Optimal maintenance of semi-markov missions

Çekyay, Bora (Dogus Author)We analyze optimal replacement and repair problems of semi-Markov missions that are composed of phases with random sequence and durations. The mission process is the minimal semi-Markov process associated with a Markov renewal process. The system is a complex one consisting of non-identical components whose failure properties depend on the mission process. We prove some monotonicity properties for the optimal replacement policy and analyze the optimal repair problem under different cost structures

Reliability, MTIT and steady-state availability analysis of systems with exponential lifetimes

Çekyay, Bora (Dogus Author)Our analysis focuses mainly on coherent systems and series connection of k-out-of-n standby subsystems with exponentially distributed component lifetimes. We analyze system reliability, mean time to failure, and steady-state availability as a function of the component failure rates. Our primary objective is provide explicit expressions for these performance measures and obtain various characterizations on their mathematical structures. This primarily involves difference of convex functions which are known to be very useful in the context of optimization problems. (C) 2014 Elsevier Inc. All rights reserved

Portfolio selection in stochastic markets with HARA utility functions

In this paper, we consider the optimal portfolio selection problem where the investor maximizes the expected utility of the terminal wealth. The utility function belongs to the HARA family which includes exponential, logarithmic, and power utility functions. The main feature of the model is that returns of the risky assets and the utility function all depend on an external process that represents the stochastic market. The states of the market describe the prevailing economic, financial, social, political and other conditions that affect the deterministic and probabilistic parameters of the model. We suppose that the random changes in the market states are depicted by a Markov chain. Dynamic programming is used to obtain an explicit characterization of the optimal policy. In particular, it is shown that optimal portfolios satisfy the separation property and the composition of the risky portfolio does not depend on the wealth of the investor. We also provide an explicit construction of the optimal wealth process and use it to determine various quantities of interest. The return-risk frontiers of the terminal wealth are shown to have linear forms. Special cases are discussed together with numerical illustrations.Portfolio optimization Dynamic programming HARA utility functions Myopic policy Efficient frontier

Inventory management with random supply and imperfect information: A hidden Markov model

In most of the papers on inventory models operating in a random environment, the state of the environment in each period is assumed to be fully observed with perfect information. However, this assumption is not realistic in most real-life situations and we provide a remedy in this paper by assuming that the environment is only partially observed with imperfect information. We accomplish this by analyzing two formulations of single-item models with periodic-review and random supply in a random environment. In the first one, supply is random due to random capacity of production and random availability of transportation. We show that state-dependent base-stock policy is optimal if the capacity and all costs are observed, while demand and availability are unobserved. In the second model, we consider a model with random availability only with fixed-ordering cost. We show that state-dependent (s,S) policy is optimal if the availability process is observable.Random supply Random environment Imperfect information Base-stock policy Dynamic programming Sufficient statistics POMDP

Performance measures for systems with Markovian missions and aging

We consider a mission-based reliability system that is designed to perform missions consisting of a random sequence of phases or stages with random durations. The mission process is described by a Markov process, and the deterioration of the system is described by a finite state Markov process whose parameters depend on the mission process. We discuss several performance measures, including mission reliability, phase reliability, as well as mean residual life and availability. We derive explicit computational formulas, and provide an illustration. We also show how our model can be applied to any coherent system with s-independent and exponentially distributed component lifetimes

Optimal maintenance of systems with Markovian mission and deterioration

We consider the maintenance of a mission-based system that is designed to perform missions consisting of a random sequence of phases or stages with random durations. A finite state Markov process describes the mission process. The age or deterioration process of the system is described by another finite state Markov process whose generator depends on the phases of the mission. We discuss optimal repair and optimal replacement problems, and characterize the optimal policies under some monotonicity assumptions. We also provide numerical illustrations to demonstrate the structure of the optimal policies

Optimal policies for inventory systems with finite capacity and partially observed Markov-modulated demand and supply processes

We analyze a single-item periodic-review inventory system with random yield and finite capacity operating in a random environment. The primary objective is to extend the model of Gallego and Hu (2004) to the more general case when the environment is only partially observable. Although our analysis is specific to inventory systems, it can also be applied to production systems by replacing the fixed capacity supplier with a fixed capacity producer. Using sufficient statistics, we consider single-period, multiple-period and infinite-period problems to show that a state-dependent modified inflated base-stock policy is optimal. Moreover, we show that the multiple-period cost converges to the infinite-period cost as the length of the planning horizon increases.Random yield Fixed capacity Random environment Modified inflated base-stock policy Dynamic programming Sufficient statistics POMDP