A two-stage stochastic programming approach for project planning with uncertain activity durations

Authors:
Guidong Zhu;Jonathan F. Bard;Gang Yu
Affiliations:
Department of Management Science & Information Systems, McCombs School of Business, The University of Texas, Austin, USA 78712;Graduate Program in Operations Research & Industrial Engineering, 1 University Station, C2200, The University of Texas, Austin, USA 78712;Department of Management Science & Information Systems, McCombs School of Business, The University of Texas, Austin, USA 78712
Venue:
Journal of Scheduling
Year:
2007

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Abstract

This paper investigates the problem of setting target finish times (due dates) for project activities with random durations. Using two-stage integer linear stochastic programming, target times are determined in the first stage followed by the development of a detailed project schedule in the second stage. The objective is to balance (1) the cost of project completion as a function of activity target times with (2) the expected penalty incurred by deviating from the specified values. It is shown that the results may be significantly different when deviations are considered, compared to when activities are scheduled as early as possible in the traditional way. For example, the optimal target completion time for a project may be greater than the makespan of the early-start schedules under any scenario. To find solutions, an exact algorithm is developed for the case without a budget constraint and is used as a part of a heuristic when crashing is permitted. All computational procedures are demonstrated on a set of 150 benchmark problems consisting of 90 activities each.