BICRITERIA RESOURCE ALLOCATION PROBLEM IN PERT NETWORKS

We develop a bicriteria model for the resource allocation problem in PERT networks, in which the total direct costs of the project as the first objective, and the mean of project completion time as the second objective are minimized. The activity durations are assumed to be independent random variables with either exponential or Erlang distributions, in which the mean of each activity duration is a non-increasing function of the amount of resource allocated to it. The direct cost of each activity is assumed to be a non-decreasing function of the amount of resource allocated to it. Finally, we use the goal attainment method to solve the related bicriteria optimal control problem numerically, by converting this problem to a related bicriteria nonlinear programming, and obtain the optimal values of the resources allocated to the activities.

[1]  James E. Kelley,et al.  Critical-path planning and scheduling , 1899, IRE-AIEE-ACM '59 (Eastern).

[2]  S. Elmaghraby.  Resource allocation via dynamic programming in activity networks , 1993 .

[3]  Jan Węglarz,et al.  Project Scheduling with Continuously-Divisible, Doubly Constrained Resources , 1981 .

[4]  Erik Demeulemeester,et al.  Optimal procedures for the discrete time/cost trade-off problem in project networks , 1996 .

[5]  James E. Kelley,et al.  Critical-Path Planning and Scheduling: Mathematical Basis , 1961 .

[6]  Vidyadhar G. Kulkarni,et al.  Markov and Markov-Regenerative pert Networks , 1986, Oper. Res..

[7]  D. R. Robinson.  A Dynamic Programming Solution to Cost-Time Tradeoff for CPM , 1975 .

[8]  and Charles K. Taft Reswick,et al.  Introduction to Dynamic Systems , 1967 .

[9]  Pierre N. Robillard,et al.  Technical Note - Expected Completion Time in Pert Networks , 1976, Oper. Res..

[10]  Cheng-Yuan Ku,et al.  Access control to two multiserver loss queues in series , 1997 .

[11]  Tadayoshi Shioyama.  Optimal control of a queuing network system with two types of customers , 1991 .

[12]  D. R. Fulkerson.  A Network Flow Computation for Project Cost Curves , 1961 .

[13]  L. Valadares Tavares.  Optimal resource profiles for program scheduling , 1987 .

[14]  S. Elmaghraby.  On the Expected Duration of PERT Type Networks , 1967 .

[15]  Zohar Laslo,et al.  Activity time-cost tradeoffs under time and cost chance constraints , 2003 .

[16]  E. B. Berman,et al.  Resource Allocation in a PERT Network Under Continuous Activity Time-Cost Functions , 1964 .

[17]  Amir Azaron,et al.  Optimal control of service rates and arrivals in Jackson networks , 2003, Eur. J. Oper. Res..

[18]  G. Thompson,et al.  Critical Path Analyses Via Chance Constrained and Stochastic Programming , 1964 .

[19]  C. T. Clingen.  Letter to the Editor-A Modification of Fulkerson's PERT Algorithm , 1964 .

[20]  R. R. Hocking,et al.  Optimum Time Compression in Project Scheduling , 1970 .

[21]  Zohar Laslo,et al.  Matrix structures and performance: the search for optimal adjustment to organizational objectives , 2001, IEEE Trans. Engineering Management.

[22]  D Golenko Ginzburg,et al.  RESOURCE SUPPORTABILITY MODEL FOR STOCHASTIC NETWORK PROJECTS UNDER A CHANCE CONSTRAINT , 2000 .

[23]  George S. Fishman.  Estimating critical path and arc probabilities in stochastic activity networks , 1985 .

[24]  John M. Burt,et al.  Conditional Monte Carlo: A Simulation Technique for Stochastic Network Analysis , 1971 .

[25]  J. J. Martin.  Distribution of the Time Through a Directed, Acyclic Network , 1965 .

[26]  Kent H. Tseng,et al.  Optimal control of arrivals to token ring networks with exhaustive service discipline , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[27]  C. Perry,et al.  Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis , 1975 .

[28]  Mark B. Garman.  More on Conditioned Sampling in the Simulation of Stochastic Networks , 1972 .

[29]  James J. Solberg,et al.  The use of cutsets in Monte Carlo analysis of stochastic networks , 1979 .