Balancing Global Project Resources Utilising a Genetic Algorithm Approach with Stochastic Resource Assignments

Globalisation in large engineering, procurement and construction companies has lead in many cases to the establishment of a number of global centres for activities such as process design, detail design, procurement and fabrication. A company with a number of such resources then faces the problem of maintaining a high percentage utilisation in each of these resource locations, multiple projects need to be processed through each of these offices and which project is handled by which office is generally more reliant on available capacity than geography, particularly in the case of engineering centres. This paper considers this problem as an extension of the well studied Resource Constrained Project Scheduling Problem (RCPSP) and utilises a modified form of our existing genetic algorithm to optimise the utilisation of multiple resource locations when scheduling multiple projects. The unique aspect of this genetic algorithm implementation is its use of stochastic resource assignments to simulate the assignment of certain of the project activities to different global facilities. The stochastic resource assignment is processed as an extension to the main chromosome and is therefore optimised along with the scheduling sequence. Introduction The Resource Constrained Project Scheduling Problem (RCPSP) is a well studied academic problem that has been shown to be well suited to optimisation via genetic algorithms. Lancaster and Ozbayrak [1] and Kolisch and Hartmann [2] provide detailed history of the work conducted in this area to date. A special case of the RCPSP occurs when one considers a company with multiple sites or office locations that can process certain activities for a number of projects. Each of the offices will be aiming at a high resource utilisation, but the more projects and the more suitable locations that can be considered the more complex the problem of optimising the project assignments. This paper considers the optimisation of this problem utilising genetic algorithms, the main objective of this research is to prove the applicability of using stochastic resource assignments to solving this type of problem. The core algorithm is based on our genetic algorithm solution to the RCPSP presented in Lancaster and Cheng [4] with and extension to cater for the optimisation of stochastically assigned resources. Section 2 details the problem being considered in further detail. Section 3 of this paper discusses the structure of the genetic algorithm. Section 4 provides the results of the application of the algorithm to the problem and finally section 5 provides our conclusions and direction of future research. The Multiple Facility Resource Levelling Problem. As a test problem we will consider an organisation concerned with the Engineering, Procurement and Construction of ten projects. The engineering of these projects can be conducted in any of the Applied Mechanics and Materials Vols. 10-12 (2008) pp 67-72 online at http://www.scientific.net © (2008) Trans Tech Publications, Switzerland Online available since 2007/Dec/06 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.33-17/04/08,12:59:00) company’s three engineering facilities worldwide. Each of the engineering facilities has a limitation on the number of man-hours per day that it has available for any given time period. Table 1 below gives the resource limitations at each of the locations. Table 1 Resource Limits Resource Limit Eng_Loc1 200 Eng_Loc2 250 Eng_Loc3 400 For the testing of this algorithm the 10 projects are included in an integrated schedule. Each of the projects is represented for this exercise only at high level i.e. One activity each for the major project phases: Engineering, Procurement, Fabrication, Construction and Commissioning as well as a final Project Completion Activity. The ten Engineering activities will be the activities subject to stochastic resource assignment, we will not consider resource assignments for the other activities for the purpose of this exercise. In the initial state the Projects are all scheduled to start immediately with no consideration for resource constraints. The objective of the problem will then be to find a feasible resource assignment solution that will maintain the imposed resource constraints and further to find the minimum duration solution under these resource constraints. The initial state resource curves are shown below for the three resources can be seen below in figure 1. Initially the resources have been arbitrarily assigned to provide a starting point for the algorithm. 0 100 200 300 400 500 600 700 800 Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Eng_Loc1 Eng_Loc2 Eng_Loc3 Fig.1 Initial Resource Assignments It can be seen that the available engineering offices could not process the projects to this schedule. The Genetic Algorithm The Genetic Algorithm used in the optimisation of this problem is based on the Fitness differential Adaptive Genetic Algorithm previously described in Lancaster and Cheng [4, 6]. In order to cater for the novelty of this specific problem the algorithm was modified in the following manner: The Chromosome was extended in order to hold the resource assignments for each of the activities identified for stochastic resource assignment. In this way the resource assignments are optimised along with the activity sequence. In order to deal with the extension specific crossover and mutation operators had to be developed that would retain the validity of the chromosomes after the genetic operations have been performed. Figure 2 below shows the structure of the extended 68 e-Engineering & Digital Enterprise Technology