An approach for identifying the most likely activity sequence in a resource-constrained stochastic network

The biggest concern of a project manager is to identify the proper sequence of activities during project planning and execution so that he or she can appropriately arrange the necessary resources under limited resource availability. The purpose of this article is to develop an approach for identifying the most likely activity sequence in a resource-constrained stochastic network. The approach consists of two stages. The first is a procedure to construct a scenario tree. In the procedure, we integrate a large enough number of sets of feasible activity sequences into a scenario tree. Each set of feasible activity sequences is generated by resource-constrained, deterministic project-scheduling problems with a configuration of randomly generated activity durations. The second stage is a backward-pruning procedure subsequently adopted to eliminate the worse branches from the scenario tree according to a specific objective function. This procedure leads to a reduced scenario tree, on which basis the most likely activity sequence can be easily identified. For demonstration purposes, a simple network example is considered.

[1]  Sergey Bushuyev,et al.  Entropy measurement as a project control tool , 1999 .

[2]  Bruce M. Woodworth,et al.  Identifying the critical sequence in a resource constrained project , 1988 .

[3]  Avraham Shtub,et al.  Project management: engineering, technology, and implementation , 1994 .

[4]  John Bowers,et al.  Criticality in Resource Constrained Networks , 1995 .

[5]  Lee W. Schruben,et al.  Simulation modeling with event graphs , 1983, CACM.

[6]  Ricki G. Ingalls,et al.  PERT Scheduling with Resource Constraints Using Qualitative Simulation Graphs , 2004 .

[7]  Giovanni Mummolo.  Measuring uncertainty and criticality in network planning by PERT-path technique , 1997 .

[8]  Vidyadhar G. Kulkarni,et al.  A classified bibliography of research on stochastic PERT networks: 1966-1987 , 1989 .

[9]  Pierpaolo Pontrandolfo,et al.  Project duration in stochastic networks by the PERT-path technique , 2000 .

[10]  Jerome D. Wiest.  Some Properties of Schedules for Large Projects with Limited Resources , 1964 .

[11]  J. Bowers.  Identifying critical activities in stochastic resource constrained networks , 1996 .

[12]  Terry Williams.  Criticality in Stochastic Networks , 1992 .

[13]  Bajis M. Dodin,et al.  Approximating the Criticality Indices of the Activities in PERT Networks , 1985 .

[14]  Andrew B. Whinston,et al.  The implementation of temporal intervals in qualitative simulation graphs , 2000, TOMC.

[15]  Robert L. Armacost,et al.  Understanding Simulation Solutions to Resource Constrained Project Scheduling Problems with Stochastic Task Durations , 1998 .

[16]  Giovanni Mummolo.  PERT-path network technique: a new approach to project planning , 1994 .