Towards Unifying Scheduling and Location Problems: A Non-Stationary Hypercube Model

Purpose – this paper aims to develop a non-stationary hypercube model capable of uniting the properties that models for both problems seek (location and shift-scheduling problems). Theoretical framework – We present the proposed model using a mixed discrete-continuous time Markov chain and compares it to a discrete-event simulation through an illustrative example. Design/methodology/approach – The method used in this paper is quantitative with a comparison between an approach of simulation and an exact model. Findings – The results show a high similarity between both models. However, the proposed model does not present noise in performance measures such as waiting times and travel times. Nevertheless, the study of their residuals revealed that the proposed model has a lower sensitivity to events, such as shift endings and imperfections in dispatch preferences. Further studies may reduce such a variation by improvements in the calculations of performance measurements. Research, Practical & Social implications – The mentioned results suggest that the proposed model may become an option for applications uniting location and shift-scheduling problems. Originality/value – When developing location problems, we seek models that are capable of representing the pertinent geographic characteristics to the problem. On the other hand, when developing shift-scheduling problems, we seek models capable of capturing transient fluctuations in the components (such as demand, service times, available workforce, among others) of such a system. Therefore, in the search to improve the daily operations of systems, such as emergency service systems (ambulances, police, firefighters) using either of the two problems individually, it may lead to flawed conclusions. Keywords - Emergency Service Systems; Queueing Theory; Hypercube non-stationary; Discrete Event Simulation; Performance Measurement.

Metric Dimension on Path-Related Graphs

Graph theory has a large number of applications in the fields of computer networking, robotics, Loran or sonar models, medical networks, electrical networking, facility location problems, navigation problems etc. It also plays an important role in studying the properties of chemical structures. In the field of telecommunication networks such as CCTV cameras, fiber optics, and cable networking, the metric dimension has a vital role. Metric dimension can help us in minimizing cost, labour, and time in the above discussed networks and in making them more efficient. Resolvability also has applications in tricky games, processing of maps or images, pattern recognitions, and robot navigation. We defined some new graphs and named them s − middle graphs, s -total graphs, symmetrical planar pyramid graph, reflection symmetrical planar pyramid graph, middle tower path graph, and reflection middle tower path graph. In the recent study, metric dimension of these path-related graphs is computed.