Context:

The analysis of the complexity of the systems involves the evolution of the models that representation of reality, logistics has advanced from a business context to the supply chain, basic models of logistics with deterministic parameters must go represent real behavior, stochastic. In this context, the combination of inventory, location and routing models with a stochastic approach applied to supply chains appears.

Method:

A systematic review of the literature was developed in the bibliographic databases, ScienceDirect, ScholarGoogle, SpringerLink, Scopus, SemanticScholar, ResearchGate and Scielo, of the 72 referenced articles, 65 % between 2015 and 2019.

Results:

From the models identified and described, a taxonomy of the models is proposed and classified into 4 kinds, three dyadic models Location Inventory Problem (LIP), Inventory Routing Problem (IRP), Location Routing problem (LRP) and a triadic model Location Inventory Routing Problem (LIRP). The stochastic parameters used in the models, the types of models, the solution methods, the contemplated objective functions, and the number of echelons in the supply chain are established, from which taxonomies of the different types of models are proposed. Lines of work for future research is presented.

Conclusions:

The evolution from deterministic to stochastic models represents an increase in complexity which forces the development of new solution methods with ability to find feasible solutions. The development of models with news measurements of performance as environmental, social and humanitarian have been of recent interest. In the last period, triadic multi-product and multi-period models take on relevance.

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