Bilevel transportation problem in neutrosophic environment

Annals of Operations Research, 2021

Developing countries scramble to contain and mitigate the spread of coronavirus disease 2019 (COVID-19), and world leaders demand equitable distribution of vaccines to trigger economic recovery. Although numerous strategies, including education, quarantine, and immunization, have been used to control COVID-19, the best method to curb this disease is vaccination. Due to the high demand for COVID 19 vaccine, developing countries must carefully identify and prioritize vulnerable populations and rationalize the vaccine allocation process. This study presents a mixed-integer linear programming model for equitable COVID-19 vaccine distribution in developing countries. Vaccines are grouped into cold, very cold, and ultra-cold categories where specific refrigeration is required for their storage and distribution. The possibility of storage for future periods, facing a shortage, budgetary considerations, manufacturer selection, order allocation, time-dependent capacities, and grouping of the...

Yugoslav Journal of Operations Research, 2016

In this paper, we present a mathematical model of delivery logistics of swine flu vaccine in a rural area. The objective is to make the medicine available at the Primary health centres of that area in such a way that the total cost (purchasing and cartage) of obtaining the flu vaccination is minimized and the demand of the demand centres is met. One more constraint is taken into consideration: once the bottle of the medicine is opened, it has to be given to a fixed number of patients requiring swine flu vaccine simultaneously, failing which, the proportion of unused medicine becomes obsolete and can not be administered to the patients. But if the bottle of medicine could not be used fully at a time then, the unused medicine can be sold back at a discounted price. Under such conditions, our next objective is to determine the size of order that must be placed so that the expected total profit per year is maximized. The methodology to achieve this objective is: first, formulate the pro...

arXiv (Cornell University), 2023

During various stages of the COVID-19 pandemic, countries implemented diverse vaccine management approaches, influenced by variations in infrastructure and socioeconomic conditions. This article provides a comprehensive overview of optimization models developed by the research community throughout the COVID-19 era, aimed at enhancing vaccine distribution and establishing a standardized framework for future pandemic preparedness. These models address critical issues such as site selection, inventory management, allocation strategies, distribution logistics, and route optimization encountered during the COVID-19 crisis. A unified framework is employed to describe the models, emphasizing their integration with epidemiological models to facilitate a holistic understanding. This article also summarizes evolving nature of literature, relevant research gaps, and authors' perspectives for model selection. Finally, future research scopes are detailed both in the context of modeling and solutions approaches.

International Journal of Enterprise Network Management

The pandemic that began in December 2019 in Wuhan, China has spread worldwide and infected millions of people across the globe. To combat COVID-19, scientists developed vaccines in record time. Without proper vaccine distribution, the country would suffer from low coverage rates and the virus would continue to spread. We are losing over 3,000 lives each day to COVID-19; this means a single day of delay in the distribution of vaccine is costing thousands of innocent lives. In this paper we have formulated a distribution model using mixed integer programming (MIP) that maximises the number of people vaccinated, minimises the cost of transportation over the entire network while ensuring widespread access.

arXiv (Cornell University), 2023

Vaccination campaigns have saved thousands of lives, reaching the farthest places in the world. These campaigns have required substantial investments and accurate coordination between several actors within the vaccine supply chain. Despite these successful strategies, the outbreak of COVID-19 has altered the objectives and rules of undertaking vaccine campaigns. Then, it is essential to consider two new facts in planning vaccination campaigns. First, some groups of infected people by the virus are more vulnerable to severe illness. Second, the virus is exceptionally contagious; sometimes, no symptoms are apparent. Accordingly, we propose a bi-objective optimization model that allows healthcare decision-makers to design effective vaccination campaigns by considering these COVID-19 characteristics and controlling the associated costs. Careful utilization of temporary and traditional vaccination centers is crucial to creating a more robust strategy. Located in suitable places, temporary centers help increase the probability of reaching groups difficult to be vaccinated while simultaneously avoiding crowd congestion and reducing the risk of spreading infections in dispensing vaccination centers. Experiments were conducted using data from an area in Santiago, Chile. The results show the model allows us to manage the resources by providing a variety of vaccination plans according to the prioritization level of each objective. Keywords OR in health services • multi-objective optimization • vaccination planning • maximum coverage • resource allocation • mixed-integer programming • last-mile distribution.

Journal of Risk and Financial Management , 2021

In this paper, a sustainable closed-loop supply chain problem is modelled in conditions of uncertainty. Due to the COVID-19 pandemic situation, the designed supply chain network seeks to deliver medical equipment to hospitals on time within a defined time window to prevent overcrowding and virus transmission. In order to achieve a suitable model for designing a sustainable closed-loop supply chain network, important decisions such as locating potential facilities, optimal flow allocation, and vehicle routing have been made to prevent the congestion of vehicles and transmission of the COVID-19 virus. Since the amount of demand in hospitals for medical equipment is unknown, the fuzzy programming method is used to control uncertain demand, and to achieve an efficient solution to the decision-making problem, the neutrosophic fuzzy method is used. The results show that the designed model and the selected solution method (the neutrosophic fuzzy method) have led to a reduction in vehicle traffic by meeting the uncertain demand of hospitals in different time windows. In this way, both the chain network costs have been reduced and medical equipment has been transferred to hospitals with social distancing.

Chemical Engineering Transactions, 2021

The global scientific community has been successful in their efforts to develop, test, and commercialize vaccines for COVID-19. However, the limited supply of these vaccines remains to be a widespread problem as different nations have started their respective vaccine rollouts. Policymakers continue to deal with the difficult task of determining how to allocate them. This research work will present how the use of mathematical models can provide valuable decision support under such conditions. Both a linear programming model and a nonlinear programming model have been developed to determine the optimal allocation of COVID-19 vaccines that minimize fatalities and COVID-19 transmission, respectively. These scenarios have to be dealt with when not enough vaccines are available, and the pandemic is still in progress. The model is capable of handling large scale allocation problems such as those intended for the general population of a country. It could also be scaled down for organization...

To the best of our knowledge, there is only one approach for solving neutrosophic cost minimization transportation problems. Since neutrosophic transportation problems are a new area of research, other researchers may be attracted to extend this approach for solving other types of neutrosophic transportation problems like neutrosophic solid transportation problems, neutrosophic time minimization transportation problems, neutrosophic transshipment problems, and so on. However, after a deep study of the existing approach, it is noticed that a mathematical incorrect assumption has been used in these existing approaches; therefore there is a need to modify these existing approaches. Keeping the same in mind, in this paper, the existing approach is modified. Furthermore, the exact results of some existing transportation problems are obtained by the modified approach.

Computers, Materials & Continua

The optimum delivery of safeguarding substances is a major part of supply chain management and a crucial issue in the mitigation against the outbreak of pandemics. A problem arises for a decision maker who wants to optimally choose a subset of candidate consumers to maximize the distributed quantities of the needed safeguarding substances within a speci c time period. A nonlinear binary mathematical programming model for the problem is formulated. The decision variables are binary ones that represent whether to choose a speci c consumer, and design constraints are formulated to keep track of the chosen route. To better illustrate the problem, objective, and problem constraints, a real application case study is presented. The case study involves the optimum delivery of safeguarding substances to several hospitals in the Al-Gharbia Governorate in Egypt. The hospitals are selected to represent the consumers of safeguarding substances, as they are the rst crucial frontline for mitigation against a pandemic outbreak. A distribution truck is used to distribute the substances from the main store to the hospitals in speci ed required quantities during a given working shift. The objective function is formulated in order to maximize the total amount of delivered quantities during the speci ed time period. The case study is solved using a novel Discrete Binary Gaining Sharing Knowledge-based Optimization algorithm (DBGSK), which involves two main stages: discrete binary junior and senior gaining and sharing stages. DBGSK has the ability of nding the solutions of the introduced problem, and the obtained results demonstrate robustness and convergence toward the optimal solutions.

Proceedings of the International Conference on Emerging Challenges: Business Transformation and Circular Economy (ICECH 2021), 2021

Logistics is one of the most important factors in any country and it has become a crucial topic due to the significant effect of Covid 19 on the world economics. Since the beginning of time, logistics is a critical link for products circulation throughout the world. When the Covid 19 pandemic came, logistics is becoming an essential role in preventing supply chain disruption. Meanwhile, transportation activity accounts for the highest portion in logistics. Therefore, improving the transportation system and optimizing the delivery method of goods are essential not only in the pandemic but also in any normal business situation. This paper focuses on optimizing the vehicle routing problem with the time window (VRPTW) by Genetic algorithm (GA) since the receiving time of the customer has some boundaries and restrictions. Furthermore, our VRPTW model include vehicle selection algorithm, which will automatically select the most efficient fleet from the set of vehicles with different capac...