Maintenance policy structure investigation and optimisation of a complex production system with intermediate buffers

Existing research about the maintenance optimisation of production systems with intermediate buffers largely assumed a series system structure. However, practical production systems often contain subsystems of ring structures, for example, rework and feedforward. The maintenance optimisation of these complex systems is difficult due to the complicated structure of maintenance policies and the large search space for optimisation. This paper proves the control limit property of the optimal condition-based maintenance policy. Based on the control limit property, approximate policy structures that incur a smaller policy space are proposed. Because the state space of a production system is often large, the objective function of the maintenance optimisation cannot be evaluated analytically. Consequently, a stochastic branch and bound (SB&B) algorithm embedding a sequential simulation procedure is proposed to determine a cost-efficient condition-based maintenance policy. Numerical studies show that the proposed maintenance policy structures can deliver a cost-efficient maintenance policy, and the performance of the SB&B algorithm is enhanced by the inclusion of a sequential simulation procedure.

Free paratopological groups

Let FP(X) be the free paratopological group on a topological space X in the sense of Markov. In this paper, we study the group FP(X) on a $P_\alpha$-space $X$ where $\alpha$ is an infinite cardinal and then we prove that the group FP(X) is an Alexandroff space if X is an Alexandroff space. Moreover, we introduce a~neighborhood base at the identity of the group FP(X) when the space X is Alexandroff and then we give some properties of this neighborhood base. As applications of these, we prove that the group FP(X) is T_0 if X is T_0, we characterize the spaces X for which the group FP(X) is a topological group and then we give a class of spaces $X$ for which the group FP(X) has the inductive limit property.

Existence, uniqueness and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order

In this paper, we apply certain measure of noncompactness and fixed point theorem of Darbo type to derive the existence and limit property of solutions to quadratic Erdélyi-Kober type integral equations of fractional order with three parameters. Moreover, we also present the uniqueness and another existence results of the solutions to the above equations. Finally, two examples are given to illustrate the obtained results.