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

Proactive resource allocation heuristics for robust project scheduling.

The well-known deterministic resource-constrained project scheduling problem (RCPSP) involves the determination of apredictive schedule (baseline schedule or pre-schedule)of the project activities that satisfies the finish-start precedence relations and the renewable resource constraints under the objective of minimizing the project duration. This pre-schedule serves as a baseline for the execution of the project. During execution, however, the project can be subject to several types of disruptions that may disturb the baseline schedule. Management must then rely on a reactive scheduling procedure for revising or reoptimizing the pre-schedule. The objective of our research is to develop procedures for allocating resources to the activities of a given baseline schedule in order to maximize its stability in the presence of activity duration variability. We propose three integer programming based heuristics and one constructive procedure for resource allocation. We derive lower bounds for schedule stability and report on computational results obtained on a set of benchmark problems.Research; Resource allocation; Project scheduling; Heuristics; Scheduling;

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;

Resource-Constrained Project Scheduling with Autonomous Learning Effects

It\u27s commonly assumed that experience leads to efficiency, yet this is largely unaccounted for in resource-constrained project scheduling. This thesis considers the idea that learning effects could allow selected activities to be completed within reduced time, if they\u27re scheduled after activities where workers learn relevant skills. This paper computationally explores the effect of this autonomous, intra-project learning on optimal makespan and problem difficulty. A learning extension is proposed to the standard RCPSP scheduling problem. Multiple parameters are considered, including project size, learning frequency, and learning intensity. A test instance generator is developed to adapt the popular PSPLIB library of scheduling problems to this model. Four different Constraint Programming model formulations are developed to efficiently solve the model. Bounding techniques are proposed for tightening optimality gaps, including four lower bounding model relaxations, an upper bounding model relaxation, and a Destructive Lower Bounding method. Hundreds of thousands of scenarios are tested to empirically determine the most efficient solution approaches and the impact of learning on project schedules. Potential makespan reduction as high as 50% is discovered, with the learning effects resembling a learning curve with a point of diminishing returns. A combination of bounding techniques is proven to produce significantly tighter optimality gaps