Multiobjective model for solving resource‐leveling problem with discounted cash flows

• DOI: http://doi.org/10.1111/itor.12253
• Published date: 01 November 2018
• Date: 01 November 2018

Intl. Trans. in Op. Res. 25 (2018) 2009–2030

DOI: 10.1111/itor.12253

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Multiobjective model for solving resource-leveling problem

with discounted cash flows

Niloofar Nikoofal Sahl Abadi, Mohsen Bagheri and Mohammad Assadi

Department of Industrial Engineering, Sadjad University of Technology, Mashhad, Iran

E-mail: nikoofal.niloo@yahoo.com[Nikoofal Sahl Abadi]; m_bagheri@sadjad.ac [Bagheri]; m.assadi.ie@gmail.com

[Assadi]

Received 31 January 2015; received in revised form 29 October 2015; accepted 23 November 2015

Abstract

Nowadays, executers are struggling to improve the economic and scheduling situation of projects. Con-

struction scheduling techniques often produce schedules that cause undesirable resource fluctuations that are

inefficient and costly to implement on site.The objective of the resource-leveling problem is to reduce resource

fluctuation related costs (hiring and firing costs) without violating the project deadline. In this article, mini-

mizing the discounted costs of resource fluctuations and minimizing the project makespanare considered in a

multiobjective model. The problem is formulated as an integer nonlinear programming model, and since the

optimization problem is NP-hard,we propose multiobjective evolutionary algorithms, namelynondominated

sorting genetic algorithm-II (NSGA-II), strength Pareto evolutionary algorithm-II (SPEA-II), and multiob-

jective particle swarm optimization (MOPSO) to solve our suggested model. To evaluate the performance of

the algorithms, experimental performance analysis on various instances is presented. Furthermore, in order

to study the performance of these algorithms, three criteria are proposed and compared with each other to

demonstrate the strengths of each applied algorithm. To validatethe results obtained for the suggested model,

we compared the results of the first objective function with a well-tuned genetic algorithm and differential

algorithm, and we also compared the makespan results with one of the popular algorithms for the resource

constraints project scheduling problem. Finally, we can observe that the NSGA-II algorithm presents better

solutions than the other two algorithms on average.

Keywords: scheduling; resource leveling; net present value; serial scheduling scheme; nondominated sorting genetic

algorithm-II; strength Pareto evolutionary algorithm-II; multiobjectiveparticle swarm optimization

1. Introduction

Project management is the processof the integration of activities in an efficient and effective method

using limited resources. Resource management is an inherent element of project management;

resource management guarantees that the project is completed on time and at cost as previously

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2010 N. Nikoofal Sahl Abadi et al. / Intl. Trans. in Op. Res. 25 (2018) 2009–2030

defined. In fact, project scheduling problemsare one of the most important problems that performers

deal while scheduling, chiefly when they need to achieve the most efficient resource usage without

increasing the prescribed makespan of a project. However, because resources are rare, their use in

the activities of the project leads to contrast in the schedule. Project scheduling problems contain

not only resource-constrained problems, but also resource-levelingproblems (RLPs), among others.

These two types of problems consider resource usage in two different manners: in the former, it is

seen as a constraint, and in the latter the problem is to make it as efficient as possible. The project

usually requires the use of one or more resources that are limited due to the availability, in which we

can present the RLP that improves project scheduling, especially in cases where even little changes

in used resources impose high costs. The aim of resource leveling is to minimize fluctuations in the

usage of resources over the project duration.

The applicationof RLP and its extensions have attracted increasinginterest from researchers: Ban-

delloni et al. (1994) proposed a model to minimize the deviation between the resource requirements

and stated desirablelevels. They presented a new optimizing approachfor resource leveling based on

nonserial dynamic programming. Younis and Saad (1996) presented a study to solve the problemof

optimal resource leveling formultisource projects, which focuseson resource leveling. The suggested

model can handle multiresource projects. Neumann and Zimmermann (1999) suggested polynomial

heuristic procedures for different types of RLPs for projects with minimumand maximum time lags

between project activities. Brucker et al. (1999) studied resource constraints scheduling with a rep-

resentation of its approaches, models, and categories in which heuristic and exact algorithms have

been represented for single-state problems. Leu et al. (1999) extended a genetic algorithm (GA) for

resource leveling to overcome other old algorithms, in which the GA has been used for showing

the difference between traditional and heuristic approaches. Leu et al. (2000) presented GAs that

were employed to overcome drawbacks of traditional construction resource-leveling algorithms.

The proposed algorithm could effectivelyprovide the optimal or near-optimal combination of mul-

tiple construction resources. Neumann and Zimmermann (2000) mentioned resource-constrained

project scheduling problems with nonregular objective functions, where general temporal con-

straints given by minimum and maximum time lags between activities are prescribed; they studied

resource leveling and net present value (NPV) problems with at most 20 activities. Leu and Hung

(2002) presented a simulation model for resource-leveling scheduling structure, in which a probable

scheduling has been considered for the problem. Furthermore, a GA has been used for solving the

problem. Ballest´

ın et al. (2007) considered the mid-term production-planning problem in make-

to-order production, which consists in scheduling production orders so that the variability in the

resource utilization overtime is minimiz ed. El-Rayes and Jun (2009) presented the resource-leveling

optimization problem in a project structure, in which negative effect of resource fluctuations on

production and costs has been studied. In addition, a GA and transmission of uncritical activities

have been used in this paper. Coughlan et al. (2010) proposed a branch-and-bound algorithm for

multi-RLPs containing 50 multimode activities where the objective was to minimize the resource

availability cost. Geng et al. (2011) suggeted an ant colony algorithm for a nonlinear RLP and

determined the start time of activities. Masmoudi and Ha¨

ıt (2011) presented a generalization of the

GA for solving the project-scheduling problem under time uncertainties within the resource-leveling

technique, in which the generalizationconsists of handling fuzzy time parameter and fuzzy resource

distribution instead of crisp ones. Dr´

otos and Kis (2011) addressed RLPs in a machine environ-

ment in which there are no precedence relations between the tasks. They proposed an exact method

C

2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies