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At least one dimensionless physical constant (i.e., a physically observable) must change for the cosmic time to make the varying speed of light (VSL) models phenomenologically feasible. Various physical constants and quantities also should be functions of cosmic time to satisfy all known local laws of physics, including special relativity, thermodynamics, and electromagnetism. Adiabatic condition is another necessary condition to keep the homogeneity and isotropy of three-dimensional space. To be a self-consistent theory, one should consider cosmic evolutions of physical constants and quantities when one derives Einstein's field equations and their solutions. All these conditions are well satisfied in the so-called minimally extended varying speed of light (meVSL) model. Unlike other VSL models, we show that the redshift-drift formula of the meVSL model is the same as a standard model. Therefore, we cannot use this as an experimental tool to verify the meVSL. Instead, one can still use the cosmological chronometers (CC) as a model-independent test of the meVSL. The current CC data cannot distinguish meVSL from the standard model (SM) when we adopt the best-fit values (or Gaussian prior) of the present values of $H_0$ and of $\Omega_{m0}$ from the Planck mission. However, the CC data prefer the meVSL when we choose Pantheon 22 data., Comment: version 3 to match the version accepted by MNRAS. 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:2011.09274

The Robertson-Walker (RW) metric allows us to apply general relativity to model the behavior of the Universe as a whole (i.e., cosmology). We can properly interpret various cosmological observations, like the cosmological redshift, the Hubble parameter, geometrical distances, and so on, if we identify fundamental observers with individual galaxies. That is to say that the interpretation of observations of modern cosmology relies on the RW metric. The RW model satisfies the cosmological principle in which the 3-space always remains isotropic and homogeneous. One can derive the cosmological redshift relation from this condition. We show that it is still possible for us to obtain consistent results in a specific time-varying speed-of-light model without spoiling the success of the standard model. The validity of this model needs to be determined by observations., Comment: 13 pages

In April 2016, Amazon won a patent for a flying warehouse that deploys unmanned aerial vehicles (UAVs) to deliver parcels to customers. In this system, the airborne fulfillment center (AFC) remains or moves at a high altitude, and UAVs are deployed from the AFC to deliver orders to customers. Smaller airships, also known as shuttles, may be used to replenish the AFC with inventory, UAVs, fuel, supplies, and staff. Amazon's AFC delivery system is a novel and challenging system that can convert same-day deliveries into 10 min deliveries and provide a wide range of UAV delivery services for Amazon Prime members. However, to operate the AFC delivery system efficiently, a quantitative operation methodology needs to be developed, which considers the related regulations and consumable replenishment. In this study, mixed-integer linear programming is developed to derive optimal operation schedules for AFC, shuttles, and UAVs simultaneously. The proposed model can be used in real time to address system changes and derive new operation schedules. The effects of system components are analyzed via a numerical experiment to provide managerial guidelines for the implementation of the AFC delivery system. Furthermore, cooperation between the new AFC delivery system and the existing stationary UAV delivery service was investigated. The results demonstrate the possibility of complementary cooperation between the two systems.

Whereas automated guided vehicles (AGVs) have traditionally been used for material handling, the utilisation of autonomous mobile robots (AMRs) is growing quickly owing to their scalability, versatility, and lower costs. In this paper, we address the pickup and delivery problem with consideration of the characteristics of AMRs in manufacturing environments. To solve the problem, we first propose a new mathematical formulation with consideration of both partial and full recharging strategies for minimisation of the total tardiness of transportation requests. We then propose two constructive heuristic algorithms with high computation speed, which are called the Transportation-Request-Initiated Grouping Algorithm (TRIGA) and the Vehicle-Initiated Grouping Algorithm (VIGA). Additionally, we develop a memetic algorithm (MA) that incorporates a genetic algorithm into local-search techniques for finding near-optimal solutions within a reasonable time. We evaluate the performance of the proposed algorithms in comparison with two dispatching rules, genetic algorithm, and neighbourhood search through simulation experiments with three sets of problem instances under different battery levels. The simulation results indicate that the proposed algorithms outperform the others with regard to the average total tardiness and the relative deviation index.

In this paper, we address the dynamic single-machine scheduling problem for minimisation of total weighted tardiness by learning of dispatching rules (DRs) from schedules. We propose a decision-tre...

Understanding the dynamics of food banks' demand from food insecurity is essential in optimizing operational costs and equitable distribution of food, especially when demand is uncertain. Hence, Gaussian Mixture Model (GMM) clustering is selected to extract patterns. The novelty is that GMM clustering is applied to identify the possible causes of food insecurity in a given region, understanding the characteristics and structure of the food assistance network in a particular region, and the clustering result is further utilized to explore the patterns of uncertain food demand behavior and its significant importance in inventory management and redistribution of surplus food thereby developing a two-stage hybrid food demand estimation model. Data obtained from a food bank network in Cleveland, Ohio, is used, and the clusters developed are studied and visualized. The results reveal that this proposed framework can make an in-depth identification of food accessibility and assistance patterns and provides better prediction accuracies of the leveraged statistical and machine learning algorithms by utilizing the GMM clustering results. Also, implementing the proposed framework for case studies based on different levels of planning led to practical results with remarkable ease and comfort intended for the respective planning team., arXiv admin note: text overlap with arXiv:1909.09453

The truck-drone hybrid delivery system uses a truck as a station for drones in addition to its delivery function and is getting attention because the strengths of these individual vehicles can be selectively and synergistically exploited. In this study, we extended the previous vehicle routing models to the hybrid delivery systems by taking into account two important practical issues: the effect of parcel weight on drone energy consumption and restricted flying areas. The flight range of the drones is heavily susceptible to the loaded weight due to the limited battery life. Drones are also not allowed to fly over sensitive facilities regulated by the Federal Aviation Administration (FAA) or temporarily in certain areas due to weather-related conditions. We developed a mathematical model that incorporates these issues and propose a two-phase constructive and search heuristic algorithm to provide computational efficiency of the real-world cases problems. The result of the numerical study demonstrates the effectiveness and efficiency of the proposed algorithm.

Cosmological observations provide more accurate values both for background evolution of the Universe and for the structure formation. These values are given by the so-called dark energy equation of state, $\omega$ and the growth index parameter, $\gamma$. From these observed parameters, one can reconstruct the model functions in scalar tensor gravity theories. However, there is a long standing debate about the (in)equality between conformally transformed frames in scalar tensor gravity models. We show that cosmological observables are frame dependent when they are described by frame independent parameter, redshift. Thus, if the cosmological observables are interpreted in one frame, then all of the observables should also be interpreted in that frame. This explicitly shows the conformal inequality of cosmological observables. Also, our method provides the model independent analysis for STG models about various observables in both frames., Comment: 14 pages, 5 figures

E-commerce and retail companies are seeking ways to cut delivery times and costs by exploring opportunities to use drones for making last mile delivery deliveries. This paper addresses the delivery concept of a truck-drone combination along with the idea of allowing autonomous drones to fly from delivery trucks, make deliveries, and fly to any available delivery truck nearby. We present a mixed integer programming (MIP) formulation that captures this scenario with the objective of minimizing the arrival time of both trucks and drones at the depot after completing the deliveries. A new algorithm based on insertion heuristics is also developed to solve large sized problems containing up to a hundred locations. Experiments are conducted to compare the MIP solutions with those obtained from different models with single truck, multiple truck and a single truck and drone system, as well as test the performance of the proposed algorithm. The numerical results demonstrate the potential operational gain when implementing the proposed drone delivery system compared to the conventional truck alone or single truck/drone delivery system.

In this paper, we address the flexible job-shop scheduling problem (FJSP) with release times for minimising the total weighted tardiness by learning dispatching rules from schedules. We propose a r...

Recently, the extension of classical vehicle routing problem (VRP) dealing with the cooperative operation of heterogeneous of vehicles has been extensively studied. In this study, we propose a vehicle-carrier routing problem (VCRP) aiming at complementary cooperative delivery that is motivated by a hybrid delivery system of a carrier and vehicles. This system consists of vehicles that provide services directly to customers, and carrier that act as mobile depots of vehicles, compensating the limited service range and capacities of the vehicles. The VCRP is modeled as a mixed-integer linear program (MILP) with two objective functions, minimization of overall delivery time and operational cost. This model escalates operational flexibility to maximize the utilization of both delivery vehicles and carrier. The effectiveness of the proposed model is demonstrated by comparing the solutions with related existing models. As a consequence, the analysis indicates that significant savings on delivery time and cost can be achieved by our model, which would further enhance logistical efficiency.

E-commerce and retail companies are seeking ways to cut delivery times and costs by exploring opportunities to use drones for making last mile delivery deliveries. In recent years, drone routing and scheduling has become a highly active area of research. This research addresses the delivery concept of a truck-drone combination along with the idea of allowing autonomous drones to fly from delivery trucks, make deliveries, and fly to delivery trucks nearby. The proposed model considers the synchronized truck drone routing model by allowing multiple drones to fly from a truck, serve customers and immediately return to the same truck for the battery swap and package retrieval. The model also takes into account both trucks and drones capacities to ensure that the amount of loads carried by each drone must not exceed its capacity and the total amount of loads in each delivery route must be less than truck’s capacity. The goal is to find the optimal routes of both trucks and drones which minimize the total arrival time of both trucks and drones at the depot after completing the deliveries. The problem can be solved by the formulated mixed integer programming (MIP) for the small size problem. Numerical results in the case study and benchmark problems are presented to show the delivery time improvement over the delivery time from other delivery types.

This research introduces the sugarcane harvesting problem for a continuous operation scenario with no seasons. A distributed control approach is proposed for a single-mill case with four harvest teams and a network of 1,250 farms. The performance of seven sequencing rules were investigated based on sugar content, relocation distance of harvest teams, and percentage of sold crops due to maximum age allowance. Results were obtained using extensive simulation-based experiments, and key insights were formulated to develop more sophisticated autonomous decisions under a distributed control approach in the future.

One of the strengths of drone is the mobility. Drone can fly without avoiding obstacles and provide services in a timely manner. However ironically, the mobility of drone cannot last for long duration due to the low battery capacity and limited loadable products. As a consequence, the use of drones may be extremely limited in a wide field of operation. One of the solutions for complementing such weaknesses of drone is the use of movable stations. Stations move across a wide field of operation and replenish consumables for drones, such as battery and service product. By visiting movable stations and replenishing consumables, drones can provide persistent service in a wide range of operation area. In this study, design and operation issues of movable unmanned aerial system (MUAS) are address for long term and persistent drone service. A two-phase optimization approach is developed to efficiently handle the system complexity. In the phase I, locations of movable stations and allocation of tasks are identified for multi-period of service duration. In the phase II, number of drones for each station and their routings are optimized based on the result of phase I. Mathematical models are proposed and verified with a case study.

With growing concern over global warming and increasing fuel costs, manufacturing facilities are seeking strategic and operational changes to achieve energy efficiency in production. On-site energy generation provides a greener and less expensive source of energy but its highly stochastic and intermittent nature makes production planning very complex. Demand Side Management (DSM) for real-time operation has emerged as an effective tool for carbon footprint reduction. In DSM, a local controller installed at the manufacturing facility uses an intelligent algorithm to make dynamic decisions for scheduling production line electrical loads. In this paper, we propose a framework for the intelligent algorithm in a job shop manufacturing facility aimed at minimizing the total electricity cost such that the total order delays are controlled. We consider a manufacturing facility with a wind mill as a source of on-site renewable electricity generation. The intelligent algorithm makes sequential decisions based on weighted objective function involving electricity cost and delay virtual queues while using different information e.g. historical decisions, current state and near future energy expectations from the wind mill. Job shop scheduling problems with traditional objective functions are NP Hard and the dimension of energy efficiency makes the problem more complicated. The intelligent algorithm developed in this paper uses Recurrent Neural Network for predicting electricity from the wind mill for the future time slots. Simulation results confirm that the proposed online algorithm framework for job shop scheduling is an effective DSM approach, outperforming the current industry practices and achieves results comparable to benchmark solutions.