Project Management

Risk Management and Optimisation Examples

Chapter 4: Research & Development Risk in Project Selection
In Book 1: Novel Six Sigma Approaches to Risk Assessment and Management

ISBN: 9781522527039

Author: Vojo Bubevski (Independent Researcher)

Abstract

The elaborated method is applied to R&D for project portfolio selection to achieve investment objectives by controlling risk. DMAIC framework applies proven stochastic techniques to risk management: 1. Define: Optimisation resolves an Efficient Frontier of portfolios for the desired range of expected return with an initially defined increment; 2. Measure: Simulation measures Efficient Frontier portfolios calculating mean return, variance, standard deviation, Sharpe Ratio, and Six Sigma metrics versus pre-specified target limits; 3. Analyse: Analysis considers mean return, Six Sigma metrics, and Sharpe Ratio and selects the portfolio with maximal Sharpe Ratio as initially the best portfolio; 4. Improve: Optimisation resolves Efficient Frontier in a narrow interval with smaller increments. Simulation measures Efficient Frontier performance including the mean return, variance, standard deviation, Sharpe Ratio, and Six Sigma metrics versus pre-specified target. The analysis identifies the maximal Sharpe Ratio portfolio, i.e., the best portfolio for implementation; 5. Control: Selected projects in the portfolio are individual projects. So, the Project Management approach is used for control.
Keywords: Research & Development; Project portfolio; Risk management; Six Sigma; DMAIC; Stochastic optimisation; Monte Carlo simulation.

The Results

The complete results of the improved Efficient Frontier portfolios are as follows. Table 5 shows the Mean Return (µ) and the Investment Fractions (F) of total funds invested in each project.

Table 5: The Investment Fractions (F) in Improved Portfolios

µ

0.15

0.155

0.16

0.165

0.17

0.175

0.18

0.185

0.19

F P1

0

0

0

0

0

0

0.0201

0.0623

0.266

F P2

0.0199

0.0349

0.0498

0.0695

0.0974

0.1249

0.1521

0.1775

0.041

F P3

0.1806

0.1761

0.1708

0.1600

0.1374

0.1141

0.0714

0

0

F P4

0.1289

0.1250

0.1202

0.1123

0.0983

0.0833

0.0505

0

0

F P5

0

0

0.0031

0.0023

0

0

0

0

0

F P6

0

0

0

0

0

0

0

0

0

F P7

0.1949

0.2183

0.2419

0.2685

0.2997

0.3317

0.3601

0.3848

0.225

F P8

0.1900

0.2132

0.2357

0.2607

0.2896

0.3181

0.3458

0.3754

0.469

F P9

0.1048

0.0651

0.0249

0

0

0

0

0

0

F P10

0.1809

0.1674

0.1536

0.1267

0.0776

0.0279

0

0

0

Total

1

1

1

1

1

1

1

1

1
 
 
 
Table 6: The Improved Efficient Frontier Portfolios’ Details

µ

0.15

0.155

0.16

0.165

0.17

0.175

0.18

0.185

0.19

V

0.0070

0.0075

0.0081

0.0087

0.0095

0.0104

0.0114

0.0128

0.0161

σ

0.0834

0.0865

0.0898

0.0934

0.0975

0.1022

0.1072

0.1130

0.1270

SR

1.1568

1.1736

1.1855

1.1931

1.1941

1.1890

1.1793

1.1637

1.0748
 
Table 6 shows the Mean Return (µ), Variance (V), Standard Deviation (σ), and Sharpe Ratio (SR) of the improved portfolios.

The improved Efficient Frontier of the Minimal Mean-Variance portfolios is presented herein. The Efficient Frontier curve shows that an increase in the expected return of the portfolio causes an increase in the portfolio Standard Deviation. Once again, the Efficient Frontier gets flattered as expected. This shows that each additional unit of Standard Deviation (i.e., risk) allowed, increases the portfolio Mean Return by less and less.

The Mean Return and Standard Deviation of Improved Efficient Frontier Portfolios are as follows: i) Mean Return – µ: 0.15; Standard Deviation: 0.0834; ii) Mean Return – µ: 0.155; Standard Deviation: 0.0865; iii) Mean Return – µ: 0.16; Standard Deviation: 0.09; iv) Mean Return – µ: 0.165; Standard Deviation: 0.0934; v) Mean Return – µ: 0.17; Standard Deviation: 0.0975; vi) Mean Return – µ: 0.175; Standard Deviation: 0.1022; vii) Mean Return – µ: 0.18; Standard Deviation: 0.1072; viii) Mean Return – µ: 0.185; Standard Deviation: 0.113; ix) Mean Return – µ: 0.19; Standard Deviation: 0.127.
 
   
Chapter 6: Project Management Risk
In Book 1: Novel Six Sigma Approaches to Risk Assessment and Management

ISBN: 9781522527039

Author: Vojo Bubevski (Independent Researcher)
 
Abstract

The presented method is applied to Project Management by using PERT-CPM critical paths to manage project risk. DMAIC framework applies proven stochastic techniques as follows: 1. Define:  Stochastic optimisation determines the critical paths; 2. Measure: Every critical path is simulated and associated risks are calculated. Six Sigma process metrics are calculated against specified targets; 3. Analyse: Simulation results are analysed and sensitivity analysis is used to identify and quantify the main contributors to the variability of the project duration time; 4. Improve: The critical paths are ranked and prioritised for management’s attention based on their associated risk factors; 5. Control: The project was not implemented, so there is no data for analysis. However, assuming that the project was implemented, a generic Project Control phase is applied.

Keywords: Operations Research; Project management; PERT-CPM; Six Sigma; DMAIC; Stochastic Optimisation; Monte Carlo simulation.

The Results

Stochastic optimisation is used to resolve the critical paths of the project.  We minimise Project Duration Time (15), with the constraint that the Activity Time Elements (VATE) must be equal or greater than the Activity Estimated Duration (AED) (13). The project start time T(1) is initialised to zero. The project time values T(2) – T(8) are adjustable and calculated by the model to achieve the optimum, subject to the constraint that they are positive numbers (2). For the optimisation, we need to specify trial values for the adjustable project times, so we specify zero to all project time values T(2) – T(8). 

Table 2: Stochastic Optimisation Results for the Project’s 10 Activities

Activity Id & Description

Activity Time Element (Months)

Estimated Duration (Months)

Activity Slack Time (Months)

1 Design Plant

12

12

0

2 Select Site

9

9

0

3 Prepare Site

13

13

0

4 Select Vendor

4

4

0

5 Produce Generator

18

18

0

6 Install Generator

4

4

0

7 Prepare Manuals

12

5

7

8 Select Personnel

16

3

13

9 Train Operators

10

9

1

10 Obtain License

6

6

0
 
The stochastic optimisation model was run to calculate the critical paths. The stochastic optimisation results are presented in Table 2 at the project activity level; and in Table 3, at the project path level. The activities that have an activity time equal to the estimated duration (Table 2) are critical path activities. The Slack Time for critical activities is zero. The non-critical activities have slack time greater than zero. 

Table 3: Stochastic Optimisation Results for the Project’s Paths

Path (Critical Indicator)

Path Activities

Path Total Duration (Months)

Path Slack Time (Months)

1 (Yes)

1-2-3-6-10

44

0

2 (Yes)

1-4-5-6-10

44

0

3 (No)

1-4-7-9-10

36

8

4 (No)

1-8-9-10

30

14
 
There are two critical paths with a total duration of 44 months and time equal to zero, i.e., path 1 & path 2 (Table 3). Paths 3 and 4 are noncritical paths with slack time greater than zero. Project managers should focus first on the critical paths’ activities, and second on the slack time associated with noncritical activities. Knowledge of those activities on the critical path and the slack associated with non-critical activities are valuable aids in managing large-scale projects. Path 1 and Path 2 are critical paths because completion requires 44 months. Any activity on these paths is a critical activity, and any delay in a critical activity will delay the whole project. Also, Path 3 and Path 4 are non-critical and have a slack of 8 and 14 months respectively.

Path 3 has a slack of 8 months and includes three critical activities, i.e., activities 1, 4, and 10; and two non-critical activities, i.e., activities 7 and 9. This means that the non-critical activities on this path can suffer a total of 8 months of delays before affecting the completion of the project.

Similarly, Path 4 has a slack of 14 months and includes two critical activities, i.e., activities 1 and 10; and two non-critical activities, i.e., activities 8 and 9. This means that the non-critical activities on this path can suffer a total of 14 months of delays before affecting the completion of the project.

Chapter 1: Improving Project Critical Path

In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter elaborates on how to reduce the risks in a project to construct a power plant by applying PERT-CPM. There are ten activities in the project with empirically estimated duration and cost. Dependencies amongst activities are defined, so a network diagram is created, determining the critical path and project duration.  Two simulations are run, one by one, to determine project duration, cost, and associated risks. Simulation-1 applies the empirically estimated durations and costs as inputs. Then Simulation-2 is run by applying the Simulation-1 result values as inputs. The results are analysed and evaluated. Also, sensitivity analysis is performed to identify and quantify the main contributors to variability and risk. It is established that the Simulation-2 solution is superior, importantly achieving a reduction in the project risk, which is the objective.

Keywords: Project risk management; PERT-CPM; Critical path; DMAIC; Financial risk management; Monte Carlo simulation; Six Sigma; Slack; Stochastic model.

The Results

Simulation 1 and Simulation 2 results including the project duration mean and the associated risk factors are presented in Table 6. The two simulations are compared considering Mean Duration (µ) in months (m), Standard Deviation (σ), and the Six Sigma process capability metrics: Process Capability (Cp), Process Capability Index (Cpk), and Sigma Level (σ-L). The comparison shows that the Simulation 2 results for the project duration are slightly increased, but the associated risk factors are improved against the Simulation-1 risk factors. This acknowledges that the risk is reduced in Simulation-2, which improved and benefited the project.

Table 6: Project Duration and Risk Factors

 

µ (m)

σ

Cp

Cpk

σ-L

Simulation-1

48.37

5.216%

0.2907

-0.286

0.2611

Simulation-2

49.7

4.738%

0.3397

0.0989

0.8220

 

Table 7: Project Cost and Risk Factors

 

µ ($)

σ

VAR

Cp

Cpk

σ-L

Simulation-1

6,180,000

4.3634%

90.885%

0.3572

-0.1372

0.4629

Simulation-2

6,313,330

4.1256%

90.858%

0.3955

0.2248

1.0525
 
Project cost and the associated risk factors are presented in Table 7. Project cost and Risk factors of the two simulations are compared considering Mean Cost (µ) in ($), Standard Deviation (σ), Value at Risk (VAR), and the Six Sigma process capability metrics: Process Capability (Cp), Process Capability Index (Cpk) and Sigma Level (σ-L).
 
Again, the comparison shows that the Simulation 2 results for the project cost are slightly increased, but the risk factors are enhanced versus Simulation-1 risk factors. Once more, this acknowledges that the risk is reduced in Simulation-2, which improved and aided the project.

 

Chapter 2: Improving Performance of an Ongoing Project 
In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)
 
Abstract 
This chapter is purposed to improve the performance of an ongoing project taking into consideration time and cost. The Short Film Project is fully established in Microsoft™ Project 2000, which is the Initial-Plan. The project is started and the completion of Task-22 is captured in Task-22-Completed-Plan. The completion of Task-30 is also captured in Task-30-Completed-Plan. Simulation is applied to all three plans in order, one by one, to calculate time, cost, and associated risks. The simulation results of a plan, are compared with the next plan which includes actual values for completed tasks. The objective of this process is to achieve the most accurate solution, which will gradually improve the ongoing project performance. In conclusion, the ongoing project performance is increasingly improved by gradually achieving risk reduction and the most accurate solution. Therefore, the objective is accomplished. 
Keywords: Microsoft™ Project, Project Risk Management, Six Sigma DMAIC, Monte Carlo Simulation

The Results

The original project’s planned total time and cost, and simulations’ total time & cost including risk factors are presented in Table 5 to provide for comparison and evaluation of results. Comparing the results of Initial-Plan’s Simulation-1, the project’s total time and cost significantly deviate from Task-22-Completed-Plan’s original, including actual values for 22 tasks; the differences are -203.77 (hrs) and -$4,653 for time and cost respectively. However, Simulation-2 of Initial-Plan results deviate much less from Task-22-Completed-Plan’s original values; the differences are only -17.45 (hrs) and -$1,174 for time and cost respectively. Even though Standard Deviations and VAR are insignificantly increased, Simulation-2 results are superior and more realistic.

Comparing the results of Simulation-2 of Initial-Plan and Simulation-3 of Task-22-Completed-Plan, the project total time and cost of both simulations deviate insignificantly from Task-30-Completed-Plan’s original values, including actual values for 30 tasks. That is: i) Simulation-2 differences are 17.45 (hrs) for time and $1,174 for cost; and ii) Simulation-3 differences are 37.6 (hrs) for time, and $1,257 for cost, i.e., slightly higher than Simulation-2. However, Simulation-3 slightly reduced the total project time and cost, significantly reduced the Standard Deviation, and increased, i.e., improved, the process capability metrics, which are the major risk factors. From a Project Risk Management perspective, this is the ultimate objective, even though VAR is increased insignificantly. Therefore, Simulation-3 results are superior and more realistic.

 

 
Chapter 3: Project Risk Analysis
InBook 3: Stochastic and Six Sigma Improvements to Project Risk Management
ISBN: 978-620-2-02905-6

Author: Vojo Bubevski 

Abstract 

This chapter presents a stochastic analysis in order to evaluate projects in terms of both, risk and return. If the projects provide the same return, the aim is how to evaluate the projects’ risk. and identify which project is riskier. Simulation is used to calculate the projects’ return and variance. The objective is to resolve the problem specified above. The evaluation determines the project with a smaller risk, which is the objective.

Keywords: Project Risk Management, Risk Analysis, Stochastic Model, Monte Carlo Simulation, Six Sigma DMAIC

The Results

In the Improve stage, the risk factors of the simulation results are compared in order to acknowledge which risk factors are better, which is the objective of this analysis. Project Return and Risk Factors are compared in Table 3.

Table 3: Project Return Risk Factors

 

µ (m)

σ

Cp

Cpk

σ-L

Project 1 Return

10%

1.000%

0.6667

0.6667

2.0000

Project 2 Return

10%

3.266%

0.2041

0.2041

0.5791

Risk factors of the two projects’ returns are compared considering the Mean (µ), Standard Deviation (σ), Process Capability (Cp), Process Capability Index (Cpk), and Sigma Level (σ-L). The comparison shows that the project returns are the same, but the risk factors of Project 1 Return are much better than Project 2 Return risk factors. This acknowledges that Project 2 is significantly riskier than Project 1. The Risk Difference of Return Equivalents risk factors is compared in Table 4.

Table 4: Risk Difference of Return Equivalents Risk Factors

 

µ ($)

σ

Cp

Cpk

σ-L

Risk Neutral Difference

0%

3.421%

0.3897

0.3897

1.1115

Risk Averse Difference

1.662%

6.416%

0.2078

0.1215

0.8921

Risk factors of the Risk Difference of Return Equivalents are compared considering the same factors as above. The comparison shows that the Risk Neutral Difference is 0%, and the Risk Averse Difference is 1.662%. The risk factors of Risk Neutral Difference are much better compared to the Risk Averse Difference risk factors. It is clear that Risk Averse Difference is significantly riskier than Risk Neutral Difference.

Chapter 4: Optimising Project Net Present Value
In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)

Abstract 
This chapter demonstrates how to optimise the Net Present Value (NPV) and Internal Rate of Return (IRR) of a commercial venue construction project, managed in Microsoft™ Project, by minimising the Total Variable Cost (TVC). Simulation and stochastic optimisation models consider uncertainty in task durations, and Risk Register is used to estimating contingencies and real-time Cash Flows to resolve NPV, IRR, and TVC. Firstly, the simulation is run, and then the optimisation is performed. The simulation and optimisation results are examined to evaluate NPV, IRR, TVC, and risk factors. Finally, the simulation and optimisation results are compared. It is concluded that optimisation significantly increases the project’s NPV and IRR with a negligible increase in associated risks, which is the objective.
Keywords: Project Risk Management, Cash Flow, Net Present Value (NPV), Internal Rate of Return (IRR), Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation.

The Results

The simulation results of project Cash Flows for the years 2012 – 2021 are presented in Table 1 and Table 2 below.

Table 1: Cash Flows in USD ($) Results for 2012 – 2016

Year

2012

2013

2014

2015

2016

Project Cost

-11,550

-223,550

-64,100

0

0

Initial Revenue Year

0

0

0

1

1

Revenue

0

0

0

140,000

154,000

Revenue Adjustment

0

0

0

-59,452

0

Fixed cost

0

0

0

-49,000

-49,000

Variable cost

0

0

0

-70,000

-77,000

Cash Flow

-11,550

-223,550

-64,100

199,548

280,000
 
Table 2: Cash Flows in USD ($) Results for 2017 – 2021

Year

2017

2018

2019

2020

2021

Project Cost

0

0

0

0

0

Initial Revenue Year

1

1

1

1

1

Revenue

169,400

186,340

204,974

225,471

248,019

Revenue Adjustment

0

0

0

0

0

Fixed cost

-49,000

-49,000

-49,000

-49000

-49000

Variable cost

-84,700

-93,170

-102,487

-112,736

-124,009

Cash Flow

303,100

328,510

356,461

387,207

421,028
 
The Cash Flow summary trend graph for the years 2012 – 2021 resolved the results.

The Cash Flow starts at -$11,550 in 2012 and drops to a minimum of -$223,550 in 2013. Then it continuously increases from the minimum in 2013 to $421,028 in 2021.

The simulation Output Values results are shown in Table 3.

Table 3: Simulation Output Values Results

Output Values

LSL-Lower

USL-Upper

TV-Target

VAR at 1%

NPV ($)

865,609.63

594,188.25

1,029,926.30

792,251

411,834.79

IRR (%)

0.58009

0.3975

0.689

0.53

0.39929

Total Variable Cost ($)

664,101.97

498,076.50

863,332.60

664,102

311,827.29

Summary Stats

Mean NPV ($)

871,813.52

Probability NPV negative

0

 

 

Chapter 5: Project Cost and Duration Optimization
In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter illustrates optimisation of project cost and duration by minimising the Net Extra Cost. The project is a residential site construction managed in Microsoft™ Project. Simulation and stochastic optimisation models consider uncertainty in tasks’ durations, to calculate the project’s duration, cost, bonuses, penalties, and Net Extra Cost. Firstly, simulation calculates the tasks durations, the project total duration, cost, bonuses, penalties, and the Net Extra Cost, including the associated risks. Then, stochastic optimisation recalculates the project’s total duration and cost by minimising the Net Extra Cost. Simulation and optimisation results are analysed to evaluate the project’s total cost and duration, and the Net Extra Cost, including the related risk factors. It is concluded that the total cost and duration of the project are significantly decreased by the optimisation, with negligible change to the associated risks, which is the objective.

Keywords: Project Risk Management, Project Cost and Duration, Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation

The Results

In the Improve stage, the simulation results are compared with the optimisation results (Table 3) in order to acknowledge if an improvement has been achieved.

Table 3: Simulation vs. Optimisation Results

Variable

Calculated

Risk-Mean

Simulation Project Total Cost ($)

63,325.42

60,462.80

Optimisation Project Total Cost ($)

53,949.25

57,912.54

Simulation Project Total Duration (Weeks)

28.36667

26.6667375

Optimisation Project Total Duration (Weeks)

25.00

26.6666647

Simulation Project Total Duration (Days)

141.83333

133.333688

Optimisation Project Total Duration (Days)

125

133.333323

Simulation Net Extra Cost ($)

4,876.17

6,052.82

Optimisation Net Extra Cost ($)

-4,500.00

-1,200.0

Project Total Cost VAR @ 1%

VAR ($)

VAR (%)

Simulation

54,431.74

90.0251768

Optimisation

51,687.00

89.2495841
 
Compared with the simulation results: i) Optimisation Calculated and Risk-Mean Total Project Cost are significantly decreased; ii) Optimisation Total Project Cost VAR is meaningfully reduced; iii) Optimisation Calculated Total Project Duration Weeks is significantly decreased; iv) Optimisation Calculated Total Project Duration Days is significantly decreased; v) Optimisation Risk-Mean Total Project Duration Weeks is negligibly decreased; vi) Optimisation Risk-Mean Total Project Duration Days is negligibly decreased; and vii) Optimisation Calculated and Risk-Mean Net Extra Cost are significantly decreased.
 
This acknowledges that an improvement has been achieved, which is the objective, as well as an important enhancement to the risk management of the project.

  

Chapter 6: Optimal Production Scenario for Oil Project
In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter applies a stochastic model to a petroleum water flood project in order to estimate recoverable oil, and to select one of four observed production schedules which generate the maximal revenue stream.  The stochastic optimisation model combines volumetric estimates, prices, costs, and production scheduling. The objective is to maximise the Cash Flow, Net Present Value (NPV), and Internal Rate of Return (IRR) for the project over an 18-year horizon. The model considers specified information about initial costs, operating costs, reservoir description, production schedules, prices, working interest, and taxes.

Keywords: Project Risk Management, Petroleum Water Flood, Production Scenarios, Cash Flow, Net Present Value (NPV), Internal Rate of Return (IRR), Six Sigma DMAIC, Stochastic Optimisation, Monte Carlo Simulation.

The Results

The DCF (Discounted Cash Flow) summary trend for years 1 – 18 shows: Cash Flow for Years 1 – 3 is $0.00 MM. From Year 3, it quickly increases, reaching a maximum of around $17.50 MM in Year 7. It then slowly reduces to zero in Year 13 and remains zero till Year 18.   The Outputs results are shown in Table 1.

 
Table 1: Outputs Results

Outputs

Calculated Value

VAR at 1%

NPV ($)

70,269,701.36

33,241,051.16

IRR (%)

0.35351

VAR (%)

Total Reserves (STB)

2,967,435

47.305
 
The project simulation NPV distribution shows as follows. The Mean NPV is $70,245,803.05; the Standard Deviation is $19,603,285.92, i.e., 27.9067%; and VAR at 1% is $70,269,701.36, i.e., 47.305%. Six Sigma target parameters are: TV = $63,105,755; LSL = TV – 30%; and USL = TV + 30%. The Six Sigma process capability metrics are Cp = 0.3219; Cpk = 0.2005; and σ-L = 0.9605. There is a 5% probability that the project NPV will be below $41,340,000; a 90% probability that it will be in the range of $41,340,000 – $105,220,000; and a 5% probability that it will be above $105,220,000.
 
In the Improve stage, four simulations are run, i.e., one simulation for each of the four possible production schedules, i.e., Production Schedule 1 simulation, Production Schedule 2 simulation, Production Schedule 3 simulation, and Production Schedule 4 simulation. The results of the simulations are compared with the optimisation results in order to acknowledge if an improvement has been achieved.

Project NPV and IRR results are presented in Table 2. The optimisation results for NPV and IRR are compared with the four simulations results considering Mean NPV (µ), Standard Deviation (σ) and Value at Risk (VAR).

Table 2: NPV and IRR Optimisation vs. Simulations’ Results

 

NPV µ $

NPV σ $

NPV VAR $

IRR µ %

IRR σ %

Optimisation

70,245,803

19,603,286

33,421,051

34.855

5.292

Production Schedule 1 Sim

70,279,369

19,734,323

32,791,218

34.857

5.329

Production Schedule 2 Sim

63,114,682

18,056,019

28,839,777

30.669

4.917

Production Schedule 3 Sim

57,826,651

16,801,838

25,905,879

28.078

4.694

Production Schedule 4 Sim

52,669,256

15,579,575

23,128,530

25.543

4.466
 
The NPV and IRR results comparison shows that the Production Schedule 1 simulation has the maximum values for NPV and IRR. Compared with the Production Schedule 1 simulation results, the optimisation results are very close. That is, Mean NPV (µ), Mean IRR (µ), and associated Standard Deviations are negligibly decreased. The NPV VAR however is slightly increased. It should be noted that these very small differences are satisfactory. This is because every run of the optimisation or simulation model produces slightly different results. 
 
The consequence is that both approaches, i.e., both optimisation and simulation, determined Production Schedule 1 be the best schedule for the project to implement. However, the simulation approach requires four simulations to be run to select the best production schedule, whereas, the optimisation approach determined the best production schedule in only one run. Hence, the optimisation approach is superior to simulation.
 
 
 
Chapter 7: Optimal Timing of Project Portfolio
In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter elaborates on how to determine the optimal timing for a corporation’s project portfolio. Stochastic optimisation is applied to schedule starting years of 10 projects in the portfolio. Stochastic optimisations are used to determine the starting years of the projects that maximise the Net Present Value (NPV) of cash flows from all the projects in the portfolio. Two optimisations are run to identify two local optimums. The two optimal solutions are compared in order to select and implement the preferred timing of the projects. In this chapter, the optimal solution with better NPV and IRR values, as well as a smaller risk, is selected. However, the selection of the preferred solution is subject to corporations’ management decisions. It should be noted that in a real-world situation, more than two local optimums are required, i.e., as many as practical, to make the decision on the optimal timing of the implementation of projects.

Keywords: Project Risk Management; Project Portfolio, Projects timing, Six Sigma, DMAIC, Monte Carlo simulation

The Results

In the Improve stage, the Optimisation 1 vs. Optimisation 2 results are presented in Table 5 for comparison.

Table 5: Optimisation 1vs. Optimisation 2 Comparison

Outputs

Calculated Value

VAR at 1%

VAR (%)

Optimisation 1 NPV ($MM)

2,054.108

1,551.16

75.515

Optimisation 2 NPV ($MM)

1,962.6

1,561.75

79.576

Optimisation 1 IRR (%)

35.351

25.85

73.124

Optimisation 2 IRR (%)

32.443

27.146

83.673
 
Optimisation 1 NPV is greater than Optimisation 2 NPV by $91.508 MM (i.e., 5% better). The NPV Value at Risk (VAR at 1%) of Optimisation 1 is reduced by $10.59 MM (i.e., 4.061% better). These differences are substantial improvements. Similarly, Optimisation 1 IRR is greater than Optimisation 2 IRR by 2.908% (i.e., 8.96% better). The IRR Value at Risk (VAR at 1%) of Optimisation 1 is reduced by 1.296% (i.e., 10.549% better). These differences are also significant improvements. 
 
The two optimal solutions are compared in order to select and implement the better timing of portfolio projects. The Optimisation 1 solution has better NPV and IRR values, as well as smaller risks. Therefore, the project timing of Optimisation 1 is selected for implementation.
 
 
 
 
Chapter 8: Cost Analysis of Project Portfolio
In Book 3: Stochastic and Six Sigma Improvements to Project Risk Management

ISBN: 978-620-2-02905-6

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter presents a stochastic cost analysis for a company’s portfolio of ten projects over 12 months. Each project is planned to start in a given month, and from that month on, it has expected costs, some of which are known (of which, some are zero) and some of which are uncertain. There are possible random delays (or, for a few projects, possible earlier starting months), which shift the cost schedule to the right (or left). Also, each project has a variable chance of failing (i.e., 5%, 10%, 15%, or 20%) in any month after its actual starting month. If it fails in a given month, that month’s costs plus any remaining months’ costs are not incurred. A simulation model is applied to calculate the variables that are required for the analysis. Four simulations are run to complete the analysis.

Keywords: Project Risk Management; Cost Analysis, Project Portfolio, Six Sigma, DMAIC, Monte Carlo simulation

 
The Results

The four sets of simulation results are presented in Table 5 for comparison. 

Table 5: Simulations’ Results Comparison

Simulation No

Failure Probability

Total Cost ($M)

T. Cost Delta ($M)

Standard

Dev. ($M)

Std. Dev. Delta ($M)

Simulation 1

5%

13,831.79

N/A

1,266.76

N/A

Simulation 2

10%

12,440.24

1,392

1,583.58

317

Simulation 3

15%

11,204.04

1,236

1,718.41

134

Simulation 4

20%

10,115.58

1,088

1,749.96

32
 
The simulation calculated the Total Cost vs, Standard Deviation. The following are the results: i) Simulation 1: Total Cost $M 13,832; Standard Deviation $M 1,267; ii) Simulation 2: Total Cost $M 12,440; Standard Deviation $M 1,584; iii) Simulation 3: Total Cost $M 11,204; Standard Deviation $M 1,718; iv) Simulation 4: Total Cost $M 10,116; Standard Deviation $M 1,750;
It should be highlighted that Simulation 1 has the smallest probability of project failure. Consequently, the associated Standard Deviation is the smallest, and the total cost is the highest one. As the failure probability gradually increases for Simulations 2, 3, and 4, the Standard Deviations (i.e., the associated risk factors) also increase. The Total Costs, however, decrease. This is because if a project fails in a given month, that month’s costs plus any remaining months’ costs are not incurred.
 
It is important to note that the rates of change from simulation to simulation, for both Total Cost and Standard Deviation, are decreasing. 
 
 
Chapter 7: Analysing Project Discounted Cash Flow
In Book 4: Risk Management for Businesses with Stochastic Six Sigma DMAIC Method

ISBN: 978-620-2-67095-1

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter analyses the Discounted Cash Flow (DCF) of a proposed project. A simulation model is designed to calculate the project’s DCF for a period of ten years. The model considers the sources of risk such as the revenue growth rate and the variable costs as a percentage of sales. The DCF is derived by taking into account the assumed investment and a given discount factor. The model calculates the Net Present Value (NPV) with the given discount factor and the Net NPV that is net of a known investment. In addition, the probability of the Net NPV being negative is calculated. The results show that the Net NPV Mean is positive with a relatively low probability of being negative. Therefore, the decision as to whether to proceed with this project will depend on the risk tolerance of the decision-makers.
Keywords: Business Risk Management, Project Risk Assessment, Finance, Cash Flow, Net Present Value, Stochastic Model, Six Sigma, DMAIC, Monte Carlo simulation

The Results

The simulation results are presented below. The attained values for NPV, Net NPV, Net NPV Mean, and Probability of Net NPV Negative are given in Table 1.

Table 1: Simulation Output Results

Data

Value

NPV

$128,884,418

Net NPV

$36,600,000

Net NPV Mean

$39,660,000

Probability of Net NPV Negative

14.9875%
 
The Cash Flow summary trend for ten years was calculated as follows. The Cash Flow starts at around $15 MM in Year 1 and then linearly increases to just over $40 MM in Year 10. 
 

Chapter 1: Optimising Project Portfolio by Considering Capital Budgeting with Financial Statement
In Book 6: Comprehensive Sensitivity Analysis of Risk for Businesses

ISBN: 978-620-2-91949-4

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter illustrates a stochastic optimisation of a project portfolio considering the projects’ capital budgeting with financial statements. There are eight proposed projects to be selected for the optimal portfolio, bearing in mind the projects’ Cash Flows, Net Present Value (NPV), Total Expenses, and Present Cost, for a period of 10 years in the future. The financial statements of the projects are simulated including several uncertain variables. Each project has a chance of falling from a technical standpoint. If it fails, it is not part of the total portfolio, that is, its NPV and costs are not included. The objective is to select the projects for the portfolio that maximise the mean portfolio NPV but to ensure with 95% confidence that the total present value of costs stays below the budget.

Keywords: Risk Assessment and Management, Project Portfolio, Optimisation, Financial Risk, Sensitivity Analysis; Monte Carlo simulation; Stochastic model.

 The Results

 The calculated Portfolio Cash Flow (CF) per Year of all projects is presented in Table 4. 

 Table 4: Portfolio Cash Flow per Year ($)

Year

2021 

2022

2023

2024 

2025

CF 

-543,333 

-526,358 

798,941 

275,965 

670,355 

 Year

2026 

2027

2028

2029

2030

CF

 650,508

954,850

1,237,922

965,937

1,030,113
 
The graph of the calculated Portfolio Cash Flow per Year of all projects was presented with value labels given in dollars ($). 
For example, the Portfolio Cash Flow is -$543,333 and -$526,358 in the Years 2021 and 2022 respectively. Then it is $798,941 in the Year 2023, etc. 
Note: The Mean results, which involve a probability distribution calculation, are lower than the calculated results, which do not use probability distributions. For example, the Mean for the Year 2023 is approximately $780,000 compared to approximately $800,000 calculated above.
Similarly, the calculated Portfolio Total Expenses (TE) per Year of all projects are presented in Table 5. 
 
Table 5: Portfolio Total Expenses per Year ($)

Year

2021 

2022

2023

2024 

2025

TE 

543,333 

700,733 

433,455 

321,264 

264,162 

 Year

2026 

2027

2028

2029

2030

TE

247,153

250,239

206,528

189,706

191,388
 
The calculated Portfolio Total Expenses per Year of all projects were with value labels given in dollars ($). For example, the Portfolio Total Expenses are $543,333 and $700,733 in the Years 2021 and 2022 respectively. Then it is $433,455 in the Year 2023, etc. 
 
 
Chapter 2: Estimating Costs of New Projects
In Book 6: Comprehensive Sensitivity Analysis of Risk for Businesses

ISBN: 978-620-2-91949-4

Author: Vojo Bubevski (Independent Researcher)

Abstract 

This chapter presents a stochastic model for estimating the costs of a new project. When submitting a budget proposal for a project, two key questions need to be answered:    1. What is the probability that the project will actually be delivered within this budget?    2. How much contingency (i.e. extra budget) should be included in order for this new revised budget level to be achieved with a certain degree of confidence? A simulation model is created to estimate the costs and calculate the required variables to answer these questions. It is assumed that each item’s actual cost will be within a min-max range. To involve uncertainties, probability distributions are applied to describe the possible costs of each item in practice. The distributions are assumed to be skewed in this case, and the parameters chosen to reflect those costs are assumed to more likely overshoot than undershoot the base case. The cost elements of the project are the model’s inputs, which are projections of historical data available.

Keywords: Risk Assessment and Management, Project Budget Proposal, Project Costs Estimation, Financial Risk, Sensitivity Analysis; Monte Carlo simulation; Stochastic model.

The Results

The Total Project Cost was calculated with Monte Carlo Simulation. The Total Project Cost Mean is $18,962.50 M with a Standard Deviation of $488.15 M, i.e., 2.574%, which is a very low risk. The Six Sigma target parameters are TV = $18,963.0 M; LSL = $18,500.0 M; and USL = $19,500.0 M. The Six Sigma process capability metrics are Cp = 0.3414; Cpk = 0.3158; and σ-L = 0.4369. There is a 5% probability that the cost will be below $18,181 M; a 90% probability that it will be in the range of $18,181 M – $19,7.