A New Approach to Determine the Critical Path in Stochastic Activity Network

Weng-Ming Chu,Chien-Hung Liu,Chang-Hung Hsu,Chien-Yu Lu,Yung-Chia Hsiao,Koan-Yuh Chang

doi:10.1155/2014/547627

Abstract

The determination of the critical path (CP) in stochastic networks is difficult. It is partly due to the randomness of path durations and partly due to the probability issue of the selection of the critical path in the network. What we are confronted with is not only the complexity among random variables but also the problem of path dependence of the network. Besides, we found that CP is not necessarily the longest (or shortest) path in the network, which was a conventional assumption in use. The Program Evaluation and Review Technique (PERT) and Critical Path Index (CPI) approaches are not able to deal with this problem efficiently. In this study, we give a new definition on the CP in stochastic network and propose a modified label-correcting tracing algorithm (M-LCTA) to solve it. Based on the numerical results, compared with Monte Carlo simulation (MCS), the proposed approach can accurately determine the CP in stochastic networks.

Highlights

The critical path (CP) does help managers in making decision for optimal resource allocation and help in doing network sensitivity analysis
The Program Evaluation and Review Technique (PERT) and Critical Path Index (CPI) approaches are not able to deal with this problem efficiently
The values of random variables are in the form of probability, which lets the selection of CP become very difficult to solve

Summary

A New Approach to Determine the Critical Path in Stochastic Activity Network

The determination of the critical path (CP) in stochastic networks is difficult. It is partly due to the randomness of path durations and partly due to the probability issue of the selection of the critical path in the network. What we are confronted with is the complexity among random variables and the problem of path dependence of the network. The Program Evaluation and Review Technique (PERT) and Critical Path Index (CPI) approaches are not able to deal with this problem efficiently. We give a new definition on the CP in stochastic network and propose a modified label-correcting tracing algorithm (M-LCTA) to solve it. Based on the numerical results, compared with Monte Carlo simulation (MCS), the proposed approach can accurately determine the CP in stochastic networks

Introduction

The Difficulty of Solving Critical Path in Stochastic Network

The Proposed Algorithm for Critical Path in a Stochastic Network

Numerical Experiments

Conflict of Interests