Dynamic Project Expediting: A Stochastic Shortest-Path Approach

Luca Bertazzi (), Riccardo Mogre () and Nikolaos Trichakis ()
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Luca Bertazzi: Department of Economics and Management, University of Brescia, 25122 Brescia, Italy
Riccardo Mogre: Durham University Business School, Durham University, Durham DH1 3LB, United Kingdom
Nikolaos Trichakis: Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142

Management Science, 2024, vol. 70, issue 6, 3748-3768

Abstract: We deal with the problem of managing a project or a complex operational process by controlling the execution pace of the activities it comprises. We consider a setting in which these activities are clearly defined, are subject to precedence constraints, and progress randomly. We formulate a discrete-time, infinite-horizon Markov decision process in which the manager reviews progress in each period and decides which activities to expedite to balance expediting costs with delay costs. We derive structural properties for this dynamic project expediting problem. These enable us then to devise exact solution methods that we show to reduce computational burden significantly. We illustrate how our method generalizes and can be used to tackle a wide range of so-called stochastic shortest-path problems that are characterized by an intuitive property and can capture other applications, including medical decision-making and disease-modeling problems. Moreover, we also deal with the state identification issue for our problem, which is a challenging task in and of itself, owing to precedence constraints. We complement our analytical results with numerical experiments, demonstrating that both our solution and state identification methods significantly outperform extant methods for a supply chain example and for various randomly generated instances.

Keywords: project management; project risk; Markov decision process; stochastic dynamic programming; stochastic shortest path (search for similar items in EconPapers)
Date: 2024
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