Strategy of solution for the inventory-routing problem based on separable cross decomposition

 

M. Elizondo-Cortés & R. Aceves-García

 

Universidad Nacional Autónoma de México. Posgrado de Ingeniería, Circuito Exterior S/N, Ciudad Universitaria Apdo. Post. 3000, Tel. 0155 5622 3282 ext. 128 Fax. 0155 5622 3282 ext. 107. mareli@avantel.net

 

Received: January 28^th, 2003.
Accepted: May 17^th, 2005.

 

Abstract

The Inventory-Routing Problem (IRP) involves a central warehouse, a fleet of trucks with finite capacity, a set of customers, and a known storage capacity. The objective is to determine when to serve each customer, as well as what route each truck should take, with the lowest expense. IRP is a NP-hard problem, this means that searching for solutions can take a very long time. A three-phase strategy is used to solve the problem. This strategy is constructed by answering the key questions: Which customers should be attended in a planned period? What volume of products should be delivered to each customer? And, which route should be followed by each truck? The second phase uses Cross Separable Decomposition to solve an Allocation Problem, in order to answer questions two and three, solving a location problem. The result is a very efficient ranking algorithm O(n³) for large cases of the IRP.

Keywords: Inventory, Routing, Cross Decomposition.

 

Resumen

El Problema de Inventario-Distribución (Inventory-Routing Problem, IRP), combina las actividades logísticas críticas de ruteo y manejo de inventarios. El objetivo es, al menor costo posible, atender las necesidades de un conjunto de clientes, utilizando una flotilla de vehículos que desde un almacén central, recorren rutas de distribución. El IRP es un problema NP-duro que en aplicaciones reales suele ser de gran tamaño. Para la solución de este problema se diseñó una estrategia conformada de tres fases, que responden a las preguntas características del IRP: 1. ¿A qué clientes atender en el horizonte de planeación? 2.¿Cuánto entregar a cada cliente? y 3. ¿Qué ruta debe seguir cada vehículo? La segunda fase, parte medular de la estrategia, utiliza la técnica de Descomposición Cruzada Separable para responder a las preguntas dos y tres, solucionando un problema de localización. El resultado es un algoritmo muy eficiente de orden O(n³) para instancias grandes del IRP.

 

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Authors Biography

Mayra Elizondo Cortés. She obtained a Master in Sciences Degree in Operational Research at the National Autonomous University of Mexico (UNAM), and a PhD in Operational Research at the same university. Her research interest include Optimization, Simulation and Logistic. She is a Teacher and Researcher in the Engineering Graduate School of the UNAM.

Ricardo Aceves García. Dr. Aceves studied Chemical Engineering at the Autonomous University of Puebla, Mexico, and obtained a Master in Sciences and a PhD. in Operational Research at the Engineering Faculty of the National Autonomous University of Mexico (UNAM). He has been working in various projects In the field of Transportation and Operational Research, both public and private organizations. At present, he is a full time Teacher and Researcher at the Engineering Faculty and Engineering Graduated School of the UNAM, and he Is a president of the Mexican Institute of Systems and Operational Research.