Title: LP relaxation-based solution algorithms for the multi-mode project scheduling with a non-renewable resource

Authors: Meral Azizoglu; Ferda Can Çetinkaya; Selin Kırbıyık Pamir

Addresses: Department of Industrial Engineering, Middle East Technical University, 06800, Ankara, Turkey ' Department of Industrial Engineering, Faculty of Engineering, Çankaya University, 06810, Etimesgut, Ankara, Turkey ' Genel Energy – Next Level Iş Merkezi Eskişehir Yolu, Dumlupınar Bulvarı No. 3A-101, Söğütözü 06500 Ankara, Turkey

Abstract: In this study, we consider a multi-mode resource allocation problem with a single non-renewable resource. We assume the resource is released at defined time points and at defined quantities. We also assume that the activity costs are charged once they are completed. Our aim is to minimise the project completion time. We formulate the problem as a pure integer programming model and show that it is strongly NP-hard. We find lower bounds by pure and mixed integer linear programming relaxations of the model and develop three heuristic procedures based on those relaxations. The results of our computational study have revealed the satisfactory performances of our lower bounds and heuristic procedures. [Received 7 December 2011; Revised 13 April 2013; Revised 4 February 2014; Accepted 11 April 2014]

Keywords: project scheduling; multi-mode resource allocation; non-renewable resources; integer programming; linear programming relaxation; heuristics; project completion time.

DOI: 10.1504/EJIE.2015.070322

European Journal of Industrial Engineering, 2015 Vol.9 No.4, pp.450 - 469

Published online: 02 Jul 2015 *

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