A Two-Phase Algorithm for a Resource Constrained Project Scheduling Problem with Discounted Cash Flows

Abstract

Abstract. This paper presents a Resource-Constrained Project Scheduling Problem (RCPSP) settled by contractual milestones. The criterion analysed here is the maximisation of aggregate discounted cash flows from the contractor's perspective, known as an RCPSP problem with Discounted Cash Flows (RCPSPDCF). The cash flows analysed here cover the contractor's cash outflows (negative cash flows), related to the commencement of individual activities, and cash inflows (positive cash flows) after the fulfilment of individual milestones. The authors propose a two-phase algorithm for solving the problem defined. In the first phase, the simulated annealing metaheuristics is used, designed to identify a forward schedule with as high total DCF as possible. In the second phase, the best first-phase schedule is improved by right shifts of activities. To this end, the procedure which iteratively shifts tasks by one unit is applied, with a view to maximising the objective function. Activity shifts take into consideration precedence and resource constraints, and they are performed for a specified resource allocation to activities. This paper also includes an analysis of the problem for a sample project. The results of computational experiments are then analysed. The experiments were run with the use of standard test problems from the Project Scheduling Problem LIBrary (PSPLIB), with additionally defined cash flows and contractual milestones.

Financial optimisation for the multi stage project scheduling problem

“…We wcześniejszych pracach autora rozważane jest wykorzystanie różnych procedur SGS uwzględniających umowne etapy projektu oraz poprawy rozwiązań przez przesunięcia czynności: w prawo (przy harmonogramowaniu wstecz) lub w lewo (przy harmonogramowaniu 9 Kolisch R.: Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation. "European Journal of Operational Research", Vol.…”

Heuristics for project scheduling with discounted cash flows optimisation

“…At time t = 8, additional arcs (6,8) and (5, 8) may appear. For the problem and right-shift algorithms analysed, such resource allocation is preferred in which these arcs do not appear, that is when all three resources required for the execution of activity 8 are transferred from activity 7 (the precedence relation occurs between activities 7 and 8 in the original AON network).…”

“…With the allocation in which additional arc (5,8) occurs, activity 5 may be rightshifted by 2 only. Now if additional arc (6,8) occurred, the right-shift of activity 6 would reduce the project NPV as the completion of milestone 3 would then be delayed.…”

“…Since then, numerous optimisation models for the RCPSP with Discounted Cash Flows (RCPSPDCF) have been considered. Recent results in this field include [2][3][4][5][6]. For a detailed description of to-date research, models and algorithms used for optimising project NPV the reader is referred to review papers, including [7,8].…”

“…In this paper, the authors analyse the project scheduling problem with limited availability of resources, with predefined milestones and a single mode of activity execution: Single-Mode RCPSP. The authors discuss their own optimisation model [4][5][6]14] with financial settlements in milestones, where the objective function is Net Present Value maximisation -aggregate discounted cash flows with the customer's payments for milestone completion, a system of penalties for late execution of project milestones and the contractor's outflows related to activity execution.…”