Minimizing Earliness-Tardiness Costs of Resource-Constrained Projects

Abstract

We consider the scheduling of interdependent subprojects incurring costs for early or tardy completion w.r.t. given milestones. Each subproject consists of several activities between which minimum and maximum start-to-start time lags have to be observed. In addition, the processing of activities takes up scarce shared resources. The problem is to determine an activity schedule complying with the temporal constraints such that the resource requirements can be matched by the capacities at any point in time and the earliness-tardiness costs of the project are minimized. For solving the resource-unconstrained version of this problem, we propose a primal and a dual algorithm which are based on the iterative calculation of locally optimal descent and ascent directions, respectively. An initial (generally resource-infeasible) schedule for the problem with resource constraints is determined by applying the primal method to the resource relaxation. Within a branch-and-bound algorithm, resource conflicts are resolved by enumerating sets of precedence constraints between activities which are executed simultaneously and whose requirements exceed the capacity of at least one resource. At each enumeration node, the corresponding relaxation is solved by the dual algorithm starting with the schedule of the father node.