Renewable Resource Constraints Research Articles

Weighted tardiness minimisation for unrelated machines with sequence-dependent and resource-constrained setups

Motivated by the need of quick job (re-)scheduling, we examine an elaborate scheduling environment under the objective of total weighted tardiness minimisation. The examined problem variant moves well beyond existing literature, as it considers unrelated machines, sequence-dependent and machine-dependent setup times, and a renewable resource constraint on the number of simultaneous setups. For this variant, we provide a relaxed MILP to calculate lower bounds, thus estimating a worst-case optimality gap. As a fast exact approach appears not plausible for instances of practical importance, we extend known (meta-)heuristics to deal with the problem at hand, coupling them with a Constraint Programming (CP) component – vital to guarantee the non-violation of the problem's constraints – which optimally allocates resources with respect to tardiness minimisation. The validity and versatility of employing different (meta-)heuristics exploiting a relaxed MILP as a quality measure are revealed by our extensive experimental study, which shows that the methods deployed have complementary strengths depending on the instance parameters. Since the problem description has been obtained from a textile manufacturer where jobs of diverse size arrive continuously under tight due dates, we also discuss the practical impact of our approach in terms of both tardiness decrease and broader managerial insights.

Unrelated Parallel Machine Scheduling with Job and Machine Acceptance and Renewable Resource Allocation

In this paper, an unrelated parallel machine scheduling problem with job (product) and machine acceptance and renewable resource constraints was considered. The main idea of this research was to establish a production facility without (or with minimum) investment in machinery, equipment, and location. This problem can be applied to many real problems. The objective was to maximize the net profit; that is, the total revenue minus the total cost, including fixed costs of jobs, job transportation costs, renting costs of machines, renting cost of resources, and transportation costs of resources. A mixed-integer linear programming (MILP) model and several heuristics (greedy, GRASP, and simulated annealing) are presented to solve the problem.

Modified Harmony Search Algorithm for Resource-Constrained Parallel Machine Scheduling Problem with Release Dates and Sequence-Dependent Setup Times

This research focuses on the problem of scheduling a set of jobs on unrelated parallel machines subject to release dates, sequence-dependent setup times, and additional renewable resource constraints. The objective is to minimize the maximum completion time (makespan). To optimize the problem, a modified harmony search (MHS) algorithm was proposed. The parameters of MHS are regulated using full factorial analysis. The MHS algorithm is examined, evaluated, and compared to the best methods known in the literature. Four algorithms were represented from similar works in the literature. A benchmark instance has been established to test the sensitivity and behavior of the problem parameters of the different algorithms. The computational results of the MHS algorithm were compared with those of other metaheuristics. The competitive performance of the developed algorithm is verified, and it was shown to provide a 42% better solution than the others.

Integrated Planning and Scheduling of Multiple Manufacturing Projects Under Resource Constraints Using Raccoon Family Optimization Algorithm

Today's dynamic environment and increasing demand for highly customized products have significantly increased the number of companies operating in the project environment. Project planning and scheduling are one of the major problems faced by managers due to resource constraints. Enterprises have to execute several projects simultaneously while sharing limited resources (i.e., human resources, equipment, and budget) among the projects to effectively meet the deadlines. Therefore, this work investigates the integrated planning and scheduling problem of multiple projects with different release dates and execution modes while considering the renewable and non-renewable resource constraints. Moreover, the raccoon family optimization (RFO) algorithm is proposed to maximize the net profit while considering the early completion bonus, penalty cost, and resource costs. In the proposed RFO algorithm, greedy search and modified genetic operators are introduced to enhance the performance and efficiency. Effectiveness of the proposed RFO algorithm is compared with the genetic algorithm (GA), raccoon optimization algorithm (ROA), and artificial bee colonial (ABC) algorithm on test cases as well as an industrial case study. The results indicate that the proposed RFO algorithm outperforms the other compared algorithms, both in terms of effectiveness and efficiency.

Automatic Clustering and Multi-Directional Scheduling Scheme for Multi-Mode Scheduling Projects

In this study, a cluster-based heuristic algorithm to solve multi-mode resource constrained project scheduling problem (MMRCPSP) is presented. The MMRCPSPs are usually challenging to schedule because each activity has multiple execution modes with renewable and non-renewable resources that are categorized as an NP-hard problem. In this paper, we propose and apply three ideas to solve an MMRCPSP. Firstly, an MMRCPSP with two objectives namely, makespan and executive cost is converted into a single mode resource-constrained project scheduling problem (RCPSP) with three objectives by relaxing the non-renewable resource constraints and then defining a corresponding penalty value. In the second phase, in the light of precedence and renewable resource constraints, the new RCPSP are scheduled by calling the multi-directional scheduling schemes (multi-dss). In the end, on the basis of three objectives’ value (namely makespan, cost, and penalty value), we defined a density-based fitness function for an evolutionary approach regarding the clustering methods on the new solution space. Our numerical results showed that the multi-dss with higher dimension regarding the automatic cluster-based fitness functions affected the performance of the evolutionary approach. Furthermore, the evolutionary approach based on multi-directional scheduling schemes prevents to trap into the local optimums by increasing the solutions’ diversity.

Algorithms for the unrelated parallel machine scheduling problem with a resource constraint

We consider the unrelated parallel machine scheduling problem with a renewable resource constraint (UPMR). For the two-machine variant of the problem, we propose a very efficient mixed-integer linear programming (MILP) model. For more than two machines, we propose a two-stage heuristic, which first uses a MILP model to calculate a lower bound and assign jobs to machines, and then uses a constraint programming (CP) model to schedule jobs on machines. If the solution of the two-stage heuristic is not proven optimal, the problem is solved using a CP model for the complete UPMR, with a hot start provided by the two-stage heuristic. New large benchmark problem instances with up to 1000 jobs are generated. Extensive computational experiments are carried out on these, as well as on smaller instances from the literature. Our algorithms obtain excellent solutions for much larger problem instances than previously proposed methods. For the UPMR with two machines, our MILP model solves all test instances to optimality in very modest computation times, greatly outperforming previously proposed methods. For the variant with more than two machines, our overall algorithm, which combines the two-stage heuristic with a full CP model, finds for the smaller instances from the literature better than or the same solutions as all previously proposed methods in considerably less computation time. Difficult types of problem instances are also identified for future research.

Resource Constrained Multi-Project Scheduling Problem with Resource Transfer Times

Scheduling multi-project is a complex decision making process. It involves the effective and timely allocation of resources to different projects. In the case of multi-project, resources are often transferred between the projects. It consumes both time and cost, when projects are situated in different geographic locations. As a result, the net present value (NPV) of multi-projects is significantly impacted by the resource transfer time. In this paper, a new genetic algorithm (GA) approach to the multi-project scheduling problem with resource transfer times is presented, where the NPV of all projects is maximized subject to renewable resource constraints. The paper also presents a heuristic approach using two phase priority rules for the same problem. We conduct a comprehensive analysis of 60 two-phase priority rules. The proposed GA approach is compared to the heuristic approach using the well-known priority rules. An extensive computational experiment is reported.

On the efficient modeling and solution of the multi-mode resource-constrained project scheduling problem with generalized precedence relations

For variants of the single-mode resource-constrained project scheduling problem, state-of-the-art exact algorithms combine a Branch and Bound algorithm with principles from Constraint Programming and Boolean Satisfiability Solving. In our paper, we propose new exact approaches extending the above principles to the multi-mode RCPSP (MRCPSP) with generalized precedence relations (GPRs). More precisely, we implemented two constraint handlers cumulativemm and gprecedencemm for the optimization framework SCIP. With the latter, one can model renewable resource constraints and GPRs in the context of multi-mode activities, respectively. Moreover, they integrate domain propagation and explanation generation techniques for the above problem characteristics. We formulate three SCIP-models for the MRCPSP with GPRs, two without and one with our constraint handler gprecedencemm. Our computational results on instances from the literature with 30, 50 and 100 activities show that the addition of this constraint handler significantly strengthens the SCIP-model. Moreover, we outperform the state-of-the-art exact approach on instances with 50 activities when imposing time limits of 27 s. In addition, we close (find the optimal solution and prove its optimality for) 289 open instances and improve the best known makespan for 271 instances from the literature.

A Honey Bee Swarm Optimization Algorithm for Minimizing the Total Costs of Resources in MRCPSP

In this paper, we solve an extended type of multimode project scheduling problem considering renewable and non-renewable resource constraints and finish-to-start precedence relations among project activities. We suppose that renewable resources are hired and are not accessible in the whole duration of the project. Therefore, there is an assigned ready date as well as a due date for each renewable resource type so that no resource can be rented before its ready date. But, the resources are allowed to be used after their due dates by incurring penalty costs. The aim is to minimize the whole charges of both renewable and nonrenewable resource usage. This problem is introduced by Khalilzadeh et al. 7 as multimode resource-constrained project scheduling problem minimizing the net present value of entire weighted resource tardiness penalty costs (MRCPSP-DCTWRTPC) in which both renewable and nonrenewable resource restrictions rely on activity mode. The problem we proposed in this paper is the extended form of the problem introduced by Khalilzadeh et al. 7 with considering the discounted cash flows of the resource costs. We call this problem multi-mode resource-constrained project scheduling problem, minimization of discounted cash flows of total weighted resource tardiness penalty cost (MRCPSP-DCTWRTPC). For this problem, we propose a novel meta-heuristic algorithm based on a Honey Bee Swarm Optimization (HBSO) approach together with a prioritization rule for project tasks and numerous improvement and local search procedures. Computational results prove the effectiveness and efficiency of the presented method. Keywords: Discounted Cash Flow, Honey Bee Swarm Optimization, Multi Modes, Project Scheduling, Resource Cost, Tardiness Penalty Cost

Resilience analysis for project scheduling with renewable resource constraint and uncertain activity durations

In the real world, project construction usually suffers various uncertain factors. Traditionally, uncertainty is modelled as either random variables or dynamic events. This paper addresses the case that the information about uncertainty is partially known when developing project schedules. The concept of resilience is introduced into project scheduling problems with resource constraint to measure a schedule's ability to absorb possible perturbation. The definition of resilience is given based on project equilibriums. Since the calculation of resilience is time intensive, a new surrogate measure is proposed to indicate schedule resilience. Correlation analysis between resilience and proposed surrogate measure is carried out. The experimental results suggest that the proposed surrogate measure is more appropriate to indicate resilience than makespan or total free slack.

On the complexity of project scheduling to minimize exposed time

We consider project scheduling where the project manager’s objective is to minimize the time from when an adversary discovers the project until the completion of the project. We analyze the complexity of the problem identifying both polynomially solvable and NP-hard versions of the problem. The complexity of the problem is seen to be dependent on the nature of renewable resource constraints, precedence constraints, and the ability to crash activities in the project.

An Improved Genetic Algorithm for Resource Constrained Project Scheduling Problem

Project scheduling with limited resources is a challenging management problem that is of immense importance to both practitioners and researchers. This problem is known to be NP-hard even under the simplifying assumptions of single renewable resource constraint, its constant availability over time and minimization of makespan as objective. This paper presents an improved Genetic Algorithm (GA) based approach for the single mode resource constrained project scheduling problem (RCPSP) with makespan minimization as objective. The proposed approach uses binary string based representations and operators for chromosomes. The approach was tested on some difficult instances with high optimality gap in the J120 data set of PSPLIB. It was found that the proposed approaches gave better results as compared to activity list based representations that are commonly used. General Terms Genetic Algorithm, Project Scheduling, Resources Allocation

An evolutionary search procedure for optimizing time–cost performance of projects under multiple renewable resource constraints

This paper presents an effective procedure for optimizing time–cost performance of multi-mode resource constrained project scheduling problems in which activities are subject to finish-start precedence constraints under renewable limited resources. Associated with each execution mode of activities, there exists a direct cost, a processing time, and a set of required renewable resources. In optimizing time–cost performance, the procedure treats the cost as a non-renewable resource whose limit can affect the duration of the project and balances cost versus time through the notion of priority-rank. This is performed by the use of a module which handles multimode projects, and since the procedure has to call this module with different limits on the cost, the effectiveness of this module plays a key role in the overall efficiency. For this reason, an effective evolutionary search technique has been developed to create the basis of this module. For testing its effectiveness, this module has been tested on 552 largest multimode benchmark instances of the PSPLIB and the results are promising: For over 98% of instances, the module finds the best available solutions in the literature. The module also produces a solution for one of these benchmark instances that is better than all of the current solutions in the literature.

Ant colony optimization-based multi-mode scheduling under renewable and nonrenewable resource constraints

Abstract An ant colony optimization (ACO)-based methodology for solving the multi-mode resource-constrained project scheduling problem (MRCPSP) considering both renewable and nonrenewable resources is presented. With regard to the MRCPSP solution consisting of activity sequencing and mode selection, two levels of pheromones are proposed to guide search in the ACO algorithm. Correspondingly, two types of heuristic information and probabilities as well as related calculation algorithms are introduced. Nonrenewable resource-constraint and elitist-rank strategy are taken into account in updating the pheromones. The flowchart of the proposed ACO algorithm is described, where a serial schedule generation scheme is incorporated to transform an ACO solution into a feasible schedule. The parameter-selection and the resultant performance of the proposed ACO methodology are investigated through a series of computational experiments. It is expected to provide an effective alternative methodology for solving the MRCPSP by utilizing the ACO theory.

A Genetic Algorithm for Solving Multi-Mode Critical Chain Project Scheduling Problem

This paper studies the application of multi-mode critical chain project scheduling problem based on genetic algorithm. A model of multi-mode critical chain project scheduling problem is addressed by combining the characteristics of multi-mode project scheduling problem and the critical chain method. Comprehensively considering the renewable resource constraints, nonrenewable resource constraints, activities with multi-mode and the uncertainty of activity duration, a bi-level genetic algorithm to solve multi-mode critical chain project scheduling problem is proposed. We use the shared benchmark from PSPLIB to test this new genetic algorithm and the results show that the algorithm in this paper has obvious superiority over most currently existing approach.

A scatter search heuristic for maximising the net present value of a resource-constrained project with fixed activity cash flows

In this paper, we present a meta-heuristic algorithm for the resource-constrained project scheduling problem with discounted cash flows. We assume fixed payments associated with the execution of project activities and develop a heuristic optimisation procedure to maximise the net present value of a project subject to the precedence and renewable resource constraints. We investigate the use of a bi-directional generation scheme and a recursive forward/backward improvement method from literature and embed them in a meta-heuristic scatter search framework. We generate a large dataset of project instances under a controlled design and report detailed computational results. The solutions and project instances can be downloaded from a website in order to facilitate comparison with future research attempts.

A multi-mode resource-constrained discrete time–cost tradeoff problem and its genetic algorithm based solution

The discrete time–cost tradeoff problem (DTCTP) is an important subject in the project scheduling theory and applications. Due to the fact that the resources used in projects in modern enterprises mainly belong to renewable resources, e.g. manpower resources, the general DTCTP is extended to a new multi-mode resource-constrained DTCTP model (MRC-DTCTP). The multi-mode resource-constrained project scheduling problem (MRCPSP) was referred and the renewable resource constraints were added to the general DTCTP. By predefining the resource price, the renewable resources are related to the project costs, including direct cost and indirect cost. Every activity can be executed in the crashing way in which the project direct costs are used to shorten the activity duration. According to the characteristics of the MRC-DTCTP, an improved genetic algorithm for solving it was developed and its effectiveness was verified by compared with the exact algorithm. Finally an entire time–cost tradeoff curve for a project network was drawn through computing project deadline problem, and the advantages of the MRC-DTCTP were investigated based on computation results.

Efficient and Optimal Capital Accumulation under a Non Renewable Resource Constraint

Accumulation de capital optimale et efficacesous une contrainte de ressource non renouvelable Le modèle usuel d’utilisation d’une ressource non renouvelable avec accumulation decapital suppose la production d’un seul type de bien qui peut être soit consommé soitinvesti. On étudie dans cet article une économie bisectorielle dans laquelle on produitun bien de consommation et un bien capital à partir d’une ressource non renouvelable,de travail et de capital. L’accumulation du capital est un processus irréversible et lecapital se déprécie au cours du temps. Dans ce cadre on réexamine les résultats classiques de la théorie de la croissance efficace et de la croissance optimale. On montreque les conditions d’efficacité de la production peuvent s’exprimer en termes des propriétés d’une fonction d’investissement dont la définition fait intervenir les caractéristiques des fonctions de production des deux secteurs, confondus dans les modèles nonsectoriels du type Dasgupta et Heal et complètement dilués dans les modèles désaggrégés du type Dixit, Hammond et Heol. On montre aussi que la règle d’Hotelling prendici la forme d’une relation entre le taux de croissance de la consommation et le taux decroissance de la productivité marginale de la ressource dans le secteur du bien deconsommation. Enfin on examine différentes formes de la règle d’Hartwick.

The impact of various activity assumptions on the lead time and resource utilization of resource-constrained projects

The well-known resource-constrained project scheduling problem (RCPSP) schedules project activities within the precedence and renewable resource constraints while minimizing the total lead time of the project. The basic problem description assumes non-pre-emptive activities with fixed durations, and has been extended to various other assumptions in the literature. In this paper, we investigate the effect of three activity assumptions on the total lead time and the total resource utilization of a project. More precisely, we investigate the influence of variable activity durations under a fixed work content, the possibility of allowing activity pre-emption and the use of fast tracking to decrease a project’s duration. We give an overview of the procedures developed in the literature and present some modifications to an existing solution approach to cope with our activity assumptions under study. We present computational results on a generated dataset and evaluate the impact of all assumptions on the quality of the schedule.

Introduction to the special issue: project scheduling under uncertainty

in the no-tation of Herroelen et al. 2000) involves the determinationof a baseline schedule that satisfies both the finish-start,zero-lag precedence constraints between the activities andthe renewable resource constraints under the objective ofminimizing the project duration (for recent comprehensiveoverviews of the literature, we refer to Demeulemeester andHerroelen 2002 and Neumann et al. 2003).During execution, however, a project may be subjectto considerable uncertainty, which may lead to numerousschedule disruptions. Activities can take longer or shorterthan primarily expected, resource requirements or availabil-ities may vary, ready times and due dates may change, newactivities might have to be inserted in the schedule, etc.In this special issue we have collected six articles that ex-amine several aspects of scheduling under uncertainty. Wedid not restrict the topics; they simply illustrate contempo-rary research in the field. The contribution of the six articlescan be summarized as follows.