Mathematical Model For Scheduling Research Articles

Mathematical scheduling model of complex industrial process combining swarm intelligence algorithm and swarm dimension reduction technology

The swarm intelligence algorithm is widely used in scheduling problems due to its superior searchability and adaptability, but it faces high computational costs and low efficiency when dealing with high-dimensional complex data. To enhance the handling of large-scale and intricate data, as well as enhance the accuracy and efficiency of scheduling, this study develops a mathematical model for industrial scheduling. The model is based on swarm intelligence algorithms such as symbiotic evolution algorithms, grey wolf algorithms, cuckoo algorithms, population dimensionality reduction techniques, and resource optimal allocation calculation methods. The final test results showed that the accuracy of the model in calculating the objective function was about 80 % in cases of high complexity and about 90 % in cases of low complexity. Compared with other algorithms, its accuracy was improved by 7 %, error rate was reduced by 50 %, time cost was reduced by about 30 %, and conversion rate was fast and more stable on average after 200 generations. The experimental results indicate that the proposed mathematical scheduling model, which integrates multiple intelligent algorithms and population dimensionality reduction technologies, has certain practices and feasibility in large-scale and multi-dimensional production for enterprises. This study combines swarm intelligence algorithms with population dimensionality reduction techniques, which is an innovative attempt at complex industrial scheduling problems.

A Deep Neural Network-Based Optimal Scheduling Decision-Making Method for Microgrids

With the rapid growth in the proportion of renewable energy access and the structural complexity of distributed energy systems, traditional microgrid (MG) scheduling methods that rely on mathematical optimization models and expert experience are facing significant challenges. Therefore, it is essential to present a novel scheduling technique with high intelligence and fast decision-making capacity to realize MGs’ automatic operation and regulation. This paper proposes an optimal scheduling decision-making method for MGs based on deep neural networks (DNN). Firstly, a typical mathematical scheduling model used for MG operation is introduced, and the limitations of current methods are analyzed. Then, a two-stage optimal scheduling framework comprising day-ahead and intra-day stages is presented. The day-ahead part is solved by mixed integer linear programming (MILP), and the intra-day part uses a convolutional neural network (CNN)—bidirectional long short-term memory (Bi LSTM) for high-speed rolling decision making, with the outputs adjusted by a power correction balance algorithm. Finally, the validity of the model and algorithm of this paper are verified by arithmetic case analysis.

A Mathematical Model for Scheduling and Assignment of Customers in Hospital Waste Collection Routes

The collection, transport, and final disposal of hospital waste may cause contamination and disease if improperly handled. Therefore, such residues are hazardous to the health of waste collectors. These wastes are generated by public agencies, such as hospitals, family health centers, dialysis centers, and private healthcare providers. In this study, a mixed-integer linear programming model is proposed for monthly customer scheduling and route assignment. The proposed approach was fulfilled according to customers’ collection frequency, truck capacity, and customer geographical location. The proposed mathematical model successfully balanced the number of customers and the workload during each day. The effectiveness of the proposed model was tested on data obtained from a waste collection company. The model has been implemented in AMPL language, and the performance of commercial solvers, GUROBI and CPLEX, to obtain an optimal solution were tested. The results show the efficiency of the proposed approach to balance the workload concerning previous scheduling is done ad hoc at the company. The use of the formulated model provides an automatic procedure that was previously performed manually. The methodology can be adapted to other companies with similar requirements.

A mathematical model for scheduling of transportation, routing, and cross-docking in the reverse logistics network of the green supply chain

Cross-docking refers to the practices of unloading materials from inbound vehicles and then loading them directly into outbound ones. Removing or minimizing warehousing costs, space requirements, as well as inventory utilization, cross-docking simplifies supply chains and makes them deliver goods to markets in a faster and more efficient manner. Accordingly, a mixed-integer linear programming ($MILP $) model is developed in the present study to schedule transportation routing and cross-docking in a reverse logistics network ($RLN$). Furthermore, different traffic modes are also considered to reduce fuel consumption, which reduces emissions and pollution. The proposed model is a multi-product, multi-stage, and non-deterministic polynomial-time that is an NP-hard problem. We use the non-dominated sorting genetic algorithm II ($NSGA-II$) to solve the model. A numerical example has been solved to illustrate the efficiency of the method.

Impact of the Learning-Forgetting Effect on Mixed-Model Production Line Sequencing

In this study, the learning-forgetting (L-F) effect is considered in a mixed-model sequencing problem to investigate its impact on makespan minimization. To this end, mathematical models of the learning and forgetting effects are modified in accordance with a mixed-model production environment, and the L-F functions for a serial workstation and multiple products are established. Subsequently, their impact on production is demonstrated via data experiments. The relationships between the learning effect, forgetting effect, product model combination, and makespan are also discussed based on the experimental results. The results show that the learning and forgetting functions can significantly affect the work time in the mathematical scheduling model and that a balanced product model combination and small MPS (minimum part set) batch can help to reduce the L-F effect.

Mathematical model for scheduling food production in hospital catering

The problem addressed in this paper was motivated by a real optimization problem of supply chain of the hospital center of Troyes (HCT). The HCT is currently seeking to review and improve its logistics processes. The implementation of techniques and methods of operational research must provide solutions to improve the efficiency of logistics activities. In this work, the studied problem focuses on the catering component of the hospital logistics. A novel mathematical model for the production scheduling of multi-products and multi-stages food processes in hospital catering is proposed. This mathematical model has been implemented in commercial solver CPLEX and it has been tested on real instances of HCT and from the literature. The implementation results of the mathematical model proposed have proved its efficiency for the scheduling of the food production process.

An internet-of-things-based production logistics optimisation method for discrete manufacturing

ABSTRACTTimely supply of production material is an important prerequisite for stable operation of discrete manufacturing systems. The difficulties of production logistics (PL) planning are increased due to the uncertainty and dynamicity in production environment. The Internet of things (IoT) provides a reliable solution for monitoring dynamic manufacturing process and obtaining real-time information. Under the uncertain manufacturing environment, this paper focusses on a PL optimisation method driven by real-time data. First, considering the uncertainty of material demands time caused by production fluctuation, the mathematical scheduling model with fuzzy time windows is established to minimise the distribution cost. Later, on the basis of the proposed two-stage operation and optimisation mechanism, an improved ant colony algorithm is designed, which introduces the factors of satisfaction degree and time windows width into state transfer rules and improves the dynamic adjustment strategy of pheromone. Finally, in a machining workshop, a case study is conducted based on the construction of real-time sensing and positioning manufacturing environment. Several numerical experiments are performed to verify the feasibility of the proposed method.

Dataflow management, dynamic load balancing, and concurrent processing for real‐time embedded vision applications using Quasar

SummaryProgramming modern embedded vision systems brings various challenges, due to the steep learning curve for programmers and the different characteristics of the devices. Quasar, a new high‐level programming language and development environment, considerably simplifies the development. Quasar has a compiler that detects and optimizes parallel programming patterns and a heterogeneous runtime that distributes the computational load over the available compute devices (CPUs and Graphical Processing Unit [GPUs]). In this paper, we focus on runtime aspects of Quasar. We show that with good approximation, the execution time of a GPU kernel function can be factorized in a compile‐time‐specific component and a runtime‐specific component. We show that this approximation leads to a computationally simple runtime load balancing rule. Moreover, the load balancing rule permits efficient implicit concurrency of kernel functions and automatic scaling to multiple compute devices (eg, multi‐CPU/GPU systems). Based on an appropriate mathematical scheduling model, we investigate the command queue size trade‐off between memory usage and device utilization. The result is a programming environment for embedded vision systems for which automatic parallelization and implicit concurrency detection allow scaling the program efficiently to multi‐CPU/GPU systems. Finally, benchmark results are provided to demonstrate the performance of our approach compared with OpenACC and CUDA (Compute Unified Device Architecture).

Exact and Heuristic Methods for Observing Task-Oriented Satellite Cluster Agent Team Formation

With the development of aerospace science and technology, Earth Observation Satellite cluster which consists of heterogeneous satellites with many kinds of payloads appears gradually. Compared with the traditional satellite systems, satellite cluster has some particular characteristics, such as large-scale, heterogeneous satellite platforms, various payloads, and the capacity of performing all the observation tasks. How to select a subset from satellite cluster to perform all observation tasks effectively with low cost is a new challenge arousing in the field of aerospace resource scheduling. This is the agent team formation problem for observation task-oriented satellite cluster. A mathematical scheduling model is built. Three novel algorithms, i.e., complete search algorithm, heuristic search algorithm, and swarm intelligence optimization algorithm, are proposed to solve the problem in different scales. Finally, some experiments are conducted to validate the effectiveness and practicability of our algorithms.

Proposing a new mathematical model and a meta-heuristic algorithm for scheduling and allocating automated guided vehicle

One of the substantial things, which has been perceived more than ever by captains of industry in recent years, is the necessity of earning competitive value. As a result, mechanisation and enhancing the level of automation of the process has become one of the most fascinating issues to researchers. In this regard one of the most appealing systems to industries is flexible manufacturing systems which contribute to achievement of higher levels of automation in business environments. Since transportation plays an essential role in flexible production systems, automated guided vehicles (AVGs) have been utilised to carry material in these systems in order to maintain the flexibility, and increase the efficiency of production and distribution throughout the system. In this paper, a mathematical model for scheduling and allocating AVGs in the manufacturing process of a specific project is proposed and in the end, a heuristic algorithm is proposed and used to solve the model problem.

Proposing a new mathematical model and a meta-heuristic algorithm for scheduling and allocating automated guided vehicle

One of the substantial things, which has been perceived more than ever by captains of industry in recent years, is the necessity of earning competitive value. As a result, mechanisation and enhancing the level of automation of the process has become one of the most fascinating issues to researchers. In this regard one of the most appealing systems to industries is flexible manufacturing systems which contribute to achievement of higher levels of automation in business environments. Since transportation plays an essential role in flexible production systems, automated guided vehicles (AVGs) have been utilised to carry material in these systems in order to maintain the flexibility, and increase the efficiency of production and distribution throughout the system. In this paper, a mathematical model for scheduling and allocating AVGs in the manufacturing process of a specific project is proposed and in the end, a heuristic algorithm is proposed and used to solve the model problem.

A mathematical model for scheduling of production process and allocation of an automatic guided vehicle in a flexible manufacturing system

A mathematical model for scheduling of production process and allocation of an automatic guided vehicle in a flexible manufacturing system

A mathematical model for scheduling of production process and allocation of an automatic guided vehicle in a flexible manufacturing system

Given that material handling in manufacturing systems is very important, many organisations use automatic guided vehicle (AGV). In recent years, many organisations have intended to have access to an optimal scheduling plan for their manufacturing and transportation system. For this reason, a mathematical model is proposed in this study for scheduling of the production process and AGV's allocation. Production time in any process, setup time, loaded/unloaded trip duration, parking spaces, and the discharge time and loading of products at each workstation are considered in the proposed model. Finally, a numerical example is used to explore the proposed model and it will be solved using GAMS software.

A novel mathematical model and multi-objective method for the low-carbon flexible job shop scheduling problem

Most conventional scheduling problems use production efficiency, cost and quality as their preeminent optimization objectives. However, because of increasing costs of energy and environmental pollution, “low-carbon scheduling” as a novel scheduling model has received increasing attention from scholars and engineers. This scheduling model focuses on reducing energy consumption and environmental pollution at the workshop level. In this paper, a new low-carbon mathematical scheduling model is proposed for the flexible job-shop environment that optimizes productivity, energy efficiency and noise reduction. In this model, the machining spindle speed — which affects production time, power and noise — is flexible and is treated as an independent decision-making variable. The methods of evaluation of productivity, energy consumption and noise are presented. A multi-objective genetic algorithm based on a simplex lattice design is proposed to solve this mixed-integer programming model effectively. The corresponding encoding/decoding method, fitness function, and crossover/mutation operators are designed specifically for the features of this problem. Three example problem instances with different scales and one Engineering case study illustrate and evaluate the performance of this method. The results demonstrate the effectiveness of the proposed model and method for the low-carbon job shop scheduling problem.

Developing a Mathematical Model for Scheduling and Determining Success Probability of Research Projects Considering Complex-Fuzzy Networks

In project management context, time management is one of the most important factors affecting project success. This paper proposes a new method to solve research project scheduling problems (RPSP) containing Fuzzy Graphical Evaluation and Review Technique (FGERT) networks. Through the deliverables of this method, a proper estimation of project completion time (PCT) and success probability can be achieved. So algorithms were developed to cover all features of the problem based on three main parameters “duration, occurrence probability, and success probability.” These developed algorithms were known as PR-FGERT (Parallel and Reversible-Fuzzy GERT networks). The main provided framework includes simplifying the network of project and taking regular steps to determine PCT and success probability. Simplifications include (1) equivalent making of parallel and series branches in fuzzy network considering the concepts of probabilistic nodes, (2) equivalent making of delay or reversible-to-itself branches and impact of changing the parameters of time and probability based on removing related branches, (3) equivalent making of simple and complex loops, and (4) an algorithm that was provided to resolve no-loop fuzzy network, after equivalent making. Finally, the performance of models was compared with existing methods. The results showed proper and real performance of models in comparison with existing methods.

Study on Shuttle Scheduling Problem in Automated Container Terminal

Owing to the shuttle in Mixed Operation Mode of Shuttle-based automated container terminal handles loading, unloading, congregation and delivery operations .simultaneously, conventional scheduling method cannot be applied. Accordingly, this paper proposed a mathematical scheduling model. The objective is to minimize shuttle operation time and deal with loading and unloading with priority while avoiding unbearable waiting time for congregation and delivery tasks. Due to the complexity of this model, a Genetic Algorithm (GA) is designed for effective solutions. Numerical experiment is conducted to examine the key factors of the problem and the performance of the proposed GA.

A mathematical model for scheduling of real-world tree-structured multi-product pipeline system

In this paper, a mathematical model to petroleum derivatives transportation scheduling is developed. The problem discussed in this paper is concerned with the scheduling of one-source tree-structured pipeline connected to several output terminals. A tree-structured pipeline is composed of a mainline conveying high-volume of petroleum products over long ways and secondary lines transporting smaller volumes over shorter distances. In such a pipeline, batches of petroleum products are pumped back-to-back at the origin of the mainline, without any separation device between them. This paper introduces a continuous mathematical representation, mixed integer linear programming, for the operational planning of tree-structured pipeline systems. Previous contributions on tree-structured pipeline planning deal with the sequence deliveries at receiving terminals, i.e., at any time only a unique terminal receives material from the pipeline. On the contrary, the proposed approach permits a receiving terminal on the mainline to simultaneously receive products when one of the secondary lines is taking material from the mainline. The problem’s aim is to find the optimal sequences of product injection and dispatching operations that satisfy product demands at minimum total cost, accounting for pumping and backordered demand costs during the specified planning horizon. The approach has been validated by solving three case studies of growing complexity.

Emergency Scheduling Model of Urban Rail Transit Based on Genetic Algorithm

Urban rail transit plays an important role in daily life and optimal emergency scheduling determines social and economic benefits. To solve emergency scheduling problem of urban rail transit, a mathematical scheduling model is proposed in this paper. Based on the characteristic of urban rail transit, this scheduling model considers the benefits of both passengers and rail transit operator. Furthermore, on the basis of the model, three sorts of emergencies, such as closure of stations, outage of metro lines and surge of passenger flow are described and formulated, thus, model is solved through several GA operations. The testing results show that the model can accurately reflect the change of rail transit network during emergencies and quickly provide an effective emergency scheduling scheme.

Research of Vehicle Scheduling with Time Window Based on Genetic Algorithm

This paper based on the genetic algorithm,introduced part search process and respectively established the mathematical scheduling model of full loads vehicle optimal scheduling with soft time windows and of non-full loads on the basis of the long distance logistics transportation situation of some companys distribution center in Shenzhen. Then programmed to achieve the scheduling of multi-vehicle touting and selection, and conducted example analysis.

Scheduling Energy Cogeneration Units under Energy Demand Uncertainty

This work presents a methodology for the scheduling of networks that consist of various energy cogeneration units (i.e., generate both electrical energy and heat) under high energy demand uncertainties of bounded form. First, a mathematical framework for the problem in question is developed, and then we present a reactive scheduling approach that relays on multiparametric programming and a receding horizon. In brief, the original mathematical scheduling model is reformulated into a multiparametric programming problem, wherein we consider as uncertain parameters: the energy demands as well as the initial and the final state of the overall system. The resulting parametric optimization problem is solved once and off-line, and afterwards a receding horizon-like approach is applied for the reactive scheduling –that acts on the fly in the energy demand realizations– by performing just function evaluations and avoiding the on-line optimization of such systems. A couple of problem instances are solved to shed light on the potential benefits of the suggested method. The proposed concept has highly practical interest and is very promising since could find application in several other optimization problems that can involve: large-scale optimization problems and process scheduling problems under uncertainty.