Identifiying project vulnerabilites can benefit organizations

Large projects are often hugely complex and expensive. If something goes wrong with a project task the knock on effects can be very costly. They may delay the project, trigger contract penalties, even force companies into bankruptcy. To provide some protection against this, organizations can develop risk management strategies that attempt to minimize the probability of mistakes and project delays. Yet organizations have limited resources, and with large projects it is difficult to know which part of the project to focus on, which element has the potential to cause the most problems.
Help is at hand for project managers, however, with the publication of new research by Daniel Kuhn and co-researchers Eli Gutin and Wolfram Wiesemann, in their paper "Interdiction Games on Markovian PERT Networks". Although when Kuhn began his research journey, he wasn't thinking of the plight of project managers around the world. Instead, he had a completely different problem in mind.
Kuhn was investigating how to derail a nuclear weapons program. Assuming someone had limited resources and wanted to target those resources at a particular part of a nuclear weapons project, what was the optimal course of action?

Finding the weak spots
Devising a solution meant deconstructing the concept of a project. As Kuhn explains, a project can be described mathematically by its different tasks. These tasks must satisfy "precedence relations" - some elements must be completed before others are started. If you are making bread you have to make the dough before doing the baking.
Projects can be represented visually using a project evaluation and review technique (PERT) network. The tasks become nodes, arrows connect the nodes indicating the order of task completion. Each task has duration – the time it takes to complete –although these are uncertain. To complete the task as quickly as possible you must start each task as soon as any required predecessor task is completed.
Next Kuhn and his co-authors considered the position of the interdictor, someone who wants to stop or delay the project. They might achieve this through a variety of means including economic sanctions, embargoes on key materials, or even more niche interventions such as the proliferation of a computer virus, for example.
Whatever method is chosen, the interdictor has limited resources, the interdiction budget, to use when trying to delay project tasks. Intuition suggests that it's best to focus resources on tasks performed in series rather than in parallel. However, there is still the considerable challenge of deciding the best tasks to act on in order to inflict maximum project delay overall.
Kuhn and his fellow researchers used game theory to model the problem and its solution. Crucially, they modelled for uncertainty in task duration. This is a very important aspect of their approach. If you assign nominal duration periods to the tasks it fails to capture the way that changing task durations can cause an accumulation of delays (caused by precedence relations) which cascade through the project. This would lead to an underestimation of the total project completion time.
Additionally, Kuhn considered the problem in a static and dynamic context. In the static context, the interdictor decides which tasks to delay at the start, then the project runs with the interdictor sticking to their original decision.
In the dynamic context the interdictor can wait to see how things develop before deciding which tasks to delay. This gives the interdictor an advantage, notes Kuhn, as it allows them to identify which tasks are taking longer and delay those. Mathematically this is more of a challenge to model, though, as it means accounting for many more possible outcomes when deciding on an optimal course of action for the interdictor. (The algorithm was tested on a project with a 100 tasks, the number of different states was in the order of 200,000 plus.)

Organizational benefits
The result of the research is an algorithm that tells someone which tasks to interdict. It does this for any given state of the project. Feed in the required information - which tasks are currently active, completed, and still to be completed, plus the resources available for interdiction actions - and the algorithm tells you the optimal decision in terms of the tasks you should try to delay, at any given moment.
The model was also extended to cover two additional situations: where the project manager is able to allocate resources to different tasks in order to speed them up; and where the interdictor tries but fails to stop a task leaving them with fewer resources and, therefore, fewer opportunities to stop other tasks.
The algorithm Kuhn and his fellow researchers have created has obvious applications for preventing nuclear weapon proliferation. However, it also has some very significant implications for business. It could, for example, be used as a risk assessment tool, identifying those project tasks with the potential to cause the most delays to a project. Project managers can then focus resources on careful management of those tasks. They could arrange special insurance for those tasks. Overall it allows for better contingency planning, and more robust project planning.
The algorithm is also relevant for competition strategy. It might allow firms to identify and poach employees that are key to the completion of critical tasks in rival firms. In a similar way firms could use patents and the enforcement of intellectual property laws to deny their rivals the use of technologies essential to the project's progress. More tangentially it could be used to identify key disease pathways to target with drug development. There are many possibilities.
Indeed, when it comes to identifying the weak link in a process, the tasks that if targeted will cause maximum damage and delay, Kuhn's black box solution really is the nuclear option.

"Interdiction Games on Markovian PERT Networks", by Daniel Kuhn, Risk Analytics and Optimization Chair, École Polytechnique Fédérale de Lausanne, Eli Gutin, Operations Research Center, Massachusetts Institute of Technology, and Wolfram Wiesemann Imperial College Business School, Imperial College London. Forthcoming in Management Science, published online in Articles in Advance 23 Sep 2014.