9,595 research outputs found

    Algorithms for scheduling projects with generalized precedence relations.

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    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.

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

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    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;

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

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    In a previous paper (De Reyck and Herroelen, 1996a), we presented an optimal procedure for the resource-constrained project scheduling problem (RCPSP) with generalised 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 project network of 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. In this paper we report new computational experience with the algorithm using a new RCPSP-GPR random problem generator developed by Schwindt (1995). A comparison with other computational results reported in the literature is included.Scheduling;

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

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    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;

    An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem.

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    In this paper we study the resource-constrained project scheduling problem with weighted earliness-tardiness penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness-tardiness penalty cost of the project subject to the finish)start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in -time environments.We introduce e depth-first branch-and-bound algorithm for the unconstrained weighted earliness-tardiness problem to compute lower bounds. The procedure has been coded in Visual C++, version 4.0 under Windows NT and has been validated on a randomly generated problem set.Studies; Scheduling; Costs; Requirements; Just-in-time;

    An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem.

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    In this paper we study the resource-constrained project scheduling problem with weighted earliness-tardinesss penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness-tardinesss penalty cost of the project subject to the finish-start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in-time environments.resource-constrained project scheduling; weighted earliness-tardiness costs; branch-and-bound; discounted cash flows; bound procedure;

    Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation

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    The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation, i.e., a hybrid of finite domain and Boolean satisfiability solving, in order to apply nogood learning and conflict-driven search on the solution generation. Our experiments show the benefit of lazy clause generation for finding an optimal solutions and proving its optimality in comparison to other state-of-the-art exact and non-exact methods. The method is highly robust: it matched or bettered the best known results on all of the 2340 instances we examined except 3, according to the currently available data on the PSPLib. Of the 631 open instances in this set it closed 573 and improved the bounds of 51 of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table

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

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    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;
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