Single stage fuzzy supply chain model with Weibull distributed demand for milk commodities

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The newsvendor model is very simple, but it is very important to study problems of supply chain coordination. This model is also called a single-cycle inventory model. In a short cycle, it is very difficult to forecast the demand. The effect of good prediction reduces inventory shortage, increases the profit and enhances competitiveness. This type of product is characterized by strong uncertainty, that means demand always changes. This creates challenges for decision makers. For newly developed products, it is very difficult to obtain the statistical demand distribution of a product. Here, we consider the demand of the milk products, which are fluctuating in nature. Hence, demand is a random variable. It is assumed that demand follows Weibull distribution. Also, there is some uncertainty in demand. It leads to the over estimation or under estimation of the parameters of the distribution. Fuzzy triangular numbers are used to obtain the uncertain demand. The lifetime of the items are very short. Thus, unsold items are sent back to the manufacturers. The retailers and manufacturers profit is obtained under decentralized and centralized supply chain. Also,the proposed single period (newsboy) inventory model is used to obtain an optimal order quantity. The proposed methodology is illustrated for milk product from Aundh market Pune, India.