Single Batch Processing Machine Research Articles

A novel carbon reduction engineering method-based deep Q-learning algorithm for energy-efficient scheduling on a single batch-processing machine in semiconductor manufacturing

The semiconductor industry is a resource-intensive sector that heavily relies on energy, water, chemicals, and raw materials. Within the semiconductor manufacturing process, the diffusion furnace, ion implantation machine, and plasma etching machine exhibit high energy demands or operate at extremely high temperatures, resulting in significant electricity consumption, which is usually carbon-intensive. To address energy conservation concerns, the industry adopts batch production technology, which allows for the simultaneous processing of multiple products. The energy-efficient parallel batch scheduling problem arises from the need to optimise product grouping and sequencing. In contrast to existing heuristics, meta-heuristics, and exact algorithms, this paper introduces the Deep Q-Network (DQN) algorithm as a novel approach to address the proposed problem. The DQN algorithm is built upon the agent’s systematic learning of scheduling rules, thereby enabling it to offer guidance for online decision-making regarding the grouping and sequencing of products. The efficacy of the algorithm is substantiated through extensive computational experiments.

Effective league championship algorithm and lower bound procedure for scheduling a single batch-processing machine with non-identical job sizes and job rejection

We address the scheduling problem of a set of non-identical size jobs on a single batch-processing machine (SBPM) wherein the scheduler can make decision whether to schedule a job in batches or not to schedule it with a job-dependent penalty. The processing time of a batch is the greatest job processing time in that batch (parallel batching or p-batching). The scheduler wants to minimize a given objective function f, where f is the total rejection penalties of the rejected jobs (rejection cost) plus the makespan of the scheduled ones. We formulate the aforementioned problem as a 0–1 mixed integer programming model. We also apply an effective dynamic programming algorithm (DPA) to calculate a lower bound (LB) on the optimal cost of the problem. To tackle the problem, we propose a grouping algorithm, based on league championship algorithm (LCA), with new updating equations maintaining the major characteristics of the original updating equations of the LCA and well-suited to the structure of the problem. For small problems, performance of the proposed LCA is compared with GAMS/CPLEX solver. For large-scale instances, a genetic algorithm is adopted as a basis for comparison. Simulated experiments confirm the performance of the proposed methods.

Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes

We consider the problem of minimizing makespan on a single batch processing machine with a limited capacity. The machine can simultaneously process a group (batch) of jobs, each of them having different sizes and processing times. The processing time of a batch is the longest processing time of all jobs in the batch. We analyze the strength of the LP-relaxations of two mixed integer linear programming (MILP) formulations: a straightforward formulation and an advanced formulation. We prove that while the LP-relaxation of the straightforward formulation can perform arbitrarily bad in providing an LP bound on the optimal makespan, the LP-relaxation of the advanced formulation have some merit in providing a relatively good bound of makespan. With a detailed analysis of the problem, we prove a number of properties of the optimal solution and derive their respective valid inequalities (VI). These VIs are exploited in a novel MILP formulation for the problem. Extensive computations reveal that, with the help of the VIs, the proposed MILP formulation can solve large instances of the problem.

Single batch processing machine scheduling with sequence-dependent setup times and multi-material parts in additive manufacturing

Additive manufacturing has been a breakthrough revolution in the manufacturing world due to the ability to economically print parts with high geometric complexity, minimal vast and dissimilar materials in the same printing process. However, some problems arise with the usage of multi-materials in AM machines. This study aims to analyze the scheduling problem of a single AM machine for printing multi-material parts. We developed a mathematical model for a single AM machine to directly minimize the makespan of a production schedule of multi-material parts and indirectly minimize the material changeovers. IBM ILOG CPLEX Optimization Studio (v12.10) is used for the development stage of the model. Some numerical examples from AM literature were handled and solutions were gathered. Effects of material changeover costs for the different numbers of materials were investigated. Results indicated that setup time depending on material changeovers becomes a critical parameter for the minimization of makespan. Higher numbers of dissimilar materials increase the completion time of the schedule. While the developed model can be used for AM machines with different material changeover difficulties, it can also be used in the printing of parts that need to be uncontaminated finished products.

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.

Just-in-time single-batch-processing machine scheduling

In this paper, we study a single-batch-processing machine (SBPM) scheduling problem by considering a just-in-time criterion. Our objective is to minimize the total weighted earliness and tardiness (WET) penalties of jobs, where the penalty rates of jobs are job-independent but the earliness and tardiness penalty rates are different, and different jobs may have different due dates. An SBPM can process several jobs simultaneously as a batch. We first model this scheduling problem using a mixed-integer linear model. We design two priority rules, i.e., earliest due date (EDD) and earliest starting time (EST), to sort jobs. Based on our analysis on the mathematical properties of this scheduling problem, we propose two heuristic algorithms AABF and ITSLS to construct and improve the near-optimal schedules. We also devise a lower bound method on a new approximate time-indexed formulation. Extensive numerical experiments demonstrate the effectiveness and efficiency of our algorithms.

Batch scheduling with incompatible job families and common due date

This paper explores incompatible batch scheduling with common due date on a single batch processing machine. The problem of minimizing the number of tardy jobs is proved to be NP-hard with respect to id-encoding, and pseudo-polynomial time algorithms for minimizing the number of tardy jobs and the weighted number of tardy jobs are presented, respectively.

Joint production-planning and distribution optimization of perishable products under a combined shipment structure: A new hybrid policy-based approach

Following the need for joint optimization of decisions in supply chains, this paper newly provides an integrated framework to efficiently fulfill a production-planning-routing problem (PPRP). In such integrated scheme, a set of perishable family-products are manufactured on a single batch-processing machine. These products are dispatched to the customers by a third-party logistics service provider with only two types of licensed eco-friendly transportation facilities. In order to efficiently deliver the manufactured products before they become unusable, we propose a combined shipment structure. To accomplish this, we formulate the problem in the context of a MILP model. In particular, we aim to establish two manufacturing policies based on both increasing and decreasing rates of production and also two delivery policies expressing distinct preferences in fulfilling the customers’ demands. In this regards, we investigate the cost structures obtained from the established integrated planning and the resulting distribution configurations as well. Further, four heuristic algorithms are developed for solving the problem with respect to each hybrid production/distribution scheme derived from the former policies. Finally, to compare the mentioned procedures, it is conducted a numerical study illustrating the preferable efficiency of the plan gained according to the hybrid of the increasing-production-rate and decreasing-delivery-distance policies.

Arc-flow approach for single batch-processing machine scheduling

We address the problem of scheduling jobs with non-identical sizes and distinct processing times on a single batch-processing machine, aiming at minimizing the makespan. The extensive literature on this NP-hard problem mostly focuses on heuristics. Using an arc-flow based optimization approach, we construct a novel formulation that represents it as a problem of determining flows in graphs. The size of the formulation increases with the machine capacity and with the number of distinct sizes and processing times among the jobs, but it does not increase with the number of jobs, which makes it very effective to solve large instances to optimality, especially when multiple jobs have equal size and processing time. We compare our model to other models from the literature, showing its clear superiority on benchmark instances and proving optimality of random instances with up to 100 million jobs.

A Self-Adaptive Differential Evolution Algorithm for Scheduling a Single Batch-Processing Machine With Arbitrary Job Sizes and Release Times.

Batch-processing machines (BPMs) can process a number of jobs at a time, which can be found in many industrial systems. This article considers a single BPM scheduling problem with unequal release times and job sizes. The goal is to assign jobs into batches without breaking the machine capacity constraint and then sort the batches to minimize the makespan. A self-adaptive differential evolution algorithm is developed for addressing the problem. In our proposed algorithm, mutation operators are adaptively chosen based on their historical performances. Also, control parameter values are adaptively determined based on their historical performances. Our proposed algorithm is compared to CPLEX, existing metaheuristics for this problem and conventional differential evolution algorithms through comprehensive experiments. The experimental results demonstrate that our proposed self-adaptive algorithm is more effective than other algorithms for this scheduling problem.

Optimizing batch-processing operations with batch-position-based learning effects

Motivated by applications in porcelain-making companies, we consider a type of optimization problems for batch-processing operations. In production, a single batch-processing machine with a fixed capacity is used to process jobs. Several jobs can be processed together if their total size is no more than the machine capacity. Batch-position-based learning effects are considered because workers become skillful gradually after they perform the processing task repeatedly. The actual processing time of a batch is a decreasing function of its position in production. The objective is to minimize makespan and we consider three different problems. In the first problem, jobs have identical sizes and we present an algorithm which can find optimal solutions in polynomial time. In the second problem, jobs have identical processing times and we show the problem is NP-hard in the strong sense. We propose an approximation algorithm with an absolute performance guarantee of 1.5 and asymptotic performance guarantee of 1.223. In the third problem, jobs have non-identical sizes and processing times simultaneously. We propose an algorithm with an absolute and asymptotic performance guarantee of 2. Besides, we present the evolution of the performance guarantee and provide managerial insights for decision makers of manufacturing companies.

Hybrid approach for a single-batch-processing machine scheduling problem with a just-in-time objective and consideration of non-identical due dates of jobs

In this paper, we study a generalized single-batch-processing machine (SBPM) scheduling problem. Given a set of jobs that differ in terms of size, processing time and due date, the generalized SBPM problem aims to cluster the jobs into batches and process each batch one at a time on a capacitated batch-processing machine such that the total earliness and tardiness of jobs, a just-in-time objective, is minimized. We investigate the intrinsic properties of the optimal solutions of the problem, based on which an effective span-limited tree search (SLTS) heuristic is developed to find the near-optimal solutions to a restricted SBPM problem with a specified processing sequence of jobs. Varying the sequence, we embed the SLTS approach into a self-adapted genetic algorithm to further explore the solution space of the original problem. A hybrid span-limited tree search and genetic algorithm approach is proposed. The results of extensive numerical experiments on various random instances with a common due date and non-identical due dates of jobs demonstrate the effectiveness and efficiency of the proposed approaches in obtaining high-quality near-optimal solutions.

Energy-efficient scheduling of a single batch processing machine with dynamic job arrival times

Research on manufacturing scheduling has historically emphasized production efficiency. With rising environmental consciousness, manufacturing companies are paying increasing attention to energy efficiency on the shop floor. Manufacturing consumes a large amount of electricity globally. The mismatch between electric supply and demand has been a huge problem, which even becomes worse when renewable energy becomes more popular. The time-of-use (TOU) pricing policy is a widely used demand response (DR) approach, trying to align demand to supply. This paper considers energy-efficient scheduling of a single batch processing machine with non-identical job sizes and release times under a TOU electric tariff so as to simultaneously minimize total electricity cost, a criterion of environmental and energy sustainability, and makespan, a criterion of productivity. A mathematical formulation is developed to optimize electricity cost and makespan. Due to computational complexity, a hybrid multi-objective meta-heuristic algorithm is developed to find the Pareto front. Two constructive heuristics are presented to group jobs into batches. Two different approaches are presented to improve total electricity costs. The performance of the proposed model and algorithms is evaluated through extensive numerical experiments. Production managers can use the model and algorithms provided in this work to make a trade-off between productivity and sustainability.

Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection

In this paper we study a single batch-processing machine scheduling model. In our model, a set of jobs having different release dates needs to be scheduled onto a single machine that can process a batch of jobs simultaneously at a time. Each batch incurs a fixed setup time and a fixed setup cost. The decision maker may reject some of the jobs by paying penalty cost so as to achieve a tight makespan, but the total rejection penalty cost is required to be no greater than a given value. Our model extends several existing batch-processing machine scheduling models in the literature. We present efficient approximation algorithms with near-linear-time complexities.

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.

Using GRASP approach and path relinking to minimise total number of tardy jobs on a single batch processing machine

This paper considers scheduling a single batch processing machine such that the total number of tardy jobs is minimised. The machine can simultaneously process several jobs as a batch as long as the machine capacity is not violated. The batch processing time is equal to the largest processing time among those jobs in the batch. As the problem under study is NP-hard solving a mathematical formulation optimality is computationally intensive. A greedy randomised adaptive search procedure (GRASP) is proposed with the assumption of arbitrary job sizes, arbitrary processing times and arbitrary due dates. A novel construction phase for the GRASP approach is proposed to improve the solution quality. In addition, a path relinking procedure is proposed for solving large-sized problems effectively. The performance of the proposed GRASP approach is evaluated by comparing its results to a commercial solver and a construction heuristic. Experimental studies suggest that GRASP is superior compared to the commercial solver and the construction heuristic.

Using GRASP Approach and Path Relinking to Minimize Total Number of Tardy Jobs on a Single Batch Processing Machine

This paper considers the problem of scheduling a single batch processing machine such that the total number of tardy jobs is minimized. The machine can simultaneously process several jobs as a batch as long as the machine capacity is not violated. The batch processing time is equal to the largest processing time among those jobs in the batch. Two decisions are made to schedule jobs on the batch processing machine, namely grouping jobs to form batches and sequencing the batches on the machines. Both the decisions are interdependent as the composition of the batch affects the processing time of the batch. The problem under study is NP-hard. Consequently, solving a mathematical formulation to find an optimal solution is computationally intensive. A Greedy Randomized Adaptive Search Procedure (GRASP) is proposed to solve the problem under study with the assumption of arbitrary job sizes, arbitrary processing times and arbitrary due dates. A novel construction phase for the GRASP approach is proposed to improve the solution quality. In addition, a path relinking procedure is proposed for solving large-sized problems effectively. The performance of the proposed GRASP approach is evaluated by comparing its results to a commercial solver (which was used to solve the mathematical model) and a construction heuristic. Experimental studies suggest that the solution obtained from the GRASP approach is superior compared to the commercial solver and the construction heuristic.

Enhanced grouping league championship and optics inspired optimization algorithms for scheduling a batch processing machine with job conflicts and non-identical job sizes

This research aims to address scheduling of a single batch processing machine, where jobs are in different sizes and have a conflicting nature with each other, in the sense that two conflicting jobs cannot share the same batch and hence, cannot be processed simultaneously by the machine. The problem is referred to as SBMC. After formulating the problem, a strong lower bound procedure is developed by transforming a relaxed version of the scheduling problem to the multiple bottleneck transportation problem (MTP) with conflicts. An efficient Lagrangian relaxation procedure is proposed, which takes advantage of decomposable nature of the relaxed problem, to attain a lower bound for MTP which in essence is a lower bound for SBMC. To solve the problem, two metaheuristic algorithms, namely the League Championship Algorithm (LCA) and Optic Inspired Optimization (OIO), are adapted and fundamentally modified to match the problem unique structure (i.e., the grouping structure) and accordingly the grouping version of these algorithms is developed. The effectiveness of the lower bound procedure, as well as algorithms, are evaluated through extensive computational experiments. To show they perform efficiently in running times and effective in finding near-optimal bounds for most of the problem instances, we generate 20 different classes of problems according to variability in job sizes, number of jobs and density of incompatibility matrix. Then, we make comparison with two of extensively used algorithms from literature, SA and GA. Our proposed algorithms obtain solutions with objective values less than 6% gap from the lower bound and outperform SA and GA algorithms, especially for large instances. Moreover, values of the lower bound procedure lie within less than 4% of objective values provided by CPLEX.

A method combining rules with genetic algorithm for minimizing makespan on a batch processing machine with preventive maintenance

This paper considers the problem of minimising makespan on a single batch processing machine with flexible periodic preventive maintenance. This problem combines two sub-problems, scheduling on a batch processing machine with jobs’ release dates considered and arranging the preventive maintenance activities on a batch processing machine. The preventive maintenance activities are flexible but the maximum continuous working time of the machine, which is allowed, is determined. A mathematical model for integrating flexible periodic preventive maintenance into batch processing machine problem is proposed, in which the grouping of jobs with incompatible job families, the starting time of batches and the preventive maintenance activities are optimised simultaneously. A method combining rules with the genetic algorithm is proposed to solve this model, in which a batching rule is proposed to group jobs with incompatible job families into batches and a modified genetic algorithm is proposed to schedule batches and arrange preventive maintenance activities. The computational results indicate the method is effective under practical problem sizes. In addition, the influences of jobs’ parameters on the performance of the method are analyzed, such as the number of jobs, the number of job families, jobs’ processing time and jobs’ release time.

A hybrid neural network approach to minimize total completion time on a single batch processing machine

AbstractIn this research, the problem of scheduling a single batch processing machine (BPM) with nonidentical job sizes is considered. The objective is to minimize the total completion time of the jobs. A BPM can process a group of jobs simultaneously as a batch as long as its capacity is not violated. The processing time of a batch is equal to the maximum processing time of all the jobs in the batch. The research problem is formulated as a mixed integer linear programming model. Since the problem under study is shown to be NP‐hard, a neural network based approach that combines a heuristic algorithm and the iterative learning approach is proposed. The computational experiments are designed to compare the effectiveness of the neural network approach with CPLEX and the other available heuristics in the literature. The results show that the proposed approach outperforms the other algorithms in terms of solution quality.