Using Markov Processes for Efficient Project Management

Abstract

An important requirement in project management is to complete it satisfactorily and within the allocated time. Delays incurred during the project will not only result in cost escalation but also in losses benefits that the end result of the project will provide. Critical Analysis Method (CPM) or Program Evaluation & Review Technique (PERT), are methodologies that identify the critical activities that cannot be delayed as the delay of such will delay the duration of the project. Accordingly, every effort has to be made to reduce such delays and the only method available to reduce such delays is to use resources in the form of material, equipment and labor efficiently. As such there does not appear in the available literature on techniques that are based on known scientific principles to bring such delays to the minimal level. The objective of this research is to use Markov process method to forecast the probability of delay in the work in the period in the following time period, based on data on delay or no delay. For convenience a day is taken as the time period, (suitable for minor projects) and activities on the critical path are treated daily. The Markov process calculations can start only after a lapse of a few days from the start which can be 5 or 10 days and the number can be increased From the sequence of delay (D) and no delay (N) up to the current period the Markov stochastic matrix A is constructed which when applied to the vector of current data will yield the probabilities for D and N for the following day. At any current period, if the forecast for the following period is delay, then extra precautions should be taken in implementing the project in the following time period.