Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

Scheduling of Batch Processors in Semiconductor Manufacturing – A Review

In this paper a review on scheduling of batch processors (SBP) in semiconductor manufacturing (SM) is presented. It classifies SBP in SM into 12 groups. The suggested classification scheme organizes the SBP in SM literature, summarizes the current research results for different problem types. The classification results are presented based on various distributions and various methodologies applied for SBP in SM are briefly highlighted. A comprehensive list of references is presented. It is hoped that, this review will provide a source for other researchers/readers interested in SBP in SM research and help simulate further interest.Singapore-MIT Alliance (SMA

Integrated Batching and Lot Streaming with Variable Sublots and Sequence-Dependent Setups in a Two-Stage Hybrid Flow Shop

Consider a paint manufacturing firm whose customers typically place orders for two or more products simultaneously: liquid primer, top coat paint, and/or undercoat paint. Each product belongs to an associated product family that can be batched together during the manufacturing process. Meanwhile, each product can be split into several sublots so that overlapping production is possible in a two-stage hybrid flow shop. Various numbers of identical capacitated machines operate in parallel at each stage. We present a mixed-integer programming (MIP) to analyze this novel integrated batching and lot streaming problem with variable sublots, incompatible job families, and sequence-dependent setup times. The model determines the number of sublots for each product, the size of each sublot, and the production sequencing for each sublot such that the sum of weighted completion time is minimized. Several numerical example problems are presented to validate the proposed formulation and to compare results with similar problems in the literature. Furthermore, an experimental design based on real industrial data is used to evaluate the performance of proposed model. Results indicate that the computational cost of solving the model is high

Heuristics for batching and sequencing in batch processing machines

In this paper, we discuss the “batch processing” problem, where there are multiple jobs to be processed in flow shops. These jobs can however be formed into batches and the number of jobs in a batch is limited by the capacity of the processing machines to accommodate the jobs. The processing time required by a batch in a machine is determined by the greatest processing time of the jobs included in the batch. Thus, the batch processing problem is a mix of batching and sequencing – the jobs need to be grouped into distinct batches, the batches then need to be sequenced through the flow shop. We apply certain newly developed heuristics to the problem and present computational results. The contributions of this paper are deriving a lower bound, and the heuristics developed and tested in this paper

Dynamic set-up rules for hybrid flow shop scheduling with parallel batching machines

An S-stage hybrid (or flexible) flow shop, with sequence-independent uniform set-up times, parallel batching machines with compatible parallel batch families (like in casting or heat treatments in furnaces, chemical or galvanic baths, painting in autoclave, etc.) has been analysed with the purpose of reducing the number of tardy jobs (and the makespan); in Graham’s notation: FPB(m_1, m_2, … , m_S)|p-batch, STsi,b|SUM(Ui). Jobs are sorted dynamically (at each new delivery); batches are closed within sliding (or rolling) time windows and processed in parallel by multiple identical machines. Computation experiments have shown the better performance on benchmarks of the two proposed heuristics based on new formulations of the critical ratio (CRsetup) considering the ratio of allowance set-up and processing time in the scheduling horizon, which improves the weighted modified operation due date rule

Performance of a Serial-Batch Processor System with Incompatible Job Families under Simple Control Policies

A typical example of a batch processor is the diffusion furnace used in wafer fabrication facilities (otherwise known as wafer fabs). In diffusion, silicon wafers are placed inside the furnace, and dopant is flown through the wafers via nitrogen gas. The higher the temperature, the faster the dopant penetrates the wafer surface. Then, a thin layer of silicon dioxide is grown, to help the dopant diffuse into the silicon. This operation can take 10 hours or more to finish processing, as compared to one or two hours for other wafer fab operations, according to Uzsoy [8]. Diffusion furnaces typically can process six to eight lots concurrently; we call the lots processed concurrently a batch. The quantity of lots loaded into the furnace does not affect the processing time. Only lots that require the same chemical recipe and temperature may be batched together at the diffusion furnace. We wish to control the production of a manufacturing system, comprised of a serial processor feeding the batch processor. The system produces different job types, and each job can only be batched together with jobs of the same type. More specifically, we explore the idea of controlling the production of the serial processor, based on the wip found in front of the batch processor. We evaluate the performance of our manufacturing system under several simple control policies under a range of loading conditions and determine which control policies perform better under which conditions. It is hoped that the results obtained from this small system could be extended to larger systems involving a batch processor, with particular emphasis placed on the applicability of such policies in wafer fabrication.Singapore-MIT Alliance (SMA

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

Mathematical Models for a Batch Scheduling Problem to Minimize Earliness and Tardiness

Purpose: Today’s manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem has been addressed to enable on-time completion of customer orders in a lean manufacturing environment. The problem is optimizing the partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components. Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid excess final product inventory. The first model is a non-linear integer programming model whereas the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented. Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times compared to the other two models. It has also been showed that the alternative model is able to solve moderate sized real-world problems. Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature owing to the inclusion of new circumstances that are present in real-world applications. Those are: customer orders consisting of multi-products made of multi-parts, processing of all parts of the same product from different orders in the same batch, and delivering the orders only when all related products are completed. This research also contributes to the literature of batch scheduling problem by presenting new optimization models.Peer Reviewe