In this article, we improve the efficiency of a turbine blade inspection robotic workcell. The workcell consists of a stationary camera and a 6-axis serial robot that is holding a blade and presenting different zones of the blade to the camera for inspection. The problem at hand consists of a 6-DOF (degree of freedom) continuous optimization of the camera placement and a discrete combinatorial optimization of the sequence of inspection poses (images). For each image, all robot configurations (up to eight) are taken into consideration. A novel combined approach is introduced, called blind dynamic particle swarm optimization (BD-PSO), to simultaneously obtain the optimal design for both domains. The objective is to minimize the cycle time of the inspection process, while avoiding any collisions. Even though PSO is vastly used in engineering problems, the novelty of our combinatorial optimization method is in its ability to be used efficiently in traveling salesman problems where the distances between the cities are unknown and subject to change. This highly unpredictable environment is the case of the inspection cell where the cycle time between two images will change for different camera placements.

A ubiquitous manufacturing (UM) system is used in manufacturing for obtaining the Internet of things solutions and provides location-based manufacturing services. Human-induced uncertainty and early termination are two complications that hamper the effectiveness of an UM system based on three-dimensional (3D) printing. To resolve these complications, several solutions were considered in this study. First, fuzzy-valued parameters were defined to determine uncertainty. Subsequently, slack was derived to determine whether to restart an early terminated 3D printing process in the same 3D printing facility. Consequently, two optimization models – a fuzzy mixed-integer linear programming model and a fuzzy mixed-integer quadratic programming model – were developed in this study. Based on the two optimization models, a fuzzy 3D printing-based UM system that considers uncertainty and early termination was developed. The effectiveness of the proposed methodology was tested by conducting a regional experiment. The experimental results revealed that the proposed methodology could shorten the average cycle time by 9% and could enable 3D printing facilities to make real-time, online reprinting decisions.

We consider a sequence of cycles of exponential single-server nodes, where the number of nodes is fixed and the number of customers grows unboundedly. We prove a central limit theorem for the cycle time distribution. We investigate the idle time structure of the bottleneck nodes and the joint sojourn time distribution that a test customer observes at the nonbottleneck nodes during a cycle. Furthermore, we study the filling behaviour of the bottleneck nodes, and show that the single bottleneck and multiple bottleneck cases lead to different asymptotic behaviours.

For a K-stage cyclic queueing network with N customers and general service times, we provide bounds on the nth departure time from each stage. Furthermore, we analyze the asymptotic tail behavior of cycle times and waiting times given that at least one service-time distribution is subexponential.

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certain weighted sums of these transforms is then solved by converting it into a linear first-order partial differential equation. The result may be used to find the density function of passage times between states in a Markov process and it is applied to derive an expression for cycle time distribution in tree-structured Markovian queueing networks.

This paper considers the two-stage cyclic queueing model consisting of one general (G) and one exponential (M) server. The strong connection between the present model and the M/G/1 model (with finite waiting room) is exploited to yield the joint distribution of the successive response times of a customer at the G queue and the M queue. This result reveals a surprising phenomenon: in general there is a difference between the joint distribution of the two successive response times at (first) the G queue and (then) the M queue, and the joint distribution of the two successive response times at (first) the M queue and (then) the G queue.

Another associated result is an expression for the cycle-time distribution. Special consideration is given to the case that the number of customers in the system tends to ∞, while the mean service times tend to 0 at an inversely proportional rate.