Modeling the supplier uncertainty with phase-type distributions in inventory problems

This study considers a stochastic inventory nnodel where the supply availability is subject to random fluctuations. The periods in which the supplier is available (ON) or unavailable (OFF) are modeled as a semi-Markov process. During ON periods the {q,r) policy is applied. During OFF periods, the amount enough to bring the inventory position to q + r is ordered as soon as the supplier becomes available again. The regenerative cycles are identifled by observing the inventory position and using the renewal reward theorem the average cost per time objective function is derived. In our study, a K-stage Phase-Type distribution for ON periods and a general distribution for OFF periods are assumed. In our study, the problem is theoretically solved for Kstage Phase-Type distributions; additionally numerical computations are made for 2-stage Phase-Type distributions. For large q values the structure of the objective function is investigated.