Entropy Based Uncertain Multi Objective Multi-Item Fixed Charge 4D Transportation Problem Involving Breakable and Substitute Items

Abstract Decision-makers always strive to build transport systems that are both profitable and sustainable. Such systems seek to satisfy transportation requirements while minimizing adverse environmental effects and enhancing economic viability. Cost savings and the reduction of the environmental impact can be boosted by improving the supply chain management and freight transportation efficiency. In the transportation systems, energy conservation, waste reduction, recyclable packaging, plastic reduction and sustainable transportation can majorly contribute to the environmental sustainability. During transportation, several types of vehicles are used and generally these vehicles use different type of fuels like petrol, diesel, CNG etc. These vehicles emit green house gases that pollute the environment. In this study, an entropy based multi-objective 4D transportation problem with breakable and substitute items is developed and examined in order to maximize profit and reduce the carbon emissions. The items have been purchased at various depots at various prices. Different types of breakable/replacement items are delivered via different routes using various types of vehicles having varying capacities. All the parameters have been taken to be zigzag uncertain variables. Different models are developed in accordance with the management and the customer decisions regarding the substitutability of items. Chance-constrained programming has been used to transform the equivalent crisp models. All the models have been solved using the intuitionistic fuzzy programming technique using the LINGO 19.0 optimization solver with x64-based system type and Intel(R) Pentium(R) CPU 4405U @ 2.10GHz, 2100 Mhz, 2 Core(s) Processor. A real life based numerical problem is presented and solved to validate the concept and the results are compared with respect to the nature of the obtained solution.