رویکرد پویا برای اندازه گیری انعطاف پذیری ماشین آلات و مسیریابی سیستم های تولید

The ability for a manufacturing system to easily adapt to various uncertainties in their production system is described as manufacturing flexibility. Over the past two decades manufacturing flexibility has become an important part of many production systems. Existing models, however, only include a few of the many technological attributes that can be found in manufacturing systems. This study considers a number of technological attributes that are common to manufacturing systems and incorporates them in the development of two manufacturing flexibility models that evaluate the performance of production systems. The first model defines a measure for machine flexibility and the second defines a measure for routing flexibility. Technological attributes such as the efficiency of processing an operation, the number of different operations a machine can perform, the fraction of an operation that can be transferred during disturbances, the probability of transferring an operation to alternative routes, are just a few of the attributes included in our flexibility models. We perform a set of tests that illustrate the strength of our models with respect to machine and routing flexibilities and highlight some of the weaknesses present in previous flexibility models.

Due to recent technological developments, customer satisfaction has grown to include the quick and efficient delivery of new products and merchandize to the shelves of retailers. To remain competitive, many companies have improved their production process by introducing manufacturing flexibility. The term manufacturing flexibility has become an exclusive expression that indicates a manufacturing system's ability to adhere to disturbances in the production process and produce customer-oriented products at low costs and greater response sensitivity to dynamically changing manufacturing systems. Manufacturing flexibility has received an increasing amount of popularity in the past two decades as it provides companies with the ability to adhere to disturbances in the production process so that new and existing products can be produced more rapidly. Also, since future customer requirements cannot be predicted, flexibility allows for a quick adaptive response to unpredictable situations in manufacturing. In fact, many successful manufacturing companies have the capacity to accommodate for several changes in product design, input, output, and the manufacturing process. Each modification can be categorized as either: an internal or an external change. Internal changes account for manufacturing modifications caused by the deterioration of machines or tools, the failure of machines or tools, or the implementation of different sequencing or dispatching rules to the production process. External changes consist of modifications made to account for customer demand and supply uncertainties. When manufacturing systems are flexible, they can respond to dynamic production necessities and requirements easily. The traditional flexibility concept is static; where manufacturing capabilities for handling uncertainties from the environment, the inputs and outputs, and the production process are considered to be fixed (Hyun and Ahn, 1992). There are several articles that detail various static flexibility models ( Hyun and Ahn, 1992, Beach et al., 2000 and Shuiabi et al., 2005); however, if the manufacturing capabilities for handling uncertainties are subject to change dynamically, the existing mathematical models fail. To account for the inherent flexibility of today's demanding manufacturing systems, the dynamic aspect of flexibility must be incorporated in the mathematical framework of the problem. Significant efforts to explore the manufacturing concept domain and measure flexibility have been made. Due to the multi-dimensional nature of manufacturing flexibility, various flexibility taxonomies have been developed. Consequently, flexibility has been studied as a physical property, a strategic tool, an attribute of decision making, and an economic indicator. Studies by Buzacott (1982), Gerwin (1987), Taymaz (1989), Gupta and Buzacott (1989), Brill and Mandelbaum (1989), Chandra and Tombak (1992), Bernado and Mohamed (1992), Nagarur (1992), Hyun and Ahn (1992), Das and Nagendra (1993), Stecke and Raman (1995), Chen and Chung (1996), and Shewchuk and Moodie (1998) are just a few amongst the many flexibility models. Many of the existing flexibility studies have only investigated the concept of flexibility in relation to a particular domain and a specific objective, instead of considering an entire manufacturing system (Gerwin, 1987 and Sarker et al., 1994). As a result, current flexibility models are simply based on a limited analysis of manufacturing systems (Koste and Malhotra, 1999). Therefore, while there are several taxonomies that attempt to define manufacturing flexibility, they are incomplete or too abstract to explain the fundamental concept of flexibility (Gupta and Buzacott, 1989 and Shewchuk and Moodie, 1998). Thus, the meaning and implementation of manufacturing flexibility still remains ambiguous (Chang et al., 2001). Subsequently, an analytical model capable of generating a clear relationship between the degree of a system's flexibility and the level of a system's performance has yet to be defined (Slack, 1987, Kumar, 1987 and Gupta and Goyal, 1989). We develop mathematical models to measure machine and routing flexibilities by integrating a variety of technological attributes and elements within manufacturing systems. Generally, machine flexibility (MF) is the degree of versatility a machine possesses with regards to performing various operations in the production process. Whereas, routing flexibility (RF) is defined as a system's ability to continue with an operation(s) despite disturbances in the production process. In order to capture the dynamic aspect of machine and routing flexibilities, we consider elements such as: the probability of assigning an operation to a machine, the probability of assigning an operation from one machine to another, the probability of transferring an operation from one machine to another, the aggregate efficiency of the material handling system for transferring an operation from one machine to another, and the availability of a machine. These models provide comprehensive flexibility measurements that may be used to evaluate and rank manufacturing systems according to their inherent flexibility. The motivation behind our model stems from the workings of Sarker et al. (1994), in which they present a survey and critical review of flexibility measures in manufacturing systems. The review provides evidence that MF and RF are two of the most fundamental and important types of flexibilities. Also, that existing MF and RF measures are not generic models and should consider more than one or two technological attributes. Although, isolated methods for measuring manufacturing flexibility have been developed, we provide a generic MF model and a generic RF model that incorporates a number of technological attributes in its design. For instance, given a manufacturing system, an investor knows the configuration and the processing capability of each machine, and the material handling system. Also the investor is familiar with the types of products produced. Thus, all necessary technological attributes that are required to value the built in machine and routing flexibilities of the manufacturing process are known. One can evaluate the flexibility of such a system using our proposed models, in which we provided two numerical examples for each type of flexibility that illustrates how machine and routing flexibilities can be measured in practice. Furthermore, embedded in these examples is a means of comparing two alternate manufacturing systems. Thus, in addition to the academic relevance of our approach, our research also presents many practical implications. The paper is organized as follows: in Section 2 we review MF definitions and technological attributes defined by previous literatures, present our MF model (2.1), and follow with numerical examples (2.2). In Section 3, we discuss the definitions and technological attributes presented in relevant literatures on RF. Next, we define and detail our RF model (3.1), which includes numerical examples (3.2). Finally, in Section 4, we present conclusions and provide suggestions for future research directions with regards to manufacturing flexibility.

We have presented two models of manufacturing flexibilities: machine flexibility and routing flexibility. Both of the flexibility measures that we define posses the capacity to capture a number of different attributes common to many manufacturing systems. The machine flexibility model considered two main operations: the initial assignment of operations to machines and transferring an operation from one machine to another during disturbances. These operations required technological parameters such as, the probability of demand occurrence of an operation, the efficiency of a machine to process an operation, the relative transferring capability of a machine with respect to another machine, the probability of transferring an operation from one machine to another, etc. Previous literatures on this topic, Das and Nagendra (1993), Nagarur (1992), and Chen and Chung (1996), at most consider only one of such technological parameters. From Section 2.2 one can observe the faults common to many previous models. As presented, our model encapsulates many, if not all of the attributes found in manufacturing systems. Thus, we provide a more representative value of machine flexibility. With regards to our routing flexibility model we also include many more routing attributes than those found in previous literatures. A few of the technological parameters that we account for include: the efficiency of alternative routes, the probability of transferring an operation to alternative routes, the number of potential routes, and the availability or utilization of alternative routes. From the numerical examples section, the value of our routing flexibility measure is much more representative than that of the existing models. For instance, as shown Nagarur (1992) reports a high RF value for a system that only contains one route linking machines together. This leaves out attributes that we account for. Our proposed flexibility models are useful tools for practitioners, which enables them to evaluate and rank their manufacturing systems according to the inherent flexibility they posses. For researchers, these models may initiate the development of more rigorous flexibility investigations that incorporate many of the factors mentioned. Future research directions for this study lie in developing a large scale simulation model of a manufacturing system that considers several products and machines. This may also include a system that deals with many different types of flexibility and performance measures, and incorporates multiple processing plants and multiple dispatching rules.