Project Scheduling in the Presence of Productivity Functions

The need for good quality project scheduling methods arises in many fields such as construction, manufacturing, and military operations, among others. In this thesis, we develop a solution methodology which determines the sequence in which the activities of the project must be processed and the resource allocation to each activity in the project to minimize the makespan of the project. We consider projects whose activities' durations are defined by convex, non-increasing time-resource trade-off functions and whose activities are not pre-emptable (i.e., once some amount of resource has been allocated to an activity, this resource level may not change while the activity is processed). The solution methodology first finds all potentially optimal sequences for a given project. However, rather than considering all possible sequences, we use special relationships between certain pairs activities to determine a priori how these pairs will be sequenced in relation to each other. Then, the optimal resource allocations are determine for each sequence and the solution with the smallest makespan is selected.