A mathematical model for the Multi-Levels Product Allocation Problem in a warehouse with compatibility constraints

The aim of this work is to address the products allocation problem in a multi-layers warehouse with compatibility constraints among the classes. The problem under study represents one of the most relevant topic in Logistics. The goal is to reduce, as much as possible, the delivery times; the inventories; the total logistic costs and to guarantee, at the same time, higher service levels (i.e., high customers satisfaction degree). In this work, a linear model to mathematically represent the problem is developed and its performance is evaluated on a set of instances, representing realistic situations. A sensitivity analysis is also carried out by considering the most relevant parameters of the model. Finally, an Iterated Local Search based heuristic is defined in order to solve large scale scenarios in a reasonable amount of time. Numerical results show that the proposed heuristic is able to find good quality solutions with a computational effort lower than that required to solve the proposed mathematical model.