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    Publication
    Bayesian analysis of doubly stochastic Markov processes in reliability
    (Cambridge University Press (CUP), 2021) Ay, Atilla; Soyer, Refik; Landon, Joshua; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631
    Markov processes play an important role in reliability analysis and particularly in modeling the stochastic evolution of survival/failure behavior of systems. The probability law of Markov processes is described by its generator or the transition rate matrix. In this paper, we suppose that the process is doubly stochastic in the sense that the generator is also stochastic. In our model, we suppose that the entries in the generator change with respect to the changing states of yet another Markov process. This process represents the random environment that the stochastic model operates in. In fact, we have a Markov modulated Markov process which can be modeled as a bivariate Markov process that can be analyzed probabilistically using Markovian analysis. In this setting, however, we are interested in Bayesian inference on model parameters. We present a computationally tractable approach using Gibbs sampling and demonstrate it by numerical illustrations. We also discuss cases that involve complete and partial data sets on both processes.
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    Optimal maintenance of semi-Markov missions
    (Cambridge University Press (CUP), 2015) Cekyay, Bora; Department of Industrial Engineering; Özekici, Süleyman; Faculty Member; Department of Industrial Engineering; College of Engineering; 32631
    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.
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    Optimal pricing and production policies of a make-to-stock system with fluctuating demand
    (Cambridge University Press (CUP), 2009) Gayon, Jean-Philippe; Talay-Degirmenci, Isilay; Department of Industrial Engineering; Department of Industrial Engineering; Karaesmen, Fikri; Örmeci, Lerzan; Faculty Member; Faculty Member; Department of Industrial Engineering; College of Engineering; College of Engineering; 3579; 32863
    We study the effects of different pricing strategies available to a production-inventory system with capacitated supply, which operates in a fluctuating demand environment. The demand depends on the environment and on the offered price. For such systems, three plausible pricing strategies are investigated: static pricing, for which only one price is used at all times, environment-dependent pricing, for which price changes with the environment, and dynamic pricing, for which price depends on both the current environment and the stock level. The objective is to find an optimal replenishment and pricing policy under each of these strategies. This article presents some structural properties of optimal replenishment policies and a numerical study that compares the performances of these three pricing strategies.
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    Solution approaches for simultaneous scheduling of jobs and operators on parallel machines
    (Gazi Üniversitesi, 2012) Edis, Emrah B.; Özkarahan, Irem; Department of Industrial Engineering; Oğuz, Ceyda; Faculty Member; Department of Industrial Engineering; College of Engineering; 6033
    Production scheduling and machine maintenance are two inseparable operational issues in multistage production systems. Previous studies attempted to deal with this issue by simplifying this problem due to the degradation uncertainties of the machines, ignoring the substantial interactions between these two tasks and leading to less efficiency of the entire production system. In this study, we fill the gap and formulate the joint optimization problem with more emphasis on the interaction between job scheduling and maintenance for a series-parallel multistage production system. Specifically, a mixed-effect degradation model is proposed to leverage the underlying interaction between job scheduling and machine maintenance. To efficiently solve this joint problem, several properties from this formulation have been derived. A two-phase method considering condition-based information, with a proactive algorithm for local intensification and a condition-based workload reallocation strategy & maintenance strategy, is then developed to address the uncertainties from the machine degradation status. A numerical study is finally borrowed to demonstrate the higher production efficiency achieved by applying the proposed method, compared with other benchmarks. —This study is motivated by a practical scenario where both job allocation and maintenance need to be determined simultaneously in the multistage production system by the operators to achieve time and cost efficiency. We focus on developing a new scheme that job scheduling and machine maintenance are able to be conducted simultaneously. Two issues are noteworthy to better implement this scheme. First, for characterizing the interaction between scheduling and maintenance, the data collected in real-time can provide a sufficient basis for the degradation path, and the production parameters can be acquired from real practice. Second, this scheme can be offered to help decision-making by a two-phase solution framework given the condition-based information during the production process. Specifically, an appropriate job allocation planning can be obtained offline in the first phase of the proposed two-phase solution framework under a limited computing resource. Meanwhile, a condition-based adjustment strategy in the second phase can update the solution based on the in-situ condition information collected from the data platform to achieve higher production efficiency.