624 REVISTA INVESTIGACION OPERACIONAL VOL. 40 , NO. 5, 624-637, 2019. OPTIMAL DECISION SUPPORT MIXTURE MODEL WITH WEIBULL DEMAND AND DETERIORATION N. K. Sahoo *1 , Bhabani S. Mohanty ** and P. K. Tripathy ** * Department of Mathematics, S.S.S. Mahavidyalaya, Dhenkanal, India ** P.G. Department of Statistics, Utkal University, Bhubaneswar, India ABSTRACT In this paper, the performance of an inventory model is explored with deteriorating items under imprecision environment where the demand follows a three-parameter Weibull distribution. Deterioration and holding cost is considered as a linear function of time. Fuzziness has been allowed to deal with imprecision. Mathematical observations of both crisp and fuzzy models have been illustrated to determine the optimal cycle time and optimal inventory cost. The demand distribution, deterioration rate and all costs of models are expressed as triangular, trapezoidal and pentagonal fuzzy numbers. Graded mean integration method is used for defuzzification. Numerical illustrations are provided to validate the applications of the model. Sensitivity analysis with useful graphs and tables are performed to analyze the variability in the optimal solution with respect to change in various system parameters. KEYWORDS: Weibull Demand, Triangular Fuzzy Number, Trapezoidal Fuzzy Number, Pentagonal Fuzzy Number, Graded Mean Integration MSC: 90B05 RESUMEN En este documento, se analiza el rendimiento de un modelo de inventario con elementos deteriorados en un entorno de imprecisión donde la demanda sigue una distribución de Weibull de tres parámetros. El deterioro y el costo de mantenimiento se consideran una función lineal del tiempo. Se ha permitido a la borrosidad lidiar con la imprecisión. Las observaciones matemáticas de los modelos nítidos y difusos se han ilustrado para determinar el tiempo de ciclo óptimo y el costo de inventario óptimo. La distribución de la demanda, la tasa de deterioro y todos los costos de los modelos se expresan como números borrosos triangulares, trapezoidales y pentagonales. Se utiliza el método de integración de medios graduados para la defuzzificación. Se proporcionan ilustraciones numéricas para validar las aplicaciones del modelo. Se realizan análisis de sensibilidad con gráficos y tablas útiles para analizar la variabilidad en la solución óptima con respecto al cambio en varios parámetros del sistema. 1. INTRODUCTION Most of the existing inventory models based on assumptions that the items can be stored indefinitely to face the future demands. Deteriorating items are common in our daily life. If the rate of deterioration is high, its impact on modeling of such an inventory system cannot be neglected. Deteriorating items refer to the items that become decayed, damaged, evaporative, expired, invalid, devaluation in course of time. But certain types of items either deteriorate or become obsolete with respect to time. The commonly used goods like fruits, vegetables, meat, foodstuffs, fashionable items, alcohol, gasoline, medicines, radioactive substances, photographic films, electronic devices, etc., where deterioration is commonly observed during their normal storage period. Inventory model with Weibull demand was considered earlier by Tadikamalla [16]. Ghosh et. al. [7] developed an inventory model with Weibull demand rate and production rate is assumed as finite. Tripathy and Pradhan [17] suggested inventory model having Weibull demand and variable deterioration rate. Covert and Philip [3], Giri et. al. [8], Ghosh and Choudhury [6] developed model with Weibull distribution deterioration with various pattern of demand. One of the weaknesses of the current model which is mostly used in business world is the unrealistic assumption of the different parameters. Fuzzy inventory models are more realistic than the traditional inventory models. The uncertainties are due to fuzziness and such cases explained in the fuzzy set theory which was demonstrated by Zadeh [21], Kaufman and Gupta [10]. Syed and Aziz [15] discussed a fuzzy inventory model using signed distance method. Chang et. al. [2], De and Rawat [4] and Jaggi et. al [9]. developed fuzzy models for deteriorating items and demand using triangular fuzzy 1 * Email:narenmaths@yahoo.co.in