Optimising Flow in an M/M/1 System with Shortage Cost: A Theory of Constraints Approach

O. Adetunji and V.S.S. Yadavalli (S. Africa)


Theory of Constraints, flow rate, buffer size, Markov queuing process


A model is presented here that shows how flow should be managed in a production environment that utilises the Theory of Constraints philosophy. It is assumed that the system is Markovian (M/M/1/∞) and that a fixed once off stipulated cost is incurred for every unit of shortage that is experienced in the production system. The system is assumed to be capacity constrained and so traffic intensity, ρ, value of less than unity is considered. This model is a more generalised form of the initial model developed in Adetunji et al [1] where it was shown that it is better to control the inventory in a TOC environment using the optimal flow rate, a process that leads to dynamic buffering than to control it using the maximum buffer size. The model here shows that when there is a positive cost of shortage incurred for lost throughput, the optimal flow rate should be less than when a zero shortage cost is assumed.

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