Dynamics of assembly production flow
Introduction
The twentieth century saw industrialized societies develop with the support of organized modern manufacturing, accompanied by a rapid increase in demand and consumption of goods. Scientific management of production systems dates back to the early twentieth century [1]. After Taylor’s pioneering work, innumerable studies have been undertaken to control, optimize, and predict production flow in factories [2], [3]. These studies have contributed to the design and management of manufacturing systems. However, the description of production flows by these theories, including the queuing theory, remains unsatisfactory, especially for complex, dynamic production systems [4], [5]. A pivotal factor impeding our understanding of production flows is the dynamic properties of a complex production system as a “many-body system”. In general, constraints pertaining to the volume of components and the finite capacity (buffer) for each job make the system dynamics complex.
This paper proposes a physical approach–suitable for dealing with dynamic phenomena–to the complex system dynamics. We use a simple model that captures the essence of the dynamics and makes it visible. In the context of nonequilibrium statistical physics, the asymmetric simple exclusion process (ASEP) [6], [7], [8] has been vigorously studied as the most archetypal model of particle flow with the exclusion (blocking) effect, and nontrivial behaviors specific to nonequilibrium systems have been discussed. In addition, the connection between the queuing theory and ASEP has been reported in recent studies [9], [10]. Thus, we find the intersection of studies on manufacturing systems and physics. Note that in the supply-chain management field, it is known that even a simple system can lead to highly complex behavior, including chaos [11], [12] and the so-called bullwhip effect [13], [14], [15], [16], [17], which has also been investigated from a physical perspective [18], [19], [20], [21].
Hopp and Spearman [22] attempted the idea of using a physical approach called factory physics to study production flow. They successfully systemized the fundamental knowledge about production systems with simple mathematics and static analyses. However, recent physical approaches using stability analyses [18], [19], [20], [21] and the formulation presented in this paper use a dynamic treatment, and are thus beyond the scope of the factory physics concept. The main goal of the present study is to uncover and understand dynamic phenomena observed in complex manufacturing systems that are beyond intuitive prediction. For this purpose, simple models are used to identify the correlation between phenomena and causes. Different from recent similar attempts [18], [19], [20], [21], we use a full discrete model–space, time, and inventories are discretized–to realize this approach. This enables us to understand the system at the microscopic level, disregarding relatively less important factors (e.g., input and output buffers at each job, and prediction and adaptation mechanisms), and to focus on the nature of “assembly”.
In this paper, we focus on a set of jobs in a single manufacturing unit that constitutes a supply chain. Each job corresponding to materials’ processing does not predict its supply and demand, but follows the state of neighboring jobs. In the absence of prediction, the bullwhip effect does not occur. The primary goal of this study is to reveal how “assembly” processes on a large production line affect the overall system. The system is perturbed by three types of fluctuations: demand fluctuations, supply fluctuations, and removal of defective products. The assembly process involves merging two or more production flows, where material provisions from these streams synchronize (couple) [23]. This significantly increases complexity when the system is under perturbations, thus making rigorous analysis of such system very challenging.
In previous studies, a set of assembly processes has been represented abstractly by a network of jobs, buffers (nodes), and topology of parts flow (links) [24], [25], [4], [23], [26]. Here, we reformulate an assembly system as an interacting particle system [6] and observe its dynamic aspects. The collective behavior of exclusive particles moving in a discrete network has received considerable attention from physicists [27], [28], [29], [30], [31]. However, the effect of particle coalescence (assembly) on these systems has not yet been fully understood.
The reminder of the paper is organized as follows. The focal model definition is given in the next section. To understand the model in detail, we first focus on the dynamics of a restricted parameter set (Section 3) and then consider variations in the fixed parameters (Section 4). Finally, we summarize the results and discuss the outlook of the study in Section 5.
Section snippets
Model
Consider a directed regular tree network whose indegree and outdegree are and 1, respectively (Fig. 1). Parts (particles) are transported along links, and at each node, different parts are assembled, generating a part for the next node. A node has a buffer of size for each incoming part; that is, a node can contain parts of one type at the same time. Hence, the stock status at a node is described by a set of parts for the buffers. The network has assembly stages, resulting in the
Fundamental phenomena
In this section, we restrict ourselves to considering the case of as the most fundamental example. These restrictions will be relaxed later. In the absence of the possibility of producing defective parts, parts flow in each link is conserved.
The case of is important for the following reasons. First, this is the minimum size that allows a stationary production flow. If each node can hold only one inventory item, products can be sent once per two steps as in ASEP. Second,
Effects of network size, buffer size, and product inspection
Now, we focus on the dependence of variations in , and on the system dynamics.
Discussion
We modeled the transportation of parts in a factory, and revealed fundamental characteristics of production flow that are caused by the effects of exclusion and coalescence of particles under supply, demand, and particle removal fluctuations.
First, we confirmed the propagation of a stockout and demand deficiency caused by a single supply error (Fig. 2). With this knowledge, we then analyzed the characteristics of the end product production rate and found steep decay for small supply-error rates
Acknowledgments
We thank Hiroshi Takahashi, Kazuya Inaba, Kenta Yoshikawa, and Naokata Komuro for useful discussions. We would also like to acknowledge Ryosuke Nishi for his valuable comments. This work was supported by JSPS Grants-in-Aid for Scientific Research (13J05086).
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