Three-layer supply chain in an imperfect production inventory model with two storage facilities under fuzzy rough environment

Abstract

Abstract This article focuses on an imperfect production inventory model considering product reliability and reworking of imperfect items in three-layer supply chain under fuzzy rough environment. In the model, the supplier receives the raw materials, all are not of perfect quality, in a lot and delivers the items of superior quality to the manufacturer and the inferior quality items are sold at a reduced price in a single batch by the end of the cent percent screening process. The manufacturer produces a mixture of perfect and imperfect quality items. A portion of the imperfect items is transformed into perfect quality items after rework. Another portion of imperfect items, termed as `less perfect quality items', is sold at a reduced price to the retailer, and the portion which cannot be either transformed to the perfect quality items or sold at a reduce price is being rejected. Here, retailer purchases both the perfect and imperfect quality items from the manufacturer to sell the items to the customers through his/her respective showrooms of finite capacities. A secondary warehouse of infinite capacity is hired by the retailer on rental basis to store the excess quantity of perfect quality items. This model considers the impact of business strategies such as optimal order size of raw materials, production rate, and unit production cost in different sectors in a collaborating marketing system that can be used in the industry, like textile, footwear, and electronics goods. An analytical method has been used to optimize the production rate and raw material order size for maximization of the average profit of the integrated model. Finally, a numerical example is given to illustrate the model.