Reliable Project Scheduling with Combination of Risk Management and Critical Chain Schedule

Shiva Mansoorzadeh Department of Manufacturing & Industrial Engineering

Universiti Teknologi Malaysia (UTM) 81310 Skudai, Johor, Malaysia Sh.mansoorzadeh@gmail.com

Sha’ri Mohd Yusof Department of Manufacturing & Industrial Engineering

Universiti Teknologi Malaysia (UTM) 81310 Skudai, Johor, Malaysia

shari@fkm.utm.my

Abstract— this paper proposes a reliable project scheduling approach, considering the integration of both risk management and critical chain schedule analysis. Various risks and uncertainties exist in projects. These may not only prevent the projects to be completed within budget and time limit, but also threaten the quality, safety and operational needs. In the proposed method the potential project risks are analyzed and risk response strategies are developed by fuzzy failure mode and effect analysis (FMEA) and then varying effect of each risk over each activity .The project total time can then be quantified and simulated by Monte Carlo simulation that is effective in uncertain conditions due to its capability of converting uncertainty to risk judgmentally in projects. Following this procedure Fault tree analysis and event tree analysis will be used to get risk mitigation. Eventually, for a reliable schedule we distribute a critical chain schedule which able to implement the project as planned and obtain reasonable Feeding Buffer time and Project Buffer time.

Keywords- Risk management; critical chain schedule; time buffer; schedule reliability

I. INTRODUCTION Every project manager must answer the fundamental

questions about the project during the project phase. Two main issues are project duration and uncertainty about task duration. In project reality, the critical path is always changed with project progress, and the project manager has no prediction to project future time. Therefore, risk management is very important to project success and it is as a critical component of managing any project [1].

Isidore and Back [2] indicated one important way of controlling risks in projects is to develop reliable project estimates and schedules. In this paper the scheduling optimization will be viewed from a reliability perspective. The risk management allows us to see the project risk as a constraint. It is assumed that a relationship always exists between some risks resided in a project and pertinent activity’s time.

To achieve the aim of this paper which is schedule reliability in project performance, the integration of risk

management and critical chain schedule model will be used to determine the best schedule reliability for a project.

II. SCHEDULE RISK MANAGEMENT Since risk management is defined as the area of project

management that identifies as many risk events as possible, minimizes their impact, manages responses to those events that do materialize (contingency plan), and provides contingency funds to cover risk events that actually materialize[3].

M. Hastak, A, Shaked and W.L. Currie [4, 5] described that the risk management process can be recognized in five principal steps of identification, analysis, evaluation, response, and monitoring. In the same sense, Williams [6] identified three factors which come together to cause extreme overruns when projects are conventionally managed: a tight time constraint, uncertainty and structural complexity (number of tasks and their level of interdependence).Also Aloini and Dulmin [7] suggested that one of the main risk effects in projects is exceeding the project time .therefore schedule risk management is the main factor in project success. In addition, accurate result in risk management can be attained by efficient risk analysis method.

III. COMPARISONOF RISK ANALYSIS METHODS The purpose of analyzing risk is to predict what happens in

the future if certain course of actions is undertaken [8].There are various techniques to perform risk analysis of projects; Some of these techniques are qualitative in nature such as risk matrix, Analytic Hierarchy Process (AHP) and some of these are quantitative for instance integration of AHP and Decision Tree, Monte Carlo Simulation, Fuzzy Logic, Failure Mode and Effect Analysis (FMEA), Fault Tree Analysis (FTA), Event Tree Analysis (ETA)which are most common In this research , quantitative analysis will be used to calculate probability and severity which leads to an accurate and effective risk assessment scheme on project schedule.

The advantages and disadvantages of these techniques are investigated to find efficient and applicable methodology. However, each of the aforementioned qualitative techniques has limitations in order to be used universally. For FMEA,

This work is partially sponsored by Universiti Teknologi Malaysia (UTM), 81310 Skudai, Malaysia

2011 IEEE Student Conference on Research and Development

978-1-4673-0102-2/11/$26.00 ©2011 IEEE 442

Puenta et al [9] and Pillay and Wang [10] believed that, the Risk Priority Number (RPN) does not differentiate between the importance of the input variables i.e., severity, occurrence, and detection during the calculation of the RPN. Braglia [11] noted that “even it is thought as a “quantitative” approach, it is really based on qualitative assessments. To address these limitations Abdelgawad and Fayek [12] had proposed a fuzzy FMEA and further combined the fuzzy FMEA with FTA and ETA. It was a complete and efficient method to find root causes and leads to mitigation strategy. Also The comparison between traditional FMEA and fuzzy FMEA which has been done with Abdelgawad ,showsin table 1 and demonstrates theefficacy of Fuzzy FMEA method.

TABLE I. COMPARISON BETWEEN TRADITIONAL FMEA AND FUZZY FMEA

Risk ID Traditional FMEA

Recommended Action

Fuzzy FMEA

Recommended

Action Risk#1 RCN=9*5*5

=225

Somewhat moderate priority to take corrective actions consider mitigation

RCN=400 Somewhat high priority to take corrective actions consider mitigation or transfer

On the other hand Ahmet and Okmen [13] proposes a new schedule risk analysis method called judgmental risk analysis process (JRAP) and offers a different project duration equation through JRAP.JRAP can be defined as a pessimistic risk analysis methodology or a hypothesis based on Monte Carlo simulation that is effective in uncertain conditions due to its capability of converting uncertainty to risk judgmentally in projects. This method focused on critical risk and their impact on activity duration, so, it can be further improved by using an applicable risk identify and quantify method such as Fuzzy FMEA.

In addition, project can be completed on time, when the risk management can be done along with time schedule reliability. One of the efficient methods known is critical chain schedule. It can assist projects to be completed earlier and with much reliable scheduling.

IV. CRITICAL CHAIN APPROACH All task in the project are subject to some degree of

uncertainly, when asked to provide an estimate of the duration, the task owner adds a safety factor in order to be ensured about the completion of the task on time. This means that in general, task duration are overestimated; in most cases, the task is not

required the entire amount of safety margin and should be completed sooner than scheduled; because the safety margin is internal to the task if it is not needed, it is wasted. For solve this problem The Critical Chain approach is established which is an extremely powerful means of gaining more predictability, productivity and speed from the project plans which is developed based on the outcome of the theory of constraints (TOC) for managing projects. Based on this argument Goldratt [14] concluded that the bottleneck of a project is the critical chain and the tasks on the critical chain must be protected by adding safety buffers. In general, Herroelen and Leus [15] reported that keeping the critical chain activities in series increases the project make-span while regularly updating the baseline schedule (the original planned schedule against which the actual implementation is compared) reduces it. The article by Elmaghraby, Herroelen and Leus [16] provides interesting insights in the use of TOC in resource constrained project scheduling. Accordingly, finding the critical chain of a project begins with removing these cushions from the task durations, leaving the average durations to use.

Obviously in critical chain approach, the size of a buffer has a significant impact on the project schedule because it show how and where to add buffers. Next section is followed by a description of the existing buffer sizing methods and comparison of them to select the efficient method.

V. COMPARISON OF TIME BUFFER APPROACHES The main question in determining the best buffer sizing

method is: how much buffer time is needed to give a 90% (or better) chance of completing the project on time. As Newbold [17] indicates, the project manager’s experience, intuition, and buffer management skills are very critical in answering this question. Nevertheless, generating buffers explicitly by using methods that take into consideration statistical fluctuations and project characteristics will allow the project manager to have better control over the project.

Figure 1. TIME BUFFER APPROCH

In this section the existing buffer sizing methods (C&PM, RSEM and adaptive buffer sizing methods) is reviewed and to discuss the advantages and disadvantages of using each. Next,

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one of these methods is introduced to generate buffer sizes which would improve the chances of a project completing on time. Leach [18] discussed buffer management and suggested the root square error method (RSEM) method for buffer sizing. Newbold [17] claims that buffers are a kind of aggregation of the risk encountered along the chain of events feeding them. Accordingly he suggests the Cut and Paste Method (C&PM) and the RSEM methods for buffer sizing. He argues that in practice there is really no need for a scientific method for buffer sizing; buffer sizes should be good enough and be adjusted based on intuitive assessment of risk [17].

A. Cut and paste method (C&PM) Assuming that the safe estimate for each task is given, the

critical chain as well as feeding chains is calculated by using 50% of the safe estimates as task durations [17]. After the critical chain has been determined, the next step is to sum the entire safety cut from the feeding chain and then take half of this sum and use it as feeding buffer. The feeding buffers are added to the end of the feeding chain where the feeding chain merges with the critical chain [19].

B. The root square error method (RSEM) Similar to the C&PM, this method uses two estimates for

each task on the feeding chain; the safe estimate and the average estimate [17]. Then the uncertainty of each task duration is calculated as equation 1:

(1)

Where, Ui is the uncertainty of task i, Si is the safe estimate

of task i and Di is the average (50%) estimate of task i, for all i in the feeding chain [17] then suggests that the standard deviation in the task duration is (Ui/2). Then the standard deviation of the feeding chain is calculated as equation 2:

(2)

Where, n is the number of activities in the feeding chain.

The assumption here is that the task completion times are independent. Equation 3 show the buffer size is then two standard deviations:

(3)

It has been suggested that in cases where there are less than

four tasks in the feeding chain, the feeding buffer should be at least equal to the longest activity in that chain [19].In additional a common assumption behind the buffer sizing methods is that 50% of the safe estimate corresponds to variability in task duration. However, as discussed Goldrat [14], 50% does not necessarily reflect the variability well since the distribution of task durations is typically skewed to the

right. That is, actual task durations can be much longer than predicted and while there might be more instances of shorter than predicted durations these deviations will be relatively small. Thus, in determining buffer sizes one should be explicit about the underlying assumption regarding task durations. In addition, when the total resource usage is close to the total resource availability, it is more likely that delays will occur. Thus, there should be larger buffers to absorb the delays. Similarly, for a given number of tasks, as the number of precedence relationships increases, it is again more likely that delays will occur. In this case the tasks are more interrelated and a delay in a task completion will influence all of its successors. Therefore, as the number of precedence relationships increases, the buffer size should also increase.

C. Adaptive procedure with density Method (APD) Walter, Rom and Sandra [19] proposed the Adaptive

Procedure with density (APD) to address C&PM and RSEM method limitation. In this method TOTPRE is total number of precedence relationships on the sub-network feeding into the critical chain , NUMTASK is total number of tasks on the sub-network and VARi is the variance of activity i. Then equation 4 illustrate, for each feeding chain:

(4)

For every activity i on the longest path terminating at the critical chain calculated through equation 5:

(5)

The value of VARi depends on the assumption regarding the distribution of task durations.

The APD method has been tested with Patterson data set which is a full factorial experiment data [20].The simulation results indicate that C&PM planned completion times will be 17–25% longer than the adaptive method. This might cause a 4-year long project to have a planned completion time of 5-years plus a possible project buffer. The RSEM generates results between these two extremes. A project manager who plans to use a method like RSEM should instead also include project characteristics as well and use something more sophisticated such as APD [19]. Thereby, the project manager main objective when selecting buffer sizing method should employ the one which generates a schedule with shorter project completion time but which can be met with a high probability.

VI. RESEARCH METHODOLOGY Risk management can identify, analyze and mitigate the

risks which exist in a project but it cannot identify or mitigate

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all of the project risks that occur. Also risk analysis focuses on some risk have high RPN therefore some risk with low RPN can together effect on project time that have not been considered in risk analysis. To solve this problem risk management should be integrated with other methods to increase schedule reliability. Critical chain schedule (CCS) is a departure from traditional project management. Since selecting critical path in CCS do not have much strong capability to identify, and analysis risks, therefore risk management can be useful for detecting risky activity in project. So, both method together help project to be finished on time which is most important factor to project success.

The method proposed in this research consists of a number of managerial steps to be carried out and an equation that offers the variation in each activity’s duration in the schedule network. The relationship between parts in the proposed methodology is shown in Fig.1. This methodology is integration of risk management and critical chain schedule in order to help project completion on-time. As can be seen in the Figure 1, this developed algorithm is summarized into the following five steps.

A. Risk analysis by combination of Fuzzy FMEA and Fuzzy AHP The first task undertaken during the conduct of this

methodology is to find out the critical risks. To identify and analyze the risk, Integration of fuzzy logic and FMEA is proposed to define the probability of occurrence (P), impact (I), and detection/control (D).Each variable is defined using membership functions (MFs) over the universe of discourse of 1 to 10 and five linguistic terms (Very High, High, Medium, Low, Very Low) for value of them. Fig.2 has showed the membership functions of probability of occurrence (P) as an example.

Figure 2. Membership functions for probability of occurrence (P)

In order to calculate impact of each risk, three factors should be considered. Impact of cost, time and quality. For this purpose the fuzzy AHP approach has been adopted to solve the multi-criteria decision-making problem by integrating of three factors into one variable named aggregated impact (AI) which is calculated in equation 6.

Al=OP (cost) x Cost Impact + OP (Time) x Time Impact + OP (Quality) x Quality Impact (6)

The overall priority (OP) for each criterion is calculated in equation 7 by taking the average of the summation of aij.

(7) aij is the relative importance of factor i over j which is calculated in equation 8:

(8)

a, represents the minimum value, b and c represents the

most likely, and d represents the maximum.

When the probability of occurrence (P), impact (I), and detection/control (D) assessed, the Risk Critical Number (RCN) should be calculated. In order to select the membership functions for the RCN, nine linguistic variables has been defined that would be sufficient to cover the universe of discourse for the RCN. Table 2 illustrated the value of this nine linguistic for RCN.

TABLE II. MEMBERSHIP FUNCTIONS OF THE RCN

Ser Critically Range Interval Cumulative Midpoint

Score Catego

ry

1 0-50 50 50 25 VL

2 50-100 50 100 75 VL-L

3 100-150 50 150 125 L

4 150-250 100 250 200 L-M

5 250-350 100 350 300 M

6 350-450 100 450 400 M-H

7 450-600 150 600 525 H

8 600-800 200 800 700 H-VH

9 800-1000 200 1000 900 VH

It is important to note that any risk event that is assessed to have an RCN that falls within the range defined by categories 5 to 9.in additional to calculate the RCN , “Risk Criticality Analyzer” (RCA) can be used. The purpose of using RCA is to support the decision-makers in assessing the level of risk criticality. It reads P, CI, TI, SI, and D from the risk register for each risk event, calculates the aggregated impact (AI) using fuzzy AHP, exports P, AI, and D to the fuzzy expert system to calculate the RCN, and presents the resultant RCN and the recommended corrective actions to the user.

B. Establishment of activity-risk factor matrix In this step of the process, activity-risk factor matrix is established. Activity-risk factor is the percentage effect of each risk over each activity.

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C. Modeling and Simulation At this step, Monte Carlo simulation (MCS) utilizes the activity-risk factor matrix developed at the third step in order to calculate the variation in activity durations. In order to enable MCS to calculate the activity duration in a stochastic manner, the following pessimistic is presented in equation 9.

(9)

Where, Min. Time is the minimum duration that an activity can be completed, Max. Time, the maximum duration that an activity can be completed, RFn, the percent effect of nth risk factor on an activity (taken from activity-risk factor matrix), Random is a random number, between 0 and 1, generated during MCS to represent the nth risk factor’s probability distribution. Once this process ends, it is possible to calculate total project time and also critical path.

D. Risk mitigation In this step some actions to prevent from delaying in project and protect a system from failure has been considered. Towards this, the utilization of the fault tree structure allows experts to understand the root causes of the risk event and supporting experts to understand which root causes are contributing the most to the occurrence of the risk event and what the fuzzy probability of the CRE is. Besides, the mitigation strategies are established that can either eliminate or reduce the chances of the occurrence of the highest ranked root causes. Event tree analysis offers for risk mitigation and understanding the impact on a risk event by considering the failure and success of the identified mitigation strategies. the fuzzy probability of failure of each mitigation strategy has been done with FTA and The probabilities of success branches are evaluated as (1-the probability of failure).eventually determine the overall probability of each path by multiplying the fuzzy probability of all the events located on the same path. This method helps improve safety integrity and minimize the risk. Figure.3 illustrated the combination of FTA and ETA.

E. Critical Chain Schedule and increasing reliability After the risk mitigation, which has been mentioned above, the critical chain schedule (CCS) is established as Figure 1 for schedule reliability.

1: Fuzzy FMEA 2: Monte Carlo Simulation

Figure 3: Integration of schedule Risk management with critical chain schedule.

Critical Chain Schedule

YES

Time be Reliable

Feeding Buffer (Based on APD method) and

simulate project Time

Add the project buffer to the end of the critical chain (Based on APD method)

Identify the critical chain

Push all the tasks based on last step

Determine 50% Duration Estimate for each Task

Determine initial Project

Plan

YES NO

Calculate Total Project Time and Comparison with

InitialPlan

YES NO YES Delay? NO Pro.of Risk

Mitigating Is High?

Asses Failure branch in ETA

Construct the ETA

Identify Mitigate Strategy

2

Conduct FTA to Find Root

Causes and Probability of

them

NO

Risk management

Acceptable?

Risk Evaluation

1

Calculate Risk

Critical Number

Identify Critical

Feeding Buffer (Based on APD method) and

simulate project Time

Add the project buffer to the end of the critical chain (Based on APD method)

Identify the critical chain

Push all the tasks based on last step

Determine 50% Duration Estimate for each Task

Determine initial Project

Plan

Monitor and

Control

Time be Reliable

Quantify Effect of Risk on each Activity(Day)

Establish Activity Risk Factor Matrix

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Figure 3. combination of FTA and ETA for Risk mitigation

VII. ONCLUSIONS The aim of this paper is to propose a time schedule based

risk management methodology that is applicable for all projects. As conceptual model for integration of risk management with critical chain schedule as a new methodology for project schedule reliability has been proposed. Despite risk management process which only identifies analyses and mitigates the risk, it has no consideration of risk impacts on the project which has not provided strong actions for enhancing project schedule reliability. Since dominant methods like the Theory of constraint and critical chain schedule have no clear systematic technique to identify and analyze the risk. Therefore, the proposed method in this paper can be emerged to address those limitations with an efficient and practical methodology for schedule risk management in industrial projects.

ACKNOWLEDGMENT Authors gratefully acknowledge the 2011 UTM

International Doctoral Fellowship (IDF) awarded by Universiti Teknologi Malaysia (UTM), through which the flow of this research was financially facilitated.

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