Contents lists available at ScienceDirect Automation in Construction journal homepage: www.elsevier.com/locate/autcon Time-cost tradeoff analysis with minimized project financing cost S.M. Reza Alavipour, David Arditi ⁎ Dept. of Civil and Architectural Engineering, Illinois Institute of Technology, Chicago, IL 60616, United States of America ARTICLEINFO Keywords: Financing optimization Construction financing Time-cost tradeoff Hybrid algorithm Loans ABSTRACT Time-cost tradeoff analysis allows a contractor to build a project using an optimal schedule that leads to minimum cost. The financing cost can be minimized if the financing decision considers different financing al- ternatives such as short-term and long-term loans and lines of credit. Financing optimization should be in- tegrated into time-cost tradeoff analysis to minimize total cost and maximize profit. This study proposes an integratedmodelthatperformstime-costtradeoffanalysisandfinancingoptimization.AhybridGALPalgorithm isintroducedtosolvetheoptimizationbycombininggeneticalgorithms(GA)andlinearprogramming(LP).The proposedmodelistestedusingsmallandlargenetworks:(1)toprovethatoptimalresultsareobtainedinterms of the financing cost and profit if the proposed integrated model is used, (2) to validate the performance and structureofeachmodel,and(3)toconfirmthepracticalityoftheproposedmodelsinlargenetworks. 1. Introduction Time-cost tradeoff analysis involves accelerated activity durations that are obtained by allocating more resources, and lead to shorter projectdurationandlowerindirectcostattheexpenseofhigherdirect cost[1,2]. Thus, schedulers can perform time-cost tradeoff analysis to find the most cost effective project duration. However, the result of time-costtradeoffanalysisdoesnotrepresentarealisticdecision,unless cashavailabilityconstraintsandfinancingcostarealsoconsidered.The assumption in time-cost tradeoff analysis that unlimited cash is avail- able during the life of a project is not realistic when retainage is withheld by the owner at the time intermediate payments are made, and when intermediate payments are delayed. As a result, the con- tractor often needs additional funds to avert deficits. Although several researchers developed different methods for opti- mizingschedulingproblems(e.g.,[3–6]),considerationoffinancingcost was neglected until 2004, when Elazouni and Gab-Allah [7] introduced “finance-based scheduling” in which construction activities are sched- uled such that financing cost is considered and cash constraints are sa- tisfied. Although some researchers have studied the finance-based sche- dulingproblem,veryfewintegratedtime-costtradeoffandfinance-based scheduling (e.g., [8–12]). A model is proposed in this research that provides an optimal schedule obtained by an optimal use of activity acceleration methods. This schedule results in minimum total cost (in- cluding optimal financing cost) and maximum profit. The proposed model differs from all models developed in past studies that integrated time-cost tradeoff and finance-based scheduling in four respects: (1) Past studies considered only a line of credit without any con- siderationofdifferentfinancingalternativesintermsofsourcesand types of financing, times of cash provisions, interest rates, and re- paymentoptions.Also,paststudiesassumedapredeterminedcredit limit (a limit that is specified by the lender) for a line of credit. Actually, according to Fathi and Afshar [13], the minimum finan- cingcostandtheoptimumfinancingschedulemaybedifferentifa credit limit that is predetermined by the lender is considered for each of the several possible financing alternatives. If lenders allow thecontractortospecifytherequiredfinancing,themodelneedsto calculate the optimal limit that minimizes the financing cost. The proposed model can handle both a predetermined credit limit spe- cifiedbythelendersandcreditlimitspecifiedbythecontractor. (2) Themodelsproposedinpaststudiesassumethatprofitdependsnot only on direct and indirect costs, but also on financing cost. However,profitcanbemaximizediffinancingcostisminimizedby using a combination of different financing alternatives. The pro- posed model calculates the total cost including the minimum fi- nancingcostbyusingdifferentfinancingalternativesinadditionto activity acceleration methods. (3) Someofthemodelsproposedinpaststudiesusegeneticalgorithms (GAs)(e.g.,[8–11])andconstraintprogramming(CP)[12]tofind an optimum schedule that results in maximum profit, but un- fortunately no attempt is made in these models to optimize finan- cing costs by considering different financing alternatives. Several typesoffinancingwithdifferentstructures,differentinterestrates, and different times and amounts of borrowing and repayment are https://doi.org/10.1016/j.autcon.2018.09.009 Received 17 September 2017; Received in revised form 13 September 2018; Accepted 19 September 2018 ⁎ Corresponding author. E-mail addresses: salavipo@hawk.iit.edu (S.M.R. Alavipour), arditi@iit.edu (D. Arditi). Automation in Construction 98 (2019) 110–121 0926-5805/ © 2018 Elsevier B.V. All rights reserved. T