In the management of a project, the project duration can often be comp
ressed by accelerating some of its activities at an additional expense
. This is the so-called time-cost tradeoff problem which has been stud
ied extensively in the project management literature. However, the dis
crete version of the problem, encountered frequently in practice and a
lso useful in modeling general time-cost relationships, has received o
nly scant and sporadic attention. Prompted by the present emphasis on
time-based competition and recent developments concerning problem comp
lexity and solution, we reexamine this important problem in this paper
. We begin by formally describing the problem and discussing the diffi
culties associated with its solution. We then provide an overview of t
he past solution approaches, identify their shortcomings, and present
a new solution approach. Next, we present network decomposition/reduct
ion as a convenient basis for solving the problem and analyzing its di
fficulty. Finally, we point to several new directions for future resea
rch, where we highlight the need for developing and evaluating effecti
ve procedures for solving the general time-cost tradeoff problem. To t
he best of our knowledge, the popular project management software pack
ages do not include provisions for time-cost tradeoff analyses. Our wo
rk, we hope, will provide the groundwork and an incentive for alleviat
ing this deficiency.