Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows

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: Lump sum payment at the terminal event, payments at prespecified event nodes, payments at prespecified time points and progress payments. For finding solutions to problems proposed, a genetic algorithm (GA) approach is employed, which uses a special crossover operator that can exploit the multi-component nature of the problem. The models are investigated at the hand of an example problem. Sensitivity analyses are performed over the mark up and the discount rate. A set of 93 problems from literature are solved under the four different payment models and resource type combinations with the GA approach employed resulting in satisfactory computation times. The GA approach is compared with a domain specific heuristic for the lump sum payment case with renewable resources and is shown to outperform it

Client-contractor bargaining on net present value in project scheduling with limited resources

The client-contractor bargaining problem addressed here is in the context of a multi-mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity-on-Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two-party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights

Client-contractor bargaining on net present value in project scheduling with limited resources

The client-contractor bargaining problem addressed here is in the context of a multi-mode resource constrained project scheduling problem with discounted cash flows, which is formulated as a progress payments model. In this model, the contractor receives payments from the client at predetermined regular time intervals. The last payment is paid at the first predetermined payment point right after project completion. The second payment model considered in this paper is the one with payments at activity completions. The project is represented on an Activity-on-Node (AON) project network. Activity durations are assumed to be deterministic. The project duration is bounded from above by a deadline imposed by the client, which constitutes a hard constraint. The bargaining objective is to maximize the bargaining objective function comprised of the objectives of both the client and the contractor. The bargaining objective function is expected to reflect the two-party nature of the problem environment and seeks a compromise between the client and the contractor. The bargaining power concept is introduced into the problem by the bargaining power weights used in the bargaining objective function. Simulated annealing algorithm and genetic algorithm approaches are proposed as solution procedures. The proposed solution methods are tested with respect to solution quality and solution times. Sensitivity analyses are conducted among different parameters used in the model, namely the profit margin, the discount rate, and the bargaining power weights

Project network models with discounted cash flows. A guided tour through recent developments.

The vast majority of the project scheduling methodologies presented in the literature have been developed with the objective of minimizing the project duration subject to precedence and other constraints. In doing so, the financial aspects of project management are largely ignored. Recent efforts have taken into account discounted cash flow and have focused on the maximalization of the net present value (npv) of the project as the more appropriate objective. In this paper we offer a guided tour through the important recent developments in the expanding field of research on deterministic and stochastic project network models with discounted cash flows. Subsequent to a close examination of the rationale behind the npv objective, we offer a taxonomy of the problems studied in the literature and critically review the major contributions. Proper attention is given to npv maximization models for the unconstrained scheduling problem with known cash flows, optimal and suboptimal scheduling procedures with various types of resource constraints, and the problem of determining both the timing and amount of payments.Scheduling; Models; Model; Discounted cash flow; Cash flow; Project scheduling; Project management; Management; Net present value; Value; Problems; Maximization; Optimal;

Pre-emptive resource-constrained multimode project scheduling using genetic algorithm: a dynamic forward approach

Purpose: The issue resource over-allocating is a big concern for project engineers in the process of scheduling project activities. Resource over-allocating drawback is frequently seen after scheduling of a project in practice which causes a schedule to be useless. Modifying an over-allocated schedule is very complicated and needs a lot of efforts and time. In this paper, a new and fast tracking method is proposed to schedule large scale projects which can help project engineers to schedule the project rapidly and with more confidence. Design/methodology/approach: In this article, a forward approach for maximizing net present value (NPV) in multi-mode resource constrained project scheduling problem while assuming discounted positive cash flows (MRCPSP-DCF) is proposed. The progress payment method is used and all resources are considered as pre-emptible. The proposed approach maximizes NPV using unscheduled resources through resource calendar in forward mode. For this purpose, a Genetic Algorithm is applied to solve. Findings: The findings show that the proposed method is an effective way to maximize NPV in MRCPSP-DCF problems while activity splitting is allowed. The proposed algorithm is very fast and can schedule experimental cases with 1000 variables and 100 resources in few seconds. The results are then compared with branch and bound method and simulated annealing algorithm and it is found the proposed genetic algorithm can provide results with better quality. Then algorithm is then applied for scheduling a hospital in practice. Originality/value: The method can be used alone or as a macro in Microsoft Office Project® Software to schedule MRCPSP-DCF problems or to modify resource over-allocated activities after scheduling a project. This can help project engineers to schedule project activities rapidly with more accuracy in practice.Peer Reviewe

An equitable approach to the payment scheduling problem in project management

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

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts. --project scheduling,modeling,resource constraints,temporal constraints,networks

Multi-project scheduling with 2-stage decomposition

A non-preemptive, zero time lag multi-project scheduling problem with multiple modes and limited renewable and nonrenewable resources is considered. A 2-stage decomposition approach is adopted to formulate the problem as a hierarchy of 0-1 mathematical programming models. At stage one, each project is reduced to a macro-activity with macro-modes resulting in a single project network where the objective is the maximization of the net present value and the cash flows are positive. For setting the time horizon three different methods are developed and tested. A genetic algorithm approach is designed for this problem, which is also employed to generate a starting solution for the exact solution procedure. Using the starting times and the resource profiles obtained in stage one each project is scheduled at stage two for minimum makespan. The result of the first stage is subjected to a post-processing procedure to distribute the remaining resource capacities. Three new test problem sets are generated with 81, 84 and 27 problems each and three different configurations of solution procedures are tested

An optimal procedure for the unconstrained max-NPV project scheduling problem with generalized precedence relations.

The unconstrained max-npv project scheduling problem involves the scheduling of the activities of a project in order to maximize its net present value. Assume a project represented in activity-on-mode (AoN) notation, in which the activities have a known duration and are subject to technological precedence constraints. Throughout each activity, a series of cash outflows and receipts may occur, which allows for the computation of a terminal cash flow value (positive or negative) upon the completion. The project is to be scheduled against a fixed deadline in the absence of resource constraints. Several procedures have been presented in the literature to cope with this problem. In this paper, we describe how one of the most efficient optimal procedures can be adapted to cope with generalized precedence relations, which introduce arbitrary minimal and maximal time lags between the start and completion of activities. The procedure has been programmed in Microsoft° Visual ++ 2.0 under Windows NT for use on a personal computer. Extensive computational results are reported.Scheduling; Optimal;

An optimal procedure for the resource-constrained project scheduling problem with discounted cash flows and generalized precedence relations.

In this paper, we study the resource-constrained project scheduling problem (RCPSP) with discounted cash flows and generalized precedence relations (further denoted as RCPSPDC-GPR). The RCPSPDC-GPR extends the RCPSP to (a) arbitrary minimal and maximal time lags between the starting and completion times of activities and (b) the non-regular objective function of maximizing the net present value of the project with positive and/or negative cash flows associated with the activities.). To the best of our knowledge, the literature on the RCPSPDC-GPR is completely void. We present a depth-first branch-and-bound algorithm in which the nodes in the search tree represent the original project network extended with extra precedence relations which resolve a number of resource conflicts. These conflicts are resolved using the concept of a minimal delaying mode (De Reyck and Herroelen, 1996b). An upper bound on the project net present value as well as several dominance rules are used to fathom large portions of the search tree. Extensive computational experience on a randomly generated benchmark problem set is obtained.Scheduling; Optimal; Discounted cash flow; Cash flow;