Financial Optimization of the Resource-Constrained Project Scheduling Problem with Milestones Payments (original) (raw)
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Decision Making in Manufacturing and Services, 2013
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.
RAIRO - Operations Research, 2013
Discrete-continuous project scheduling problems with positive discounted cash flows and the maximization of the NPV are considered. We deal with a class of these problems with an arbitrary number of discrete resources and one continuous, renewable resource. Activities are nonpreemptable, and the processing rate of an activity is a continuous, increasing function of the amount of the continuous resource allotted to the activity at a time. Three common payment models-Lump Sum Payment, Payments at Activity Completion times, and payments in Equal Time Intervals are analyzed. Formulations of mathematical programming problems for an optimal continuous resource allocation for each payment model are presented. Applications of two local search metaheuristics-Tabu Search and Simulated Annealing are proposed. The algorithms are compared on a basis of computational experiments. Some conclusions and directions for future research are pointed out.
A metaheuristic scheduling procedure for resource-constrained projects with cash flows
Naval Research Logistics, 1999
Resource-constrained project scheduling problems with cash flows (RCPSPCF) are complex, combinatorial optimization problems. Many heuristics have been reported in the literature that produce reasonable schedules in limited project environments. However, the lack of a heuristic that dominates under differing project conditions can lead to a suboptimal choice of an appropriate heuristic for scheduling any given project. This may result in poor schedules and monetary losses. This paper reports on the application of the tabu search metaheuristic procedure for the RCPSPCF. Strategies for neighborhood generation and candidate selection that exploit the special features of the problem are combined with a simple multiheuristic start procedure. Extensive experimentation, with multiple data sets and comparison with an upper bound, indicates a significant improvement, both in project Net Present Value (NPV) as well as the number of projects, where the metaheuristic outperforms the best known heuristics in the literature. More specifically, this procedure produces the best schedules in over 85% of the projects tested, in contrast to the best single-pass heuristics which have been shown to dominate in at most 20% of the same cases. This iterative, general purpose heuristic is able to adapt significantly better to the complex interactions of the many critical parameters of the RCPSPCF than single-pass heuristics that use more specific information about each project environment.
Project resource investment problem under progress payment model
Journal of Industrial and Systems Engineering, 2018
As a general branch of project scheduling problems, resource investment problem (RIP) considers resource availabilities as decision variables to determine a level of employed resources minimizing the costs of the project. In addition to costs (cash outflows), researchers in the later extensions of the RIP took payments (cash inflows) received from clients into account and used the net present value (NPV) of project cash flows as a financial criterion evaluating the profitability of the project. A striking point in a financial view of the project scheduling is how cash inflows are paid by the client. There are different payment models in the literature of which progress payment is highly common in practice. In this paper, resource investment problem with maximization of the NPV under progress payment model is investigated. A new mathematical model is developed for the problem and then two metaheuristic algorithms based on the genetic algorithm (GA) and simulated annealing algorithm (...
Multi-mode capital-constrained project payment scheduling model considering bonus-penalty structure
International Journal of Management Science and Engineering Management, 2019
In this paper, a multi-mode capital-constrained project payment scheduling problem with bonuspenalty structure is developed where activities can be performed under one of several possible modes and a bonus-penalty structure exists at project deadline. The objective is to assign activity modes and progress payments so as to maximize the net present value (NPV) of the contractor under the constraint of capital availability. The event-based method is employed to construct the mathematical model and Tabu search (TS) is used to solve the strongly NP-hard problem. Using a randomly generated dataset, we compare the performance of our solution with benchmarks generated by Simulated annealing (SA), Random sampling (RS), and Multi-start iterative improvement (MSII) methods, and demonstrate that the proposed TS is superior. Moreover, the effects of several key parameters on the contractor's NPV are investigated. We show that the contractor's NPV grows with the increase in the contractor's initial capital availability, the payment number, and the rewarding rate in bonus-penalty structure.
An equitable approach to the payment scheduling problem in project management
European Journal of Operational Research, 2000
This study reports on a new approach to the payment scheduling problem. In this approach, the amount and timing of the payments made by the client and received by the contractor are determined so as to achieve an equitable solution. An equitable solution is defined as one where both the contractor and the client deviate from their respective ideal solutions by an equal percentage. The ideal solutions for the contractor and the client result from having a lump sum payment at the start and end of the project respectively. A double loop genetic algorithm is proposed to solve for an equitable solution. The outer loop represents the client and the inner loop the contractor. The inner loop corresponds to a multi-mode resource constrained project scheduling problem with the objective of maximizing the contractor's net present value for a given payment distribution. When searching for an equitable solution, information flows between the outer and inner loops regarding the payment distribution over the event nodes and the timing of these payments. An example problem is solved and analyzed. A set of 93 problems from the literature are solved and some computational results are reported.
Annals of Operations Research, 2001
In this paper, the multi-mode resource constrained project scheduling problem with discounted cash flows is considered. The objective is the maximization of the net present value of all cash flows. Time value of money is taken into consideration, and cash in-and outflows are associated with activities and/or events. The resources can be of renewable, nonrenewable, and doubly constrained resource types. Four payment models are considered: