A Simple Heuristic Approach for Step Fixed Charge Bulk Transportation Problem

Abstract

The classical transportation problem (CTP) is a particular kind of optimization problem. It involves determining the most cost-effective way to transport a uniform product from several suppliers (sources) to several consumers (destinations). In the real-world scenario, transportation of goods often involves fulfilling the demand of multiple destinations from a single source. However, a source can fulfill the demand of multiple destinations, which is known as bulk transportation problem. Sometimes, the shipment of these goods involves some fixed cost along with a variable cost. Generally, in logistics and transportation, a fixed charge denotes an unchanging expense incurred each time a shipment is sent from one location to another, irrespective of the shipment's volume. Fixed charges can include costs such as setup costs, handling costs, loading or unloading costs or any other costs that remain constant regardless of shipment volume. This fixed cost was earlier in-curred in the context of classical transportation problems only. In literature, the fixed cost was not introduced in the bulk transportation problem (BTP) which should be an essential part of the BTP in the current scenario. Considering this gap, the fixed cost is taken as a step function, which uses some fixed costs for each route and keeps them constant until a particular number of quantities is reached after which it increases in multiple. The branching method in modified form is used to solve the numerical problem, which then converges upon the optimal solution.