PROJECT RISK QUANTIFIER AND OPTIMAL PROJECT ACCELERATOR – USING MACHINE LEARNING AND STOCHASTIC SIMULATION TO OPTIMIZE PROJECT COMPLETION DATES AND COSTS Larry M. Deschaine, Samantha R. Pack, Frederick A. Zafran, Janardan J. Patel Science Application International Corporation – Address correspondence to:
[email protected] ABSTRACT
INTRODUCTION
Program managers routinely make decisions that affect projects in all phases. These decisions often control hundreds of thousands or millions of dollars of resources and personnel. A tremendous amount of energy has been applied to developing project management tools such as scheduling software and the like. These systems can sometimes be limited by two fundamental impediments; the project variables such as task duration and cost are typically assumed to be precisely known, and the project relationships are not always simple linear functions. These impediments can sometimes adversely affect the effectiveness of even the most expert project manager. This work describes a tool that combines risk assessment with optimization to optimize project management decisions. These tools consist of a project variable risk assessment by using stochastic inputs for project variables such as task duration and cost instead of single value point estimates. This analysis provides probability distributions for intermediate milestone or total project costs and completion dates. By employing a MonteCarlo simulation technique, the manager can focus project monitoring resources from output the details the percentage of the time a task will fall on the critical path. This can be done at the bidding stage to evaluate the project risk/reward level or at the project kick-off stages to optimize the project baseline schedule. If project slippage begins to occur, the manager can then implement a machine learning software algorithm known as genetic algorithm or genetic programming, that will optimize which project tasks to accelerate to recover schedule at the minimum cost under deterministic or uncertain (i. e. stochastic) conditions. These results are immediately discernable and readily explainable to management. A summary of the theoretical basis and applicability for the techniques are provided.
When beginning a typical project, one of the first management activities is to acquire and assemble all of the tasks descriptions, duration, and costs into a commercial off the shelf (COTS) scheduling package. The project's schedule logic, or task interdependencies, is then added and a baseline schedule is produced. An example of the product produced from this type of scheduling activity is shown on Figure 1. This information consists of the main elements:
Key Words: Project management, scheduling, optimization, genetic algorithms, genetic programming, stochastic simulation, machine learning, and artificial intelligence.
• • • • • •
Project Start Date; Individual Task Duration; Individual Task Costs; The Project Critical Path; Project Completion Date Estimate, and; Project Cost Estimate.
When the initial schedule is produced, the management team conducts a sensitivity, or reality check. This consists of, among other items, the following key questions: • • • •
How real are these estimates? What could be the variation(s)? What activities are most critical to manage to avoid cost overruns or schedule slippage? If the schedule slips, how do we best recover in terms of cost and effectiveness?
The example project has the following estimates to these questions: • • • •
Project Start Date – September 30, 1999; Project Completion Date – December 9, 1999; Project Duration – 49 Days, and; Project Cost - $117,500.
The work presented below represents the output from the “Project Risk Quantifier and Optimal Project Accelerator” Science Applications International Corporation – 1999.
PROJECT RISK QUANTIFICATION The first step in the analysis is to include the uncertainty in the project information, specifically the task duration and cost estimates. To accomplish this task, a software algorithm that allows for distributions of time and cost, as opposed to point estimates, was applied. The value of using a distribution for cost and time estimates is quite clear. If a program scheduler uses the average estimate for task cost and duration, then the project has about a average chance of succeeding. This success rate on project management performance is not acceptable in the industry. On the other hand, if the project scheduler adds contingency throughout the project, the project cost and delivery time may become so bloated as to not be acceptable to the client, or the company may not win the contract at all. Performing a project risk assessment allows both the project manager and the management review team to assess the sensitivity to the project from various conditions which may affect the project, and to rank these in order of which tasks to focus management time. These concepts are best shown through example.
to the project task duration or cost estimates. For simplicity, a risk distribution in the form of a triangle was used throughout this project. For example, the task duration input for task ID #3 “Mob and Install Access Road” is given as RiskTriangle (2,3,4). This notation indicates the task cannot take less than 2 days or more than 4 days, and will likely take 3 days. The actual distribution is then calculated such that the area under the RiskTriangle (2,3,4) is equal to 1.0. A simulation of the project was conducted using the MonteCarlo technique. This technique randomly picks task durations from the distributions provided and calculates the results of the total project duration and cost. It also calculates the frequency that an individual task appeared on the critical path. By simulation this project 10,000 times, a very good picture is developed that specifically describes the project performance under the expected variations in the task durations. As seen on Figure 2 in the @Risk Critical Index Column, certain tasks are always on the critical path (with 100% certainty), and certain tasks are never and almost never (with 0 to 7% certainty), on the critical paths. This analysis quickly and specifically identifies which tasks are important to monitor with management resources, and which tasks are of less importance.
Critical Path Analysis. The critical path of a project is the shortest time that a project can be conducted if all the tasks on the critical path are completed according to the estimates. In the optimization arena, the critical path can be thought of as the constraint on project completion time, shorter times are not in the feasible region of the solution space. Seasoned project managers know that a project of any reasonable complexity does not have only one distinct critical path, but may have many that change throughout the project, as actual project performance information becomes available. To assess the sensitivity on the critical path to variations on project task duration, the point estimates in the original schedule were changed to probabilistic distributions. These are shown on Figure 2. Virtually any distribution can be added
The statistics from the analysis also provide for a rank order correlation of these tasks. This result is shown on Table 1.0. As can be seen in this figure, the key tasks to monitor are: • • • •
Building Erection; Start-up, Acceptance, and Demobilization; Install Above Ground Piping, and; Excavate for and Frame Foundation.
Note that in this list, the “Install Above Ground Piping” task is the third most important task for the project with respect to project completion, but only falls on the critical path 94% of the time. This is because that the duration of the task is longer than some of the other tasks that are on the critical path 100% of the time and hence affects the final outcome more if it slips. This rank order analysis is key in addition to the critical path index analysis where complex and variable tasks durations are present in a project.
Project Completion Time Analysis. Using point estimates, the project completion time was estimated to be 49 days, or December 9, 1999. The project completion estimate is provided in Figure 3. Shown on this figure, there is a small chance that the project could be finished as early as November 28, 1999 and is most certainly expected to be finished before December 16, 1999. There is only a 50% probability that this project would finish on the December 9, 1999 estimated date. This information is crucial not only for internal project management, but also to managing client expectations. Project Completion Cost Analysis. Using point estimates, the project completion cost was estimated to be $117,500. The project completion cost estimate is provided in Figure 4. Shown on this figure, their a small chance that the project could be finished for as little as $100,000 but could cost as much as $125,000. There is about an 80% probability that this project would cost the estimated $117,500. This information is crucial for internal project management as many of these types of projects are fixed price and project overruns are funded by profits. Note that the probability of time completion (50%) and the probability of cost compliance (80%) are different. This is due to the non-linearity in costs versus project duration, and is very important to know when balancing and optimizing individual and multiple projects.
OPTIMAL PROJECT RECOVERY Any seasoned project manager knows that schedules slip. It is the best project manager that can recover from project slippage while minimizing drain on the project’s or company’s financial resources. The SAIC “Project Risk Quantifier and Optimal Project Accelerator” uses a combination of optimization techniques to help find the best method to schedule recovery. This is critical since project slippage can, depending on the size of the project, cost from a few thousand dollars per day to hundreds of thousands of dollars. Optimal project acceleration is a complex problem due the interrelationships of the tasks, the non-linearity in the costs, the possibility of if-then logic in the schedule, and the like. The structure of the challenge is provided by the project schedule, such that the solution is on of “constant” optimization. Specifically, SAIC uses
algorithms that decide which tasks to fund that will reduce the project schedule to the desired duration for the minimal cost. Techniques range from linear programming, genetic algorithms, genetic programming, optimization under uncertainty and the like, An example of optimal schedule acceleration is shown on Figure 5. Note that this cost structure is slightly different than shown in Figure 4. Figure 5 used a time and materials cost structure that was dependent on task duration, so that if schedule days were saved by chance, cost was saved also. In this example, we complicated the challenge by adding a cost penalty for forcibly accelerate the schedule by choice, rather than relying on a chance that a task may take less time. This is a very real scenario that managers face. The information that the model provides is the following: • • •
Project Accelerator Input: Cost of Acceleration per task per day; Maximum acceleration achievable per task.
And the model will provide: • • • •
Which tasks to accelerate; How many days to accelerate; The task cost for acceleration; The overall new project cost and schedule.
Using this information, the project manager is enabled, in conjunction with other management intervention strategies as appropriate, to then authorize individual task leader to accelerate task for schedule recover to meet delivery dates at the least cost. The optimization can be designed to: •
Minimize the cost of project acceleration subject to a fixed delivery date;
•
Minimize the cost of project acceleration under uncertainty subject to schedule completeness date variance limitations;
As well as many other objectives and options. REFERENCES Deschaine, L. M. Pack, S. R., Zafran, F. A., Patel, J. J., Holt, E. L., “SAIC Project Risk Quantifier and Optimal Project Accelerator”, 1999. Peer Reviewed by M. J. Ades, Ph. D., PE, MBA
Figure 1. Standard Project Management: Remediation Construction Project
Figure 2. Advanced Project Management: Monte Carlo Simulation to Identify Likelihood of Tasks on Critical Path
Table 1 Rank Order Coefficients for the Key Tasks to Monitor to Meet Project Completion Schedule Task Description
Rank Order Coefficient
•
Key Task # 1: Building Erection
0.49
•
Key Task #2: Start-up, Acceptance, and Demobilization
0.49
•
Key Task #3: Install Above Ground Piping
0.48
•
Key Task #4: Excavate for and Frame Foundation
0.24
F ig u re 3 . P ro je c t C o m p le tio n T im e D is trib u tio n : V a ria n c e fro m U n c e rta in T a s k D u ra tio n
D a te
11 -D ec 13 -D ec 15 -D ec
9D ec
7D ec
5D ec
3D ec
1D ec
28 -N ov 29 -N ov
100% 80% 60% 40% 20% 0%
Figure 4. D istribution for Total Project C ost B ased on U ncertain Task D uration Length 100% 80% 60% 40% 20%
12 2. 5
12 0
11 7. 5
11 5
11 2. 5
11 0
10 7. 5
10 5
10 2. 5
10 0
0%
$ V alues in Thousands
Figure 5. Optimal Task Selection for Duration Management $180,000
Total Project Cost (Dollars)
$160,000 $140,000 $120,000 $100,000 $80,000 $60,000 $40,000 $20,000 $35
40
45
50
Total Project Duration (Days)
55
60
