Abstract:Consider a project during the life cycle of which there are cash payouts and in-flows. To better meet his financial commitments, the project owner would like to meet all deadlines without running out of cash. We show that the cash availability objective is similar to the total weighted flowtime used to measure work-in-progress performance in the scheduling and inventory control literatures. In this article we provide several specialized solution methods for the problem of minimizing total weighted flowtime in an arbitrary acyclic project network, subject to activity release times and due dates, where the activity weights may be positive or negative and represent cash in-and out-flows. We describe the structure of an optimal solution and provide several efficient algorithms and their complexity based on mincost and maxflow formulations. © 2006 Wiley Periodicals, Inc. Naval Research Logistics 53: 272-284, 2006 Keywords: cash availability; project scheduling; network optimization; algorithms; discounting
MOTIVATION AND LITERATURE REVIEWConsider the cash in-and out-flows associated with each activity of a project. Multiply each cash flow by the amount of time from the time it is committed until project completion. This product is measured in money-time. The project objective proposed in this article is the sum of these products over all cash flows associated with the activities. This sum is called cash availability. The associated optimization problem is to identify a schedule that maximizes cash availability.The notion of cash availability as a means for evaluating projects is discussed by Goldratt [6]. The author suggests cash availability as an alternative measure for financial evaluation of projects. Today the two most popular methods for evaluating projects are the Payback period and the Net Present Value (NPV).Unlike manufactured products, projects may not require storing materials at sites controlled by the project owner. This is, for instance, the case with construction projects. Such projects often involve hundreds of subcontractors. Partial payments are made to subcontractors according to bilateral agreements. Such payments are only recovered by the Correspondence to: G. L. Vairaktarakis (gxv5@weatherhead. cwru.edu) project owner upon project completion, much the same way that work-in-process costs are captured by manufacturers upon selling finished goods. Evidently, cash availability is the project equivalent of work-in-progress (WIP) inventory costs in production. A lean manufacturer wants to minimize the investment in WIP in the same way that a project owner wants to minimize the average cash amount needed throughout the lifetime of the project. WIP costs are measured using total weighted flowtime. This measure is a sum of n products, one for every job. Associated with each job i is the product of the inventory value w i committed to initiate (or complete) the job, multiplied by the length of time t i for which this amount is committed. Following the usual assumption that an order of n job...