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