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This research is designed to optimize the business process of a green tea dealer, who is a key supply chain partner of the Sri Lankan tea industry. The most appropriate trips for each vehicle in multiple trip routing systems are identified to minimize the total cost by considering the traveling distance.

The study has followed the concepts in vehicle routing problems and mixed-integer programming mathematical techniques. The model was coded with the Python programming language and was solved with the CPLEX Optimization solver version 12.10. In total, 20 data instances were used from the subjected green tea dealer for the validation of the model.

The result of the numerical experiment showed the ability to access supply over the full capacity of the available fleet. The model achieved optimal traveling distance for all the instances, with the capability of saving 17% of daily transpiration cost as an average.

This study contributes to the three index mixed-integer programing model formulation through in-depth analysis and combination of several extensions of vehicle routing problem.

This study contributes to the three index mixed-integer programming model formulation through in-depth analysis and combination of several extensions of the vehicle routing problem.

The proposed model provides a cost-effective optimal routing plan to the green tea dealer, which satisfies all the practical situations by following the multiple trip vehicle routing problems. Licensee green tea dealer is able to have an optimal fleet size, which is always less than the original fleet size. Elimination of a vehicle from the fleet has the capability of reducing the workforce. Hence, this provides managerial implication for the optimal fleet sizing and route designing.

Developing an optimization model for a tea dealer in Sri Lankan context is important, as this a complex real world case which has a significant importance in export economy of the country and which has not been analyzed or optimized through any previous research effort.

This study proposed an optimal model to examine the relationship between the Bitcoin price and six macroeconomic variables – the Bitcoin price, Standard and Poor's 500 volatility index, US treasury 10-year yield, US consumer price index, gold price and dollar index. It also examined the effectiveness of the vector error correction model (VECM) in analyzing the interrelationship among these variables. The authors employed the following approach: first, the authors sampled the period August 2010–February 2022. This is because Bitcoin achieved a market capitalization of more than US$1 tn over this period, gaining market attention and acceptance from retail, corporate and institutional investors. Second, the authors employed a VECM with the six macroeconomic variables. Finally, the authors expanded the long-run equilibrium relationship (time-invariant cointegration)-based VECM to develop a time-varying cointegration (TVC) VECM. The authors estimated the TVC VECM using the Chebyshev polynomial specification based on various information criteria. The results showed that the Bitcoin price can be modeled with the VECM (p = 1, r = 1). The TVC approach generated more explanatory power for Bitcoin pricing, indicating the effectiveness of the approach for modeling the long-run relationship between Bitcoin price and macroeconomic variables.

Image segmentation is one of the most essential tasks in image processing applications. It is a valuable tool in many oriented applications such as health-care systems, pattern recognition, traffic control, surveillance systems, etc. However, an accurate segmentation is a critical task since finding a correct model that fits a different type of image processing application is a persistent problem. This paper develops a novel segmentation model that aims to be a unified model using any kind of image processing application. The proposed precise and parallel segmentation model (PPSM) combines the three benchmark distribution thresholding techniques to estimate an optimum threshold value that leads to optimum extraction of the segmented region: Gaussian, lognormal and gamma distributions. Moreover, a parallel boosting algorithm is proposed to improve the performance of the developed segmentation algorithm and minimize its computational cost. To evaluate the effectiveness of the proposed PPSM, different benchmark data sets for image segmentation are used such as Planet Hunters 2 (PH2), the International Skin Imaging Collaboration (ISIC), Microsoft Research in Cambridge (MSRC), the Berkley Segmentation Benchmark Data set (BSDS) and Common Objects in COntext (COCO). The obtained results indicate the efficacy of the proposed model in achieving high accuracy with significant processing time reduction compared to other segmentation models and using different types and fields of benchmarking data sets.

The proposed PPSM combines the three benchmark distribution thresholding techniques to estimate an optimum threshold value that leads to optimum extraction of the segmented region: Gaussian, lognormal and gamma distributions.

On the basis of the achieved results, it can be observed that the proposed PPSM–minimum cross-entropy thresholding (PPSM–MCET)-based segmentation model is a robust, accurate and highly consistent method with high-performance ability.

A novel hybrid segmentation model is constructed exploiting a combination of Gaussian, gamma and lognormal distributions using MCET. Moreover, and to provide an accurate and high-performance thresholding with minimum computational cost, the proposed PPSM uses a parallel processing method to minimize the computational effort in MCET computing. The proposed model might be used as a valuable tool in many oriented applications such as health-care systems, pattern recognition, traffic control, surveillance systems, etc.