Improved Golden-Section Algorithm for the Multi-Item Replenishment Problem

 

S. Hernández*¹, I. Flores², J.A. Vázquez¹

 

¹ Departamento de Ingeniería Industrial Instituto Tecnológico de Celaya Antonio García Cubas s/n, Celaya, México, C.P. 38010 *E-mail: salvador.hernandez@itcelaya.edu.mx

² División de Estudios de Posgrado Facultad de Ingeniería Universidad Nacional Autónoma de México Circuito Universitario s/n, Distrito Federal, México, C.P. 04510.

 

ABSTRACT

This paper presents a procedure for solving instances of the joint replenishment problem using the golden-section method. The algorithm includes an iterative method for obtaining a narrowing search range for the continuous variable in order to carry out less iterations. We studied the behavior of the algorithm experimentally and made comparisons with the heuristic technique known as RAND, solving randomly-generated problems. The results showed that the golden-section algorithm with the proposed improvements obtains the optimum solution for up to 100% of the problems solved, it is very stable when faced with the increase in the number of products in the problem and the runtime is notably competitive. The procedure is easy to implement and useful for professionals working in planning.

Keywords: line search methods, golden section, inventory management, joint replenishment.

 

RESUMEN

Se muestra un método basado en sección dorada para resolver instancias del problema de reaprovisionamiento de productos múltiples. El algoritmo incluye un método iterativo para obtener un intervalo de búsqueda más pequeño. Se estudió el desempeño del algoritmo de manera experimental realizando las comparaciones con el algoritmo RAND, resolviendo instancias generadas aleatoriamente. Los resultados muestran que el algoritmo de sección dorada obtiene la solución óptima hasta en el 100% de las instancias resueltas, es estable frente al número de productos y el tiempo de ejecución es competitivo. El algoritmo es sencillo de implementar y muy útil para profesionistas dedicados a la planeación y control de inventarios.

 

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