Problem: A company has a special purpose processing area that makes parts used throughout the company. A variety of different parts are made on a single machine and transported to various locations within the company for storage until they are needed in that area. The company has a very experienced employee who does the analysis of the parts currently available throughout the company and then decides what part type is to be made next at this machine. The part-needs analysis and release for processing is performed by this employee in two steps. The needs-analysis step takes 1/2 hour on average, but with the variety of parts to be analyzed, this time is exponentially distributed. Historical data indicates that 7 of every 9 parts analyses results in a standard part-type release and, since the part processing information is already on file, the part order is then released to the machine immediately.

Two of every nine analyses, however, results in the need for a special-purpose part for which the processing data are not available. Thus, this employee then develops a complete processing plan for the part. This processing plan development time averages an additional 2.5 hours. Due to the variety of the special purpose parts, it has been observed that this extra preparation time also is exponentially distributed. The order development employee is additionally charged with keeping the flow of jobs within the machine area reasonably smooth and timely. Towards this objective, the employee has developed the following release strategy. If there are 3 part orders already in the machining area, the employee holds the current completed order at her desk until a part has been completed and shipped. Then the "ready" order is given to the machine area personnel. If there is a completed (but blocked) order on the analyses employee's desk, no new order analysis is started until the blocked order has been cleared and been released to the machining area.

The machining area has only one machine and the average time for processing an order is 70 minutes. Due to the variety of part types, this processing time is exponentially distributed. Develop a model of the special parts processing workstation (order analyses through processing). This encompasses the analyses employee and the machine (there is an operator for the machine and it is not necessary to keep track of this operator). First draw a diagram of every possible configuration that this workstation can encounter. From this set of configurations, develop a state-space representation for these configurations. Then draw a rate-connected state diagram relating all of these configurations. Develop the steady-state equations for the rate-state diagram. Solve these equations for the steady-state probabilities. And finally, develop the workstation performance measures for this problem (machine utilization, orderdevelopment employee utilization, and throughput).