342 REVISTA INVESTIGACION OPERACIONAL VOL. 40 , NO. 3, 342-355, 2019 OPTIMAL PRODUCTION INTEGRATED INVENTORY MODEL WITH QUADRATIC DEMAND FOR DETERIORATING ITEMS UNDER INFLATION USING GENETIC ALGORITHM Isha Talati and Poonam Mishra * Faculty, Department of Mathematics & Computer Science, School of Technology, Pandit Deendayal Petroleum University. ABSTRACT: This paper is a production integrated inventory model between manufacturer and retailer with quadratic demand and time dependent deterioration. Paper also considers effect of inflation on total cost. Manufacturer offers lot size dependent ordering cost to boost higher orders as well as it decreases manufacturer’s inventory holding cost significantly. Total cost of model is obtained using both classical optimization technique and genetic algorithm. Results clearly show that GA has succeeded in obtaining global minimum whereas classical method has stuck with local minimum. For using classical optimization technique we have used Maple 18 whereas for genetic algorithm we have used MATLAB R2013a.The optimal solution of this model is illustrated using numerical example. Sensitivity for inflation and other parameters of demand has been carried out to analyse their effect on total cost. This paper will encourage researchers involve in inventory and supply chain management to optimize complex problems using different evolutionary search algorithm in order to reach to global optimum. KEYWORDS: Integrated inventory, time dependent deterioration, genetic algorithm, lot size dependent ordering cost, time dependent quadratic demand, inflation MSC: 90B05 RESUMEN: Este documento es un modelo de inventario integrado de producción entre el fabricante y el minorista con demanda cuadrática y deterioro dependiente del tiempo. El documento también considera el efecto de la inflación en el costo total. El fabricante ofrece un costo de pedido dependiente del tamaño del lote para impulsar pedidos más altos y también disminuye significativamente el costo de mantenimiento del inventario del fabricante. El costo total del modelo se obtiene utilizando la técnica de optimización clásica y el algoritmo genético. Los resultados muestran claramente que GA ha logrado obtener el mínimo global mientras que el método clásico se ha quedado con el mínimo local. Para utilizar la técnica de optimización clásica, hemos utilizado Maple 18, mientras que para el algoritmo genético hemos utilizado MATLAB R2013a. La solución óptima de este modelo se ilustra mediante un ejemplo numérico. La sensibilidad para la inflación y otros parámetros de la demanda se han llevado a cabo para analizar su efecto sobre el costo total. Este documento alentará a los investigadores a participar en el inventario y en la gestión de la cadena de suministro para optimizar problemas complejos utilizando diferentes algoritmos de búsqueda evolutiva con el fin de alcanzar el óptimo global. PALABRAS CLAVE: Inventario integrado, deterioro dependiente del tiempo, algoritmo genético, tamaño del lote dependiente del costo de la orden, demanda cuadrática dependiente del tiempo, inflación 1. INTRODUCTION Till a recent past every member of supply chain was managing its own inventory in isolation and minimizes its cost individually. But later researchers realised that optimization of cost or profit with respect to only one member could be at the cost of other members. This will not lead to a long term authentic inventory model. Therefore researchers started proposing integrated model where joint profit or cost is optimized and at the same time individual profits are studied. Goyal (1976): firstly made integrated model for single supplier and single customer so that either both the parties get economical benefit or no one at least get loss. Banerjee (1986): extended that model for joint optimal total cost for purchaser and vendor. Goyal & Gunasekaran (1995): formulated joint optimal model for deteriorating items. Rau et al. (2006): extended optimal total cost among the supplier, the producer, and the buyer. Cárdenas-Barrón et al. (2011): optimized integrated inventory model using arithmetic–geometric inequality. Chung & Cárdenas-Barrón (2014): formulated two- echelon model using promotional tool when demand depends on sales team’s initiatives. Sarkar et al. (2014):