Bi-objective optimization of three echelon supply chain involving truck selection and loading using NSGA-II with heuristics algorithm

• Cost minimized in a mix-product three echelon supply chain while maintaining service level.
• A heuristic algorithm is used for optimal truck selection and loading along with NSGA-II.
• Type and number of truck moving in each path in each time period is determined.
• Number of products of each type carried by each of these trucks is also calculated.

This paper models a three echelon supply chain distribution problem considering multiple time periods, multi-products and uncertain demands. To take the problem closer to reality we consider multiple truck types and focus on the truck selection and loading sub-problem. Truck selection is important because the quantity of goods to be transported varies regularly and also because different trucks have different hiring cost, mileage and speed. Truck loading is important when considering the optimal loading pattern of products having different shapes and sizes on trucks, which themselves have distinct loading capacities. The two objectives considered here are the cost and responsiveness of the supply chain. The distribution problem is solved using the non-dominated sorting genetic algorithm (NSGA-II). However, the genetic algorithms compromise the optimality of the sub-problems while optimizing the entire system. But the optimality of truck selection and loading sub-problem is non-compromisable in nature. Hence a heuristic algorithm is used innovatively along with the NSGA-II to produce much better solutions. To make our model more realistic, the distribution chain is modelled as a push–pull based supply chain having multiple time periods and using demand aggregation over time. Using a separate algorithm also gives the advantage of utilizing the difference in nature of the push and pull part of the supply chain by giving every individual truck different objectives. Real life like data is generated and the optimality gap between the heuristic and non-heuristic approach is calculated. A clear improvement in objectives can be seen while using the heuristic approach.