A note on a robust inventory model with stock-dependent demand

We investigate an inventory model with stock-dependent demand where larger pile of stock displayed leads the customer to purchase more. The dependency of demand on the inventory level is modelled as a monomial function whose shape and scale parameters are stochastic. We present a linear regression-based method for constructing ellipsoidal representations of the parameter uncertainty, which are subsequently incorporated into the inventory model under the robust optimisation framework. We show that the resulting robust optimisation model can be transformed into an equivalent convex programme, and also prove that a robust optimal inventory replenishment policy is of the base-stock type. Through a numerical illustration of the proposed approach and a performance analysis based upon Monte Carlo simulation, we demonstrate that robust optimal order decisions exhibit a unique advantage over deterministic ones.