THE APPLICATION OF QUEUEING THEORY:Example 3—How Many Tool Cribs?

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Example 3—How Many Tool Cribs?

The MECHANICAL COMPANY is designing a new plant. This plant will need to include one or more tool cribs in the factory area to store tools required by the shop mechanics. The tools will be handed out by clerks as the mechanics arrive and request them and will be returned to the clerks when they are no longer needed. In existing plants, there have been frequent complaints from supervisors that their mechanics have had to waste too much time traveling to tool cribs and waiting to be served, so it appears that there should be more tool cribs and more clerks in the new plant. On the other hand, management is exerting pressure to reduce overhead in the new plant, and this reduction would lead to fewer tool cribs and fewer clerks. To resolve these conflicting pressures, an OR study is to be con- ducted to determine just how many tool cribs and clerks the new plant should have.

Each tool crib constitutes a queueing system, with the clerks as its servers and the mechanics as its customers. Based on previous experience, it is estimated that the time required by a tool crib clerk to service a mechanic has an exponential distribution, with a mean of -- minute. Judging from the anticipated number of mechanics in the entire factory area, it is also predicted that they would require this service randomly but at a mean rate of 2 mechanics per minute. Therefore, it was decided to use the M/M/s model of Sec. 17.6 to represent each queueing system. With 1 hour as the unit of time, 120. If only one tool crib were to be provided, also would be 120. With more than one tool crib, this mean arrival rate would be divided among the different queueing systems.

The total cost to the company of each tool crib clerk is about $20 per hour. The cap- ital recovery costs, upkeep costs, and so forth associated with each tool crib provided are estimated to be $16 per working hour. While a mechanic is busy, the value to the company of his or her output averages about $48 per hour.

Sections 26.3 and 26.4 include discussions of how this (and additional) information was used to make the required decisions.

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