Batch-processing Machine Scheduling Problem Research Articles

An Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Batch Processing and Time-of-Use Electricity Prices

The extensive consumption of energy in manufacturing has led to a large amount of greenhouse gas emissions that have caused an enormous effect on the environment. Therefore, investigating how to reduce energy consumption in manufacturing is of great significance to cleaner production. This paper considers an energy-conscious unrelated parallel batch processing machine scheduling problem under time-of-use (TOU) electricity prices. Under TOU, electricity prices vary for different periods of a day. This problem is grouping jobs into batches, assigning the batches to machines and allocating time to the batches so as to minimize the total electricity cost. A mixed-integer linear programming model and two groups of heuristics are proposed to solve this problem. The first group of heuristics first forms batches, assigns the batches to machines and finally allocates time to the batches, while the second group of heuristics first assigns jobs to machines, batches the jobs on each machine and finally allocates time to each batch. The computational results show that the SPT-FBLPT-P1 heuristic in the second group can provide high-quality solutions for large-scaled instances in a short time, in which the jobs are assigned to the machines based on the shortest processing time rule, the jobs on each machine are batched following the full-batch longest processing time algorithm, and the time is allocated to each batch following an integer programming approach. The MDEC-FBLPT-P1 heuristic that uses the minimum difference of the power consumption algorithm to assign the jobs also performed well.

Parallel Batch Processing Machine Scheduling Under Two-Dimensional Bin-Packing Constraints

The parallel batch processing machine scheduling problem with two-dimensional bin packing constraints (PBS-2D) has appeared in many industrial environments, but the research on this problem is still not sufficient. In this article, we use the 2-D rectangular packing constraints to describe the spatial geometric layout of jobs more accurately, and propose a mixed integer linear programming (MILP) model to minimize the makespan of PBS-2D. According to the in-depth analysis of the problem properties, PBS-2D is separated into three subproblems, which are job-machine assignment, 2-D job placement, and job sequence optimization. An improved biased random key genetic algorithm (OBRKGA) is proposed to solve job-machine assignment and job sequence optimization. This algorithm generates the initial population based on the idea of orthogonal experimental design, so that the whole solution space can be scanned evenly when generating the initial solution, making the algorithm be more likely to find better solutions for subsequent evolution. At the same time, a bin packing algorithm based on best fit is designed to handle 2-D job placement problem. Finally, the algorithms are tested on a large number of randomly generated instances, the results show that OBRKGA outperformed the original BRKGA, the classical moth-flame optimization algorithm, particle swarm optimization algorithm, gravity search algorithm, and MILP.

Scheduling a single batch processing machine with non-identical two-dimensional job sizes

This paper considers a single batch processing machine scheduling problem with non-identical two-dimensional job sizes. Jobs may be rotated but must be placed orthogonally without overlapping in the machine. The machine can simultaneously process a batch of jobs as long as its two-dimensional capacity is not exceeded. The processing time of a batch is defined by the longest processing time of all jobs in the batch. The objective is to assign jobs to batches considering the machine capacity constraint such that the makespan is minimized. An improved mixed integer programming formulation is proposed to reduce the solution space. 16 heuristics, combining four job sequencing, two batch selection, and two job placement alternatives, are investigated. The effectiveness of the model and heuristics is analyzed through a comprehensive experimental study. The results show that the LPTBFSA heuristic outperforms the others, in which jobs are sorted in decreasing processing time, a batch is selected for each job based on the best-fit algorithm, and a job is placed in the selected batch following the “as compact as possible” packing principle. The LPTFFSA heuristic also works well, in which the first-fit algorithm is used to select a batch for each job.

Machine scheduling with orientation selection and two-dimensional packing for additive manufacturing

In recent years, additive manufacturing (AM) gains increasing attention in manufacturing industries due to the growing demands, and the corresponding machine scheduling problems also attract many researchers. In this paper, we study a new unrelated parallel batch processing machine scheduling problem arose in AM, which requires to simultaneously assign parts to batches, determine the orientation of parts, pack the parts to the two-dimensional surface, and allocate the batches to machines. It is the first work to consider the orientation selection for parts in machine scheduling with the objective to minimize the makespan. To solve this problem, we first present a mixed integer linear programming model. Then, a simulated annealing algorithm with designed packing strategies based on the skyline representation of packing pattern is developed. Moreover, data structure Trie is introduced to accelerate the whole procedure and four post-optimization methods are designed to further refine solutions. Finally, a comprehensive computational study is conducted. The efficiency of our heuristic algorithms is verified and the best packing strategy for this problem is identified. The advantage of considering multiple orientations of parts in machine scheduling is demonstrated by comparisons with scenarios of fixed orientation.

Exact algorithms to minimize makespan on single and parallel batch processing machines

Batch-processing machine scheduling problem is one of the challenging problems in the machine scheduling literature where machines are capable of processing a batch of jobs simultaneously. In this paper, we tackle single and parallel batch processing machine scheduling problems with the objective of minimizing makespan. We propose a reformulation for parallel batch processing machine scheduling, which is based on decomposition in two levels, and an exact algorithm for its solution. To the best of our knowledge, there is no exact algorithm to solve this problem in the literature, except for its formulations solved by off-the-shelf solvers. In the first part of the proposed algorithm, we solve the single batch processing machine problem by a column-and-cut generation algorithm that provides a lower bound for the parallel machine problem. The second part of our proposed algorithm employs a search mechanism to find the minimum makespan for the parallel machine problem, which entails the solution of the reformulation of this problem by column generation at every iteration. The novel aspect of this column generation algorithm is the integration of batch generation and machine schedule generation in a single pricing subproblem. We test the performance of the proposed algorithms on randomly generated instances and show that, on average, they outperform the off-the-shelf solver. The major findings are that the single machine problem provides tight lower and upper bounds for the parallel machine problem, and the proposed algorithm for the parallel machine problem solves more instances to optimality than that for the single machine problem.

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.

Optimisation of burn-in time considering the hidden loss of quality deviations in the manufacturing process

The burn-in test time is an important parameter of the complex batch processing machine scheduling problem. The omission of the loss of quality deviations in manufacturing generates a non-comprehensive and imperfect result in the optimisation of burn-in time, which hinders the identification of proactive and economical optimisation strategies to prevent infant failure in manufacturing. To solve this problem, this study visualises and quantifies for the first time the hidden loss caused by quality deviations in manufacturing and uses it as a newly added constraint to optimise the burn-in time. Firstly, a quality loss model composed of visible yield loss and warranty costs related to measurable but undetectable reliability vulnerabilities is defined. Secondly, the loss effects of growing defects are measured during the burn-in test, and the optimal burn-in time expressed by the proposed quality loss model is traded off between the additional burn-in cost and the decreased quality loss for an acceptable low infant failure rate. Finally, the effectiveness of the proposed optimisation approach is demonstrated using actual data from a control board with a high infant failure rate. Results show that the proposed method can systematically combine the fundamental loss of quality deviations in the optimisation of burn-in time, which supplements the commonly used optimality criteria, with the upstream loss of quality deviations in the form of manufacturing defects.

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.

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.

Reduction of power consumption and carbon footprints by applying multi-objective optimisation via genetic algorithms

Firms heavily emphasise reducing carbon footprint, an area warranting further improvement. This study examines carbon footprint within the context of production scheduling. Two multi-objective scheduling problems involving economic- and environmental-related criteria are studied: (1) a batch-processing machine scheduling problem to minimise the total weighted tardiness and carbon footprint simultaneously; (2) a triple-criteria scheduling problem involving of a hybrid flow shop consisting of a batch-processing machine followed by two parallel-processing machines, in which the shop attempts to minimise the total weighted tardiness, carbon footprint and peak power. Since the above problems are treated as a true multi-objective optimisation problem, decision-makers should select a solution among the trade-off solutions provided in the Pareto-optimal set. Therefore, the non-dominated sorting-based genetic algorithm II (NSGA-II) is implemented, which identifies the set of approximate efficient schedules to both multi-objective scheduling problems. Moreover, an adaptive multi-objective genetic algorithm (AMGA) is developed to generate the reference Pareto front, which validates the results that are obtained using NSGA-II. Results of this study demonstrate both the effectiveness of AMGA in converging to the true Pareto-optimal set and the efficiency of NSGA-II.

The burn-in test scheduling problem with batch dependent processing time and sequence dependent setup time

The burn-in test scheduling problem (BTSP) is a variation of the complex batch processing machine scheduling problem, which is also a generalisation of the liquid crystal injection scheduling problem with incompatible product families and classical identical parallel machine problem. In the case we investigated on the BTSP, the jobs are clustered by their product families. The product families can be clustered by different product groups. In the same product group, jobs with different product families can be processed as a batch. The batch processing time is dependent on the longest processing time of those jobs in that batch. Setup times between two consecutive batches of different product groups on the same batch machine are sequentially dependent. In addition, the unequal ready times are considered in the BTSP which involves the decisions of batch formation and batch scheduling in order to minimise the total machine workload without violating due dates and the limited machine capacity restrictions. Since the BTSP involves constraints on unequal ready time, batch dependent processing time, and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with compatible product families or incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Consequently, this paper proposes a mixed integer programming model to solve the BTSP exactly. In addition, two efficient solution procedures which solve the BTSP are also presented.

Research on computational intelligence algorithms with adaptive learning approach for scheduling problems with batch processing machines

This paper presents a general kind of flow shop scheduling problem in a manufacturing supply chain where a group of jobs can be processed on a machine simultaneously. Examples of such environment occur in chemical processes, semiconductor industries, electronics manufacturing, wafer fabrication, and pharmaceutical industries, etc. In this problem not only should the sequence of jobs be determined but also the formation of batches is considered as a new variable in the model. The problem under investigation is NP-hard for cost of total earliness; total tardiness and makespan as objectives. During recent years, the nature-inspired computational intelligent algorithms are successfully employed for achieving the optimum design of supply chain structures. Hence, three effective computational intelligence algorithms including a hybrid genetic algorithm (HGA), a hybrid simulated annealing (HSA) and an improved discrete particle swarm optimization (PSO) algorithm are developed and analyzed for solving the batch processing machine scheduling problem addressed in current paper. Furthermore, an adaptive learning approach which is inspired by the training weights in artificial neural network (ANN) environment is embedded into the algorithms so as to enhance the quality of solutions. An extensive simulation experiments is conducted and the performance of algorithms is compared with the traditional genetic algorithm, particle swarm optimization, some well known dispatching rules such as STPT, LTPT, SBMPT, LBMPT, EDD, MST and also with the powerful commercial solver LINGO. The attained results show the appropriate performance of our algorithms.

The liquid crystal injection scheduling problem (LCISP)

In this paper, the liquid crystal injection scheduling problem (LCISP) involving the constraints on limited maximum waiting times, unequal ready times, and machine setup times is considered to form the batches with incompatible product families and to sequence those batches on identical parallel batch processing machines. The batch scheduling problem, LCISP, has many applications, especially in thin film transistor liquid crystal display (TFT-LCD) factories at the cell assembly stage. In the LCISP, the objective is to minimise the total machine workload without violating the limited maximum waiting time restriction. Furthermore, machine setup times that are sequence dependent for two consecutive batches classified into different product families on the same machine are also considered. Since the LCISP involves constraints on limited maximum waiting times and sequence dependent setup times, it is more difficult to solve than the classical parallel batch processing machine scheduling problem with incompatible product families. These restrictions mean that the existing methods cannot be applied into real-world factories directly. Therefore, this paper proposes a mixed integer programming model to solve the LCISP exactly. In addition, two efficient solution procedures which solve the LCISP are also presented.

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.

Scheduling a single batch-processing machine with arbitrary job sizes and incompatible job families: An ant colony framework

This paper investigates the first attempt on the batch-processing machine scheduling problem, where the machine can process multiple jobs simultaneously, using an ant colony optimization metaheuristic. We consider the scheduling problem of a single batch-processing machine with incompatible job families and the performance measure of minimizing total weighted completion time. Jobs of a given family have an identical processing time and are characterized by arbitrary sizes and weights. Based on a number of developed heuristic approaches, we propose an ant colony framework (ACF) in two versions, which are distinguished by the type of embedded heuristic information. Each version is also investigated in two formats, that is the pure ACF and the hybridized ACF. To verify the performance of our framework, comparisons are made based on using a set of well-known existing heuristic and meta-heuristic algorithms taken from the literature, on a diverse set of artificially generated test problem instances. Computational results show the high performance of the proposed framework and signify its ability to outperform the comparator algorithms in most cases as the problem size increases.

On‐line algorithms for minimizing makespan on batch processing machines

We consider problem of scheduling jobs on-line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on-line algorithms with worst-case ratio (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst-case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on-line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001

On‐line algorithms for minimizing makespan on batch processing machines

AbstractWe consider problem of scheduling jobs on‐line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on‐line algorithms with worst‐case ratio $(\sqrt{5}+1)/2$ (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst‐case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on‐line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001