Model approximation for batch flow shop scheduling with fixed batch sizes

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.United States. Department of Homeland Security. Science and Technology Directorate (Contract HSHQDC-13-C-B0052)United States. Air Force Research Laboratory (Contract FA8750-09-2-0219)ATK Thiokol Inc

Clips: a capacity and lead time integrated procedure for scheduling.

We propose a general procedure to address real life job shop scheduling problems. The shop typically produces a variety of products, each with its own arrival stream, its own route through the shop and a given customer due date. The procedure first determines the manufacturing lot sizes for each product. The objective is to minimize the expected lead time and therefore we model the production environment as a queueing network. Given these lead times, release dates are set dynamically. This in turn creates a time window for every manufacturing order in which the various operations have to be sequenced. The sequencing logic is based on a Extended Shifting Bottleneck Procedure. These three major decisions are next incorporated into a four phase hierarchical operational implementation scheme. A small numerical example is used to illustrate the methodology. The final objective however is to develop a procedure that is useful for large, real life shops. We therefore report on a real life application.Model; Models; Applications; Product; Scheduling;

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Bütünleşik tedarik zinciri çizelgeleme modelleri: Bir literatür taraması

Research on integration of supply chain and scheduling is relatively recent, and number of studies on this topic is increasing. This study provides a comprehensive literature survey about Integrated Supply Chain Scheduling (ISCS) models to help identify deficiencies in this area. For this purpose, it is thought that this study will contribute in terms of guiding researchers working in this field. In this study, existing literature on ISCS problems are reviewed and summarized by introducing the new classification scheme. The studies were categorized by considering the features such as the number of customers (single or multiple), product lifespan (limited or unlimited), order sizes (equal or general), vehicle characteristics (limited/sufficient and homogeneous/heterogeneous), machine configurations and number of objective function (single or multi objective). In addition, properties of mathematical models applied for problems and solution approaches are also discussed.Bütünleşik Tedarik Zinciri Çizelgeleme (BTZÇ) üzerine yapılan araştırmalar nispeten yenidir ve bu konu üzerine yapılan çalışma sayısı artmaktadır. Bu çalışma, bu alandaki eksiklikleri tespit etmeye yardımcı olmak için BTZÇ modelleri hakkında kapsamlı bir literatür araştırması sunmaktadır. Bu amaçla, bu çalışmanın bu alanda çalışan araştırmacılara rehberlik etmesi açısından katkı sağlayacağı düşünülmektedir. Bu çalışmada, BTZÇ problemleri üzerine mevcut literatür gözden geçirilmiş ve yeni sınıflandırma şeması tanıtılarak çalışmalar özetlenmiştir. Çalışmalar; tek veya çoklu müşteri sayısı, sipariş büyüklüğü tipi (eşit veya genel), ürün ömrü (sınırlı veya sınırsız), araç karakteristikleri (sınırlı/yeterli ve homojen/heterojen), makine konfigürasyonları ve amaç fonksiyonu sayısı (tek veya çok amaçlı) gibi özellikler dikkate alınarak kategorize edildi. Ayrıca problemler için uygulanan matematiksel modellerin özellikleri ve çözüm yaklaşımları da tartışılmıştır

Scheduling reentrant jobs on parallel machines with a remote server

This paper explores a specific combinatorial problem relating to re-entrant jobs on parallel primary machines, with a remote server machine. A middle operation is required by each job on the server before it returns to its primary processing machine. The problem is inspired by the logistics of a semi-automated micro-biology laboratory. The testing programme in the laboratory corresponds roughly to a hybrid flowshop, whose bottleneck stage is the subject of study. We demonstrate the NP-hard nature of the problem, and provide various structural features. A heuristic is developed and tested on randomly generated benchmark data. Results indicate solutions reliably within 1.5% of optimum. We also provide a greedy 2-approximation algorithm. Test on real-life data from the microbiology laboratory indicate a 20% saving relative to current practice, which is more than can be achieved currently with 3 instead of 2 people staffing the primary machines

Capacity Planning and Leadtime management

In this paper we discuss a framework for capacity planning and lead time management in manufacturing companies, with an emphasis on the machine shop. First we show how queueing models can be used to find approximations of the mean and the variance of manufacturing shop lead times. These quantities often serve as a basis to set a fixed planned lead time in an MRP-controlled environment. A major drawback of a fixed planned lead time is the ignorance of the correlation between actual work loads and the lead times that can be realized under a limited capacity flexibility. To overcome this problem, we develop a method that determines the earliest possible completion time of any arriving job, without sacrificing the delivery performance of any other job in the shop. This earliest completion time is then taken to be the delivery date and thereby determines a workload-dependent planned lead time. We compare this capacity planning procedure with a fixed planned lead time approach (as in MRP), with a procedure in which lead times are estimated based on the amount of work in the shop, and with a workload-oriented release procedure. Numerical experiments so far show an excellent performance of the capacity planning procedure

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

E-POLCA to control multi-product, multi-machine job shops.

Control; Job; University; Research;

Heuristics for scheduling a two-stage hybrid flow shop with parallel batching machines: application at a hospital sterilisation plant

The model of a two-stage hybrid (or flexible) flow shop, with sequence-independent uniform setup times, parallel batching machines and parallel batches has been analysed with the purpose of reducing the number of tardy jobs and the makespan in a sterilisation plant. Jobs are processed in parallel batches by multiple identical parallel machines. Manual operations preceding each of the two stages have been dealt with as machine setup with standardised times and are sequence-independent. A mixed-integer model is proposed. Two heuristics have been tested on real benchmark data from an existing sterilisation plant: constrained size of parallel batches and fixed time slots. Computation experiments performed on combinations of machines and operator numbers suggest balancing the two stages by assigning operators proportionally to the setup time requirements