Technical Note—Managing a Secret Project

Abstract

We study project scheduling in a competitive setting taking the perspective of a project manager with an adversary, using a Stackelberg game format. The project manager seeks to limit the adversary's opportunity to react to the project and therefore wants to manage the project in a way that keeps the adversary “in the dark” as long as possible while completing the project on time. We formulate and illustrate a new form of project management problem for secret projects where the project manager uses a combination of deception, task scheduling, and crashing to minimize the time between when the adversary initiates a response to the project to when the project is completed. We propose a novel mixed-integer linear programming formulation for the problem and determine characteristics of optimal schedules in this context. Using a detailed example of nuclear weapons development, we illustrate the interconnectedness of the deception, task scheduling, and crashing, and how these influence adversary behavior.

Timely exposure of a secret project: Which activities to monitor?

“…Pinker et al (), the same authors analyze the complexity status for different variants of the problem. Our finding that a late‐start schedule defines a dominant attacker strategy reinforces the results of Pinker et al (, ), who have also identified conditions under which a late‐start schedule is optimal.…”

“…Thus, we can model the harm by a function h : ℝ ≥0 → ℝ that is nonincreasing in the length of the time window between project discovery and completion. Pinker et al () call this time window the exposed time . The highest possible harm h (0) occurs if the project remains secret until completion.…”

“…Below, we briefly review these domains and position our work. A number of articles within the field of project management study the problem of planning (Pinker, Szmerekovsky, & Tilson, 2013, interdicting (Brown, Carlyle, Harney, Skroch, & Wood, 2009;Brown, Carlyle, Royset, & Wood, 2005), or estimating the progress (Godfrey, Cunningham, & Tran, 2007;Godfrey & Mifflin, 2009) of a secret project. The main difference with our work is that these articles do not explicitly model the defender's decision of monitoring tasks and do not consider a probabilistic discovery process.…”

“…Harney et al (2006) describe the tasks necessary to produce "a first small batch of nuclear weapons" together with their durations and precedence constraints. The project-which has also served as an example in (Brown et al, 2009;Gutin, Kuhn, & Wiesemann, 2014;Pinker et al, 2013)-consists of 124 nondummy tasks that can be grouped into five main parts as listed in Table 5. The table's third and fourth column give each part's start and end time (in weeks) under the late-start schedule with a deadline equal to the project's minimum makespan of 468 weeks.…”

Interdiction Games on Markovian PERT Networks

“…Among others, they show that problem (1) can be solved in polynomial time via dynamic programming, but the problem becomes strongly -hard if the proliferator can expedite project tasks. Pinker et al (2013) consider a proliferator that manages a covert project so as to minimize the interdictor's reaction time window. The authors assume that the interdictor only acts once she is sufficiently confident about the malicious intentions of the project manager.…”