Stationary Inventory policy

Assuming demand is stationary and independently distributed across periods Di = D we further obtain that G y ) = Gi y ) since the single-period game is the same in each period. By restricting consideration to the stationary inventory policy yi — yj t = 1,2,..., we can find the solution to the multi-period game as a sequence of the solutions to a single-period game Gi yi) which is... 

In this example, the matrix F is unstable (eigenvalues= 0,1 ), but = = Hy. Thus, the Kalman filter for this model converges to a steady state, and so the framework in this paper can still be used to devise and characterize appropriate classes of stationary inventory policies for the ARIMA(0,1,1) case. In fact, a detailed treatment of this model is provided in Graves (1999). 

For the revenue management problem, an example of a stationary deterministic policy is to order quantity q = if the inventory level s < ij, for chosen constants and to set the price... 

Production decisions may change based on the structure of the demand (deterministic vs. stochastic, stationary). Inventory review policies (periodic review vs. continuous review) may affect the production decisions as well. 

Veinott, A. 1965. Optimal policy for a multi-product, dynamic, non-stationary inventory problem. Management Sci. 12 206-222. 

Many research problems that address pricing and production decisions with fixed production set-up cost fall within the area of the Economic Order Quantity (EOQ) model). The general EOQ model inventory model has been studied frequently in inventory literature (see [164] for a review). The problem consists of multiple periods in a fixed time horizon, with a stationary deterministic function in each period ordering or production costs have a fixed and variable component. Since demand is deterministic, the optimal policy will leave zero inventory at the end of each time cycle, so each period may be considered... 

In [34], Chen and Simchi-Levi consider the infinite horizon model with stationary parameters and general demand processes. They show that in this case, the (s, 5, p) policy identified by Thomas is optimal under both the average and discounted expected profit criteria. They further consider the problem with continuous inventory review in [35], and show that a stationary (s, S,p) policy is optimal for both the discounted and average proft models with general demand functions and general inter-arrival time distribution. 

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