Abstract:

The present paper aims to study the important characteristics of the Transportation Problem, highlighting the aspects that can be processed using elements of Graph Theory (i.e., assignment problems, optimal route), in order to optimize the transport in pandemic conditions, taking into account the minimum length of the road that can be taken to the destination, as well as the efficiency of supply: sanitary units, production units, commercial and food units. Transportation problem is a linear programming problem to which certain (set) restrictions are associated, aiming at optimizing the result, minimum transport cost from supplier to beneficiary. Given that the Hungarian algorithm applies to allocation problems, we can think of much more complex problems. For example, one can implement a hybrid algorithm, starting from the transport problem and combining the assignment problem (hungarian algorithm) with specific algorithms for determining the optimal path in a graph (Dijkstra, Ford, Bellman-Kalaba), where the nodes of the graph represent the departments within an institution, e.g., the sections of the considered medical units. Also, the considered graph will be seen as a complex network that can be used in robotic swarm problems, where its nodes have certain characteristics and in turn represent graphs whose components are simple nodes. In this regard, we will consider the following issue, the implementation of the hybrid algorithm for: designing specific medical circuits in a medical unit, efficient allocation of medical team members to critical patients, so that travel and response time is as short as possible, and the result of the medical procedure to be optimal.