The payment scheduling problem

Richard C. Grinold

Naval Research Logistics Quarterly, 1972, vol. 19, issue 1, 123-136

Abstract: Large complicated projects with interdependent activities can be described by project networks. Arcs represent activities, nodes represent events, and the network's structure defines the relation between activities and events. A schedule associates an occurrence time with each event: the project can be scheduled in several different ways. We assume that a known amount of cash changes hands at each event. Given any schedule the present value of all cash transactions can be calculated. The payment scheduling problem looks for a schedule that maximizes the present value of all transactions. This problem was first introduced by Russell [2]; it is a nonlinear program with linear constraints and a nonconcave objective. This paper demonstrates that the payment scheduling problem can be transformed into an equivalent linear program. The linear program has the structure of a weighted distribution problem and an efficient procedure is presented for its solution. The algorithm requires the solution of triangular systems of equations with all matrix coefficients equal to ± or 0.

Date: 1972
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Persistent link: https://EconPapers.repec.org/RePEc:wly:navlog:v:19:y:1972:i:1:p:123-136

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