Browsing by Subject "Base-Stock Policy"

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Open Access
Finite perturbation analysis methods for optimization of inventory systems with non-stationary Markov-modulated demand and partial information
(2018-01) Güleçyüz, Süheyl
The state of the economy may fluctuate due to several factors, and the customer demand is a affected from the fluctuations of the state of the economy. Although the inventory holders can predict the state of the economy based on the demand realizations, they generally do not have the true state information. The lack of information can be extended to the transition probabilities in the state, and the demand distributions associated with each state. Further extensions may include the actual number of demand states. We consider a single-item, periodic-review inventory system with Markov-modulated discrete-valued demand, constant lead time, and full backlogging. The true demand distribution state is partially observed based on the realized demands. We study the infinite horizon average cost minimization problem, in which the optimal inventory replenishment policy is a state-dependent base-stock policy. We develop a local search method based on finite perturbation analysis (FPA) to find the base-stock levels for a finite number of discretized state beliefs. We then extend our search method to the unknown transition matrix and demand distribution case. We compare the FPA-based local search algorithm with a myopic base-stock policy, the Viterbi algorithm, and the sufficient statistics method, in terms of the average cost. Finally, we analyze how the average cost changes with respect to the estimated number of demand states when the actual number of states is unknown.
Open Access
Structural results for average-cost inventory models with partially observed Markov-modulated demand
(2018-05) Avcı, Harun
We consider a discrete-time in nite-horizon inventory system with full backlogging, deterministic replenishment lead time, and Markov-modulated demand. The actual state of demand can only be imperfectly estimated based on past demand data. We model the inventory replenishment problem as a Markov decision process with an uncountable state space consisting of both the inventory position and the most recent belief about the actual state of demand. When the demand state evolves according to an ergodic Markov chain, using the vanishing discount method along with a coupling argument, we prove the existence of an optimal average cost that is independent of the initial system state. With this result, we establish the average-cost optimality of a belief-dependent base-stock policy. We then discretize the belief space into a regular grid. The average cost under our discretization converges to the optimal average cost as the number of grid points grows large. Finally, we conduct numerical experiments to evaluate the use of a myopic belief-dependent base-stock policy as a heuristic. On a test bed of 108 instances, the average cost under the myopic policy deviates by no more than a few percent from the best lower bound on the optimal average cost obtained from our discretization.