A multi-path delivery system with random refusal against online booking using Type-2 fuzzy logic-based fireworks algorithm

With the development of the internet and the availability of smart phones, online shopping and the number of digital buyers have increased enormously under the present social context (COVID-19). The major pitfall of this marketing system is the random non-availability of/refusal by customers. Nowadays, with the development of infrastructure, there are several route connections among the different locations worldwide. Considering these, we formulate some multi-path routing for goods delivery with refusal problems (MPRfGDwRPs) against online booking having different route connections between nodes (customers) and solved by a novel Type-2 fuzzy logic based fireworks algorithm (T2FLFWA) developed for discrete problems with probability-based selection and generation based prime mutation. In T2FLFWA, inferences are drawn to obtain the amplitude coefficient against the assumed spark number and iteration ratio. Some instances from TSPLIB are solved and supremacy of T2FLFWA is established through ANOVA test. In MPRfGDwRP, a delivery man starts with goods from a warehouse against customers' online demands under cash-on-delivery or cash-on bookings systems and delivers the appropriate goods to the respective customers located at different locations. The random refusal or non-availability of customers is considered. The optimum travel plan and appropriate routes between the nodes are selected for minimum total cost. The models are illustrated numerically through a real-life problem. Some managerial conclusions are drawn. The novelty of the investigation is that for the first time, T2FLFWA for discrete problems is developed, delivery man's routing plan with multiple paths between nodes with refusals is formulated and its solution using T2FLFWA is presented.