Feasible Schedule Research Articles

An artificial immune differential evolution algorithm for scheduling a distributed heterogeneous flexible flowshop

This paper studies a distributed heterogeneous flexible flowshop problem (DHFFP) with sequence-dependent setup and transport times, where each job has a release time and each production stage has multiple unrelated parallel machines. An integer linear programming (ILP) model and a new artificial immune differential evolution (AIDE) algorithm are proposed aiming to minimize the makespan and total tardiness simultaneously. Firstly, the AIDE employs a two-dimensional vector encoding scheme including the information of job permutation and factory allocation for solution representation. In addition, a dynamic decoding scheme is designed to construct a feasible schedule. Secondly, three distributed Nawaz–Enscore–Ham (NEH) based constructive heuristics are presented to provide the initial antibody population. Thirdly, a discrete differential evolution algorithm is introduced to mutate the cloned antibodies. Further, clonal suppression is applied by eliminating the antibodies with lower stimulation values. Simulated annealing (SA) based local search is incorporated with four problem-specific neighborhood structures to enhance the algorithm. Finally, the optimal values of the algorithmic parameters are determined by the orthogonal test. Some numerical experiments of the ILP model on small-scale instances are conducted to show the effectiveness of the proposed AIDE algorithm. The AIDE algorithm is also compared with several existing algorithms for different scale instances. The results demonstrate that the AIDE algorithm generates average relative percentage deviation of 12.51% and 7.99% respectively for small & medium-scale instances and large-scale instances, which is the best-performing among all algorithms.

FTSC: Fault-tolerant scheduling and control co-design for distributed real-time system

Ensuring control stability is essential for safety-critical systems. Task redundancy is one commonly employed technique to enhance control performance in applications afflicted by intermittent faults. While increasing the number of replicas can improve control performance, it also introduces challenges in terms of scheduling and mapping. Prior research primarily focuses on controller design to enhance control performance, with limited consideration given to fault tolerance and scheduling in a combined manner. In this paper, we propose a co-design scheme of Fault-Tolerant Scheduling and Control (FTSC), which aims to provide stable control performance along with feasible mapping and scheduling solutions. We present a comprehensive formulation that encompasses mapping, scheduling, and fault tolerance, optimizing control performance into a Mixed Integer Linear Programming (MILP) framework. The problem of task redundancy can either be addressed through a heuristic algorithm efficiently or be solved in a MILP-based approach with a better solution. A case study is conducted to demonstrate the effectiveness of our proposed scheme, highlighting its ability to reduce system control costs while meeting real-time, reliability, and schedulability constraints.

Bag-of-Tasks Scheduling with Rejection in Large Computing Systems

We are given a set of [Formula: see text] identical parallel machines and a set of [Formula: see text] jobs in large computing systems, where each job [Formula: see text] consists of a bag of [Formula: see text] identical tasks with a processing time [Formula: see text], and has a rejection penalty [Formula: see text]. Job [Formula: see text] is either accepted in which case all the [Formula: see text] tasks must be processed by one of the machines, or rejected which incurs a rejection penalty [Formula: see text]. The problem of bag-of-tasks scheduling with rejection is to find a feasible schedule, so as to minimize the makespan plus the total rejection penalty of all rejected jobs. In this paper, we present a polynomial time approximation scheme.

A late-mover genetic algorithm for resource-constrained project-scheduling problems

The Resource-Constrained Project Scheduling Problem (RCPSP) plays a critical role in various management applications. Despite its importance, research efforts are still ongoing to improve lower bounds and reduce deviation values. This study aims to develop an innovative and straightforward algorithm for RCPSPs by integrating the “1+1” evolution strategy into a genetic algorithm framework. Unlike most existing studies, the proposed algorithm eliminates the need for parameter tuning and utilizes real-valued numbers and path representation as chromosomes. Consequently, it does not require priority rules to construct a feasible schedule. The algorithm's performance is evaluated using the RCPSP benchmark and compared to alternative algorithms, such as cWSA, Hybrid PSO, and EESHHO. The experimental results demonstrate that the proposed algorithm is competitive, while the exploration capability remains a challenge for further investigation.

Determining optimal fuel delivery strategies under uncertainty

During the preparation before a hurricane makes landfall, affected individuals may be asked to evacuate. Large and small-scale evacuations can cause rapid increases in the demand for gasoline fuel. However, during a hurricane vessels carrying gas may be delayed and/or rerouted, adding to the difficulty of providing the necessary gas in affected areas. In this work, we determine alternate delivery locations and times for vessels carrying fuel that are scheduled to arrive and deliver fuel at ports impacted by an approaching hurricane. Motivated by Hurricane Irma in Florida, we develop a multi-period stochastic scheduling model that incorporates hurricane (weather) advisories, fuel delivery schedules, port storage capacities, and port docking capacities. Our model determines the best schedule based on two objectives: (1) minimize the total unmet demand at each port, and (2) minimize inequities in unmet demands among the ports. We also present a case study and a numerical experiment based on fuel delivery data from ports in Florida. Among our key findings is that port availability is the driving factor in determining feasible schedules for vessel gas deliveries. We also present a scheduling heuristic that dynamically adapts to weather advisories so as to minimize the impact of unmet demand in the affected areas.

A heuristic solution framework for the resource-constrained multi-aircraft scheduling problem with transfer of resources and aircraft

Efficient and feasible flight deck operation scheduling plan is of great significance for improving the sortie rate of carrier aircraft. Oxygen filling, fueling, and other operations of each carrier aircraft are executed in the pre-flight preparation stage. Different personnel, support equipments, and supply resources, are required while different operations are being executed. To date, most approaches proposed in the literature are based on the unrealistic assumption that the transfer process of carrier aircraft can be ignored. To close this gap, the resource-constrained multi-aircraft scheduling problem on the flight deck is examined in this study. The main contributions of the study are as follows. First, by considering the transfer process of aircraft on the flight deck operations, the model formulation of resource-constrained multi-aircraft scheduling problem is established. Second, the parallel and serial scheduling framework are proposed, where parking spot priority rules and resource allocation rules are presented to select the most suitable resources. Third, a modified genetic programming algorithm is presented for obtaining efficient activity priority rules. Fourth, the well-performed scheduling framework, priority rules, and allocation rules are selected by conducting computational experiments. Furthermore, experiment results show that the parallel scheduling framework outperforms the serial framework in most experiments (average outperformance is 10.19%), and the parking spot priority rules slightly affect the serial scheduling framework.

A genetic algorithm for scheduling open shops with conflict graphs to minimize the makespan

The open shop problem with conflict graph consists of scheduling jobs on an open shop system subject to conflict constraints given by a simple undirected graph G, called the conflict graph. In this graph, each vertex represents a job, and jobs that are adjacent in G are in conflict, i.e. they cannot be processed at the same time on different machines. The problem of finding a feasible schedule that minimizes the maximum completion time is known to be NP-hard even on two machines. In this paper, we present mixed integer linear programming models, lower bounds, and genetic algorithms for this problem. Extensive computational experiments are conducted on a large set of instances derived from well-known benchmarks of the basic open shop problem. The results show the effectiveness of the genetic algorithm that solves to optimality at least 93.490% of the instances and the average deviation from the lower bounds is within 0.475%. Furthermore, the algorithm improves the upper bounds obtained by the mathematical formulations and outperforms the existing heuristics.

Deep Reinforcement Learning Based Unit Commitment Scheduling under Load and Wind Power Uncertainty

The intermittent nature of renewable energy sources and fluctuating electricity demand induce significant uncertainty that needs to be tackled with computationally efficient solution techniques to provide reliable and cost-effective generation schedules of power systems. In this work, we present a deep reinforcement learning (DRL) based approach for the day-ahead scheduling of generation resources under demand and wind power uncertainties. The proposed approach yields a causal policy relying only on historical uncertainty realizations and forecast data that is trained with an actor-critic-based reinforcement learning algorithm. Through safe exploration, the DRL-based approach guarantees a feasible commitment schedule without any operational constraint violations. We conduct computational experiments on the IEEE 39-bus and 118-bus test cases to demonstrate the effectiveness of the proposed solution strategy and improvement over existing approaches, including a deterministic approach with point forecasts and the stochastic dual dynamic integer programming method. The results show that the proposed approach enjoys superior performance in terms of computational efficiency and incurred operational costs, with significant reduction in penalty costs caused by insufficient net load supply than the deterministic approach.

A two-stage partial fixing approach for solving the residency block scheduling problem.

We consider constructing feasible annual block schedules for residents in a medical training program. We must satisfy coverage requirements to guarantee an acceptable staffing level for different services in the hospital as well as education requirements to ensure residents receive appropriate training to pursue their individual (sub-)specialty interests. The complex requirement structure makes this resident block scheduling problem a complicated combinatorial optimization problem. Solving a conventional integer program formulation for certain practical instances directly using traditional solution techniques will result in unacceptably slow performance. To address this, we propose a partial fixing approach, which completes the schedule construction iteratively through two sequential stages. The first stage focuses on the resident assignments for a small set of predetermined services through solving a much smaller and easier problem relaxation, while the second stage completes the rest of the schedule construction after fixing those assignments specified by the first stage's solution. We develop cut generation mechanisms to prune off the bad decisions made by the first stage if infeasibility arises in the second stage. We additionally propose a network-based model to assist us with an effective service selection for the first stage to work on the corresponding resident assignments to achieve an efficient and robust performance of the proposed two-stage iterative approach. Experiments using real-world inputs from our clinical collaborator show that our approach can speed up the schedule construction at least 5 times for all instances and even over 100 times for some huge-size instances compared to applying traditional techniques directly.

A multi-stage stochastic programming model for the unit commitment of conventional and virtual power plants bidding in the day-ahead and ancillary services markets

As more uncontrollable renewable energy sources are present in the power generation portfolio, the need of more detailed and reliable tools for the optimal operation of energy systems has increased in the last years. This work presents a multi-stage stochastic Mixed Integer Linear Program with binary recourse for optimizing the day-ahead unit commitment of power plants and virtual power plants operating in the day-ahead and ancillary services markets. Scenarios reproduce the uncertainty of the ancillary services market requests, and production of photovoltaic panels. A novel decomposition algorithm is proposed to tackle the challenging multistage stochastic program. The methodology is tested on three types of large power plants: a natural gas-fired combined cycle, a combined heat and power combined cycle with thermal storage, and a virtual power plant integrating a combined cycle with battery and photovoltaic fields. Compared to the typical deterministic unit commitment approach, the proposed stochastic optimization approach allows to increase the revenues of the conventional power plant up to 13.58% and, for the combined heat and power and virtual power plant case, it allows finding a feasible and efficient operational scheduling.

A fast data-driven optimization method of multi-area combined economic emission dispatch

To provide more feasible schemes for power system optimization management and operation, the interconnection of power grids in different areas is inevitable. Naturally, the multi-area combined economic/emission dispatch (MACEED) problem becomes a more important decision problem. However, as the dimensions of MACEED problems increase, existing studies may not obtain feasible scheduling decisions in a suitable time. On this background, MACEED problems are transferred into computational expensive problems. In order to solve high-dimensional, large-scale MACEED problems, a data-driven surrogate-assisted approach is proposed. First, a feature engineering-based support vector regression surrogate model is proposed to replace the traditional objective functions in high-dimensional MACEED problems. Second, knowledge distillation is applied as a freezing and fine-tuning mechanism for the improved support vector regression surrogate models, which significantly reduces the time required to build surrogate models. Third, an improved non-dominated sorting genetic algorithm-III is proposed to obtain feasible solutions to high-dimensional MACEED problem. The proposed algorithm enhances the convergence and diversity of optimal solutions. The effectiveness of the proposed data-driven approach is demonstrated through simulations of a four-area 40-unit test system under different constraints.

Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs

We consider the scheduling of jobs with multiple weights on a single machine for minimizing the total weighted number of tardy jobs. In this setting, each job has m weights (or equivalently, the jobs have m weighting vectors), and thus we have m criteria, each of which is to minimize the total weighted number of tardy jobs under a corresponding weighting vector of the jobs. For this scheduling model, the feasibility problem aims to find a feasible schedule such that each criterion is upper bounded by its threshold value, and the Pareto scheduling problem aims to find all the Pareto-optimal points and for each one a corresponding Pareto-optimal schedule. Although the two problems have not been studied before, it is implied in the literature that both of them are unary NP-hard when m is an arbitrary number. We show in this paper that, in the case where m is a fixed number, the two problems are solvable in pseudo-polynomial time, the feasibility problem admits a dual-fully polynomial-time approximation scheme, and the Pareto-scheduling problem admits a fully polynomial-time approximation scheme.

A Two-Step Approach to Scheduling a Class of Two-Stage Flow Shops in Automotive Glass Manufacturing

Driven from real-life applications, this work aims to cope with the scheduling problem of automotive glass manufacturing systems, that is characterized as a two-stage flow-shop with small batches, inevitable setup time for different product changeover at the first stage, and un-interruption requirement at the second stage. To the best knowledge of the authors, there is no report on this topic from other research groups. Our previous study presents a method to assign all batches to each machine at the first stage only without sequencing the assigned batches, resulting in an incomplete schedule. To cope with this problem, if a mathematical programming method is directly applied to minimize the makespan of the production process, binary variables should be introduced to describe the processing sequence of all the products, not only the batches, resulting in huge number of binary variables for the model. Thus, it is necessary and challenging to search for a method to solve the problem efficiently. Due to the mandatory requirement that the second stage should keep working continuously without interruption, solution feasibility is essential. Therefore, the key to solve the addressed problem is how to guarantee the solution feasibility. To do so, we present a method to determine the minimal size of each batch such that the second stage can continuously work without interruption if the sizes of all batches are same. Then, the conditions under which a feasible schedule exists are derived. Based on the conditions, we are able to develop a two-step solution method. At the first step, an integer linear program (ILP) is formulated for handling the batch allocation problem at the first stage. By the ILP, we need then to distinguish the batches only, greatly reducing the number of variables and constraints. Then, the batches assigned to each machine at the first stage are optimally sequenced at the second step by an algorithm with polynomial complexity. In this way, by the proposed method, the computational complexity is greatly reduced in comparison with the problem formulation without the established feasibility conditions. To validate the proposed approach, we carry out extensive experiments on a real case from an automotive glass manufacturer. We run ILP on CPLEX for testing. For large-size problems, we set 3600 s as the longest time for getting a solution and a gap of 1% for the lower bound of solutions. The results show that CPLEX can solve 96.83% cases. Moreover, we can obtain good solutions with the maximum gap of 4.9416% for the unsolved cases.

Evaluation of ROTARIX® Booster Dose Vaccination at 9 Months for Safety and Enhanced Anti-Rotavirus Immunity in Zambian Children: A Randomised Controlled Trial.

Oral rotavirus vaccines show diminished immunogenicity in low-resource settings where rotavirus burden is highest. This study assessed the safety and immune boosting effect of a third dose of oral ROTARIX® (GlaxoSmithKline) vaccine administered at 9 months of age. A total of 214 infants aged 6 to 12 weeks were randomised to receive two doses of ROTARIX® as per standard schedule with other routine vaccinations or an additional third dose of ROTARIX® administered at 9 months old concomitantly with measles/rubella vaccination. Plasma collected pre-vaccination, 1 month after first- and second-dose vaccination, at 9 months old before receipt of third ROTARIX® dose and/or measles/rubella vaccination, and at 12 months old were assayed for rotavirus-specific IgA (RV-IgA). Geometric mean RV-IgA at 12 months of age and the incidence of clinical adverse events 1 month following administration of the third dose of ROTARIX® among infants in the intervention arm were compared between infants in the two arms. We found no significant difference in RV-IgA titres at 12 months between the two arms. Our findings showed that rotavirus vaccines are immunogenic in Zambian infants but with modest vaccine seroconversion rates in low-income settings. Importantly, however, a third dose of oral ROTARIX® vaccine was shown to be safe when administered concomitantly with measles/rubella vaccine at 9 months of age in Zambia. This speaks to opportunities for enhancing rotavirus vaccine immunity within feasible schedules in the national immunization program.

Online Throughput Maximization on Unrelated Machines: Commitment is No Burden

We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on a single or multiple possibly unrelated machines that maximizes the number of jobs that complete before their deadline. Due to strong impossibility results for competitive analysis on a single machine, we require that jobs contain some slack ɛ > 0, which means that the feasible time window for scheduling a job is at least 1+ɛ times its processing time on each eligible machine. Our contribution is two-fold: (i) We give the first non-trivial online algorithms for throughput maximization on unrelated machines, and (ii), this is the main focus of our paper, we answer the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs. This is very relevant, e.g., in providing cloud-computing services, and disallows last-minute rejections of critical tasks. We present an algorithm for unrelated machines that is \(\Theta (\frac{1}{\varepsilon })\) -competitive when the scheduler must commit upon starting a job. Somewhat surprisingly, this is the same optimal performance bound (up to constants) as for scheduling without commitment on a single machine. If commitment decisions must be made before a job’s slack becomes less than a δ-fraction of its size, we prove a competitive ratio of \(\mathcal {O}(\frac{1}{\varepsilon - \delta })\) for 0 < δ < ɛ. This result nicely interpolates between commitment upon starting a job and commitment upon arrival. For the latter commitment model, it is known that no (randomized) online algorithm admits any bounded competitive ratio. While we mainly focus on scheduling without migration, our results also hold when comparing against a migratory optimal solution in case of identical machines.

Using Machine Learning to Include Planners’ Preferences in Railway Crew Scheduling Optimization

In crew scheduling, optimization models can become complex when a large number of penalty terms is included in the objective function to take planners’ preferences into account. Planners’ preferences often include nonmonetary aspects for which both the mathematical formulation and the assignment of appropriate penalty costs can be difficult. We address this problem by using machine learning to learn and predict planners’ preferences. We train a random forest classifier on planner feedback regarding duties from their daily work in railway crew scheduling. Our data set contains over 16,000 duties that planners labeled as good or bad. The trained model predicts the probability that a duty is perceived as bad by the planners. We present a novel approach to replace the large construct of penalty terms in a crew scheduling optimization model by a single term that penalizes duties proportionally to the predicted probability of being assessed as unfavorable by a planner. By integrating this probability into the optimization model, we generate schedules that include more duties with preferred characteristics. We increase the mean planner acceptance probability by more than 12% while only facing a marginal increase in costs compared with the original approach that utilizes a set of multiple penalty terms. Our approach combines machine learning to detect complex patterns regarding favorable duty characteristics and optimization to create feasible and cost-efficient crew schedules. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1196 .

Single machine Pareto scheduling with positional deadlines and agreeable release and processing times

<abstract><p>This paper studies the problem of scheduling $ n $ jobs on a single machine to minimize total completion time and maximum cost, simultaneously. Each job is associated with a positional deadline that indicates the largest ordinal number of this job in any feasible schedule. The jobs have agreeable release and processing times, meaning that jobs with larger release times also have larger processing times. The agreeability assumption is reasonable since both the single-criterion problems (without positional deadline constraints) of minimizing total completion time and maximum lateness on a single machine with arbitrary release and processing times are strongly NP-hard. An $ O(n^3) $-time Pareto optimal algorithm is presented. The previously known algorithms only solve two special cases of the agreeability assumption: either the case of equal release times in $ O(n^4) $ time, or the case of equal processing times (without positional deadline constraints) in $ O(n^3) $ time.</p></abstract>

Research on Software Project Schedule Planning Technology Based on the Integration of PERT and CPM

Make a feasible schedule planning for software project, is the foundation to carry out an orderly software project activity, is the key to success of the project. To solve the difficulties of schedule planning, this article studies the science technology and methods, including four aspects: First, using network chart to show the dependencies between activities, including Precedence Diagram Method and Arrow Diagram Method; Second, Program Evaluation and Review Technique is used to evaluate the time of the project activity; Third, the critical path method of determining the project total duration, including deduce from calculation formula of active time and determine the critical path; Fourth, duration compression method based on progress compression factor method. According to the situation of many technologies and methods, studied the main factors considered by selecting techniques and methods. Results show that using scientific technology and method to make the schedule planning, will reduce the workload of planning, improve the accuracy of the plan and have high practical value.

Optimized Scheduling of Periodic Hard Real-Time Multicore Systems

Multicore systems were developed to provide a substantial performance increase over monocore systems. But shared hardware resources are a problem as they add unpredictable delays that affect the schedulability of multicore hard real-time systems. In recent years much effort has been put into modelling interference and proposing scheduling techniques to mitigate its negative effect. Using one of these models, we propose a scheduling technique, based on Integer Linear Programming (ILP) that, in combination with a task to core allocator, not only achieves a feasible schedule but also reduces the interference produced by shared hardware resources in the context of hard real-time multicore systems. The evaluation shows how both the interference is reduced (≈ 83.47%) and the schedulability is increased (≈ 12.25%) compared to traditional heuristics.

A Novel Control-Theory-Based Approach to Scheduling of High-Throughput Screening System for Enzymatic Assay

Nowadays, high-throughput screening (HTS) systems are widely used in pharmaceutical industries and laboratories for the discovery of new drugs and biomedical substances. It is important to efficiently schedule them so as to reduce the cost. In the operation of an HTS system, a microplate may visit some resources more than once and complex time window constraints are imposed on some activities and activity sequences. Moreover, with the consistency requirement, a one-microplate cyclic schedule is necessary. Thus, its scheduling problem is very challenging. This article studies the scheduling problem of an HTS system for an enzymatic assay, a typical application of HTSs, from the perspective of control theory. The system is modeled by resource-oriented Petri nets (ROPNs). With the model, necessary and sufficient conditions under which a feasible cyclic schedule exists are established. Then, we determine how many microplates should be in the system for concurrent processing and the transition firing sequence to obtain the activity sequence for an optimal and feasible schedule. In this way, a feasible and optimal cyclic schedule can be found by very simple computations, which shows that polynomial algorithms for an optimal schedule exist, while the existing studies apply mathematical programming with exponential computation complexity. Also, its efficient implementation is given.