Imprecise modified solid green traveling purchaser problem for substitute items using quantum-inspired genetic algorithm

Abstract This paper develops a modified formulation of the traveling purchaser problem (TPP), in capacitated markets with the availability of both original and substitute products where purchaser focuses on minimizing an imprecise procurement cost using multiple vehicle types. We also develop an environment-friendly green procurement planning through suitable penalty/credit structure. The motivation for this study emerges from a hub and spoke procurement planning model, with a focus on environmental concerns following regulations and customer sentiments. To obtain the solution with faster execution time, a quantum-inspired genetic algorithm with in vitro fertilization (IVF) crossover and mutation operator is developed. Our results illustrate the non-linear change in the number of markets selection, routing and procurement planning with changes in product availability and substitutes. We show that the designing of suitable carbon credit/penalty structure is essential to obtain a green network with minor compromises in travel and transportation costs. The flexibility of multiple vehicle types reduces both cost and emission significantly. As a part of the methodological contribution, the superiority of our heuristic is established by testing on benchmark TPP instances using a rigorous statistical test.