Scheduling Problem Research Articles

Two-stage coordinated scheduling of hydrogen-integrated multi-energy virtual power plant in joint capacity, energy, and ancillary service markets

With the emergence of distributed resources (DRs), developing an effective, profitable, and green management method is of great importance. Virtual power plant (VPP) can aggregate various DRs, optimize their schedules, and participate in electricity markets uniformly to earn profit. The optimal scheduling problem in spot market has been widely studied, however, few studies have extended the services of VPP to the long-term scale. This paper proposes a coordinated scheduling method for a multi-energy virtual power plant (MEVPP), considering the integration of hydrogen facilities. A holistic market framework, including capacity market, energy market (EM), and ancillary service market (ASM) is developed jointly for the coordination among the annual capacity schedule, daily energy schedule, and daily reserve schedule of MEVPP. A hybrid hydrogen storage system including daily hydrogen storage and seasonal hydrogen storage is modeled to achieve both intraday and cross-seasonal peak shaving. Stochastic programming is used to tackle the uncertainties and risk management is considered by conditional value at risk. With the help of numerical analysis in case studies, it can be concluded that the proposed coordinated scheduling method can improve the economy of MEVPP. The profit from joint market decreases the total cost by about 52 %. The capacity adequacy and flexibility of MEVPP can be improved by the coordination of capacity and reserve services. The hybrid hydrogen storage system can realize the efficient integration of hydrogen and increase hydrogen production and consumption by about 9 %.

The Electric Vehicle Routing and Overnight Charging Scheduling Problem on a Multigraph

In the electric vehicle (EV) routing and overnight charging scheduling problem, a fleet of EVs must serve the demand of a set of customers with time windows. The problem consists in finding a set of minimum cost routes and determining an overnight EV charging schedule that ensures the routes’ feasibility. Because (i) travel time and energy consumption are conflicting resources, (ii) the overnight charging operations take considerable time, and (iii) the charging infrastructure at the depot is limited, we model the problem on a multigraph where each arc between two vertices represents a path with a different resource consumption trade-off. To solve the problem, we design a branch-price-and-cut algorithm that implements state-of-the-art techniques, including the ng-path relaxation, subset-row inequalities, and a specialized labeling algorithm. We report computational results showing that the method solves to optimality instances with up to 50 customers. We also present experiments evaluating the benefits of modeling the problem on a multigraph rather than on the more classical 1-graph representation. History: Accepted by Andra Lodi, Area Editor for Design and Analysis of Algorithms—Discrete. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada through the Discovery grants [Grant RGPIN-2023-03791]. It was also partially funded by HEC Montréal through the research professorship on Clean Transportation Analytics. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0404 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0404 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Some new results on rough interval linear programming problems and their application to scheduling and fixed-charge transportation problems

This paper focuses on linear programming problems in a rough interval environment. By introducing four linear programming problems, an attempt is being made to propose some results on optimal value of a linear programming problem with rough interval parameters. To obtain optimal solutions of a linear programming problem with rough interval data, constraints of the four proposed linear problems are applied. In this regard, firstly, the largest and the smallest feasible spaces for a linear constraint set with rough interval coefficients and parameters are introduced. Then, a rough interval for optimal value of such problems is obtained. Further, an upper approximation interval and a lower approximation interval as the optimal solutions of linear programming problems with rough interval parameters are achieved. Moreover, two solution concepts, surely and possibly solutions, are defined. Some numerical examples demonstrate the validity of the results. In particular, a scheduling problem and a fixed-charge transportation problem (FCTP) under rough interval uncertainty are investigated.

Fleet repositioning in the tramp ship routing and scheduling problem with bunker optimization: A matheuristic solution approach

This paper investigates an important planning problem faced by dry bulk shipping operators, referred to as the Tramp Ship Routing and Scheduling Problem with Bunker Optimization (TSRSPBO). The problem is to maximize the overall profit of a fleet of vessels by selecting cargoes and determining ship routes and schedules. We consider this problem under a set of practically relevant features such as flexibility in cargo quantities, as well as bunkering decisions on where to procure fuel and how much. As a particularly novel feature, we address the regional allocation of vessels at the end of the planning period to be well prepared for meeting (uncertain) future demand. To incorporate this, we consider the TSRSPBO as a two-stage stochastic programming problem, where cargo selection, routing, and bunkering decisions are solved in the first-stage problem, and the recourse cost of fleet repositioning is considered in the second stage. We present arc flow and path flow formulations, where the latter employs a priori generation of feasible routes as input. For solving realistically sized instances, we propose a matheuristic based on an Adaptive Large Neighborhood Search (ALNS) framework that iteratively generates columns and solves the path flow model. Computational experiments based on real data show that this matheuristic finds high-quality solutions for large test instances with 120 cargoes, 30 vessels, and ten bunker ports in less than one hour. Also, considering the TSRSPBO as a two-stage stochastic problem achieves the highest profits and is solved almost as quickly as the deterministic problem variant.

Minimizing total completion time and makespan for a multi-scenario bi-criteria parallel machine scheduling problem

Multi-criteria scheduling problems under uncertainty remain a relatively unexplored topic in theoretical computer science despite substantial practical interests. This work studies a bi-objective identical parallel machine scheduling problem under uncertainty, in which the first objective is to minimize the total completion time, and the second is to minimize the makespan. Especially a job’s processing time is assumed to be represented by a polynomial function with respect to scenario u∈U, where U⊂R+ is an interval containing an infinite number of scenarios.In this work, we are looking for a compact and complete description of the set of possibly optimal solutions, along with their objective function values, over the set of scenarios or an approximation with a performance guarantee. First, to better understand the characteristics of the studied problem, we consider two single-objective problems: parallel machine scheduling problem under uncertainty with the total completion time and makespan criterion, respectively. For the problem with the total completion time criterion, we demonstrate that the set of possibly optimal schedules can be found in polynomial time. In contrast, for the problem with the makespan criterion, we provide a (1+ϵ)-approximation algorithm. For the bi-objective problem, we provide a 2-approximation algorithm for any number of parallel machines and a (1+ϵ)-approximation algorithm where a fixed number of parallel machines is considered.

Simulation-based emergency department staffing and scheduling optimization considering part-time work shifts

Emergency department (ED) physicians have long been in short supply, which causes serious overcrowding and the excessive waiting of patients in many countries. ED managers are under great pressure to make staffing and scheduling decisions. To address this problem, this paper introduces part-time work shifts with fixed starting times and durations in peak hours to increase the flexibility and reduce patients’ waiting times. Then, a two-stage framework is proposed to optimize the weekly staffing and scheduling decisions with both fixed and part-time work shifts. Stage I is a weekly staffing problem to determine the number of physicians for both types of work shifts. The weekly staffing problem is decomposed and then solved using a simulation optimization method. Specifically, an adaptive partitioning empirical stochastic branch and bound (ESB&B-AP) algorithm is proposed by employing adaptive cut-generation methods in the process of feasible region partitioning, which significantly improves the searching efficiency of the algorithm. Stage II is a scheduling problem to determine the work schedules of physicians based on a predetermined set of work patterns. Numerical experiments validate the advantages of part-time work shifts, as well as the effectiveness of the two-stage optimization framework and the ESB&B-AP algorithm.

Dynamic scheduling of hybrid flow shop problem with uncertain process time and flexible maintenance using NeuroEvolution of Augmenting Topologies

AbstractA hybrid flow shop is pivotal in modern manufacturing systems, where various emergencies and disturbances occur within the smart manufacturing context. Efficiently solving the dynamic hybrid flow shop scheduling problem (HFSP), characterised by dynamic release times, uncertain job processing times, and flexible machine maintenance has become a significant research focus. A NeuroEvolution of Augmenting Topologies (NEAT) algorithm is proposed to minimise the maximum completion time. To improve the NEAT algorithm's efficiency and effectiveness, several features were integrated: a multi‐agent system with autonomous interaction and centralised training to develop the parallel machine scheduling policy, a maintenance‐related scheduling action for optimal maintenance decision learning, and a proactive scheduling action to avoid waiting for jobs at decision moments, thereby exploring a broader solution space. The performance of the trained NEAT model was experimentally compared with the Deep Q‐Network (DQN) and five classical priority dispatching rules (PDRs) across various problem scales. The results show that the NEAT algorithm achieves better solutions and responds more quickly to dynamic changes than DQN and PDRs. Furthermore, generalisation test results demonstrate NEAT's rapid problem‐solving ability on test instances different from the training set.

Mathematical optimization strategy for online scheduling of complex manufacturing systems based on thermal energy optimization and fuzzy mathematical model

With the rapid development of the manufacturing industry and the advancement of the intelligent process, the scheduling problem of complex manufacturing systems becomes more and more complicated, especially in the aspect of energy management and optimization. This study aims to propose an online scheduling mathematical optimization strategy based on thermal energy optimization and fuzzy mathematical model, so as to improve the scheduling efficiency and resource allocation rationality of complex manufacturing systems under different production conditions. A scheduling model considering thermal energy utilization rate, production priority and real-time demand is established by using fuzzy mathematics. The model deals with the uncertain factors by fuzzy logic and solves them by genetic algorithm to realize the dynamic adjustment and optimal scheduling of production resources. Through the experimental verification of a complex manufacturing system, the improvement of scheduling efficiency not only reduces the operating cost, but also improves the flexibility and response speed of the system. The fuzzy mathematical model based on thermal energy optimization provides an effective on-line scheduling strategy for complex manufacturing systems, which can realize efficient scheduling and energy management in dynamic environment.

A Multi-Objective Hybrid Algorithm for the Casting Scheduling Problem with Unrelated Batch Processing Machine

A Multi-Objective Hybrid Algorithm for the Casting Scheduling Problem with Unrelated Batch Processing Machine

Machine Learning based Algorithm Selection and Genetic Algorithms for serial-batch scheduling

Whenever combinatorial optimization problems cannot be solved by exact solution methods in reasonable time, tailor-made algorithms (heuristics, meta-heuristics) are developed. Often, these heuristics exploit structural properties and perform well on selected subsets of the problem space. For example, this is how the two best-known construction heuristics solve the scheduling problem investigated in this study (i.e., the scheduling of parallel serial-batch processing machines with incompatible job families, restricted batch capacities, arbitrary batch capacity demands, and sequence-dependent setup times). However, when the properties change, the performance of one algorithm might decrease, and another algorithm might have been the better choice. To resolve this issue, we propose using Machine Learning to exploit the strengths of different algorithms and to select the probably best-performing algorithm for each problem instance individually. To that, we investigate a variety of methods from the “learning-to-rank” literature and propose several adaptations. Furthermore, because there is no algorithm for the considered scheduling problem that is capable to explore the entire solution space, we developed two Genetic Algorithms for the improvement of initial solutions computed by the selected algorithms. Here, we put special emphasis on ensuring that the solution representation (encoding) reflects the entire solution space and that the operators (e.g., for recombination and mutation) are appropriate to explore and exploit this space completely. Our computational experiments show an average increase of 39.19% in solution quality.

A multi-objective genetic algorithm based on two-stage reinforcement learning for green flexible shop scheduling problem considering machine speed

The consumption of energy and resources in the manufacturing industry has garnered significant attention due to the increasingly severe environmental issues. Green shop scheduling research is focused on optimizing economic and environmental indicators within the current manufacturing model. This paper specifically addresses the flexibility of job-shop scheduling problem considering machine speed (CMS-FJSP), as different machine speeds during the production process can impact energy and resource consumption. The objectives of this study include minimizing the makespan, total energy consumption, and tool wear. To tackle this problem, a multi-objective genetic algorithm that incorporates a two-stage reinforcement learning approach is proposed. In light of the characteristics of the problem, a three-layer encoding approach is suggested, which encompasses machine allocation, operation sequencing, and machine speed selection. Additionally, a decoding method that integrates energy-saving strategies is proposed to enhance the optimization process. To improve the quality of the population, three distinct initialization methods have been developed. Furthermore, a parameter adjustment strategy informed by two-stage reinforcement learning is introduced. This strategy incorporates a state set and action set tailored to the unique characteristics of two-stage reinforcement learning, alongside corresponding reward mechanisms. In 30 test cases, the proposed algorithm demonstrates superior uniformity and convergence compared to five classical algorithms. In a practical case within a hydraulic component production workshop conducted at a hydraulic component company, the proposed algorithm generates 26 scheduling schemes with different focuses, achieving a 14.39% reduction in makespan, a 2.13% decrease in energy consumption, and a 10.65% reduction in tool wear.

A multi-objective dynamical artificial bee colony for energy-efficient fuzzy hybrid flow shop scheduling with batch processing machines

Energy-efficient hybrid flow shop scheduling problem (EHFSP) with batch processing machines (BPMs) is rarely considered, let alone EHFSP with BPMs and uncertainty. In this study, an energy-efficient fuzzy hybrid flow shop scheduling problem (EFHFSP) with BPMs at a middle stage and no precedence between some stages is solved, and a multi-objective dynamical artificial bee colony algorithm (MODABC) is presented to simultaneously minimize fuzzy makespan and total fuzzy energy consumption. To produce high quality solutions, a swarm decision is used to dynamically determine the employed bee swarm and onlooker bee swarm, a dynamical employed bee phase is implemented, and an onlooker bee phase with adaptive communication is given. The diversity reinforcement strategy and an adaptive scout phase are also adopted. Extensive experiments are conducted, and the optimal combination of key parameters for the proposed algorithm is determined by the Taguchi method. The computational results demonstrate that the new strategies of MODABC are effective, and MODABC is very competitive in solving the considered EFHFSP.

Multi-stage hybrid flow shop scheduling problem with lag, unloading, and transportation times

Multi-stage hybrid flow shop scheduling problem with lag, unloading, and transportation times

New heuristics for the 2-stage assembly scheduling problem with total earliness and tardiness minimisation: A computational evaluation

Traditionally, scheduling literature has focused mainly on solving problems related to processing jobs with non-assembly operations. Despite the growing interest in the assembly literature in recent years, knowledge of the problem is still in its early stages in many aspects. In this regard, we are not aware of any previous contributions that address the assembly scheduling problem with just-in-time objectives. To fill this gap, this paper studies the 2-stage assembly scheduling problem minimising the sum of total earliness and total tardiness. We first analyse the relationship between the decision problem and the generation of the due dates of the jobs, and identify the equivalences with different related decision problems depending on the instances. The properties and conclusions obtained in the analysis are applied to design two constructive heuristics and a composite heuristic. To evaluate our proposals, different heuristics from the state-of-the-art of related scheduling problems are adapted, and a computational evaluation is carried out. The excellent behaviour of the proposed algorithms is demonstrated by an extensive computational evaluation.

Deep reinforcement learning assisted memetic scheduling of drones for railway catenary deicing

Icy rainfall and snowfall in 2024 Spring Festival struck the high-speed railway catenary systems and caused serious traffic disruptions in central and eastern China. Deicing drones are an effective method in response to these freezing events due to their fast speed and high environmental tolerance. However, the large disaster-affected area and the large scale and complexity of catenary networks make deicing drone scheduling a very difficult problem. In this paper, we formulate two versions of deicing drone scheduling problem, one for single drone scheduling and the other for multiple drone scheduling. Unlike most existing vehicle/drone routing problems, our problem aims to minimize the total negative effect caused by the freezing events on train operations, which reflects the prime concern of the decision-maker and is highly complex. To efficiently solve the problem, we propose a reinforcement learning assisted memetic optimization algorithm, which integrates global mutation and a set of neighborhood search operators adaptively selected by deep reinforcement learning. Computational results on real-world problem instances demonstrate its significant performance advantages over selected popular optimization algorithms in the literature.

Integrated two-stage multi-factory assembly scheduling with maintenance considerations

ABSTRACT In the dynamic landscape of contemporary industry, integrating maintenance practices with production scheduling is essential for sustaining operational efficiency and competitiveness. This study addresses a two-stage multi-factory assembly scheduling problem, introducing an innovative approach that incorporates maintenance practices to enhance system reliability in the face of unexpected machine failures. For deterministic scheduling, a tailored mixed-integer programming model is presented to minimise the makespan. This model is extended to formulate a stochastic schedule, accommodating unforeseen machine breakdowns through stochastic distributions. The extension includes the integration of preventive and corrective maintenance activities into an integrated two-stage multi-factory assembly scheduling problem. To solve the resulting optimisation problem, a decomposition algorithm utilising an exact solver is proposed. This approach breaks down the main model into smaller models, addressing computational challenges. Comparative analyses against the widely adopted CPLEX software across various instances validate the effectiveness of our approach. A significant finding from this comparison is that our decomposition algorithm outperforms the exact solver, achieving the optimal solution at a faster rate. In sensitivity analyses, the results underscore the superior solution-finding capability of our integrated stochastic model compared to maintenance heuristics from existing literature.

Enhancing airline connectivity: An optimisation approach for flight scheduling in multi-hub networks with bank structures

While one salient characteristic of hub airports lies in connecting passengers, the full-service airlines in North America concentrate their networks spatially over a number of hubs. Having witnessed the emerging multi-hub network, this paper investigated the flight scheduling problem under a multi-hub configuration, taking a well-defined bank structure and airport operational restrictions into account. An integrated non-convex Mixed-Integer Nonlinear Programming (MINLP) approach was proposed to enhance airline connectivity, considering different combinations of traffic flow direction and connecting times. To verify the scalability and effectiveness of the proposed model, a comprehensive case study has been undertaken with real-world scheduling data from Air China, which was solved by a novel problem-specific Selective Simulated Annealing (SSA) algorithm. Substantial improvements were achieved without sacrificing the scheduling efficiency. Precisely, the programme adjusted the flights during a typical operational day in a timely manner. The post-optimisation outcomes have witnessed its effectiveness with a 17.97%, 17.06%, 22.41% and 53.86% increase in airline connectivity at its four major hub airports (Chengdu Shangliu, Beijing Capital, Shanghai Pudong and Hongqiao) in China, respectively. A clear pattern of the bank structure also confirms its positive impact on airline connectivity under the multi-hub network configuration. Lastly, a comparative analysis for the distribution of all feasible connections further highlights the critical challenge concerning the role of the hubs in a multi-hub network. More specifically, Air China’s multi-hub network systematically performs better on Domestic-International routes, due to flight schedule, frequencies, geographical placements and detours. Among the four hub airports, Beijing Capital International Airport stands out as a dominant one, which implies its potential to serve as a robust international hub airport.

Large-scale hydropower dispatching system based on cloud platform and its key technologies

In the past decade, the rapid expansion of hydropower capacity in China brings challenges to hydropower dispatching in data management and operation scheduling. In data management, the scale of hydropower operation data increases explosively, presenting typical big data features. In operation scheduling, the optimization of hydropower system operations is a high-dimension, nonconvex, and nonlinear problem. Conventional optimization methods encounter the “dimensionality disaster”, and cannot solve the scheduling problem efficiently. To deal with these challenges, by analyzing the data characteristics and operation scheduling requirements, this paper develops a large-scale hydropower dispatching system based on the cloud platform. The dispatching system consists of four layers: data access layer, cloud platform layer, data sharing layer, and application layer, which has good scalability and flexibility in data management and operation scheduling. In the application layer, key technologies based on the big data and cloud computing resources of the dispatching system are proposed to carry out the optimal operation of hydropower systems, including distributed parallel dynamic programming (DPDP) for long-/medium-term scheduling and data mining-based method (DMM) for short-term scheduling. Finally, the dispatching system is applied to the operation of hydropower systems in southwest China. Results indicate that: 1) The developed dispatching system is capable of processing 18 million data records per day, with a peak processing speed of 10,000 data requests per second, fulfilling the requirements for hydropower dispatching. 2) In long-term generation scheduling, under varying levels of runoff and plant scales, DPDP has demonstrated a remarkable reduction in computing time compared to dynamic programming, obtaining the same optimal solution with over 90 % less computational time. 3) In short-term peak shaving operation, on typical dry and wet days, the computing time of DMM is 7.2 s and 7.5 s, respectively, far less than the time of mixed-integer linear programming, and the maximum residual load obtained by DMM is lower than historical observations, indicating its effectiveness.

Flexible assembly job shop scheduling problem considering reconfigurable machine: A cooperative co-evolutionary matheuristic algorithm

With popularity of mass customization, enterprises urgently need to improve reconfigurability to handle rapidly changing market demands. Reconfigurable machines have been widely applied in the flexible assembly job shop. These reconfigurable machines can be equipped with various and limited auxiliary modules (AMs) to provide multiple alternative functions to manufacture numerous products. Therefore, this study addresses flexible assembly job shop scheduling problem considering reconfigurable machines with limited AMs to minimize makespan. First, a mixed-integer linear programming (MILP) model is formulated to define the problem. Then, a cooperative co-evolutionary matheuristic algorithm (CCMA) is presented to efficiently tackle large-scale FAJSP-RM problem. In this algorithm, a MILP-based evolution method, which relies on a decomposed MILP (D-MILP) with known sequence decisions, is proposed to explore the optimal machine and AM assignments. Meanwhile, a collaborative initialization and dual collaborative strategy are proposed to improve the performance of the proposed CCMA. Comprehensive experiments are conducted on 720 instances, extended from the well-known Fdata and BRdata benchmarks, to evaluate the proposed MILP model and CCMA algorithm. The results illustrate that the MILP model can produce optimal solutions for small-scale instances. The MILP-based evolution method improves the performance of the CCMA algorithm by 12.63, and the CCMA outperforms other well-known algorithms from numerical, statistical, differential and stable analysis.

Multi-guided population co-evolutionary algorithm based on multiple similarity decomposition for large-scale flexible job shop scheduling problem

As manufacturing shifts towards large-scale production, the size of the workshop increases, and its search space exponentially expands. It is difficult for existing algorithms to obtain an ideal scheduling solution in an acceptable time. For the large-scale flexible job shop scheduling problem (LSFJSP), a multi-guided population co-evolutionary algorithm based on multiple similarity decomposition (MPCSD) is designed. Faced with the problem of high dimensionality and complex solution space, a multiple similarity decomposition strategy is proposed. It proceeds to group based on similarity information at the dimension and population level. To obtain convergence-preferred and diversity-preferred dimension groupings, a training-set solution selection method is proposed. Inspired by the idea of divide-and-conquer, a multi-guided co-evolutionary strategy is proposed. It improves the exploration efficiency of the algorithm in the search space. To test effectiveness on more complex LSFJSP, a set of large-scale test problems including LS1-12 are designed. On LS1-12, MPCSD is compared with seven other algorithms to demonstrate its superiority. MPCSD performed best on 11, 7, and 10 of the 12 test problems on Inverted Generational Distance (IGD), Hypervolume (HV) and Schott’s Spacing Metric (SP), respectively. Meanwhile, the Relative Deviation (RD) results showed that MPCSD obtained the best fitness performance.