Integrated time–cost tradeoff and resources leveling problems with allowed activity splitting

• Published date: 01 January 2019
• Date: 01 January 2019
• Author: Abdulrahim Shamayleh,Fekrat El‐Wehedi,Moncer Hariga
• DOI: http://doi.org/10.1111/itor.12329

Intl. Trans. in Op. Res. 26 (2019) 80–99

DOI: 10.1111/itor.12329

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Integrated time–cost tradeoff and resources leveling problems

with allowed activity splitting

Moncer Hariga, Abdulrahim Shamayleh and Fekrat El-Wehedi

Industrial Engineering, American University of Sharjah, Sharjah, United Arab Emirates

E-mail: mhariga@aus.edu [Hariga]; ashamayleh@aus.edu[Shamayleh]; felwehedi@aus.edu [El-Wehedi]

Received 12 September 2015; receivedin revised form 10 April 2016; accepted 21 June 2016

Abstract

Resource leveling and time–cost tradeoff are among the most challenging optimization problems in project

management. These two problems areusually addressed separately because each problem optimizes different

objective functions.In this paper, we developan integrated model that addresses both problems when activities

are allowed to split for better utilization of resources. The formulated mixed integer linear program (MILP)

model considers the tradeoff between the crashing-dependent costs; direct and indirect costs, and resource

utilization related costs; acquiring, releasing, and splitting costs. The model can be used as a decision tool

to determine whether crashing is recommended when decision makers are also concerned with the better

utilization of project’s resources. A one-way sensitivity analysis was conducted to assess total cost savings

achieved through the integrationof time–cost tradeoff and resource leveling problems. Another experimental

study was undertaken to evaluate the performance of the MILP runtime.

Keywords:project scheduling; resource leveling; time–cost tradeoff; activity splitting; optimization

1. Introduction

Application of project management practicesis growing in all types of industries. Currently, project

management concepts and techniques are mostly applied to help organizations to complete their

projects on time, within budget, and to meet customers’ specifications. Project planning process

involves identifying project activities, such as estimates of their durations and costs, precedence

relationships between activities, cost for each of the required resources, total project cost, and

project completion time before the project is executed. Project resources are broadly classified

into consumable and renewable resources. Consumable resources are used up, whereas renewable

resources havelimited availability. One of the major concerns of project managers is the completion

of the project at the earliest possible date with least cost while ensuring high and even utilization of

the project’s renewable resources.

Limiting the amount of resources and constraining the project completion time are the two com-

mon types of constraints in project management. Resource-constrained projects must be finished

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M. Hariga et al. / Intl. Trans.in Op. Res. 26 (2019) 80–99 81

as soon as possible, but without exceeding the available amount resources (Gagnon et al., 2012).

Usually,for this type of projects, the completion time determined by the critical path method (CPM)

is surpassed because of the limitation on the cost of resources. Time-limited projects must finish

by a certain time with minimum time variation in resource utilization over the project lifespan

(Menesi and Hegazi, 2015). In the scheduling of time-constrained projects, agreed upon deadline

in the project contract or the completion time set by CPM is to be honored in order to avoid delay

penalties. The decision therefore is to optimally allocate available resources to project’s activities

by minimizing the fluctuation of their utilization over time. Larson and Gray (2014) pointed that

projects with irregular resource requirements over time are difficult to manage and their resource

utilization may be very poor. Moreover, the adjustment of the amount of resources, in response

to the time-varying requirement, results in additional acquiring and releasing costs. According to

Karaa and Nasr (1986), varying the utilization of a specific resource requires significant costs due

to extra charges such as hiring, firing, overtime, and idle resources.

Resource leveling is a well-known technique adopted in time-limited projects for effective utiliza-

tion and allocation of resources. The goal is to balance demand for resources with the available

supply while minimizing the fluctuations in resource utilization. Among the approaches used for

resource leveling, activitysplitting allows activities to be interrupted for some periods of time to level

the utilization of resources, therefore allowing them to be run atdifferent intervals using noncritical

activities’ idle times. Son and Mattila (2004) explained that identifying which activities to be split is

a realistic approach to the resource leveling problem. However,activity splitting introduces an extra

cost associated with interrupting and later restarting the activity. Therefore, for time-constrained

projects, project managers have to develop a schedule that achieves a balance between the costs of

acquiring and releasing resources incurred due to the fluctuation in their utilization over time as

well as the cost associated with activity splitting.

In the planning phase of the project life cycle, project managers face the decision of allocating

appropriate resources, including labor resources with the right number and skills, equipment with

the required efficiency and productivity to complete the project activities. In other words, project

managers have to select an execution mode for each activity from a set of alternative modes with

different processing times and costs. The challenge for the project manager is therefore to compare

the benefits of shortening project duration with the resulting costs. This problem is well known

in the project management literature as project crashing, also known as time–cost tradeoff (TCT)

analysis. It is a project scheduling tool commonly used to expedite project completion by reducing

the duration of some activities at a minimum cost.

Typically, project decision makers face project crashing and resources leveling decisions sequen-

tially where a schedule with the minimum duration is developed first using TCT analysis, and

then the resources are leveled using the floats of the noncritical activities in the resultant schedule.

However, attempting to minimize the total operations costs related to the reduction of the project

duration without considering the costs incurred as a result of the variations in the resources uti-

lization (costs of acquiring and releasing the resources, and activity splitting cost) over time and

vice versa may result in a suboptimal project schedule. Therefore, the main contribution of this

paper is the development of a MILP model that integrates crashing and leveling problems with the

possibility of splitting activities to provide least-cost project schedule having well-adjusted resource

utilization and reduced project duration.

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2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies