Scheduling a project to maximize

its net present value: An integer

programming approach

Kum Khiong Yang

Decision Sciences Department, National University of Singapore, Kent Ridge, Singapore $0511,$ Singapore

F$.$ Brian Talbot

Operations Management Department, University of Michigan, Ann Arbor, MI $48109-1234,$ USA

James H$.$ Patterson

Operations Management Department, Indiana University, Bloomington, IN $47405,$ USA

Received June $1990$; revised August $1991$

Abstract: We describe an integer programming algorithm for determining scheduled start and finish

times for the activities of a project subject to resource limitations during each period of the schedule

duration. The objective is to maximize the net present value of the project to the firm. A depth$-$first

branch and bound solution procedure searches over the feasible set of finish or completion times for

each of the activities of the project. Fathoming criteria based upon the concept of a network cut

originally developed to solve the duration minimization version of this problem are extended in this

paper to solve the net present value problem. These fathoming decision rules prevent many potentially

inferior solutions from being explicitly evaluated. Computational experience reported demonstrates the

efficacy of the approach.

Keywords: Scheduling; Net present value; Integer programming

$1.$ Introduction

The application of optimization techniques to

cost control has lagged far behind those directed

at optimizing other measures of project perfor$-$

mance. A review of the literature reveals that

previous research has been focused primarily on

the objective of minimizing project duration

$[1,2,5,9,10,17-20].$ This is unfortunate when one

considers th~it the single inducement leading to

the involvement in any project is the project's

Correspondence to: Prof. J$.$H$.$ Patterson, Operations Manage$-$

ment Department, Indiana University,Bloomington,IN $47405,$

USA.

potential of becoming a lucrative venture. Even if

a manager cannot limit attention to the pecuniary

aspects of a project alone, these aspects cannot

be treated in cavalier fashion.

The procedure described in this paper deter$-$

mines activity completion times that maximize the

net present value $($NPV$)$ of the project to the

firm. Multiple limited$-$resources influence when

activities can be performed, as in the resource$-$

constrained, duration minimization version of this

problem. In maximizing NPV$,$ we assume that the

start of each activity requires an initial capital

investment that is recovered upon completion of

the activity. Cash flows $($cash payments and cash

disbursements$)$ occur during the performance of

$0377-2217/93/$$$06\mathrm{.}001993-$ Elsevier Science Publishers B$.$V$.$ All rights reserved

app$($a$)$ write a brief report summarizing the paper; and$/$or$,$

$($b$)$ solve an example to illustrate the results in the paperroach