Z.M. Avsar

Capacitated two-echelon inventory models for repairable item systems

In this paper, we consider two-echelon maintenance systems with repair facilities both at a number of local service centers (called bases) and at a central location. Each repair facility may be considered to be a job shop and is modeled as a (limited capacity) open queuing network, while any transport from the central facility to the bases (and vice versa) is modeled as an ample server. At all bases as well as at the central repair facility, ready-for-use spare parts are kept in stock. Once an item in the field fails, it is returned to one of the bases and replaced by a ready-for-use item from the spare parts stock, if available. The returned failed item is either repaired at the base or shipped to and repaired at the central facility. In the case of local repair, the item is added to the local spare parts stock as a ready-for-use item after repair. If a repair at the central facility is needed, the base orders an item from the central spare parts stock to replenish its local stock, while the failed item is added to the central stock after repair. Orders are satisfied on a first-come-first-serve basis while any requirement that cannot be satisfied immediately either at the bases or at the central facility is backlogged.

A decomposition approach for undiscounted two-person zero-sum stochastic games

Abstract. Two-person zero-sum stochastic games are considered under the long-run average expected payoff criterion. State and action spaces are assumed finite. By making use of the concept of maximal communicating classes, the following decomposition algorithm is introduced for solving two-person zero-sum stochastic games: First, the state space is decomposed into maximal communicating classes. Then, these classes are organized in an hierarchical order where each level may contain more than one maximal communicating class. Best stationary strategies for the states in a maximal communicating class at a level are determined by using the best stationary strategies of the states in the previous levels that are accessible from that class. At the initial level, a restricted game is defined for each closed maximal communicating class and these restricted games are solved independently. It is shown that the proposed decomposition algorithm is exact in the sense that the solution obtained from the decomposition procedure gives the best stationary strategies for the original stochastic game.

Markov decision processes with restricted observations: Finite horizon case

In this article we consider a Markov decision process subject to the constraints that result from some observability restrictions. We assume that the state of the Markov process under consideration is unobservable. The states are grouped so that the group that a state belongs to is observable. So, we want to find an optimal decision rule depending on the observable groups instead of the states. This means that the same decision applies to all the states in the same group. We prove that a deterministic optimal policy exists for the finite horizon. An algorithm is developed to compute policies minimizing the total expected discounted cost over a finite horizon.

A note on two-person zero-sum communicating stochastic games

For undiscounted two-person zero-sum communicating stochastic games with finite state and action spaces, a solution procedure is proposed that exploits the communication property, i.e., working with irreducible games over restricted strategy spaces. The proposed procedure gives the value of the communicating game with an arbitrarily small error when the value is independent of the initial state.

Undiscounted two-person zero-sum communicating stochastic games

Consider two-person zero-sum communicating stochastic games with finite state and finite action spaces under the long-run average payoff criterion. A communicating game is irreducible on a restricted strategy space where every pair of action is taken with positive probability. The proposed approach applies Hoffman and Karps (1996) algorithm for irreducible games successively over a sequence of restricted strategy spaces that gets larger until an /spl epsiv/-optimal stationary policy pair is obtained for any /spl epsiv/>0. This algorithm is convergent for the games that have optimal strategies with a value independent of the initial state.