Continuous inventory control with stochastic and non-stationary Markovian demand

Non-stationary demand is common in many industrial settings and accounting for the non-stationarity in the demand process significantly complicates the analysis of inventory policies. This work presents an efficient computational framework, which utilizes a Markovian representation, to model and solve for the stochastic and non-stationary performance measures of an inventory system. The non-stationary and stochastic characteristics of the demand process are captured by an approximate Phase-type distribution. The differential equations corresponding to the Markovian representation are presented along with an algorithmic approach to numerically solve for the non-stationary performance measures. Time-dependent (st, St) continuous replenishment policies with a fixed ordering cost are investigated over a finite time horizon. The trade-off between the computational complexity and cost effectiveness of the policies are investigated numerically under different cost and demand distribution parameters. The numerical study also investigates the accuracy of using the time-dependent Phase-type distribution to capture key descriptors of the non-stationary demand process.