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 and has been validated on a randomly generated problem set.