CONTINUOUS-REVIEW INVENTORY PROBLEM WITH RANDOM SUPPLY INTERRUPTIONS

This paper considers a continuous-review stochastic inventory problem with random demand and random lead-time where supply may be disrupted due to machine breakdowns, strikes or other randomly occurring events. The supplier availability is modelled as a semi-Markov process (more specifically, as an alternating renewal process). The standard (q, r) policy is used when the supplier is available (ON), i.e., when the inv entory position reaches the reorder point r, q units are ordered to ra ise the inventory position to the target level of R = q + r. The form of the policy changes when the supplier becomes unavailable (OFF) in w hich case orders cannot be placed when the reorder point r is reached. However, as soon as the supplier becomes available again one orders e nough to bring the inventory position up to the target level of R. The regenerative cycles are identified by observing the inventory positio n process. We construct the average cost per time objective function u sing the renewal reward theorem. It is assumed that the duration of th e ON period is E-k (i.e., k-stage Erlangian) and the OFF period is gen eral. In analogy with queuing notation we call this an E-k/G system. B y employing the 'method of stages', we obtain a problem with a larger state space for the ON/OFF stochastic process; but the resulting ON pr ocess can now be analyzed using Markovian techniques. For asymptotic v alues of q, the objective function assumes a particularly simple form which is shown to be convex under mild restrictions on the density fun ctions of demand. Numerical examples illustrate the results. (C) 1997 Elsevier Science B.V.