The contractor time–cost–credit trade‐off problem: integer programming model, heuristic solution, and business insights

• Published date: 01 November 2020
• DOI: http://doi.org/10.1111/itor.12764
• Author: Sameh Al‐Shihabi,Mohammad M. AlDurgam
• Date: 01 November 2020

Intl. Trans. in Op. Res. 27 (2020) 2841–2877

DOI: 10.1111/itor.12764

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The contractor time–cost–credit trade-off problem: integer

programming model, heuristic solution, and business insights

Sameh Al-Shihabia,∗and Mohammad M. AlDurgamb

aS P Jain School of Global Management, Sydney, Australia

bSystems Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran,Kingdom of Saudi Arabia

E-mail: shihabi.sameh@spjain.org [Al-Shihabi]; aldurgam@kfupm.edu.sa [AlDurgam]

Received 29 October 2018; receivedin revised form 21 October 2019; accepted 6 December 2019

Abstract

Contractors in the construction sector face several trade-offs between time and cost. The time–cost trade-off

(TCT) is one of these trade-offs where contractors can reduce a project completion time by assigning more

resources to activities,which means spending more money, to shorten the execution times of project activities.

On the other hand, contractors who finance their projects through credit lines from banks such that if they

reach their credit limits, then the start times of some project activities can be delayed until cash is available

again, which might lead to an increase in the project execution time; thus, contractors need to consider the

time–credit trade-off. In this work, we simultaneously consider these two trade-offs that affect the project

completion time and use mixed integer linear programming (MILP) to model the contractor time–cost–credit

trade-off (TCCT) problem. The MILP model minimizes the project execution time given the contractor’s

budgetary and financial constraints. In addition to the MILP model, we also develop a heuristic solution

algorithm to solve the problem. Through a set of benchmark instances, we study the effectiveness of the

heuristic algorithm and the computation time of the exact model. It is found that a good upper bound

for the MILP results in less computation time. We also study some practical aspects of the problem where

we highlight the importance of expediting contractor payments in addition to selecting a financially stable

contractor. Finally, we use our MILP model to help a contractor bid for a project.

Keywords:finance-based scheduling; integer programming; scheduling

1. Introduction

Managing cash is an important task when executing projectsin the construction sector. Mismanage-

ment of cash flow is the main reason for contractors’ failures in the construction sector according

to Zayed and Liu (2014). If contractors do not have enough cash to support their activity execution

schedules, then they need to change their baseline plans by delaying or temporarily stopping some

∗Corresponding author.

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2842 S. Al-Shihabi and M. M. AlDurgam / Intl. Trans. in Op. Res.27 (2020) 2841–2877

Fig. 1. Expense versus income profile.

of the activities until money is available, which leads to missing their project due dates (Assaf and

Al-Hejji, 2006) or even fail to finish projects (Arditi et al., 2000). Thus, it is better to work with a

realistic project plan that takes into account the financial constraints instead of a schedule that is

subject to continuous alterations due to cash availability problems.

The contract between the sponsor and the contractor defines a reimbursementperiod such that the

contractor invoices the sponsor forthe cost of the work performed during this period. The sponsor,

however, does not spontaneously pay the contractor and delays the payments. For example, in the

United States, contractors may request payments at the end of the month and sponsors pay the

contractors a month later (Hinze, 2011); however, this payment lag might exceed one month, as

discussed in Arditi and Chotibhongs (2005). In Australia,several state governments use project bank

accounts to expedite subcontractor payments to be paid on time, for example, Western Australia

Government (2017) and Queensland Government (2017). To guarantee the contractor’s job, the

sponsor retains part of the payments. The sum of these retentions is called retainage and is usually

paid at the end of the project (Park et al., 2005).

Figure 1 depicts the cumulativeproject expenditures and sponsor payments of a typical contractor

(Hendrickson, 2008). These two factors, payment delay and retainage, force contractors to rely on

external financing sources since they prefer not to use their own retained earnings (Elazouni and

Metwally, 2005). Among the different available financing options, line of credit (LOC) is the most

common method used to finance projects (Ahuja, 1976). The Surety Information Office (SIO),

which is an office that collects data on surety bonds in the United States, has identified six warning

indicators that show that a construction company may be in distress. One of these indicators is that

LOC is constantly borrowed to the limit (Peterson, 2009).

Contractors withdraw cash from their bank accounts to pay their expenditures such that their

withdrawals do not exceed an approved credit limit (CL), but they also deposit money back to

this account after being reimbursed by the sponsors. Henceforth, we call the condition (constraint)

of not exceeding the CL as the CL constraint. Due to this constraint, especially if the CL is not

high enough, activities’ start times might be delayed until money is deposited back to the bank

account after receiving the payments from the contractor. This problem, minimizing the project

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S. Al-Shihabi and M. M. AlDurgam / Intl. Trans. in Op. Res.27 (2020) 2841–2877 2843

execution time subject to the CL constraint, is called the finance-based scheduling problem (FBSP)

in Elazouni and Gab-Allah (2004) where integer programming (IP) is used to model and optimize

this problem. The project execution time according to FBSP is greater than the one found using the

critical path method (CPM) technique (Kelly and Walker 1959) since the start times of activities, of

which some might be critical, might be delayed due to cash unavailability. Delaying the start times

of activities is called extension in Elazouni and Gab-Allah (2004). Thus, FBSP is about the trade-off

between the CL and project duration.

The resource-constrained project scheduling problem (RCPSP) is considered as the elemental

scheduling problem in project management (e.g., Palacio and Larrea, 2017; Chakrabortty et al.,

2020). According to ¨

Ozdamar and Ulusoy (1995), resources in projectmanagement can be classified

as renewable, nonrenewable, and doublyconstrained. Renewable resources (e.g., labor) are fixed for

a period and are renewed every period (Homberger, 2007). Nonrenewable resources (e.g., budget)

are fixed for the whole project. Doubly constrained resources (e.g., working hours of consultants)

are fixed with respect to the project and period. Available cash, as a resource, is different from the

three discussed classifications because none of the criteria used for classification considers the case

where the use of a resource in one period might affect its availability in the next period. Financial

resources can be considered as a new set of resource that needs to be added to the three previously

known resources.

Another practical, cash-related practice is shortening activity times, consequently the project

duration, by committing more resources to these activities, which implies spending more money to

accelerate the execution of these activities. The option of reducing activity times is called crashing,

and the problem of minimizing project duration given the crashing option is called the time–cost

trade-off problem (TCTP) (e.g., Siemens, 1971; Kerzner and Kerzner, 2017). The relationship be-

tween time and cost might be linear (Kelley Jr (1961)) leading to LTCTP, continuous(Moussourakis

and Haksever, 2009) leading to CTCTP, and discrete (De et al., 1997) leading to DTCTP. In the

construction industry, the used time units are discrete; therefore, we assume a discrete relationship

between time and cost. Linear and continuous relationships can be made discrete to comply with

the time unit used in the construction industry.

In summary, the lower CL is, the more time the contractor needs to execute the project, and the

higher the project budget is, the less time the contractor needs to complete the project if the project

activities can be crashed. Contractors need to think of these two trade-offs during the bidding and

execution phases of any project. For example, at the bidding stage, contractors need to know their

capabilities regarding time and cost given their financial limitations. Similarly, when executing the

project, a contractor can crash some of the activities to shorten the projectduration if the contractor

is late and needs to pay a lateness penalty.

Researchers have considered variants to this problem earlier (e.g., El-Abbasy et al., 2016, 2017;

Alavipour and Arditi, 2019a); however, and to the authors’ knowledge, no exacttechnique has been

used to solve this problem; instead, researchers have relied on meta-heuristics to solve this problem.

A common excuse to avoid using exact methods, especially IP, is the time needed to solve this

problem compared to genetic algorithm (GA). In an industry like construction, in which project

durations might exceed a year, spending an extra hour or two hours to solve a problem is a must

investment, given the high cost of the projects.

In this paper, we develop a mixed integer linear program (MILP) model to capture the trade-

off between extension and crashing. We call this problem the discrete time, cost, and credit

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International Transactionsin Operational Research C

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