Influence of a cloudy fuzzy environment for deteriorating products with ramp-type demand under a supply chain management

Even if a new product is launched, that is a deteriorating type; there is a chance of imperfect production due to its deteriorating nature. Then, the producer faces trouble since the production starts and the trouble is the deteriorating rate of those products. One sure fact is that the longer a deteriorating product stays in the production unit or warehouse, the lesser its shelf-life will be when it reaches the retailer and, finally, consumers. During this entire process, one of the most troublesome things is the uncertain nature of the deterioration rate of the product. This study examines the above-stated scenario when the deterioration rate affects the newly launched products from the production of the product to the selling of the product. In this process, the product loses its shelf-life gradually, where inflation exists in the market. This implies that inflation happens for the time value of money but with the depreciating value of the shelf-life of a product. Because of the depreciating shelf-life, the retailer faces a shortage of the products in the market. As it is a newly launched product, an increasing demand happens over time, and a ramp-type demand pattern justifies the market demand for this type of product. To ensure the minimum cost of the supply chain, two different types of deteriorating rates are tested in this study: crisp deterioration rate and uncertain deterioration rate. A fuzzy and cloudy fuzzy sets are used to check the uncertain deterioration rates. A global minimum cost is found using the classical optimization methods. Results show that the cloudy fuzzy environment for a deterioration rate obtains the global minimum supply chain cost. The global minimum cost of the supply chain in the cloudy fuzzy environment is 2.54% less than the fuzzy environment and 1.95% less than the crisp environment. The optimal time is minimal in the cloudy fuzzy environment, followed by the crisp and fuzzy environments. Sensitivity analysis and managerial insights are discussed for generating insights from this study.