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 heuristic procedure to solve the project staffing problem with discrete time/resource trade-offs and personnel scheduling constraints

Highlights • Project staffing with discrete time/resource trade-offs and calendar constraints. • An iterated local search procedure is proposed. • Different problem decomposition techniques are applied. Abstract When scheduling projects under resource constraints, assumptions are typically made with respect to the resource availability and activities are planned each with its own duration and resource requirements. In resource scheduling, important assumptions are made with respect to the staffing requirements. Both problems are typically solved in a sequential manner leading to a suboptimal outcome. We integrate these two interrelated scheduling problems to determine the optimal personnel budget that minimises the overall cost. Integrating these problems increases the scheduling flexibility, which improves the overall performance. In addition, we consider some resource demand flexibility in this research as an activity can be performed in multiple modes. In this paper, we present an iterated local search procedure for the integrated multi-mode project scheduling and personnel staffing problem. Detailed computational experiments are presented to evaluate different decomposition heuristics and comparison is made with alternative optimisation techniques

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 transport scheduling under multiple resource constraints

This paper presents a heuristic for the dynamic vehicle scheduling problem with multiple resource capacity constraints. In the envisaged application, an automated transport system using Automated Guided Vehicles, bottleneck resources are (1) vehicles, (2) docks for loading/unloading, (3) vehicle parking places, and (4) load storage space. This problem is hard, because interrelated activities (loading, transportation, unloading) at several geographical locations have to be scheduled under multiple resource constraints, where the bottleneck resource varies over time. Besides, the method should be suitable for real-time planning. We developed a dedicated serial scheduling method and analyzed its dynamic behavior using discrete event simulation. We found that our method is very well able to find good vehicle schedules satisfying all resource constraints. For comparison, we used a simple approach where we left out the resource constraints and extended the processing times by statistically estimated waiting times to account for finite capacities. We found that our newly designed method finds better schedules in terms of service levels

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

Short-Term Resource Allocation and Management

Almost all sectors of the economy, such as, government, healthcare, education, ship repair, construction, and manufacturing require project management. A key component of project management deals with scheduling of tasks such that limited resources are utilized in an effective manner. Current research on resource constrained project-scheduling has been classified as: a) Single project with single mode for various tasks, b) Single project with multiple task modes, c) Multiple projects with single task mode, and d) Multiple projects with multiple task modes.;This work extends the current multi-project, multi-mode scheduling techniques. The resources can be renewable, and non-renewable. In addition, it focuses on short term scheduling, that is, scheduling on an hourly, daily, or weekly basis. Long term scheduling assumes a stable system, that is, resources, priorities, and other constraints do no change during the scheduling period. In this research, short term scheduling assumes a dynamic system, that is, resources, priorities, and other constraints change over time.;A hybrid approach is proposed to address the dynamic nature of the problem. It is based on discrete event simulation and a set of empirical rules provided by the project manager. The project manager is assumed to be highly knowledgeable about the project. He/she is regarded as an integral part of the system. Such an approach is better suited to deal with real world scheduling. The proposed approach does not seek to provide a single optimum solution, instead, it generates a series of feasible solutions, along with the impact of each solution on schedule and cost.;Two project case studies dealing with finding an optimum solution were selected from the literature. The proposed technique was applied to the data set in these studies. In both cases the proposed approach found the optimum solution. The model was then applied to two additional problems to test the features that could not be tested on the dataset from the literature.;As for practical implications, the proposed approach enhances the decision making process, by providing more resource allocation flexibility, and results in improved solutions in terms of total project duration and cost. From an academic viewpoint, this research enriches the existing literature, as it provides an extension of the resource constrained project scheduling problems, a discrete event simulation and four cases studies which highlights relevant issues to model properly the complexity of real-life projects

Medium-term optimization-based approach for the integration of production planning, scheduling and maintenance

A medium-term optimization-based approach is proposed for the integration of production planning, scheduling and maintenance. The problem presented in this work considers a multiproduct single-stage batch process plant with parallel units and limited resources. An MILP continuous-time formulation is developed based on the main ideas of travelling salesman problem and precedence-based constraints to deal with, sequence-dependent unit performance decay, flexible recovery operations, resource availability and product lifetime. Small scheduling examples have been solved and compared with adapted formulations from the literature, based on discrete-time and global-time events, demonstrating the effectiveness of the proposed solution approach. Additional planning and scheduling problems have been proposed by considering several time periods. Multi-period examples have been efficiently solved by the model showing the applicability of the solution approach for medium-size problems

Loop pipelining with resource and timing constraints

Developing efficient programs for many of the current parallel computers is not easy due to the architectural complexity of those machines. The wide variety of machine organizations often makes it more difficult to port an existing program than to reprogram it completely. Therefore, powerful translators are necessary to generate effective code and free the programmer from concerns about the specific characteristics of the target machine. This work focuses on techniques to be used by an important class of translators, whose objective is to transform sequential programs into equivalent more parallel programs. The transformations are performed at instruction level in order to exploit low level parallelism and increase memory locality.Most of the current applications are programmed in languages which do not allow us to express parallelism between high-level sentences (as Pascal, C or Fortran). Furthermore, a lot of applications written ten or more years ago are still used today, and it is not feasible to rewrite such applications for many reasons (not only technical reasons, but also economic ones). Translators enable programmers to write the application in a familiar sequential programming language, without concerning their selves with the architecture of the target machine. Current compilers for parallel architectures not only translate a program written on a high-level language to the appropriate machine language, but also perform some transformations in the final code in order to execute the program in a more parallel way. The transformations improve the performance in the execution of the program by making use of the knowledge that the compiler has about the machine architecture. The semantics of the program remain intact after any transformation.Experiments show that limiting parallelization to basic blocks not included in loops limits maximum speedup. This is because loops often comprise a large portion of the parallelism available to be exploited in a program. For this reason, a lot of effort has been devoted in the recent years to parallelize loop execution. Several parallel computer architectures and compilation techniques have been proposed to exploit such a parallelism at different granularities. Multiprocessors exploit coarse grained parallelism by distributing entire loop iterations to different processors. Systems oriented to the high-level synthesis (HLS) of VLSI circuits, superscalar processors and very long instruction word (VLIW) processors exploit fine-grained parallelism at instruction level. This work addresses fine-grained parallelization of loops addressed to the HLS of VLSI circuits. Two algorithms are proposed for resource constraints and for timing constraints. An algorithm to reduce the number of registers required to execute a loop in a given architecture is also proposed.Postprint (published version