An integrated inventory model of imperfect quality products with fuzzy chance constraints

In this paper, we consider a network of supplier, producer, retailer and customer which synchronizes a series of inter-related business process in terms of integrated supply chain production inventory model. The whole system is considered for a finite time period with imprecise inventory costs. There are imprecise chance constraints on the transportation costs for both producer, retailer and also a fuzzy space constraint for producer is considered. The objective of the model is to minimize the total inventory related cost to find: (i) optimal collection rate incurred by the supplier for supplying raw materials to producer, (ii) the optimal procurement rate of the producer and (iii) the optimal replenishment of the retailer from the producer on the basis of the customer’s demand. Rommelfanger method [28, 29] is used to handle fuzzy inequalities. The fuzzy model provides the decision maker with alternative decision plans for different degrees of satisfaction. This proposal is tested by using an illustrative numerical example.