Single Batch Processing Machine Research Articles

A modified particle swarm optimization algorithm for a batch-processing machine scheduling problem with arbitrary release times and non-identical job sizes

Abstract This paper presents a modified particle swarm optimization (MPSO) algorithm to minimize the maximum lateness for the single batch-processing machine problem with non-identical job sizes and release dates. The MPSO algorithm incorporated a diversification and a local search strategy into a basic particle swarm optimization algorithm. This incorporation enables the proposed algorithm to have a good balance between exploration and exploitation that yields high search efficiency. Additionally, a dynamic programming method is proposed to calculate a relevant value for each particle. The MPSO algorithm was tested in problems from the literature without release dates and newly generated problems with release dates. Computational results show the advantages of combining the diversification strategy, and local search methods. The performance of the proposed MPSO is competitive. For the problems without release dates, the MPSO algorithm could find 80 optimal solutions and improve 68 solutions for all benchmark instances. For the problems with job release dates, the MPSO algorithm also significantly outperformed the other two algorithms with respect to solution quality within the same computational time.

An Efficient Bi-objective Genetic Algorithm for the Single Batch-Processing Machine Scheduling Problem with Sequence Dependent Family Setup Time and Non-identical Job Sizes

This paper considers the problem of minimizing make-span and maximum tardiness simultaneously for scheduling jobs under non-identical job sizes, dynamic job arrivals, incompatible job families,and sequence-dependentfamily setup time on the single batch- processor, where split size of jobs is allowed between batches. At first, a new Mixed Integer Linear Programming (MILP) model is proposed for this problem; then, it is solved by -constraint method.Since this problem is NP-hard, a bi-objective genetic algorithm (BOGA) is offered for real-sized problems. The efficiency of the proposed BOGA is evaluated to be comparedwith many test problemsby -constraint method based on performance measures. The results show that the proposed BOGAis found to be more efficient and faster than the -constraint method in generating Pareto fronts in most cases.

Scheduling Batch Processing Machine Using Max–Min Ant System Algorithm Improved by a Local Search Method

The problem of minimizing the makespan on single batch processing machine is studied in this paper. Both job sizes and processing time are nonidentical and the processing time of each batch is determined by the job with the longest processing time in the batch. Max–Min Ant System (MMAS) algorithm is developed to solve the problem. A local search method MJE (Multiple Jobs Exchange) is proposed to improve the performance of the algorithm by adjusting jobs between batches. Preliminary experiment is conducted to determine the parameters of MMAS. The performance of the proposed MMAS algorithm is compared with CPLEX as well as several other algorithms including ant cycle (AC) algorithm, genetic algorithm (GA), and two heuristics, First Fit Longest Processing Time (FFLPT) and Best Fit Longest Processing Time (BFLPT), through numerical experiment. The experiment results show that MMAS outperformed others especially for large population size.

Scheduling batch processing machine problem with non-identical job sizes via artificial immune system

This paper considers a single batch processing machine problem, in this problem, jobs with release time and size will be assigned into some batches and processed aiming to minimize makespan. Given that this problem is NP-hard, an immunoglobulin-based artificial immune system (IAIS) algorithm is used to solve the problem. The proposed IAIS algorithm has two meaningful features. First, the searching area is limited in the somatic recombination process in order to decrease the computational time. Second, several local search methods are mixed for use in each run to change neighbor and escape from local optimum. Comparisons with an algorithm for the problem are shown to verify proposed IAIS. Comparisons results have shown that the proposed IAIS algorithm has a better performance than the existing algorithm.

Single batch processing machine scheduling with two-dimensional bin packing constraints

We study the problem of minimizing the makespan for jobs on a single batch processing machine (BPM). A BMP can process several jobs as a batch simultaneously. Unlike the classic batch processing machine scheduling problems in which the capacity of a machine is modeled as one-dimensional knapsack constraints, in this research, the machine's capacity is represented by a two-dimensional rectangle and a job occupies a rectangle of its dimensions, i.e., width and height, while being processed on the machine. The processing time and the dimensions of the jobs are non-identical. A batch's processing time equals to the longest processing time of jobs in the batch. A batch is feasible only if the jobs can be placed in the machine without overlapping with each other. Arising from practical industrial applications such as advanced manufacturing and wafer fabrication, this problem is a generalization of both the classic single BPM scheduling problem and the two-dimensional bin packing problem (2D-BPP), which are both proven to be NP-hard. Thus, it is NP-hard as well. We present a mixed integer programming (MIP) model for this problem. We also develop heuristic algorithms to tackle this problem, including four single-sequence based heuristics, a biased random-key genetic algorithm (BRKGA), and a hybrid bin loading (HBL) algorithm. The performances of the MIP model and proposed algorithms are compared based on a set of random generated instances.

A Bi-criterion Simulated Annealing Method for a Single Batch-processing Machine Scheduling Problem with Dynamic Job Release Times

This paper is motivated by a sterilization operation in a professional waste disposal services, and models the operation as the problem of single batch-processing machine (BPM) scheduling with the objectives of minimizing the makespan and the total weighted number of tardy orders that has not been considered in the literature. The considered problem is NP-hard such that two simulated annealing algorithms (SA1 and SA2) are developed in this work. SA1 uses multi-search directions to find Pareto-optimal solutions by eleven combinations of weights, as to SA2 applied the SMOSA of Suman to solve the considered problem. A computational experiment is conducted and the solutions for each instance obtained by SA1 and SA2 respectively are compared. Computational results reveal that SA1 is significantly better than SA2 because SA1 changes different search directions by two parameters.

A Note on “Two new approaches for a two-stage hybrid flowshop problem with a single batch processing machine under waiting time constraint”

The two-stage flow shop scheduling problem with a batch processing machine and limited waiting time was studied in the paper entitled “Two new approaches for a two-stage hybrid flowshop problem with a single batch processing machine under waiting time constraint” [Chung, T.-P., Sun, H., Liao, C.-J., 2016, Computers &Industrial Engineering, 10.1016/j.cie.2016.11.031]. In the original paper, this problem was formulated as a mixed-integer linear programming model. However, this model is not correct and the blocking time is confusing. In this note, a correct mixed-integer linear programming model is proposed and the confusing blocking time is discussed. Numerical experiments are conducted to illustrate the necessity of correction.

Two new approaches for a two-stage hybrid flowshop problem with a single batch processing machine under waiting time constraint

This paper investigates a two-stage hybrid flowshop problem with a single batch processing machine in the first stage and a single machine in the second stage. In this problem, each job has an individual release time and they are grouped into several batches. The batch processing machine can process a batch (limited number) of jobs simultaneously. To be more practical, the waiting time between the batch processing machine and the single machine is restricted in the two-stage hybrid flowshop problem. The objective is to minimize the makespan. To the best of our knowledge, few study researches the problem which is common in many real-life applications. Two immunoglobulin-based artificial immune system (IAIS) algorithms are developed to solve the problem which is NP-hard. The proposed IAIS algorithms provide different encoding and decoding ways to solve the problem. To verify proposed IAISs, comparisons with existing algorithms are made. Two lower bounds are also proposed to test solution quality. Computational results have shown that the proposed IAIS algorithms for the two-stage hybrid flowshop problem are quite stable and efficient.

Integrated scheduling on a batch machine to minimize production, inventory and distribution costs

We consider the problem of scheduling a set of jobs on a single batch-processing machine. Each job has a size and a processing time. The jobs are batched together and scheduled on the batch-processing machine, provided that the total size does not exceed the machine capacity. The processing time of the batch is the longest processing time among all the jobs in the batch. There is a single vehicle to deliver the final products to the customer. If the vehicle has not returned, completed batches will be put into the inventory. In this paper, we consider the problem of minimizing the production, delivery and inventory costs. We show that if the jobs have the same size, there is an O(nlog n)-time algorithm to find an optimal solution. If the jobs have the same processing time, there is a fast approximation algorithm with an absolute worst-case ratio less than 1.783 and an asymptotic worst-case ratio equal to 11/9. When the jobs have arbitrary sizes and arbitrary processing times, there is a fast approximation algorithm with absolute and asymptotic worst-case ratios less than or equal to 2, respectively.

Minimizing total flow time on a batch processing machine using a hybrid max–min ant system

A single batch processing machine scheduling problem with non-identical job sizes to minimize the total flow time is investigated. The problem is formulated as a binary mixed integer programming model. Since the research problem is shown to be NP-hard, a hybrid metaheuristic algorithm based on the max–min ant system (MMAS) is proposed. MMAS is an ant colony optimization algorithm derived from ant system. In the proposed algorithm, first, a sequence of jobs is constructed based on the MMAS algorithm. Then, a dynamic programming algorithm is applied to obtain the optimal batching for the given job sequence. At last, an effective local search procedure is embedded in the algorithm for finding higher quality solutions. The performance of the proposed algorithm is compared with CPLEX and available heuristics in the literature. Computational results demonstrate the efficacy of the proposed algorithm in terms of the solution quality.

Local search algorithm with path relinking for single batch-processing machine scheduling problem

The single batch-processing machine problem is to minimize makespan, which has broad applications, including engineering fundamentals and theoretical background. The machine can process several jobs as a batch simultaneously, and every job has three different attributes: job size, processing time, and job arrival. In this paper, a hybrid local search algorithm with path relinking (LP) is devised to solve the problem. We not only generate an optimal initial solution firstly but also pay more attention to improving the solution quality. Three kinds of local searches are applied to enhance the diversity of solutions; the path relinking is adopted to explore better solutions through local tracks connecting the current solution and the best in the elite set. With these approaches, it can keep a balanced rate between exploratory and exploitative capacity. Computational experiments on 40 benchmark instances indicate that LP has the superior convergence and robust performance and it surpasses the current state-of-the-art methods such as genetic algorithm and ant colony optimization, especially for large instances.

A modified imperialist competitive algorithm for scheduling single batch-processing machine with fuzzy due date

This paper considers a fuzzy single batch-processing machine (SBPM) scheduling problem and aims to make it closer to a real-world application through a fuzzy set theory. For this purpose, jobs’ due dates are set to be fuzzy numbers and the membership function of a fuzzy due date assigned to each job represents the degree of satisfaction that a decision maker has with the completion time of that job. The objective is to maximize the total degree of satisfaction or equivalently to minimize the total degree of dissatisfaction over given jobs. Then, the fuzzy mathematical programming model is presented. To solve the model, we propose the imperialist competitive algorithm (ICA) and modify the assimilation policy (i.e., colonies moving) and imperialistic competition in order to overcome its immature convergence and improve its performances. Moreover, due to the significant role of parameters on the quality of random search algorithms, a robust calibration is applied on the parameters using the Taguchi optimization technique. To evaluate the proposed ICA, several random test problems are generated and its performance is compared to the traditional ICA, simulated annealing (SA), particle swarm optimization (PSO), genetic algorithm (GA), ant colony optimization (ACO), and earliest due date (EDD). The obtained computational results demonstrate the superiority and robustness of the modified ICA.

Earliness–tardiness minimization on scheduling a batch processing machine with non-identical job sizes

This paper considers the scheduling problem of minimizing earliness–tardiness (E/T) on a single batch processing machine with a common due date. The problem is extended to the environment of non-identical job sizes. First, a mathematical model is formulated, which is tested effectively under IBM ILOG CPLEX using the constraint programming solver. Then several optimal properties are given to schedule batches effectively, and by introducing the concept of ARB (Attribute Ratio of Batch), it is proven that the ARB of each batch should be made as small as possible in order to minimize the objective, designed as the heuristic information for assigning jobs into batches. Based on these properties, a heuristic algorithm MARB (Minimum Attribute Ratio of Batch) for batch forming is proposed, and a hybrid genetic algorithm is developed for the problem under study by combining GA (genetic algorithm) with MARB. Experimental results demonstrate that the proposed algorithm outperforms other algorithms in the literature, both for small and large problem instances.

A Hyperheuristic Approach for Intercell Scheduling With Single Processing Machines and Batch Processing Machines

Intercell transfers in cellular manufacturing systems disrupt the philosophy of creating independent cells, but are essential for enterprises to reduce production costs. The problem of intercell scheduling with single processing machines and batch processing machines is considered in this paper, which involves an assignment subproblem, a sequencing subproblem, and a batch formation subproblem. An ant colony optimization (ACO)-based hyperheuristic (ABH) is developed in this paper, searching assignment rules for parts, sequencing rules for single processing machines, and batch formation rules for batch processing machines, simultaneously, and then using the obtained combinatorial rules to generate scheduling solutions. Computational results show that ABH is an effective and significantly efficient approach to provide near-optimum solutions even when CPLEX shows poor performance, and as compared to genetic algorithm that is widely used in hyperheuristics, ABH has better performance with respect to the problem addressed in this paper.

Constrained binary artificial bee colony to minimize the makespan for single machine batch processing with non-identical job sizes

This paper proposes an artificial bee colony approach to minimize the makespan for a single batch-processing machine. The single batch-processing problem is characterized by discontinuity in the objective function and having integer variables. Since the problem under study is NP-hard, an artificial bee colony approach is proposed. The penalty function method is used to convert the constrained problem to unconstrained problem, which is then solved by the ABC algorithm. A procedure to generate initial solutions is presented, which is based on filling partially filled batches first. The analysis in the article shows that the colony size, the value of the penalty parameter, the penalty function iteration, the ABC iteration, and maximum trials per food source all have a significant effect on the performance of the ABC algorithm; however, no pattern can be established.

Grouping evolution strategies: An effective approach for grouping problems

Many combinatorial optimization problems include a grouping (or assignment) phase wherein a set of items are partitioned into disjoint groups or sets. Introduced in 1994, the grouping genetic algorithm (GGA) is the most established heuristic for grouping problems which exploits the structural information along with the grouping nature of these problems to steer the search process. The aim of this paper is to evaluate the grouping version of the classic evolution strategies (ES) which originally maintain the well-known Gaussian mutation, recombination and selection operators for optimizing non-linear real-valued functions. Introducing the grouping evolution strategies (GES) to optimize the grouping problems that are intrinsically discrete, requests for developing a new mutation operator which works with groups of items rather than scalars and is respondent to the structure of grouping problems. As a source of variation, GES employs a mutation operator which shares a same rationale with the original ES mutation in the way that it works in continuous space while the consequences are used in discrete search space. A two phase heuristic procedure is developed to generate a complete feasible solution from the output of the mutation process. An extensive comparative study is conducted to evaluate the performance of GES versus GGA and GPSO (a recently proposed grouping particle swarm optimization algorithm) on test problem instances of the single batch-processing machine scheduling problem and the bin-packing problem. While these problems share exactly a same grouping structure and the performance of GES on both problems is reliable, switching from one problem to another deteriorates the performance of GGA. Though such a deficiency is not observed in the performance of GPSO, it is still inferior to GES on the single batch-processing machine scheduling test problem instances. Beside such empirical outcomes, the paper conveys a number of core strengths that the design of GES supports them but the design of GGA does not address them.

Minimization of makespan for the single batch-processing machine scheduling problem with considering aging effect and multi-maintenance activities

This paper considers the single batch-processing machine scheduling problem with aging effect and multi-maintenance activity concept. Real processing time of jobs increases due to machine’s aging effect. Maintenance time is constant and the machine returns to its initial condition after each maintenance activity and the aging effect starts anew. Our scheduling problem is under assumptions: non identical job sizes and dynamic job arrivals. We have to determine jointly (1) the maintenance frequencies, (2) the position of the maintenance activities on the machine, (3) the grouping of the jobs into the batches, and (4) the sequence of the batches on the machine, to minimize makespan. At first, we formulate the problem as a mathematical model. Since this problem has been proved to be NP-hard; therefore, a heuristic and two meta-heuristic algorithms are offered for the real-sized problems. The performance of the proposed algorithms is analyzed on the various test problems based on the considered measures.

A heuristic-search genetic algorithm for multi-stage hybrid flow shop scheduling with single processing machines and batch processing machines

This paper addresses the scheduling problem for a multi-stage hybrid flow shop (HFS) with single processing machines and batch processing machines. Each stage consists of nonidentical machines in parallel, and only one of the stages is composed of batch processing machines. Such a variant of the HFS problem is derived from the actual manufacturing of complex products in the equipment manufacturing industry. Aiming at minimizing the maximum completion time and minimizing the total weighted tardiness, respectively, a heuristic-search genetic algorithm (HSGA) is developed in this paper, which selects assignment rules for parts, sequencing rules for machines (including single processing machines and batch processing machines), and batch formation rules for batch processing machines, simultaneously. Then parts and machines are scheduled using the obtained combinatorial heuristic rules. Since the search space composed of the heuristic rules is much smaller than that composed of the schedules, the HSGA results in lower complexity and higher computational efficiency. Computational results indicate that as compared with meta-heuristics that search for scheduling solutions directly, the HSGA has a significant advantage with respect to the computational efficiency. As compared with combinatorial heuristic rules, other heuristic-search approaches, and the CPLEX, the HSGA provides better optimizational performance and is especially suitable to solve large dimension scheduling problems.

Hybrid metaheuristics for solving a fuzzy single batch-processing machine scheduling problem.

This paper deals with a problem of minimizing total weighted tardiness of jobs in a real-world single batch-processing machine (SBPM) scheduling in the presence of fuzzy due date. In this paper, first a fuzzy mixed integer linear programming model is developed. Then, due to the complexity of the problem, which is NP-hard, we design two hybrid metaheuristics called GA-VNS and VNS-SA applying the advantages of genetic algorithm (GA), variable neighborhood search (VNS), and simulated annealing (SA) frameworks. Besides, we propose three fuzzy earliest due date heuristics to solve the given problem. Through computational experiments with several random test problems, a robust calibration is applied on the parameters. Finally, computational results on different-scale test problems are presented to compare the proposed algorithms.

Minimising makespan on a single batch processing machine with dynamic job arrivals and non-identical job sizes

Batch scheduling is a prevalent policy in many industries such as burn-in operations in semiconductor manufacturing and heat treatment operations in metalworking. In this paper, we consider the problem of minimising makespan on a single batch processing machine in the presence of dynamic job arrivals and non-identical job sizes. The problem under study is NP-hard. Consequently, we develop a number of efficient construction heuristics. The performance of the proposed heuristics is evaluated by comparing their results to two lower bounds, and other solution approaches published in the literature, namely the first-fit longest processing time-earliest release time (FFLPT-ERT) heuristic, hybrid genetic algorithm (HGA), joint genetic algorithm and dynamic programming (GA+DP) approach and ant colony optimisation (ACO) algorithm. The computational experiments demonstrate the superiority of the proposed heuristics with respect to solution quality, especially for the problems with small size jobs. Moreover, the computational costs of the proposed heuristics are very low.