An exact procedure for the resource-constrained weighted earliness–tardiness project scheduling problem

In this paper we study the resource-constrained project scheduling problem with weighted earliness–tardiness penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness–tardiness penalty cost of the project subject to the finish–start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in-time environments. We introduce a depth-first branch-and-bound algorithm which makes use of extra precedence relations to resolve resource conflicts and relies on a fast recursive search algorithm for the unconstrained weighted earliness–tardiness problem to compute lower bounds. The procedure has been coded in Visual C++, version 4.0 under Windows NT. Both the recursive search algorithm and the branch-and-bound procedure have been validated on a randomly generated problem set.