Resource-constrained Scheduling Research Articles

Lagrangian relaxation-based lower bound for resource-constrained modulo scheduling

Abstract In this work we propose a Lagrangian relaxation of a time indexed integer programming formulation to compute a lower bound for the resource-constrained modulo scheduling problem (RCMSP). Solving the RCMSP consists in finding a 1-periodic schedule minimizing the period subject to both temporal and resource constraints. This work is inspired by Mohring et al results [Mohring, R.H., A. S. Schulz, F. Stork and M. Uetz Solving Project Scheduling Problems by Minimum Cut Computations , Management Science. 49 (2003), 330–350] for the (non cyclic) resource constrained project scheduling problem, where each subproblem solved within the subgradient optimization is equivalent to a minimum cut problem. Experimental results, presented on instruction scheduling instances from the STMicroelectronics ST200 VLIW processor family, underline the interest of the proposed method.

Modeling methods and a branch and cut algorithm for pharmaceutical clinical trial planning using stochastic programming

We discuss methods for the solution of a multi-stage stochastic programming formulation for the resource-constrained scheduling of clinical trials in the pharmaceutical research and development pipeline. First, we present a number of theoretical properties to reduce the size and improve the tightness of the formulation, focusing primarily on non-anticipativity constraints. Second, we develop a novel branch and cut algorithm where necessary non-anticipativity constraints that are unlikely to be active are removed from the initial formulation and only added if they are violated within the search tree. We improve the performance of our algorithm by combining different node selection strategies and exploring different approaches to constraint violation checking.

A fuzzy random resource-constrained scheduling model with multiple projects and its application to a working procedure in a large-scale water conservancy and hydropower construction project

The aim of this paper is to deal with resource-constrained multiple project scheduling problems (rc-mPSP) under a fuzzy random environment by a hybrid genetic algorithm with fuzzy logic controller (flc-hGA), to a large-scale water conservancy and hydropower construction project in the southwest region of China, whose main project is a dam embankment. The objective functions in this paper are to minimize the total project time (that is the sum of the completion time for all projects) and to minimize the total tardiness penalty of multiple projects, which is the sum of penalty costs for all the projects. After describing the problem of the working procedure in the project and presenting the mathematical formulation model of a resource-constrained project scheduling problem under a fuzzy random environment, we give some definitions and discuss some properties of fuzzy random variables. Then, a method of solving solution sets of fuzzy random multiple objective programming problems is proposed. Because traditional optimization techniques could not cope with the rc-mPSP under a fuzzy random environment effectively, we present a new approach based on the hybrid genetic algorithm (hGA). In order to improve its efficiency, the proposed method hybridized with the fuzzy logic controller (flc) concept for auto-tuning the GA parameters is presented. For the practical problems in this paper, flc-hGA is proved the most effective and most appropriate compared with other approaches. The computer generated results validate the effectiveness of the proposed model and algorithm in solving large-scale practical problems.

A GRASP for a resource-constrained scheduling problem

This paper is devoted to the approximate resolution of a strongly NP-hard real world resource-constrained scheduling problem, which arises in relation to the operability of certain high availability real time distributed systems. We present a fast and pragmatic algorithm based on the GRASP metaheuristic and, building on previous research on exact resolution methods, extensive computational results demonstrating its practical ability to find solutions within a few percents to optimality on a wide spectrum of hard instances.

Minimizing the total weighted completion time in the relocation problem

This paper studies the minimization of total weighted completion time in the relocation problem on a single machine. The relocation problem, formulated from an area redevelopment project, can be treated as a resource-constrained scheduling problem. In this paper, we show four special cases to be NP-hard in the strong sense. Problem equivalence between the unit-weighted case and the UET (unit-execution-time) case is established. For two further restricted special cases, we present a polynomial time approximation algorithm and show its performance ratio to be 2.

Automatic design of application-specific reconfigurable processor extensions with UPaK synthesis kernel

This article presents a new tool for automatic design of application-specific reconfigurable processor extensions based on UPaK (Abstract U nified Pa tterns Based Synthesis K ernel for Hardware and Software Systems). We introduce a complete design flow that identifies new instructions, selects specific instructions and schedules a considered application on the newly created reconfigurable architecture. The identified extensions are implemented as specialized sequential or parallel instructions. These instructions are executed on a reconfigurable unit implementing all merged patterns. Our method uses specially developed algorithms for subgraph isomorphism that are implemented as graph matching constraints. These constraints together with separate algorithms are able to efficiently identify computational patterns and carry out application mapping and scheduling. Our methods can handle both time-constrained and resource-constrained scheduling. Experimental results show that the presented method provides high coverage of application graphs with small number of patterns and ensures high application execution speedup both for sequential and parallel application execution with reconfigurable processor extensions implementing selected patterns.

Applying Genetic Algorithm to Resource Constrained Multi-Project Scheduling Problems

Resource-constrained multi-project scheduling problems (RCMPSP) consider precedence relationship among activities and the capacity constraints of multiple resources for multiple projects. RCMPSP are NP-hard due to these practical constraints indicating an exponential calculation time to reach optimal solution. In order to improve the speed and the performance of problem solving, heuristic approaches are widely applied to solve RCMPSP. This research proposes Hybrid Genetic Algorithm (HGA) and heuristic approach to solve RCMPSP with an objective to minimize the total tardiness. HGA is compared with three typical heuristics for RCMPSP: Maximum Total Work Content, Earliest Due Date, and Minimum Slack. Two typical RCMPSP from literature are used as a test bed for performance evaluation. The results demonstrate that HGA outperforms the three heuristic methods in term of the total tardiness.

Using novel particle swarm optimization scheme to solve resource-constrained scheduling problem in PSPLIB

This investigation proposes an improved particle swam optimization (PSO) approach to solve the resource-constrained scheduling problem. Two proposed rules named delay local search rule and bidirectional scheduling rule for PSO to solve scheduling problem are proposed and evaluated. These two suggested rules applied in proposed PSO facilitate finding global minimum (minimum makespan). The delay local search enables some activities delayed and altering the decided start processing time, and being capable of escaping from local minimum. The bidirectional scheduling rule which combines forward and backward scheduling to expand the searching area in the solution space for obtaining potential optimal solution. Moreover, to speed up the production of feasible solution, a critical path is adopted in this study. The critical path method is used to generate heuristic value in scheduling process. The simulation results reveal that the proposed approach in this investigation is novel and efficient for resource-constrained class scheduling problem.

Resource-constrained scheduling for continuous repetitive projects with time-based production units

In construction projects of highways, pipelines, and tunnels, labor and equipment continuously move in a linear geographic layout. This class of continuous repetitive projects encounters the resource-constrained problem when there are limits on the availabilities of resources (labor and equipment). Conventional scheduling models divide continuous repetitive projects into space segments. The premise is that crews would maintain the same production rate in each space segment. However, when the length of segment is indivisible by the production rate, this assumption leads to an inefficient schedule which asks the crews to change their production rate, a reflection of their size, composition, and associated equipment, in the middle of a time period. Unproductive time would then be spent in extra preparation and unnecessary warming up. Another drawback is that production units divided in space cannot be directly linked to the time-based payment schedule. In light of these shortcomings, this paper presents a scheduling model to find the optimal set of production rates in different time periods for each crew, considering limited availability of resources. To be practical, the proposed model addresses work continuity while maintaining lead-time and lead-distance between operations. The optimization problem is solved by an evolutionary strategy algorithm, which is easy to program and takes less execution time, with no need for selection and crossover process. A real-life project is used to validate the performance of the proposed model in terms of effectiveness, efficiency, and stability.

Improved genetic algorithm for resource-constrained scheduling of large projects

The generalized model of the resource-constrained project scheduling problem (RCPSP) is valuable because it can be incorporated into the advanced computational methods of commercial project management software for practical applications. A construction schedule generated by most commercial project management programs does not guarantee its optimality when the resources are limited. This paper presents an improved elitist genetic algorithm (GA) for resource-constrained scheduling of large projects. The proposed algorithm allocates multiple renewable resources to activities of a single large-sized project to achieve the objective of minimizing the project duration. A permutation-based decoding procedure is developed using the improved parallel schedule generation scheme. A new parameter, named transformation power, is created in the transformation method of the improved algorithm to ensure that the individual selection process performs correctly. Extensive computational results using a standard set of large-sized multiple resource-constrained project scheduling problems are presented to demonstrate the performance and accuracy of the algorithm.

Activity Prioritization Under Resource Constraints Using a Utility Index Method

Resource availability constraints are a typical real-life construction scheduling problem; a problem that limits a constructor's ability to execute and deliver a project as originally planned. It is, thus, imperative that developed project schedules should have not only well-thought project logic networks (successor/predecessor information and activity durations) but also resource assignments (including cost) for each activity in the network so that the effects of resource constraints can effectively be accounted for. The paper presents a new approach to resource-constrained scheduling that allows for activity prioritization when a project is subject to limited resources. The methodology proposed is based on a utility index, hereby defined as the ratio of the number of required resources for a specific activity to the total number of required resources among competing activities. A dynamic programming technique is adopted to maximize the utility value for each activity so that the resource allocation among competing activities, as suggested by the method, results in the minimum overall project duration.

Delay analysis in resource-constrained schedules

The schedule for construction delay analysis should consider resources because it is acknowledged that a schedule without resources is not realistic. However, the conventional resource-constrained scheduling (RCS) technique is not properly operated for the widely accepted delay analysis techniques such as the contemporaneous period analysis (CPA) and the “but-for” method. The “CPM + RCS” method for rescheduling to analyze delay impacts may cause unexpected activity sequence changes and the “RCS-only” method does not reflect the time impact of the duration reduction of an activity and may cause substantial project completion delay by a minor change in the activity duration. This study analyzes the problems that arise when CPA and the “but-for” method are performed on the basis of the conventional RCS technique and shows how the resource-constrained critical path method can be utilized in those delay analyses that have advantages as compared with the RCS technique.

Project-oriented task scheduling for mobile robot team

This paper presents a project-oriented framework for multi-robot task scheduling. An agent-based architecture is designed to schedule tasks where robots are considered as resources. The study focused on the problems when the number of available robots is less than the required number. In this case, the problem becomes a resource-constrained scheduling problem. Initially, tasks are scheduled by using Critical path method (CPM), resource leveling method is used to smooth the deviation between the resource requirements and available resource levels, and tasks are allocated to robots. As robots perform their tasks, a monitoring agent observes them and tasks are rescheduled if the difference between the planned and actual completion time of tasks exceeds a predefined threshold. Effectiveness of the proposed approach is shown by using a nine-task two-robot project simulation.

Heuristic algorithm for the resource-constrained scheduling problem during high-level synthesis

Scheduling is considered the most important task in a high-level synthesis process. A heuristic algorithm based on the A* search to find optimal schedules quickly is presented. This algorithm reduces the computational effort required to obtain the best schedules on a pre-defined datapath by effectively pruning the non-promising search space. The pruning method is accomplished by an admissible heuristic that estimates the schedule length, or the cost, of a search node represented by a partially scheduled data flow graph. The search node with the least cost is considered the most promising candidate and is expanded next, avoiding an exhaustive search of the problem space. When the costs of the candidate search nodes are identical, the A* search is guided by a depth-first search to speed up the computation. Experimental results on several well known benchmarks with varying resource constraints show the effectiveness of the proposed algorithm. Multicycle, pipelined and chaining execution of operations are supported.

A general resource-constrained scheduling framework for multistage batch facilities with sequence-dependent changeovers

This work introduces a new MILP sequential approach to the short-term scheduling of multistage batch plants that accounts for sequence-dependent changeover times, intermediate due dates and limited availability of renewable resources. It relies on a continuous-time formulation based on the general precedence notion that uses different sets of binary variables to handle allocation and sequencing decisions. To avoid resource overloading, additional constraints in terms of sequencing variables and a new set of 0-1 overlapping variables are presented. They allow tracking the set of tasks requiring the same resource and running in parallel at the start of another process operation. In this way, the proposed formulation involves a reasonable number of binary variables and constraints and features a very good computational behavior, even in the presence of hard bottleneck resources. Four illustrative examples, one of them including multiple bottleneck resources shared by several processing stages, have been efficiently solved.

Maximizing the reward in the relocation problem with generalized due dates

The relocation problem, based on a public housing project in Boston, USA, is a generalized resource-constrained scheduling problem in which the amount of resources (new housing units) returned by a completed job (building) is not necessarily the same as the amount of resources (original housing units) it started out with for processing. In this paper we consider a variant where several generalized due dates are specified to define the number of new housing units that should be built in the entire duration of the project. Generalized due dates are different from conventional due dates in that they are job independent and common to all jobs. In the present study each generalized due date is given to specify an expected percentage of completion of the project. Given an initial number of temporary housing units, the goal is to find a feasible reconstruction sequence that maximizes the total reward over all generalized due dates. This paper investigates the time complexity of the problem. Two upper bounds and a dominance property are proposed for the design of branch-and-bound algorithms. Computational experiments are carried out to assess the efficiency of the proposed properties. The results show that the proposed properties can significantly reduce the time required for producing an optimal schedule.

Improved bounds for scheduling conflicting jobs with minsum criteria

We consider a general class of scheduling problems where a set of conflicting jobs needs to be scheduled (preemptively or nonpreemptively) on a set of machines so as to minimize the weighted sum of completion times. The conflicts among jobs are formed as an arbitrary conflict graph. Building on the framework of Queyranne and Sviridenko [2002b], we present a general technique for reducing the weighted sum of completion-times problem to the classical makespan minimization problem. Using this technique, we improve the best-known results for scheduling conflicting jobs with the min-sum objective, on several fundamental classes of graphs, including line graphs, ( k + 1)-claw-free graphs, and perfect graphs. In particular, we obtain the first constant-factor approximation ratio for nonpreemptive scheduling on interval graphs. We also improve the results of Kim [2003] for scheduling jobs on line graphs and for resource-constrained scheduling.

Resource-constrained critical path analysis based on discrete event simulation and particle swarm optimization

The absence of a valid resource-constrained critical path method (CPM) not only hampers the widespread use of mainstream project scheduling software in construction management practice, but also destabilizes the very foundation of any sophisticated, CPM-based time or cost analysis in construction scheduling research. This has motivated us into developing an innovative, fully-automated solution to resource-constrained CPM called the Simplified Simulation-based Scheduling system (short as S3). S3 takes advantage of the simplified discrete event simulation approach (SDESA) and the evolutionary optimization technique called particle swarm optimizer (PSO) to automate the formulation of a resource-constrained schedule with the shortest total project duration. We clarify basic issues of resource scheduling, elaborate on the formation of a CPM simulation model by SDESA, present PSO algorithms, and discuss the PSO solution formulation and simulation–optimization interaction in relation to the development of S3 software. In order to introduce S3 to construction schedulers, we also reference the relevant functionalities and features of Primavera Project Planner (P3) and Microsoft Project, which are applied alongside S3 in two case studies. The first case is a classic textbook example while the second case is based on a real drainage project in Hong Kong. In both cases, S3 eclipses the current CPM software with respect of (1) shortening the total project duration; (2) optimizing provisions of resources of various types; and (3) producing valid total float values to guide schedule implementation.

On a resource-constrained scheduling problem with application to distributed systems reconfiguration

This paper is devoted to the study of a resource-constrained scheduling problem, the Process Move Programming problem, which arises in relation to the operability of certain high availability real-time distributed systems. Informally, this problem consists, starting from an arbitrary initial distribution of processes on the processors of a distributed system, in finding the least disruptive sequence of operations (non-impacting process migrations or temporary process interruptions) at the end of which the system ends up in another predefined arbitrary state. The main constraint is that the capacity of the processors must not be exceeded during the reconfiguration. After a brief survey of the literature, we prove the NP-hardness of the problem and exhibit a few polynomial special cases. We then present a branch-and-bound algorithm for the general case along with computational results demonstrating its practical relevance. The paper is concluded by a discussion on further research.

Strong valid inequalities for the resource-constrained scheduling problem with uniform resource requirements

We consider the resource-constrained scheduling problem when each job’s resource requirements remain constant over its processing time. We study a time-indexed formulation of the problem, providing facet-defining inequalities for a projection of the resulting polyhedron that exploit the resource limitations inherent in the problem. Lifting procedures are then provided for obtaining strong valid inequalities for the original polyhedron. Computational results are presented to demonstrate the strength of these inequalities.