A study of multi-objective restricted multi-item fixed charge transportation problem considering different types of demands

In this paper, we formulate a multi-objective fixed charge transportation problem (FCTP) for multiple items, considering availability of multiple modes of transport along each pair of origin and destination. The variable cost of each item, the fixed cost and the transport time are considered to be different for each mode of transport. It is also considered that some items are mutually incompatible and cannot be transported in the same mode of transport. Two models of the multi-item FCTP are presented, considering the demands of items as crisp and interval numbers, respectively. The transportation problem is then posed as a multi-objective optimization problem (MOOP), in which the objectives are to minimize the total cost and total transport time. For the model with interval demands, the instances are only solved, in which, for each item, the sum total of demands of an item at different destinations is at least the sum total of availabilities of the item at different origins. For each model, a set of four numerical examples are solved using two multi-objective evolutionary algorithms (MOEAs), namely, Non-dominated Soring Genetic Algorithm-II (NSGA-II) and Strength Pareto Evolutionary Algorithm 2 (SPEA2). A comparative study of the computational results are made in terms of four performance index, namely, RNI value, Hyper-volume (HV), Inverted Generational Distance (IGD) and Spread. The computational results clearly indicates that NSGA-II outperforms SPEA2 for all the numerical examples, in terms of generating better approximate Pareto front with respect to dominance, diversity and spread. (C) 2022 Elsevier B.V. All rights reserved.