Simulated Annealing and Tabu Search for Discrete-Continuous Project Scheduling with Discounted Cash Flows

Abstract

Discrete-continuous project scheduling problems with positive discounted cash flows and the maximization of the NPV are considered. We deal with a class of these problems with an arbitrary number of discrete resources and one continuous, renewable resource. Activities are nonpreemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. Three common payment models – Lump Sum Payment, Payments at Activity Completion times, and payments in Equal Time Intervals are analyzed. Formulations of mathematical programming problems for an optimal continuous resource allocation for each payment model are presented. Applications of two local search metaheuristics – Tabu Search and Simulated Annealing are proposed. The algorithms are compared on a basis of computational experiments. Some conclusions and directions for future research are pointed out.