Exact and flexible solution approach to a critical chain project management problem
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Exact and flexible solution approach to a critical chain project management problem Hiroyuki Goto 1
& Alan T. Murray
2
Accepted: 15 October 2020/ # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
An important component in critical chain project management is a scheduling methodology to support resource constraints. Given task duration estimates and precedence relations along with resource designation for each task, one seeks to adhere to a target due date as well as to shorten the estimated makespan. Key are two types of time buffers to absorb potential delays accumulated from preceding tasks, and this makes the problem complex and hard to solve. The “good enough” strategy has been prevalent in research, focusing on the development of heuristic solution methods. There has been only one attempt to minimize estimated makespan, wherein discrete algebra is utilized. The method is, however, inflexible as you must compose a search space. Even the slightest extension requires a major recast of the approach. Hence, we develop a new approach to find an exact optimal solution in an efficient manner. Given a project instance, an optimization problem is constructed as a mixed-integer linear-program, for which an exact solution can be found using an off-the-shelf solver. While the problem is NP hard, larger-scale project instances, including up to 30 tasks, can be solved within a practical time standard. Extension with respect to resource assignment is easily accomplished. Experimental results highlight the significance of the developed framework. Keywords Project scheduling . Resource constrained . Critical chain . Exact optimal solution . Mixed-integer linear-programming
1 Introduction The critical chain project management (CCPM) [1, 2] framework provides a good solution for project planning. A project is deemed successful if it completes early or on time. Positively * Hiroyuki Goto goto–[email protected]
1
Department of Industrial and Systems Engineering, Hosei University, Koganei, Tokyo 185-8584, Japan
2
Department of Geography, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
Constraints
taking into account potential delays impacted by unforeseen incidents, the CCPM framework aims to shorten lead time along with specific disciplines. Among others, a scheduling methodology is an important quantitative component in the holistic framework. Constrained by resource availability, a schedule is planned to achieve shorter lead time, i.e. shorter makespan. A problem to minimize the estimated makespan is comprised as a class of resource constrained project scheduling problems (RCPSPs). Given tasks with uncertain duration estimates along with precedence relations, the scheduling framework aims to shorten the estimated makespan averting delay in due date. The specific procedure was initially unveiled as a business approach [1]. With reports of significant improvements on real projects [3–5] as well as broad academic interest, the methodology attracted the attention of both pr
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