Modelling and solving the integrated inventory-location-routing problem in a multi-period and multi-perishable product supply chain with uncertainty: Lagrangian relaxation algorithm

In this article a three-echelon supply chain, consisting of a supplier, a number of distribution centers (DCs), and a number of retailers (customers) is modeled in form of the integrated inventory- location - routing problem (ILRP), in a way that perishable products are delivered to the customers in a limited time horizon, consisting of several time periods. The retailers' demand is stochastic and follows normal distribution with certain mean and standard deviation. The transportation fleet is heterogeneous, and distribution centers use a timetable, which will prevent interference of the vehicles operation and also allocation of a vehicle to more than one distribution center in each time period. Lagrangian Relaxation Method is used to solve the resulted model and determine the lower bound; and a heuristic algorithm is provided to feasibilize the result of the Lagrangian Relaxation Algorithm and determine the upper bound.