Periodic Review Perturbed Demand Inventory Models with Stochastic Demand

Perturbed demand models penalize retailers for stock-outs by altering future demand, opposed to the classic method of penalizing stock-outs by imposing a cost proportional to the number of stock-outs. In this paper we consider a periodic-review, perturbed-demand inventory model with stochastic demand. Current consumer willingness to purchase the product after stock-out occurs is captured by a state variable referred to as demand deflation. First we consider the infinite horizon case with instantaneous delivery where we show that the optimal policy converges in steady state and has a base-stock structure that is dependent on demand deflation. Next, we extend the model to include positive reorder lead times and show the optimal policy converges but does not take on an easy to characterize policy. Lastly we consider the finite horizon version of this problem. Due to the computational complexity of this problem we develop heuristics which are shown to have small deviations from optimal gain.;Each perturbed demand problem variation can be formulated and solved as a Markov decision process (MDP) to determine the optimal policy and expected gain. For perturbed demand models, the optimal policy takes on a more complex structure than typical penalty cost models because the order quantity is dependent on current inventory and demand deflation. In traditional penalty cost models there is an optimal policy corresponding to a specific penalty cost value, but the value of the penalty cost can be difficult to determine. Our perturbed demand model creates a common reality in which these penalty cost policies can be tested. The penalty cost policy resulting in the best gain within our perturbed demand reality is one way to estimate the value of the penalty cost which most accurately represents customer behavior.