Cohen & Keren
GENERATING UPLOADING AND MONITORING PROJECT RISK PROFILES
Y. Cohen1 and B. Keren2
1Department of Industrial Engineering, The Open University of Israel
118 Ravutzki, P.O.Box 808, Raanana 43107
2Department of Industrial Engineering, Sami Shmoon College of Engineering,
Beer-Sheva 84100
ABSTRACT
This paper presents a new technique for modeling and monitoring risks in projects. The generated risk profile could be a major contributor to risk analysis, risk leveling and risk mitigation in project planning and scheduling. The proposed methodology illustrates how a project risk profile could be constructed utilizing a dynamic Poisson compound process for the project risks. The proposed risk profiles visually illustrate the vulnerabilities of the project, identifying the problematic issues and periods. The difficulties in constructing and maintaining the risk profiles will be discussed and ways to overcome these difficulties.
1. INTRODUCTION
Project risk management is one of nine major project management knowledge areas defined by the Project Management Institute (PMI) [1]. Significant part of this knowledge is documented in the Project Management Body of Knowledge (PMBOK). Most of the project management literature contains trials to quantify the probability and the damage of risks [2]. Typically time dimension in risk-management is related to delays [3].
It is customary to map risks into four general categories [4]: (1) High probability and high damage risks (2) High probability and small damage risks, (3) Low probability and high damage risks, and (4) Low probability low damage risks. In general, corporations try to avoid or eliminate the risks in the first category (the most probable and expansive), they try to mitigating the chances and effects of the second category, they try to insure large parts of the third category, and the risks in the fourth group are tolerable so in many cases they are simply assumed. Kendrick [5] differentiates between schedule risks, resources risks, and activity risks.
This paper assumes that risks with high probabilities are being managed perfectly and concentrate on the low probability risks with chances of less than 10% of occurrence. Many risks may fall in this category during a project's lifetime. Some examples are: fires, storms, traffic accidents, job hazards, strikes, blackout, litigation, etc. In this paper we develop the time dimension of the risks as risk profiles. The basic assumption in this paper is that different risky events (such as a traffic accident, a blackout, and jump in the prices of raw materials) are independent of each other. The independence between different risky events provide sound theoretical basis for the proposed model. Overall the model seeks to represent profile of risks along the project and to enable managing risks.
The major idea in this paper is to represent risk profile on a time line and spot the most risky time-intervals. Obviously the risks and their intensity are strongly related to various activities. This means that project scheduling is a pre-requisite to risk profiling. Once each activity start time is determined the risk profile can be constructed.
Unlike resource leveling, risk leveling can be done in several ways, and re-scheduling is only one of them. Mitigating risks could be done by reducing the probability for risk realization, reducing its damage, insuring, and sharing the risks with partners, investors, or banks. The treatment of each risky interval must consider the specific activities that are being carried out in the specific interval. Since the situation is very unique for each individual interval, this paper does not deal with mitigating risks, and is focused only on the part of generating the risk profile.
Any process that generates independent events along the timeline must generate independent intervals between any two adjacent events. This means that a realization of a risk does not change its probability to occur in the future. In other words the distribution of intervals between any two sequential events is memory-less, and the only memory-less distribution type that exists is the exponential distribution [6]. Any arrival process with exponentially distributed intervals has a Poisson distributed arrival rate [7]. Therefore, we can conclude that if the occurrences of risks of certain type are independent of each other, they form a Poisson process [7].It is customary to express the expected rate value of a Poison process as lambda (l). The sum of several Poisson arrivals is a Poisson process with expected value being the sum of the expected rates:
.1
In case that the process intensity changes over time, the process is defined as a non-homogeneous Poisson process having expected value as a function of time - l(t) [8]. The Poisson distribution only deals with the frequency of occurrence. For each risk type the damage has a certain probability distribution. So the overall damage of a specific type of risk is a compound non-homogeneous Poisson process [9]. For a monetary value of damage x, having expected value E(x) - the expected value of the compound Poisson process is l(t)E(x). So it is not so surprising that the sum of a compound Poisson processes is also a compound Poisson process: While l(t) is just the sum of the individual li(t), E(x) is a weighted average of the E(x)i:
.2
2. GENERATING THE PROFILE FOR A SINGLE RISK TYPE
In this section we shell construct a risk profile for falling in a construction site. This will show the most risky time intervals for falling in a house construction project. Fall occurrences are assumed to be independent of each other, and arrive at an average rate that is related to the state of the building and the activities done. So what do we do? What steps do we take?
2.1 The Steps for Risk Profile Construction
Step 1: Schedule the project in any regular manner that is used in the company (determining the start and finish time of each activity).
Step 2: Once an initial schedule exists, execute resource leveling, and move the activities so that resource consumption never exceeds the resource availability. At the end of this stage we must have a clear plan of exactly when each activity is done and by whom. Only after such a plan is in place can we start dealing with risk.
Step 3: Identify the most falling prone construction stages . Suppose that the most risk prone stages are as follows:
· After digging for foundations and before putting the foundation concrete.
· After concrete foundations were built and before covering them with supporting material.
· Special vulnerabilities exist before laying the floor
· High risk exist while constructing the roof
Step 4: Draw the construction schedule on a time line. If needed, resource leveling may be employed to ensure the feasibility of the time line.
Step 5: Draw a graph of the average risk rate in the project as a function of time. The monetary risk is estimated according to the vulnerabilities at each moment. An example of this graph is depicted in figure 1.
Figure 1. Example of risk profile of worker safety hazards as a function of time, for a house construction project.
3. RISK PROFILE FOR SEVERAL INDEPENDENT RISK TYPES
A general rule in stochastic processes is that the sum of Poison processes is a Poisson process and sum of compound Poisson processes is also a compound Poisson process [9]. This powerful rule enables generating the aggregate risk profile for the project as a stacked graph of all the considered risk profiles. This is depicted in figure 2. In figure 2 we see that several graphs of different and independent risk sources could be summed to give the overall risk curve. However, figure 2 also show that this could lead to very risky intervals (with very high risk level). This gives the motivation for risk leveling.
3. CONCLUSIONS
This paper has shown that significant part of risk management could be modeled using compound Poisson processes. The paper explained how to construct a profile for a single risk type, and how to generate an inclusive project risk profile. It then discussed ways of risk leveling, and showed some new insights as to the reasons for insurance.
Figure 2. Example of aggregate risk profile of 4 independent risk factors
4. REFERENCES
[1] PMI Standards Committee. A guide to the project management body of knowledge (forth edition). Project Management Institute: Newtown Square, PA. 2008.
[2] Kerzner, H. Project management: a systems approach to planning, scheduling, and controlling (10th edition). Haboken, NJ: John Wiley and Sons. 2009.
[3] Van de Vonder, S., Demeulemeester E., Leus R. and W. Herroelen, Proactive-reactive project scheduling trade-offs and procedures .In: Josefowska J. & Weglarz J. (Eds.). Perspectives in Modern Project Scheduling, pp. 25-51, Springer: New-York: NY. 2006.
[4] Marrison C., . The Fundamentals of Risk Measurement, McGraw-Hill. 2002.
[5] Kendrick T., Identifying and Managing Project Risk: Essential Tools for Failure-Proofing Your Project, Second edition, AMACOM. 2009.
[6] Ross, M. S., Introduction to Probability Models, Ninth Edition. Elsevier-Academic Press: Burlington, MA. 2007.
[7] Ross, M. S.. Stochastic Processes, second edition. Wiley; New York, NY. 1995.
[8] Majeske, K. D., A non-homogeneous Poisson process predictive model for automobile warranty claims. Reliability Engineering and System Safety, 92 (2), pp. 243-251. 2007.
[9] Grandell, J., Mixed Poisson Processes (Monographs on Statistics & Applied Probability), Chapman & Hall/CRC: London/Suffolk, UK. 1997.