Activity sequencing in some discrete-continuous project scheduling problems with discounted cash inflows

Abstract

In this work discrete-continuous project scheduling problems with discounted cash flows are considered. These problems are characterized by the fact that activities of a project simultaneously require for their execution discrete and continuous resources. A class of these problems is considered, where the number of discrete resources is arbitrary, and there is one continuous, limited, renewable resource. Activities are non-preemptable, and the processing rate of an activity is a continuous, increasing, and convex function of the amount of the continuous resource allotted to the activity at a time. A positive cash flow is associated with each activity. The objective is to maximize the net present value. It is shown that sequential schedules are optimal for the considered class of problems. Four payment models are considered: lump-sum payment at the completion of the project, payments at activity completion times, payments at equal time intervals, and progress payments. Some rules of optimal activity sequencing are proved for the payment models.