Analysis of a (Q, r, T) inventory policy with deterministic and random yields when future supply is uncertain

This paper considers a stochastic inventory model where the quantity ordered sometimes may not be available due to strikes, etc. We represent the supplier's availability process as a two-state continuous time Markov chain where one state corresponds to availability and the other state corresponds to unavailability of the supplier. The problem is to determine the reorder point, the order quantity when the system is found in ON state, and how long to wait before the next order if the system is in OFF state. It is assumed that the state of the system is identified at a cost. Using the renewal reward theorem we construct the objective function as the long-run average cost. Numerical sensitivity analysis results are provided. We also analyze the problem when the yield (i.e., amount received, if available) is random, and discuss an example with Beta distributed yield.