Resource-constrained project scheduling.

Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;

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

Local search methods for the discrete time/resource trade-off problem in project networks.

Abstract: In this paper we consider the discrete time/resource trade-off problem in project networks. Given a project network consisting of nodes (activities) and arcs (technological precedence relations specifying that an activity can only start when al of its predecessors have been completed), in which the duration of the activities is a discrete, on-increasing function of the amount of a single renewable resource committed to it, the discrete time/resource trade-off problem minimizes the project makespan subject to precedence constraints and a single renewable resource constraint. For each activity a work content is specified such that all execution modes (duration-resource pairs) for performing the activity are allowed as long as the product of the duration and the resource requirement is at least as large as the specified work content. We present a tabu search procedure which is based on subdividing the problem into a mode assignment phase and a resource-constrained project scheduling phase with fixed mode assignments. Extensive computational experience, including a comparison with other local search methods, is reported.Scheduling; Methods; Networks; Product; Assignment;

Dynamic resource constrained multi-project scheduling problem with weighted earliness/tardiness costs

In this study, a conceptual framework is given for the dynamic multi-project scheduling problem with weighted earliness/tardiness costs (DRCMPSPWET) and a mathematical programming formulation of the problem is provided. In DRCMPSPWET, a project arrives on top of an existing project portfolio and a due date has to be quoted for the new project while minimizing the costs of schedule changes. The objective function consists of the weighted earliness tardiness costs of the activities of the existing projects in the current baseline schedule plus a term that increases linearly with the anticipated completion time of the new project. An iterated local search based approach is developed for large instances of this problem. In order to analyze the performance and behavior of the proposed method, a new multi-project data set is created by controlling the total number of activities, the due date tightness, the due date range, the number of resource types, and the completion time factor in an instance. A series of computational experiments are carried out to test the performance of the local search approach. Exact solutions are provided for the small instances. The results indicate that the local search heuristic performs well in terms of both solution quality and solution time

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

Solution and quality robust project scheduling: a methodological framework.

The vast majority of the research efforts in project scheduling over the past several years has concentrated on the development of exact and suboptimal procedures for the generation of a baseline schedule assuming complete information and a deterministic environment. During execution, however, projects may be the subject of considerable uncertainty, which may lead to numerous schedule disruptions. Predictive-reactive scheduling refers to the process where a baseline schedule is developed prior to the start of the project and updated if necessary during project execution. It is the objective of this paper to review possible procedures for the generation of proactive (robust) schedules, which are as well as possible protected against schedule disruptions, and for the deployment of reactive scheduling procedures that may be used to revise or re-optimize the baseline schedule when unexpected events occur. We also offer a methodological framework that should allow project management to identify the proper scheduling methodology for different project scheduling environments. Finally, we survey the basics of Critical Chain scheduling and indicate in which environments it is useful.Framework; Information; Management; Processes; Project management; Project scheduling; Project scheduling under uncertainty; Stability; Robust scheduling; Quality; Scheduling; Stability; Uncertainty;

Railway scheduling reduces the expected project makespan.

The Critical Chain Scheduling and Buffer Management (CC/BM) methodology, proposed by Goldratt (1997), introduced the concepts of feeding buffers, project buffers and resource buffers as well as the roadrunner mentality. This last concept, in which activities are started as soon as possible, was introduced in order to speed up projects by taking advantage of predecessors finishing early. Later on, the railway scheduling concept of never starting activities earlier than planned was introduced as a way to increase the stability of the project, typically at the cost of an increase in the expected project makespan. In this paper, we will indicate a realistic situation in which railway scheduling improves both the stability and the expected project makespan over roadrunner scheduling.Railway scheduling; Roadrunner scheduling; Feeding buffer; Priority list; Resource availability;

Algorithms for scheduling projects with generalized precedence relations.

Project scheduling under the assumption of renewable resource constraints and generalized precedence relations, i.e. arbitrary minimal and maximal time lags between the starting and completion times of the activities of the project, constitutes an important and challenging problem. Over the past few years considerable progress has been made in the use of exact solution procedure for this problem type and its variants. We review the fundamental logic and report new computational experience with a branch-and-bound procedure for optimally solving resource-constrained project scheduling problems with generalized precedence relations of the precedence diagramming type, i.e. start-start, start-finish, finish-start and finish-finish relations with minimal time lags for minimizing the project makespan. Subsequently, we review and report new results for several branch-and -bound procedures for the case of generalized precedence relations, including both minimal and maximal time lags, and demonstrate how the solution methodology can be expected to cope with other regular and nonregular objective functions such a smaximizing the net present value of a project.Networks; Problems; Scheduling; Algorithms; Functions; Net present value;

Optimization Algorithms in Project Scheduling

Scheduling, or planning in a general perspective, is the backbone of project management; thus, the successful implementation of project scheduling is a key factor to projects’ success. Due to its complexity and challenging nature, scheduling has become one of the most famous research topics within the operational research context, and it has been widely researched in practical applications within various industries, especially manufacturing, construction, and computer engineering. Accordingly, the literature is rich with many implementations of different optimization algorithms and their extensions within the project scheduling problem (PSP) analysis field. This study is intended to exhibit the general modelling of the PSP, and to survey the implementations of various optimization algorithms adopted for solving the different types of the PSP