The stochastic location-routing-inventory problem of perishable products with reneging and balking

The transport of perishable products is in need of specific control and safety operations, either due to their short shelf life or their particular storage circumstances. This study investigates an extended Location-routing-inventory problem (LRIP) for perishable products, in which a two-phase hybrid mathematical model is developed. In the first phase, the location-routing problem (LRP) is formulated with stochastic demands and travel time, and then in the second phase, a queue system is employed to model the inventory control problem based on the established locations and routes. Moreover, the effects of reneging and balking behaviors are studied in the second phase, and hereby, holding, shortage, product expiration, customer waiting times, and customer loss costs are calculated. To tackle the complexity of the problem, an improved genetic algorithm (IGA) is designed and is compared with the classic genetic algorithm (GA) and GAMS software. Finally, two small and large-sized illustrative examples and then different problem instances are taken into account to test the applicability of the suggested methodology. The obtained results demonstrate that the developed methodology of the research has an appropriate performance to deal with the high complexity of the problem.