.002556 
C3 
0.015893 
0.738 
0.3 
0.003519 
Sub3 
0.019504 
0.695 
0.3 
0.004067 
Sup3 
0.017976 
0.719 
0.3 
0.003877 
O1 
0.01765 
0.633 
0.3 
0.003352 
O2 
0.017296 
0.61 
0.3 
0.003165 
O3 
0.010495 
0.511 
0.3 
0.001609 
O4 
0.02141 
0.719 
0.3 
0.004618 
O5 
0.020461 
0.686 
0.3 
0.004211 
1 Sum W*E*P = 
0.910941 
Factors 
Weight (W) 
Effect(E) 
P 
W*E*P 
F6 
0.02192 
0.796 
0.3 
0.005234 
F7 
0.01648 
0.659 
0.3 
0.003258 
F8 
0.018614 
0.729 
0.3 
0.004071 
F9 
0.015617 
0.666 
0.3 
0.00312 
F10 
0.014745 
0.664 
0.3 
0.002937 
F11 
0.011054 
0.605 
0.3 
0.002006 
F12 
0.01094 
0.611 
0.3 
0.002005 
P1 
0.019067 
0.734 
0.3 
0.004199 
P2 
0.011678 
0.572 
0.3 
0.002004 
P3 
0.014461 
0.658 
0.3 
0.002855 
P4 
0.019148 
0.747 
0.3 
0.004291 
D1 
0.017889 
0.708 
0.3 
0.0038 
D2 
0.009527 
0.532 
0.3 
0.001521 
D3 
0.01139 
0.525 
0.3 
0.001794 
D4 
0.018397 
0.715 
0.3 
0.003946 
D5 
0.012533 
0.635 
0.3 
0.002388 
D6 
0.022081 
0.813 
0.3 
0.005386 
D7 
0.017897 
0.739 
0.3 
0.003968 
D8 
0.005282 
0.652 
0.3 
0.001033 
D9 
0.02268 
0.856 
0.3 
0.005824 
C1 
0.016145 
0.689 
0.3 
0.003337 
C2 
0.013209 
0.645 
0.3 
0.002556 
C3 
0.015893 
0.738 
0.3 
0.003519 
C4 
0.00896 
0.554 
0.3 
0.001489 
Sub1 
0.014268 
0.624 
0.3 
0.002671 
Sub2 
0.012922 
0.658 
0.3 
0.002551 
Sub3 
0.019504 
0.695 
0.3 
0.004067 
Sub4 
0.013296 
0.582 
0.3 
0.002321 
Sup1 
0.016153 
0.652 
0.3 
0.00316 
Sup2 
0.014114 
0.627 
0.3 
0.002655 
Sup3 
0.017976 
0.719 
0.3 
0.003877 
Sup4 
0.01203 
0.555 
0.3 
0.002003 
O1 
0.01765 
0.633 
0.3 
0.003352 
O2 
0.017296 
0.61 
0.3 
0.003165 
1 + Sum W*P*E 
1.106362 
$$\begin{array}{l}f(x)=\{\begin{array}{l}\left(xSA\right)*\frac{CA}{DA}IfxSAand\left(xSA\right)1andx\le FA\\ 1*\frac{CA}{DA}IfxSAandx\le FAand\left(xSA\right)\ge 1\\ \left(FAFA\right)*\frac{CA}{DA}If\left(xSA\right)and\left(x=FA\right)and\left(xSA\right)1and\left(FAx\right)1)\\ 0otherwise\end{array}\text{}Eq.\text{}3\\ \end{array}$$
Where x is a deterministic variable that indicates the start time of the activity’s direct cost representation. The value of the variable x can range from one day to the extended total duration. SA is a stochastic variable; it shows the start time of activity A. FA is a deterministic variable that shows the finish time of activity A. CA is a deterministic variable and indicates the direct cost of activity A. DA is a deterministic variable that gives the duration of activity A. This equation has been defined for each day in the project duration, for each of the project’s activities. After the representation of the direct cost of each activity’s day, the total direct cost of each day can be calculated.
Were${E}_{t}$ is the cash outflow during a typical period t, and ${N}_{t1}$ is the cumulative net balance at the end of period t1. The cumulative net balance at the end of period t after receiving payment ${P}_{t}$ is defined as ${N}_{t}$ . At the end of period t1, ${N}_{t1}$ can be calculated from equation 5.
Where ${F}_{t1}$ − is the cumulative balance, Pt1 is the payment received, and ${N}_{t1}$ is the cumulative net balance. When contractors decide to pay the financing costs at the end of the project, the periodical financing costs are compounded by applying equation 6:
$${\widehat{I}}_{t}={\displaystyle \sum _{l=1}^{t}{I}_{l}{\left(1+r\right)}^{tl}}\text{}Eq.\text{}6$$
Where ${\widehat{I}}_{t}$ is the cumulative financing cost, r interest rate. Thus, the cumulative balance at the end of period t, including accumulated financing costs, is represented by ${\widehat{F}}_{t}$ which is calculated as:
$${\widehat{F}}_{t}={F}_{t}+{\widehat{I}}_{t}\text{}Eq.\text{}7$$
The cumulative net balance including the financing cost is thus ${\widehat{N}}_{t}$ :
$${\widehat{N}}_{t}={\widehat{F}}_{t}+{P}_{t}\text{}Eq.\text{}8$$
The positive value of ${\widehat{N}}_{t}$ at the end of the last period L represents the corporate profit.
The calculation of cash flow parameters depends on the activities’ cash outflow and inflow. The cash outflow for a week depends on the total direct cost of the activities in that week plus overhead. The cash inflow is the cash outflow plus the markup, as the project contract is for cost plus fees. In this research, a stochastic interest rate is defined by collecting data for the interest rate of the last 10 years and using the bestfit option in @RISK. The interest rate is defined as a triangular probability distribution with a mean value of 0.19%, minimum value of 0.125% and maximum value of 0.25%. The weekly cash outflow and cash inflow transactions were determined and adjusted to incorporate the impact of the qualitative factors. The weekly cash outflow is calculated based on the total direct cost of the activities plus overhead, multiplied by 1.106, which represents the impact of the cash outflow qualitative factors. The weekly cash inflow is calculated based on the weekly cash outflow plus markup multiplied by 0.91, which represents the impact of the cash inflow qualitative factors. Cash inflow and Cash outflow can be calculated using equations 9, 10 and 11.
where ${E}_{t}$ is the cash outflow at time period t, n is the number of days comprising the time period,${D}_{i}$ is the sum of the total direct cost of all the activities ongoing during one unit of the time period t, OH is the overhead, and $Cout$ factor is stochastic variable, it is the cash outflow factors’ impact.
${P}_{t}$ is the cash inflow transaction for the disbursements at time period t. ${E}_{t2}$ is the cash outflow at time period t2; $Cin$ factor is the cash inflow factors’ impact, it is stochastic variable.
The cashflow is developed from the contractors’ perspective. Contractors often procure funds from banks by establishing creditline accounts. Cash flow parameters include maximum negative cumulative balance; project profit and financing cost are calculated using equation 1 till equation 5 that were used before in an earlier study by Elazouni, 2009. These equations are illustrated in details in the background section.
the start time of activity B as
; the start time of activity C as
And the start time of activity D as
Where FA and FB are deterministic variables that represent the finish times of activities A and B, respectively. The start time of activity E is defined as
$$f\left(x\right)=FBx\in \left\{6,7,8,9,10,11,12,13,14,15,16\right\}\text{}Eq.\text{}15$$ Where FB is a deterministic variable it represents the finish time of activity B. The start time of activity F is defined as
$$f\left(x\right)=\{\begin{array}{c}FBifFBFC\\ FCotherwise\end{array}x\in \left\{12,13,14,15,16,17\right\}\text{}Eq.\text{}16$$
Where FB and FC are deterministic variables that represent the finish times of activities B and C, respectively. The start time of activity G is defined as
$$\begin{array}{l}f\left(x\right)=\{\begin{array}{l}FDifFDFEandFDFF\\ FEifFEFDandFEFF\\ FFifFFFDandFFFE\end{array}x\in \left\{17,18,19,20,21,22\right\}\text{}Eq.\text{}17\\ \end{array}$$
Where FD, FE and FF are deterministic variables representing the finish times of activities D, E and F, respectively.
The advantage of using these models is that they allow the dependencies between the activities to be maintained while applying the Monte Carlo simulation. This is achieved by running the simulation through a number of iterations, suddenly stopping the simulation and saving the resulted new schedules. This procedure was repeated approximately ten times for each extension increment. We thus saved several different schedules which could then be easily checked for the dependencies between activities. Moreover, this procedure ensures that the activities’ start times are within the range of the early start time to the late start time plus the extension increment. The direct cost of each activity was verified and calculated for each generated schedule based on the new start and finish times of the activities. The cash outflows and inflows were checked as well, as were the calculations of the other cash flow parameters: the financing cost, the maximum negative cumulative balance and the project profit.
The results in Table 4 indicate that the mean value of the maximum cumulative negative balance decreases with the increase of the extension increment. The mean values of the maximum cumulative negative balance for 0, 5, 10 and 15day extension increments are $46,298.09, $44,586.89, $42,893.05 and $41,377.81, respectively. Whenever the duration is increased, the number of activities that are ongoing during any period decreases. Accordingly, the amount of cash that a contractor borrows during any period decreases and consequently the maximum negative cumulative balance decreases.
The results in Table 4 indicate that the project profit increases with the increase of the extension increment. The mean values of the profit for the 0, 5, 10 and 15day extension increments are $21,912.93, $21,923.3, $21,930.91 and $21,940.38, respectively. In the current project, which represents a cost plus contract, the profit varies exclusively according to the variations of the financing cost. The lower the financing cost, the higher the profit. Since the financing cost decreases with the increase of the extension increment, the profit increases with the increase of the extension increment. As presented in Table 4 and Table 5 the mean value of the financing cost and the maximum negative cumulative balance decrease with the increase of the extension. Moreover, their values increase from scenario I to scenario II due to the incorporated qualitative factors, which consequently increase the cash out and decrease the cash inflow transactions. The results indicate that the mean value of the financing cost for scenarios I and II are $397.25 and $432.67, respectively, with an extension increment of 5 days. The results also show that the mean values of the maximum negative cumulative balance for scenarios I and II are $44,586.9 and $47,972.99, respectively. The project profit increases from scenario I to scenario II; the results indicate the mean profit values for scenarios I and II are $21,912 and $23,224.60, respectively, for an extension increment of 5 days. It can be observed that the project profit has no fixed trends with the extensions of 5, 10 or 15 days for scenario II, due to the stochastic impact of the qualitative factors.
Scenario 
Cash flow Parameters 
Ranges 
Extension Increment 

Scenario I 

0 days 
5days 
10 days 
15 days 

Minimum 
269.6 
257.8 
244.33 
258.17 

Maximum 
542.95 
547.4 
544.8 
520.86 

Mean 
404.71 
397.25 
390.58 
384.47 


Minimum 
41320.12 
33680.39 
29549.44 
30407.61 

Maximum 
51414.77 
56155.39 
55991.18 
55809.91 

Mean 
46298.09 
44586.89 
42893.05 
41377.81 

D 
Minimum 
40 days 
42 days 
45 days 
48 days 

Maximum 
40 days 
45 days 
50 days 
55 days 

Mean 
40 days 
44 days 
49 days 
54 days 


Minimum 
20586.59 
20476.9 
20318.11 
20684.43 

Maximum 
23044.9 
23563.09 
24571.32 
23100.67 

Mean 
21912.93 
21923.26 
21930.91 
21940.38 
Scenario 
Cash flow Parameters 
Ranges 
Extension Increment 

Scenario II 
$${\widehat{I}}_{t}(\$)$$ (Financing cost) 
0 days 
5days 
10 days 
15 days 

Minimum 
276 
285.8 
284.6 
278.16 

Maximum 
628 
603.1 
587.3 
565.57 

Mean 
440.9 
432.4 
425.22 
418.3 

$${\widehat{F}}_{t}(\$)$$
(Max negative Balance) 
Minimum 
40753.94 
35999 
32989.38 
31846.97 

Maximum 
58894 
58137 
58372.4 
57329.97 

Mean 
50004.15 
47958.5 
46128.7 
44581.67 

D 
Minimum 
40 days 
42 days 
47 days 
49 days 

Maximum 
40 days 
45 days 
50 days 
55 days 

Mean 
40 days 
44 days 
49 days 
54 days 

$${\widehat{N}}_{t}(\$)$$
(Net Project Profit) 
Minimum 
19898 
20113.6 
22573.27 
22742.51 

Maximum 
27430 
26260.6 
24054.43 
23830.9 

Mean 
23224.6 
23239.22 
23238.2 
23245.6 
As illustrated in Table 6 and Table 7, the impact of the activities on the cash flow parameters are presented by the regression coefficient of each activity. The high value of the regression coefficient of an activity in relation to an output indicates the degree of impact that activity has on this output. The positive value of the regression coefficient indicates a directly proportional relationship between the activity and the output. Table 6 and Table 7 present the results of the three extension increments in scenarios I and II, respectively. Table 6 presents the regression coefficients of all the activities in scenario I with an extension increment of five days, activity B has the highest regression coefficients to the financing cost and to the project profit. The regression coefficient values of activity B to the financing cost and project profit are 0.059 and 0.059, respectively. Activities B and A have the highest regression coefficient value to the maximum negative cumulative balance. The regression coefficient values of activities B and A are 0.407 and 0.38. Activity G has the highest regression coefficient value to the project duration. The regression coefficient value of activity G is 0.133.
In scenario I and with an extension increment of 10 days, activities B and O have the highest regression coefficients to the financing cost. The regression coefficient values of activities B and O are 0.097 and 0.1, respectively. Activity B has the highest regression coefficient value to the project profit and the maximum negative cumulative balance. The regression coefficient values of activity B to the project profit and to the maximum negative cumulative balance are 0.097 and 0.437, respectively. Activities O, L and F have the highest regression coefficient value to the project duration. The regression coefficient value of activities O, L and F are 0.132, 0.116 and 0.111, respectively.
Scenario 
Scenario I 

Extension 
5 days 
10 days 
15 days 

Cash Flow parameters 



D 



D 



D 
Activities 

A 
0.023 
0.38 
0.023 
0.099 
0.034 
0.238 
0.034 
0 
0.044 
0.24 
0.044 
0.121 
B 
0.059 
0.407 
0.059 
0 
0.097 
0.437 
0.097 
0.101 
0.118 
0.398 
0.118 
0.156 
C 
0.022 
0.155 
0.022 
0 
0.041 
0.239 
0.041 
0.085 
0.054 
0.208 
0.054 
0.138 
D 
 
0.06 
 
0 
 
0.11 
 
0 
 
0.103 
 
0 
E 
 
 
 
0.106 
 
0.079 
 
0.086 
0.021 
0.089 
0.021 
0.088 
F 
 
 
 
0.093 
 
0.108 
 
0.111 
0.022 
0.16 
0.022 
0.147 
G 
 
0.082 
 
0.133 
 
 
 
0.094 
 
 
 
 
H 
 
0.216 
 
0.128 
 
0.14 
 
0 
 
0.097 
 
0.089 
I 
 
0.126 
 
0 
 
 
 
0.108 
 
 
 
0.106 
J 
 
 
 
0 
 
 
 
0.085 
 
 
 
0.195 
K 
 
0.171 
 
0.116 
 
0.169 
 
0.103 
 
0.157 
 
0.149 
L 
 
 
 
0.078 
 
 
 
0.116 
 
 
 
0.087 
M 
 
 
 
0.14 
 
 
 
0.104 
 
 
 
0.096 
N 
 
0.159 
 
 
 
0.116 
 
 
0.029 
0.143 
0.029 
0.077 
O 
 
 
 
0.081 
0.1 
0.063 
 
0.132 
0.12 
 
 
0.185 
Scenario 
Scenario II 

Extension 
5 days 
10 days 
15 days 

Cash Flow parameters 



D 



D 



D 
Activities 

A 
 
0.26 
 
0 
 
 
 
0.158 
0.029 
0.182 
0.029 
0.081 
B 
0.03 
0.247 
0.03 
0 
0.117 
 
0.117 
0.1 
0.076 
0.373 
0.076 
0.113 
C 
 
0.184 
 
0.124 
 
 
 
0.155 
 
0.254 
 
0.138 
D 
 
0.163 
 
0 
 
 
 
0.103 
 
0.098 
 
0.126 
E 
 
 
 
0 
 
 
 
0.119 
 
 
 
0.09 
F 
 
 
 
0 
 
 
 
0 
 
0.211 
 
0.08 
G 
 
 
 
0.095 
 
 
 
0.18 
 
 
 
0.119 
H 
 
 
 
0 
 
 
 
0.148 
 
0.155 
 
0.087 
I 
 
 
 
0.088 
 
 
 
0 
 
 
 
0.146 
J 
 
 
 
0.1 
 
 
 
0.151 
 
 
 
0.105 
K 
 
0.235 
 
0 
 
 
 
 
 
0.188 
 
 
L 
 
 
 
 
 
 
 
0.124 
 
 
 
0.202 
M 
 
 
 
0.108 
 
 
 
0.077 
 
 
 
0.138 
N 
 
0.142 
 
0.091 
 
 
 
0.089 
 
0.185 
 
0.112 
O 
 
 
 
0.111 
0.1 
 
 
0.091 
0.09 
 
 
0.132 
Scenarios 
Financial Parameters 
Extension Increment 
Critical Activities 

Rank 
5days 
10 days 
15 days 

Scenario I 
$${\widehat{I}}_{t}$$

Rank1 
Activity B 
Activity 
Activity O 
O 
Rank2 
Activity A 
Activity B 
Activity B 
B 

Rank3 
Activity C 
Activity C 
Activity C 
C 

$${\widehat{F}}_{t}$$
(Max negative Balance) 
Rank1 
Activity B 
Activity B 
Activity B 
B 

Rank2 
Activity A 
Activity C 
Activity A 
A 

Rank3 
Activity H 
Activity A 
Activity C 
C 

D 
Rank1 
Activity M 
Activity O 
Activity J 
O 

Rank2 
Activity G 
Activity L 
Activity O 
 

Rank3 
Activity H 
Activity F 
Activity B 
 

$${\widehat{N}}_{t}$$
( Net Project Profit) 
Rank1 
Activity B 
Activity B 
Activity B 
B 

Rank2 
Activity A 
Activity C 
Activity C 
C 

Rank3 
Activity C 
Activity A 
Activity A 
A 

Scenario II 
$${\widehat{I}}_{t}$$
(Financing cost) 
Rank1 
Activity B 
Activity B 
Activity O 
B 
Rank 2 
 
Activity O 
Activity B 
O 

Rank3 
 
 
Activity A 
 

$${\widehat{F}}_{t}$$
(Max negative Balance) 
Rank 1 
Activity A 
 
Activity B 
B 

Rank 2 
Activity B 
 
Activity C 
 

Rank 3 
Activity K 
 
Activity F 
 

D 
Rank 1 
Activity C 
Activity A 
Activity I 
 

Rank 2 
Activity O 
Activity C 
Activity C 
C 

Rank 3 
Activity M 
Activity G 
Activity M 
M 

$${\widehat{N}}_{t}$$
(Net Project Profit) 
Rank 1 
Activity B 
Activity B 
Activity B 
B 

Rank 2 
 
 
Activity A 
 
The results indicate that the mean value of the financing cost and the maximum negative cumulative balance decrease with the increase of the time extension. Moreover, their values increase from scenario I to scenario III due to the incorporated qualitative factors, which consequently increase the cash outflow and decrease the cash inflow transactions. Since the financing cost decreases with the increase of the extension increment, the profit also increases with the increase of the extension increment. According to the results, the schedule generated with a 10day extension in Case Scenario I is considered to be the best schedule. This generated schedule indicates total project duration 45 days, a maximum project profit of $24,571.32, a maximum negative cumulative balance of $55,991.18 and a maximum financing cost of $544.8. The terminology of activities’ criticality was introduced to describe the sensitivity of the individual cashflow parameters to the delays in the activities’ start times. The criticality of activities is an indication of the number of times an activity determines the outputs over the number of the simulation runs. Assessing activities’ criticality helps managers focus on and prioritize the activities that should be completed on time. Consequently, allows practitioners assess potential risk associated with the project finance needs. The study considered cost plus fee contract. It is recommended in future work to develop the methodology to include different type of contracts. In this research, the durations of activities are deterministic. However, future work could consider the uncertainty in the duration of activities, which would make the alternative generated schedules more accurate. Moreover, this would help in studying the impact of activity durations on the project cash flow. In addition, it could be a very useful way to measure the activities’ criticality.
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