ORIGINAL PAPER Single stage fuzzy supply chain model with Weibull distributed demand for milk commodities M. R. Bhosale 1 • R. V. Latpate 1 Received: 10 April 2019 / Accepted: 5 July 2019 Ó Springer Nature Switzerland AG 2019 Abstract 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 char- acterized 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. Keywords Single period inventory model  Fuzzy random variable  Signed distance defuzzification method  Optimal order quantity  Perishable items 1 Introduction In the supply chain, there are several stakeholders like manufacturers, wholesalers, distributors, retailers, and customers. The prime objective of the supply chain is to satisfy the customer’s demand. Every entity in the supply chain tries to satisfy this objective. If every entity included in the supply chain does their work efficiently and con- sistently, then the performance of the supply chain will be improved substantially. If all entities are independent of each other and they are taking their decision independently, then the supply chain is called as a decentralized supply chain. If all the entities are related to each other and the decision is taken by a central authority, then it is called as a centralized supply chain. In a centralized decision making system, there exists a central authority to take the decision, whereas in a decentralized system every individual entity can take their own decisions. The supply chain is a real network. Each stage of the supply chain is connected through the flow of products. This flow of products is in both directions. In the traditional supply chain, the focus of the integration of the supply chain network is the single objective such as minimize the cost or maximize the profit. Supply chain designs how to choose the entities and dis- tribute goods to satisfy the customers demand and mini- mize the total cost. Erlenkotter (1989) presented the classical economic order quantity model with known constant demand. In the inventory system, there exists parameters and constants which are uncertain. Fuzzy set theory is widely used in various fields for different problems which are related to the supply chain. When parameters and constants are uncertain then, they are usually treated as probability the- ory. In some cases, uncertainties can be defined as fuzzi- ness or vagueness, which are characterized by fuzzy & R. V. Latpate rvl@unipune.ac.in 1 Department of Statistics, Savitribai Phule Pune University, Pune 411007, India 123 Granular Computing https://doi.org/10.1007/s41066-019-00186-2