Production Scheduling Problems Research Articles

Two meta-heuristic algorithms for optimizing a multi-objective supply chain scheduling problem in an identical parallel machines environment

Optimizing the trade-off between crucial decisions has been a prominent issue to help decision-makers for synchronizing the production scheduling and distribution planning in supply chain management. In this article, a bi-objective integrated scheduling problem of production and distribution is addressed in a production environment with identical parallel machines. Besides, two objective functions are considered as measures for customer satisfaction and reduction of the manufacturer’s costs. The first objective is considered aiming at minimizing the total weighted tardiness and total operation time. The second objective is considered aiming at minimizing the total cost of the company’s reputational damage due to the number of tardy orders, total earliness penalty, and total batch delivery costs. First, a mathematical programming model is developed for the problem. Then, two well-known meta-heuristic algorithms are designed to spot near-optimal solutions since the problem is strongly NP-hard. A multi-objective particle swarm optimization (MOPSO) is designed using a mutation function, followed by a non-dominated sorting genetic algorithm (NSGA-II) with a one-point crossover operator and a heuristic mutation operator. The experiments on MOPSO and NSGA-II are carried out on small, medium, and large scale problems. Moreover, the performance of the two algorithms is compared according to some comparing criteria. The computational results reveal that the NSGA-II performs highly better than the MOPSO algorithm in small scale problems. In the case of medium and large scale problems, the efficiency of the MOPSO algorithm was significantly improved. Nevertheless, the NSGA-II performs robustly in the most important criteria.

Production scheduling problem of automobile mixed model assembly line

Nowadays, the mode of production has changed from mass production to multi variety and small batch production, and mixed model assembly line has emerged. Mixed model assembly is widely used in automobile enterprises. This paper summarizes the theory and method of automobile mixed model assembly line scheduling, analyzes its characteristics and difficulties, summarizes the related optimization objectives, and introduces the related algorithms, so as to make the scheduling problem of mixed model assembly line more clear.

Production optimization by using integer linear programming under a practical approach

This paper addresses the problem of production scheduling under a practical approach, which seeks to find out what would be the product mix to ensure the company to obtain the most useful, also requires that these combinations of products obtained from quickly and efficiently contributing thus to achieve lower costs associated with production. A specific mathematical model based on integer linear programming applied specifically to the product mix is presented, as well as the results obtained from the practical problem from the use of the model in integer linear programming, the use of the software and considering the own conditions of the problem addressed here.

Production scheduling problem and solver improvement via integration of the grey wolf optimizer into the augmented Lagrangian relaxation method

In open-pit mines, the long-term production scheduling problem is a mixed-integer programming optimization problem. Usually, it is tricky to reach the true optimal solution to the long-term production scheduling problem due to its complexity and dimensions. However, owing to its high-dimensional and combinatorial nature, the long-term production scheduling problem hinders the development of a precise mathematical optimization technique that can solve the whole problem for any real-size block model. In this paper, a hybrid model is introduced to solve the long-term production scheduling problem, taking into account grade uncertainty assisted by the augmented Lagrangian relaxation and the grey wolf optimizer methods. The hybrid augmented Lagrangian relaxation–the grey wolf optimizer technique is recommended to solve the long-term production scheduling problem to improve its performance and, consequently, speed up the convergence. The proposed model has been compared with the results of the hybrid methods gained from the classic Lagrangian relaxation and augmented Lagrangian relaxation methods integrated with the bat algorithm, particle swarm optimization, genetic algorithm, the traditional subgradient method, and conventional method without using the Lagrangian approach. The fallouts point out that better presentation is gained by the augmented Lagrangian relaxation–the grey wolf optimizer method in terms of net present value, average ore grade, and CPU time. Moreover, the cumulative net present value by the proposed model is 13.39% more than the conventional method.

A Hybrid Genetic Algorithm for Integrated Production and Distribution Scheduling Problem with Outsourcing Allowed

In this paper, we studied a new integrated production scheduling, vehicle routing, inventory and outsourcing problem. The production phase considers parallel machine scheduling including setup times with outsourcing allowed and the distribution phase considered batch delivery by a fleet of homogenous vehicles with respect to holding cost of completed jobs. The objective of the Mixed Integer Linear Programming (MILP) formulated model is to minimize the total costs including production, outsourcing, holding, tardiness and distribution fixed and variable costs. Due to the nondeterministic polynomial time (Np)-hardness of the problem, we derive a number of dominance properties for the optimal solution and combine them with a Genetic Algorithm (GA) to solve the problem. To assess the efficiency and effectiveness of the proposed hybrid algorithm, we conduct the computational study on randomly generated instances. Sensitivity analyses showed the impacts of the parameters on the objective function were incorporated. In order to evaluate the significance of the differences among the results obtained by GA and GADP one-tailed paired t tests were performed and interval plots were depicted.

A novel multi-objective optimization algorithm for the integrated scheduling of flexible job shops considering preventive maintenance activities and transportation processes

Most production scheduling problems, including standard flexible job shop scheduling problems, assume that machines are continuously available. However, in most cases, due to preventive maintenance activities, machines may not be available for a certain time. Meanwhile, in the entire workshop production process, the transportation process of workpieces cannot be ignored. Therefore, the impact of transportation on the production planning should be considered in the scheduling process. To consider both preventive maintenance and transportation processes in the flexible job shop scheduling problem, this paper proposes a flexible job shop scheduling problem considering preventive maintenance activities and transportation processes and establishes a multi-objective flexible job shop scheduling model optimizing the total energy consumption and total makespan. Furthermore, a multi-region division sampling strategy-based multi-objective optimization algorithm integrated with a genetic algorithm and a differential evolution algorithm (MDSS-MOGA-DE) is proposed to solve the model. In the proposed algorithm, a multi-region division sampling strategy and two evaluation functions are utilized to improve the diversity of solutions. In addition, this paper combines a genetic operation and a differential operation to further enhance the search ability of the algorithm. The validity of the algorithm is verified by a real case. The computational results reveal that the proposed model and algorithm obtain appropriate results and have the potential to be applied to other similar problems.

A hybrid multi-level optimisation framework for integrated production scheduling and vehicle routing with flexible departure time

This paper investigates an integrated scheduling problem of production and outbound distribution with flexible vehicle departure time in a time-sensitive make-to-order supply chain. We develop a hybrid multi-level optimisation framework by decomposing the problem into three sub-problems, including vehicle assignment, parallel machines scheduling and distribution scheduling. In this framework, we propose an efficient procedure to obtain the optimal vehicle departure time and utilise metaheuristics and heuristics to obtain the values of other decision variables. Results from extensive numerical experiments indicate that the proposed framework can solve small-scale instances optimally, and for large-scale instances it also shows the better performance than the compared genetic algorithm in terms of convergence and solution quality. Besides, the distribution cost can be reduced by setting flexible vehicle departure time.

Modified Migrating Birds Optimization for Solving the Low-carbon Scheduling Problem

Production scheduling problems have historically emphasized cycle time without involving the environmental factors. In the study, a low-carbon scheduling problem in a flexible job shop is considered to minimize the energy consumption, which mainly consists of two parts: the useful part and the wasted part. First, a mathematical model is built based on the features of the workshop. Second, a modified migrating bird's optimization (MMBO) is developed to obtain the optimal solution. In the MMBO, a population initialization scheme is designed to enhance the solution quality and convergence speed. Five types of neighborhood structures are introduced to create neighborhood solutions. Furthermore, a local search method and a reset mechanism are developed to improve the computational results. Finally, experimental results validate that the MMBO is effective and feasible.

An energy-aware scheduling algorithm under maximum power consumption constraints

This research investigates the production scheduling problems under maximum power consumption constraints. Probabilistic models are developed to model dispatching-dependent and stochastic machine energy consumption. A multi-objective scheduling algorithm called the energy-aware scheduling optimization method is proposed in this study to enhance both production and energy efficiency. The explicit consideration of the probabilistic energy consumption constraint and the following factors makes this work distinct from other existing studies in the literature: 1) dispatching-dependent energy consumption of machines, 2) stochastic energy consumption of machines, 3) parallel machines with different production rates and energy consumption pattern, and 4) maximum power consumption constraints. The proposed three-stage algorithm can quickly generate near-optimal solutions and outperforms other algorithms in terms of energy efficiency, makespan, and computation time. While minimizing the total energy consumption in the first and second stages, the proposed algorithm generates a detailed production schedule under the probabilistic constraint of peak energy consumption in the third stage. Numerical results show the superiority of the scheduling solution with regard to quality and computational time in real problems instances from manufacturing industry. While the scheduling solution is optimal in total energy consumption, the makespan is within 0.6 % of the optimal on average.

Crowdsource-enabled integrated production and transportation scheduling for smart city logistics

With city logistics becoming more and more important, increasing attention has been paid to the ‘last-mile delivery’ in urban areas. We investigate a novel crowdsource-enabled integrated production and transportation scheduling problem in the paper. The problem is first formulated into a mixed-integer linear program and its strong NP-hardness is proved. To better understand this complex problem, two sub-problems: a production and transportation scheduling problem and a crowdsourced bid selection problem are analysed. Based on problem properties, a Genetic Algorithm (GA) and a lower bound (LB) are developed to solve the original problem. Experimental results with up to 100 customers show that the GA outperforms the well-known commercial MIP solver CPLEX. Especially, (1) the GA can yield near-optimal solutions for all the tested instances with an average gap of 10.17% from the lower bound, while CPLEX provides feasible solutions only for instances with no more than 30 customers; (2) the average computation time of the GA is only 0.93% of that required by CPLEX; Besides, sensitivity analysis demonstrates advantages of introducing crowdsourced delivery into city logistics.

Improving performance of open-pit mine production scheduling problem under grade uncertainty by hybrid algorithms

One of the surface mining methods is open-pit mining, by which a pit is dug to extract ore or waste downwards from the earth’s surface. In the mining industry, one of the most significant difficulties is long-term production scheduling (LTPS) of the open-pit mines. Deterministic and uncertainty-based approaches are identified as the main strategies, which have been widely used to cope with this problem. Within the last few years, many researchers have highly considered a new computational type, which is less costly, i.e., meta-heuristic methods, so as to solve the mine design and production scheduling problem. Although the optimality of the final solution cannot be guaranteed, they are able to produce sufficiently good solutions with relatively less computational costs. In the present paper, two hybrid models between augmented Lagrangian relaxation (ALR) and a particle swarm optimization (PSO) and ALR and bat algorithm (BA) are suggested so that the LTPS problem is solved under the condition of grade uncertainty. It is suggested to carry out the ALR method on the LTPS problem to improve its performance and accelerate the convergence. Moreover, the Lagrangian coefficients are updated by using PSO and BA. The presented models have been compared with the outcomes of the ALR-genetic algorithm, the ALR-traditional sub-gradient method, and the conventional method without using the Lagrangian approach. The results indicated that the ALR is considered a more efficient approach which can solve a large-scale problem and make a valid solution. Hence, it is more effectual than the conventional method. Furthermore, the time and cost of computation are diminished by the proposed hybrid strategies. The CPU time using the ALR-BA method is about 7.4% higher than the ALR-PSO approach.

Color-Coating Scheduling With a Multiobjective Evolutionary Algorithm Based on Decomposition and Dynamic Local Search

The color-coated steel coil is a high value-added product for steel enterprises, and its production process is affected by multiple factors. How to provide operators with appropriate scheduling schemes is the key to improve the economic benefits of enterprises. In this article, for the scheduling of a single color-coating turn, we establish a multiobjective optimization model that minimizes the number of insertions of transition coils, the thickness jump penalty of adjacent coils, and the switching times of the backup rollers. To address this problem, we propose a piecewise coding approach to ensure that each individual meets the production constraints. Besides, a multiobjective evolutionary algorithm (MOEA) based on decomposition and dynamic local search (D-DLS) strategy is proposed (MOEA/D-DLS). More specifically, the color-coating multiobjective scheduling problem is decomposed into a series of single-objective subproblems and optimized simultaneously. Furthermore, based on the speed of evolution of these subproblems, local search is performed on partial subproblems dynamically. The proposed algorithm is used to solve eight multiobjective scheduling problem instances of color-coating with different scales, and the experimental results demonstrate that the proposed algorithm is very effective compared with four state-of-the-art algorithms. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Practical production scheduling problems in iron & steel industry generally need to optimize conflicting objectives simultaneously, which is very hard for practitioners to make appropriate decisions with manual experience. The decomposition-based multiobjective evolutionary algorithm (MOEA) can help practitioners of color-coating scheduling to achieve a set of Pareto optimal decisions with good distribution and tradeoff among three objectives. Since the scheduling of the other production lines shares many similarities with our problem, the proposed model and algorithm can also be applicable to these problems.

Production planning and scheduling problem of continuous parallel lines with demand uncertainty and different production capacities

Abstract Production planning and scheduling problems are highly interdependent as scheduling provides optimum allocation of resources and planning is an optimum utilization of these allocated resources to serve multiple customers. Researchers have solved production planning and scheduling problems by the sequential method. But, in this case, the solution obtained by the production planning problem may not be feasible for scheduling method. Hence, production planning and scheduling problems must be solved simultaneously. Therefore, in this work, a mathematical model is developed to integrate production planning and scheduling problems. The solution to this integrated planning and scheduling problem is attempted by using a discrete artificial bee colony (DABC) algorithm. To speed up the DABC algorithm, a k-means clustering algorithm is used in the initial population generation phase. This k-means clustering algorithm will help to converge the algorithm in lesser time. A real-life case study of a soap manufacturing industry is presented to demonstrate the effectiveness of the proposed approach. An objective function to minimize overall cost, which comprises the processing cost, material cost, utility cost, and changeover cost, is considered. The results obtained by using DABC algorithm are compared with those obtained by CPLEX software. There is a saving of ₹2 23 324 for weeks 1–4 in overall cost compared with the results obtained by using CPLEX software.

A Comprehensive Study of Several Meta-Heuristic Algorithms for Open-Pit Mine Production Scheduling Problem Considering Grade Uncertainty

It is significant to discover a global optimization in the problems dealing with large dimensional scales to increase the quality of decision-making in the mining operation. It has been broadly confirmed that the long-term production scheduling (LTPS) problem performs a main role in mining projects to develop the performance regarding the obtainability of constraints, while maximizing the whole profits of the project in a specific period. There is a requirement for improving the scheduling methodologies to get a good solution since the production scheduling problems are non-deterministic polynomial-time hard. The current paper introduces the hybrid models so as to solve the LTPS problem under the condition of grade uncertainty with the contribution of Lagrangian relaxation (LR), particle swarm optimization (PSO), firefly algorithm (FA), and bat algorithm (BA). In fact, the LTPS problem is solved under the condition of grade uncertainty. It is proposed to use the LR technique on the LTPS problem and develop its performance, speeding up the convergence. Furthermore, PSO, FA, and BA are projected to bring up-to-date the Lagrangian multipliers. The consequences of the case study specifies that the LR method is more influential than the traditional linearization method to clarify the large-scale problem and make an acceptable solution. The results obtained point out that a better presentation is gained by LR–FA in comparison with LR-PSO, LR-BA, LR-Genetic Algorithm (GA), and traditional methods in terms of the summation net present value. Moreover, the CPU time by the LR-FA method is approximately 16.2% upper than the other methods.

Bir Metal Fabrikası İçin İş Çizelgeleme Yazılımı Hazırlanması

In order to maintain continuity in today's competitive environment, companies provide products and services that are produced with higher quality and cheaper. Continuous production techniques and production systems technology production plant has become more complex and control of simple production activities has become more difficult. The production planning option is capable of planning and planning the production of the production, available, identified and required equipment, wherever and wherever we want. The production scheduling problem is to determine the order in which a certain number of jobs must be loaded on a certain number of machines. Different scheduling options to solve production scheduling problems. The common goal of all methods is to use all existing orders. The solution of these methods is done with Gantt diagrams. On this page a work scheduling package program has been implemented in a factory produces software, metal production. The program is C# language software and the program is Access. The aim of the program is to facilitate the scheduling process so that firms can examine the charts according to different methods, make the comparison, use the most accurate method.

Joint optimization of opportunistic maintenance and production scheduling considering batch production mode and varying operational conditions

The joint optimization of production scheduling and maintenance has been a hot topic. Most of the existing publications assume that the operational condition (OC) of a machine is constant during the entire production task. However, it is practical that a machine may experience several different OCs due to the requirement of different jobs. The varying OC may impact the deterioration of machines and their maintenance decisions. In addition, in a batch production system, a maintenance action has to be advanced before or postponed after a processing batch. Even if a machine is maintained preventively, it cannot be renewed since preventive maintenance (PM) is usually imperfect. In addition, minimal repair should be considered, which is costly and time consuming upon machine failure. The above concerns are practical but insufficiently considered in an integrated manner. Due to this integration, the complexity of the joint optimization problem is enhanced. An improved genetic algorithm (GA) based on random keys, convex set theory and the Jaya algorithm is proposed to solve the joint optimization problem of opportunistic PM and production scheduling in a batch production system under varying OCs. A series of comparative cases are conducted to illustrate the effectiveness of the proposed methods.

Two calibrated meta-heuristics to solve an integrated scheduling problem of production and air transportation with the interval due date

Contrary to previous methods in production management, today’s approaches mainly focus on the whole supply chain parties’ considerations. Considering production planning and distribution, as the two main functions in supply chain (SC) management, in an integrated manner in order to enhance the SC advantages is one of today’s main dilemma. Here, we have firstly proposed and investigated the integrated production and air transportation scheduling problem with time windows for the due date to minimize the total SC costs. Since the problem was NP-hard, two new coordinated and integrated solution procedures have been presented based on meta-heuristics. Four algorithms (i.e., simulated annealing (SA), genetic algorithm, particle swarm optimization/district PSO (PSO/DPSO), and hybrid variable neighborhood search–simulated annealing (H-VNS–SA)) have been developed in both procedures. For the first time in literature, we probe different encoding schemes in the proposed algorithms. In addition, by using Taguchi experimental design, the parameters of the algorithms have been tuned. Besides, to study the behavior of the algorithms, different problem sizes have been generated and the results of two procedures have been compared together and discussed. Finally, a comparison of the proposed algorithms with some state-of-art optimized algorithms has been presented to prove statistically better performance of the proposed algorithms in most cases.

Application of an improved Lagrangian relaxation approach in the constrained long-term production scheduling problem under grade uncertainty

In open-pit mines, the long-term production scheduling (LTPS) problem is a mixed-integer programming problem and is considered as a class of NP-hard problems that has to be solved in a reasonably small time owing to the operational requirements. The LTPS problem cannot be considered a well-solved problem. The current article presents hybrid models to elucidate the LTPS problem regarding grade uncertainty with the involvement of Lagrangian relaxation and augmented Lagrangian relaxation (ALR) with metaheuristic methods, firefly algorithm (FA) and bat algorithm. The results demonstrate that the ALR-FA has the best results in terms of net present value, average ore grade and computational time, and it is significantly better than the conventional method. Finally, analysis of the results shows that the proposed method generates a near-optimal solution within a reasonable time; thus, it could be a good proposition for use in the industry.

Design of mathematical models for the integration of purchase and production lot-sizing and scheduling problems under demand uncertainty

This study addresses the multi-level lot-sizing and scheduling problem with complex setups and considers supplier selection with quantity discounts and multiple modes of transportation. The present research proposes a mixed-integer linear programming (MILP) model in which the purchase lot-sizing from multiple suppliers, production lot-sizing with multiple machines and scheduling of various products of different families are accomplished at the same time. However, these decisions are not integrated in traditional environments and are taken separately. In this study, two different types of lot-sizing models called aggregated and disaggregated are developed for the problem to evaluate and compare the computational efficiency of them under deterministic and stochastic demands and provide some managerial insights. To deal with the stochastic demands, Chance-Constrained Programming (CCP) approach is applied. Based on the results of this study, the average profit of the separated (purchase from production) lot-sizing model under demand choice flexibility and stochastic demand is 24% and 22% less than the integrated model, respectively. Moreover, the results also confirm the effect of discount structure on the amount of purchases, productions, revenues and costs.

Deep Learning-Based Dynamic Scheduling for Semiconductor Manufacturing With High Uncertainty of Automated Material Handling System Capability

Recently, the transportation capability of the automated material handling system (AMHS) has emerged as a major barrier to the semiconductor fabrication facility (FAB), because it can limit the FAB production capacity. In this study, we propose a prediction method for a machine allocation problem of production scheduling in consideration with the AMHS’s constraints. The proposed method dynamically targets a machine for the next process by identifying diverse production conditions. We use a deep neural network-based dynamic scheduling method considering the overall production environment, which includes the remaining processing time, facility states, transportation time and traffic congestion, work-in-process distribution, and intermediate buffer states. To demonstrate the superiority and efficiency of the proposed method, we conducted experimental studies to compare the proposed model with the existing priority rule-based and analytic models under the static and dynamic environments. From the results, we verify that the proposed dynamic scheduling system can enhance the performance of existing AMHS and reduce machine starvation and production losses.