Groupe d’études et de recherche en analyse des décisions

G-88-05

Loading an N M/G/1 Queue-Like Job Shop

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We consider a queue-like job shop in which a single resource (such as an operator, a robot, etc.) loads jobs onto machines. Jobs arrive at a station at known Poisson rates, and await (in a FCFS queue) for the resource to visit their queue so that they may be loaded (if the machine is free). The loading resource is assumed to "walk" through all stations following a predetermined order, stopping at a station only if a job has completed processing and if the machine's queue is not empty. The amount of time required to load a job is a random variable with known distribution function while the amount of time, net of loading, that the resource spends "walking" and returning to a given station is also known.

Our purposes in this paper are two-fold. First, due to the complex analytical structure of the problem presented, we use reasonable approximations to characterize the operating characteristics of the individual queues such as machine idleness, virtual delays etc., (justified through numerical analysis) and second, to provide a manufacturing economic analysis of the loading resource in terms of its characteristics (walking time, loading times, loading-unloading technology and costs) and the manufacturing characteristics of such a job shop. In addition, a specific problem is investigated, for which we use a computer program to evaluate the sensitivity of our model to selected parameters and to the approximations made.

The importance of this problem arises hand in hand with the increased use of automation in manufacturing and the adoption of flexible and just-in-time manufacturing concepts (e.g. see Buzacott and Shantikumar [4]). For example, firms such as Renault, G.M. and other car manufacturers have invested extensively in loading resources to reduce loading time, and facilitate the switching of machining from job to job, and thereby increasing machining efficiency and adaptability. In some respects, the strategic notions of just-in-time and flexibility are fueling and are fueled by a gradual reduction of machine conversion and loading costs. our analysis provides a theoretical and practical framework for studying these problems.

, 39 pages