The low density parity check codes whose performance is closest to the Shannon limit are`Gallager codes' based on irregular graphs. We compare alternative methods for constructing these graphs and present two results. First, we nd a`super{Poisson' construction which gives a small improvement in empirical performance over a random construction. Second, whereas Gallager codes normally take N 2 time to encode, we investigate constructions of regular and irregular Gallager codes which allow more rapid encoding and have smaller memory requirements in the encoder. We nd that thesè fast{encoding' Gallager codes have equally good performance.

Uncertainty and variety have been established as the fundamental reasons for needing manufacturing flexibility at a plant level. However, the sole focus on uncertainty and variety often leads to the neglect of factors that influence flexibility requirements at the system and resource levels. To address this neglect, this article considers the role of manufacturing resource configuration in influencing the need for mix flexibility. This article begins by revisiting literature that reviews the plant level drivers for needing mix flexibility. These relationships are captured in a preliminary framework. Subsequently, by applying constructs from Coordination Theory, the role of manufacturing resource configuration in influencing mix flexibility requirements is outlined. The preliminary framework is then revised and tested via a case study. The article concludes by arguing that the traditional focus on plant level factors influencing mix flexibility requirements should be expanded to consider the role of manufacturing resource configuration in influencing mix flexibility requirements at the system and resource levels.

Purpose – Mix flexibility is a critical manufacturing flexibility type needed to produce a company's range of products. Oftentimes, multiple products are produced on shared resources which require coordination mechanisms to ensure their effective utilization. This paper aims to explore the applicability of the product wheel concept as a coordination mechanism that can be used to manage shared resources in operational mix flexibility achievement in process industries. Design/methodology/approach – The product wheel concept is a construct from the theory of lean manufacturing adoption in process industries. This construct is applied as a sequencing coordination mechanism, where similar products are grouped together to run consecutively in a production schedule. A single case study is used to illustrate the development and evaluation of a product wheel design. Findings – The results show that the product wheel concept does achieve the aim of grouping similar products in the production schedule, and, as such, can be used to improve the production planning process through the reduction of the number of time-intensive changeovers without sacrificing product availability to meet customer demand. The product wheel, however, is not a mathematical optimization technique; but is instead a heuristic technique which requires the use of judgment and experience to achieve an optimal design. Originality/value – A theoretical contribution to the study of mix flexibility has been made, where the application of the product wheel construct presents a novel approach to the study of operational mix flexibility achievement, via the sequencing of products on shared manufacturing resources.

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Purpose -The purpose of this paper is to address a research gap relating to the understanding of how one type of manufacturing flexibility -mix flexibility -is achieved during day-to-day operations. Design/methodology/approach -Constructs from coordination theory are used in order to understand the way in which physical manufacturing resources are coordinated during daily operations to produce a company's product mix. A multiple case study methodology is used to investigate the applicability of these constructs in the flour milling industry. Subsequently, a conceptual framework is proposed which captures the coordination mechanisms used in the achievement of mix flexibility. Findings -The paper finds that mix flexibility requirements influence how a company achieves mix flexibility. Further, the findings indicate that, at an operational level, mix flexibility is achieved via the use of coordination mechanisms to manage specific dependencies relating to mix flexibility requirements.Research limitations/implications -Mix flexibility achievement was studied in a single industry. Future research can test the applicability of the conceptual framework in other manufacturing settings. Originality/value -An empirical contribution to the study of manufacturing flexibility achievement has been made, where the application of constructs from coordination theory presents a novel approach to the study of manufacturing flexibility achievement.