An imperfect production model with energy consumption, GHG emissions and fuzzy demand under a sustainable supply chain

In this article, an integrated two-level supply chain model is described in two different scenarios by treating the demand rate as a triangular fuzzy number. In the first scenario, the retailer offers a price discount for customers on the backorders; it encourages the customer to wait for the product. In the second scenario, the retailer does not provide any discount; instead, an investment is made to reduce lost sales during the stock-out. In both scenarios, the shortages are allowed, and it is partially back-ordered. Two different cases are discussed within these scenarios with two different production functions related to the process quality and production rate. The signed distance method is employed to handle the fuzzified parameter. This research aims to minimize the total expected cost of the supply chain model under each scenario with energy consumption and greenhouse gas emissions during the production process. Moreover, to investigate how changes in the production rate affect the quality of products produced and the entire model’s total cost under the effects of backorder price discounts and lost sales reduction. An iterative algorithm is followed to acquire numerical results. To demonstrate the model, some numerical instances, sensitivity analysis and managerial insights are provided.