More-for-Less Paradox in Time Minimization Transportation Problem with Mixed Constraints

Abstract

In emergency situations, such as at the time of the outbreak of infectious viruses (COVID-19, SARS, Ebola, MERS, etc.), strike of natural disasters (Earthquakes, tsunamis, cyclones, etc.), wars, terrorist attacks, etc., where distributing essential goods and services in minimum possible time is a major logistical challenge, the concept of more-for-less paradox could be helpful. In a minimization type transportation problem, this paradoxical situation occurs when the value of objective function falls below the optimum value by shipping a large number of total goods. In this article, a unified algorithm is developed to identify and resolve the existence of paradoxical situation in the time minimization transportation problem with mixed constraints using right-hand side parametric formulation. Using this prior approach, the paradoxical solution (if exists) can be found first, followed by an optimal solution. If the paradoxical part does not exist, it gets neglected. The conditions governing the existence of more transportation flow in less shipping time enable the decision-maker to extend the optimal solution in search of more-for-less opportunity at the time of emergency. The validity of an algorithm has been tested through numerical illustrations and by computational observations on matlab.