Title: Optimal resource allocation in activity networks - stochastic environment

Authors: Salah E. Elmaghraby; Girish Ramachandra

Addresses: Department of Industrial and Systems Engineering, The Graduate Program in Operations Research, North Carolina State University, Raleigh NC, 27695-7906, USA ' Knowledge Foundry Business Solutions Pvt. Ltd., 344, 20th Main, Koramangala 8th Block, Bangalore – 560095, India

Abstract: We treat the problem of optimally allocating a single resource under uncertainty to minimise the sum of resource cost and tardiness cost. We assume that the work content of an activity is the source of the 'internal' uncertainty - as opposed to the 'external' uncertainty. When the work content is known only in probability, we discuss the approach via stochastic programming and demonstrate its inadequacy. We treat the special case when the work content is exponentially distributed. This results in a continuous-time Markov chain with a single absorbing state. We establish convexity of the cost function and develop a policy iteration-like approach that achieves the optimum in finite number of steps. In case of arbitrary probability distribution of the work content, we develop a simulation-based optimisation method that incorporates sampling optimisation and variance reduction techniques.

Keywords: activity networks; resource allocation; stochastic work content; phase-type distributions; uncertainty; simulation; sampling optimisation; variance reduction; continuous-time Markov chain.

DOI: 10.1504/IJPOM.2014.059745

International Journal of Project Organisation and Management, 2014 Vol.6 No.1/2, pp.67 - 95

Published online: 24 May 2014 *

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