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We start the analysis of manufacturing systems by first explaining the way we perceive them. Then we will focus on some simple cases of work stations with and without failures and demonstrate how these systems can be analyzed. A work station can be thought of as a work place in the shop floor as depicted in Fig3.1, where jobs arrive to be processed or machined. They are kept in the buffer zone (work-in-process (WIP) inventory) until their process begins and are transferred to other areas in the facility after their process is completed. The machines may experience random failures. Our approach in studying work stations in manufacturing environments is to perceive them as queueing systems. The flow of incoming jobs, either one by one or in batches, forms the arrival stream, which can be identified by the statistical characteristics of the time between consecutive arrivals. Service times are usually the processing times of jobs in the work station. Processing times may be augmented by random failures and repairs. Thus, a work station may very well be looked at as a queueing system with single or multiple servers, with finite or infinite waiting room (input buffer), and with a service policy depending on the operating characteristics of the work place. Queueing theory is a fairly well-developed field, and a considerable amount of research is being done on a variety of queueing systems and queueing networks. We demonstrate in this and other chapters that with some level of abstraction, queueing theory and queueing networks can be very useful in the analysis and design of manufacturing systems. In fact, queueing modeling of numerous systems have already been studied and can be found in Gross and Harris ([1974]), Cooper ([1990]), and Kleinrock ([1975]), among various others. Next we give a short introduction on the formulation and the analysis of queueing systems.

Various manufacturing facilities in different industrial sectors have some type of series arrangements of production stages. Jobs in a variety of forms are transferred from one stage to another to be processed in some order and leave the system as finished or semifinished products. The flexibility generated by computer-controlled machinery enables production stages to handle a variety of operations. This in turn creates a sequence of intelligent work stations in the shop floor, processing or assembling different types of products. Each work station may consist of one or more machines, one or more operators (robots may also be involved), and a workin-process buffer, as depicted in a rather abstract form in Fig4.1. Upon process completion at a work station, jobs join the work-in-process buffer at the next work station, if space is available. Conceivably, some cases may require repetition of a certain process or a set of processes for a number of times. Some of the work stations may process jobs in batches. Transfer of jobs from one station to another is usually done by means of vehicles or conveyors. Eventually, jobs depart from the system, which may happen practically at any of the work stations. In general, flow lines are push-type systems where little attention is given to the finished-product inventory. The line is to produce as much as it can with the assumption that all finished products are either used or demanded. Otherwise, it has to stop producing when there is an excessive accumulation of finished products. Those systems are known as pull-type systems and will be discussed in Chapter 7.

Transfer lines are common in industries such as food, automotive, electronics, and pharmaceutical, among many others. A transfer line is a synchronous production line consisting of several work stations in series integrated into one system by a common transfer mechanism and a control system. Each station is a stopping point at which operations (machining, inspection, etc.) are performed on the work pieces. The main feature of transfer lines is that the machines are connected through conveyors and the units on the entire conveyor system move one slot at a time synchronously. The transfer points in time are determined by the maximum of the unit processing times at all the stations, which is referred to as the cycle time. Typical examples of these systems are filling and packaging lines in the pharmaceutical and food industries, and the assembly lines in various other industries. Transfer lines operate like a single machine when all the machines are up and producing one unit per cycle. However, they experience failures like any other production line. Different manufacturing practices may necessitate different line designs. Also, the procedures as to what to do when a failure occurs may vary from one manufacturing environment to another. For instance, the entire system may stop, or parts of the system may remain unaffected by a failure and may continue to operate utilizing the conveyor segments and the buffer storages. The units on failed machines may be discarded, reworked, or processed further for the remaining unfinished work after the repair is completed. In food and pharmaceutical manufacturing facilities, depending on the cost and the perishability concerns, the unit on a failed machine may be removed and discarded.

A manufacturing system can be viewed as an arrangement of tasks and processes, properly put together, to transform a selected group of raw materials and semifinished products to a set of finished products. The three basic functions of manufacturing are procurement, production and distribution. Clearly, there are other functions in a supporting, role such as planning, design, accounting, personnel management, and marketing, among others. The raw material is procured and converted through the production process to semifinished units, which are sometimes referred to as assemblies or subassemblies, and to finished products to be finally stored in the warehouse to meet the customer demand. Distribution deals with the transfer of the finished products to warehouses at different locations. The flow of materials shown in Fig1.1 depicts the various stages of manufacturing.

This chapter provides a refresher on probability and random processes that is essential for a healthy coverage of the remaining chapters of this book. The review will be done to the extent of our interest in the context of manufacturing systems.

In Chapters 4 and 5, we studied multistage, push-type manufacturing systems in the context of production lines. In push-type systems, the production schedule is decided based on the demand forecasts, in an upstream part of the system. That is, attention is not given to the immediate market response which may have a significant impact on the finished-product inventory levels. Therefore, push-type systems have difficulties in promptly adapting to the changes in the market, such as demand fluctuations. The forecasting effort itself is a source of considerable error in the master schedule. In practice, to circumvent this difficulty, the inventories are kept at high levels. Notice, for instance, that the production lines we have studied earlier assume a finished-product warehouse of unlimited capacity.