A Supply-Chain Production Inventory Model with Warehouse Facilities Under Fuzzy Environment

In reality, there are different types of supply-chain system for production. One such type may be that a producer purchases raw materials from several vendors and the finished products are sold to a retailer. The retailer may plan to procure in large quantity to avail the price discount, transportation advantage, etc., and adopt for warehouse facilities system-one warehouse at the market place from where sale is conducted and the other (if necessary) at a distance away from the market place from which the units are transported to the market warehouse (MW) continuously to keep MW full. This motivated us to take up the following three supply-chain production inventory models. In the first model, the above mentioned type two warehouse supply chain model (SCM) is considered with imprecise stock dependent demand and in this model the objective goal is assumed to be fuzzy. There are budget and space constraints which are also in fuzzy nature. The fuzziness are defuzzified following possibility, necessity and credibility measures. In the second model (i) nature of collection of raw-material is different; (ii) demand is increasing with time in a decreasing rate, (iii) selling price of the partial backlogging units depends on the waiting time of the customers. The model is formulated with defective production system and learning effect which is fuzzy in nature. Learning effect i.e., experience is introduced in reducing the defective rate in production. In last model, an integrated production-inventory model is presented for a supplier, manufacturer, and retailer supply chain under conditionally permissible delay in payments in uncertain environments. The supplier produces the item at a certain rate, which is a decision variable, and purchases the item to the manufacturer. The manufacturer has also purchased and produced the item in a finite rate. The manufacturer sells the product to the retailer and also gives the delay in payment to the retailer. The retailer purchases the item from the manufacture to sell it to the customers. Ideal costs of supplier, manufacturer, and retailer have been taken into account. The SCMs have been developed and solved analytically fuzzy environments, and finally, corresponding individual profits are calculated numerically and graphically.