Exact Expressions for the First Two Moments of Job Flow Time in a Job Shop

Abstract

This paper presents analytical expressions for the moments of job flow time in a job shop by computing the moments of a random number of random variables assuming that the job shop satisfies the sufficient conditions of the Jackson decomposition principle. The mathematical equivalence of the proposed method to the Laplace transform method is shown and then demonstrated in a simple example. Then, expressions for the moments of job flow time in more realistic (and more complex) job shop settings are derived by computing the moments of a random number of random variables, provided that expressions for the moments of job flow time are available for the corresponding single stage shop. It is shown that the analytical expressions developed are exact as long as the assumptions of the Jackson decomposition principle hold. Any violation of these assumptions makes the derived expressions approximations, and their accuracy should be tested by simulation.