A four valued neutrosophic multi-objective optimization for managing pandemics in a network of healthcare systems

Decision making under uncertainty has been always a challenge due to probabilistic and non-probabilistic behavior of situations. Moreover, most of the models are based on a set of assumptions and unknown parameters, making it difficult for the analyst to incorporate all of them in the decision making. Extent of literature depicts the extensive use of probabilistic models in which their deterministic form employs expected values and standard deviation while ignoring the extreme values. While, non-probabilistic models such as fuzzy multi-objective optimization model incorporate extreme values based on the type of membership function used in the model. Most of the fuzzy multi-objective models engage extreme values such as best and worst solutions to cater to uncertainty. However, in addition to the uncertainty the decision-making process the analyst may face the truth, falsity, and contradiction in the results. To deal with this problem this research proposes a four valued neutrosophic multi-objective optimization model. It uses membership function for each objective and each situation such as uncertainty, truth, falsity, and contraction and its final formulation achieves the satisfaction level of each objective. To demonstrate the practical application of the model a case study of healthcare network is presented. The case study is about managing the resources in a network of healthcare system during uncertain situation such as the Pandemic Covid-19. Due to the increased number of patients number of hospitals were over burden/over utilized while others were underutilized. Unlike traditional approach of patient transfer, this research proposes sharing of vital resources such as doctors/nurses, ambulances, and portable ventilators among the hospitals. In addition to sharing, if shortages still exist then our model will allow hospitals to outsource the resources or acquire them from the donors . Hence, the case study combines sharing, outsourcing, and donation to meet the needs of hospitals while considering three objectives cost, resilience, and responsiveness. The cost function includes sharing, transportation, operating, and inventory holding cost. The resilience objective measures how quickly the system absorbs the changing demand pattern of patients and the responsiveness shows how quickly patients get their services without delays. To optimize the multi-objective problem, case study results help us to solv the problem by using four neutrosophic multi-objective optimization methods. The results were then compared with the other methods such as goal programming, interactive multi-objective fuzzy programing. The results depicted the exceptional performance of four valued neutrosophic multi-objectives. The findings of this research are useful for the policy makers, government, and operation managers in healthcare department.
Keywords: Four valued neutrosophic multi-objective optimization; Resource sharing; Donation; Outsourcing; Resilience; Responsiveness