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;

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 classification of predictive-reactive project scheduling procedures.

The vast majority of the project scheduling research efforts over the past several years have concentrated on the development of workable predictive baseline schedules, assuming complete information and a static and deterministic environment. During execution, however, a project may be subject to numerous schedule disruptions. Proactive-reactive project scheduling procedures try to cope with these disruptions through the combination of a proactive scheduling procedure for generating predictive baseline schedules that are hopefully robust in that they incorporate safety time to absorb anticipated disruptions with a reactive procedure that is invoked when a schedule breakage occurs during project execution.proactive-reactive project scheduling; time uncertainty; stability; timely project completion; preselective strategies; resource constraints; trade-off; complexity; stability; management; makespan; networks; subject; job;

An investigation of resource-allocation decisions by means of project networks.

This paper investigates the relationship between resource allocation and ES-policies, which are a type of scheduling policies introduced for stochastic scheduling and which can be represented by a directed acyclic graph. We present a formal treatment of resource flows as are presentation of resource-allocation decisions, extending the existing literature. A number of complexity results are established, showing that a number of recently proposed objective functions for evaluating the quality of ES-policies lead to difficult problems. Finally, some reflections are provided on possible effciency enhancements to enumeration algorithms for ES-policies.Complexity; Project scheduling; Resource allocation; Resource constraints;

The complexity of generating robust resource-constrained baseline schedules.

Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that will change little when variations in the input parameters arise. Robustness can also be achieved by making the schedule makespan insensitive to variability. In this paper, we describe models for the generation of stable and insensitive baseline schedules for resource-constrained scheduling problems and present results on their complexity status. We start from a project scheduling viewpoint and derive results on machine scheduling sub-problems.Complexity; Information; Product scheduling; Robustness; sensitivity; stability;

An overview of recent research results and future research avenues using simulation studies in project management

This paper gives an overview of three simulation studies in dynamic project scheduling integrating baseline scheduling with risk analysis and project control. This integration is known in the literature as dynamic scheduling. An integrated project control method is presented using a project control simulation approach that combines the three topics into a single decision support system. The method makes use of Monte Carlo simulations and connects schedule risk analysis (SRA) with earned value management (EVM). A corrective action mechanism is added to the simulation model to measure the efficiency of two alternative project control methods. At the end of the paper, a summary of recent and state-of-the-art results is given, and directions for future research based on a new research study are presented

Stability and resource allocation in project planning.

The majority of resource-constrained project scheduling efforts assumes perfect information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule is executed. In reality, project activities are subject to considerable uncertainty, which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed resource allocation problem. We report on computational results obtained on a set of benchmark problems.Constraint satisfaction; Information; Model; Planning; Problems; Project management; Project planning; Project scheduling; Resource allocati; Scheduling; Stability; Uncertainty; Variability;

A branch-and-bound algorithm for stable scheduling in single-machine production systems.

Robust scheduling aims at the construction of a schedule that is protected against uncertain events. A stable schedule is a robust schedule that will change little when variations in the input parameters arise. This paper proposes a branch-and-bound algorithm for optimally solving a single-machine scheduling problem with stability objective, when a single job is anticipated to be disrupted.Branch-and-bound; Construction; Event; Job; Robust scheduling; Robustness; Scheduling; Single-machine scheduling; Stability; Systems; Uncertainty;

A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations.

We present an optimal procedure for the resource-constrained project scheduling problem (RCPSP) with generalized precedence relations (further denoted as RCPSP-GPR) with the objective of minimizing the project makespan. The RCPSP-GPR extends the RCPSP to arbitrary minimal and maximal time lags between the starting and completion times of activities. The procedure is 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 resource conflict present in the parent node. Resource conflicts are resolved using the concept of minimal delaying alternatives, i.e. minimal sets of activities which, when delayed, release enough resources to resolve the conflict. Precedence and resource-based lower bounds as well as dominance rules are used to fathom large portions of the search tree. The procedure can be extended to other regular measures of performance by some minor modifications. Even non-regular measures of performance, such as the maximinization of the net present value of the project or resource levelling objectives, can be handled. The procedure has been programmed in Microsoft* Visual C++ for use on a personal computer. Extensive computational experience is obtained.Scheduling;