A green supply chain production inventory model with uncertain holding cost

A green supply chain (GrSC) model with two plants facilities is formulated under uncertain environment. At first suppliers receive the deteriorating items in a lot and supplies the fresh units to manufacturer for production. Manufacturer has two plants: plant-1 and plant-2. Manufacturer purchases these fresh raw materials at a constant rate from supplier to manufacture the main product in plant-1. Retailer-I has purchased this product from manufacturer of plant-1 to sale it to the customers. The residue units of plant-1 has transferred to plant-2 with constant rate to manufacture another usable by-product. Retailer-II then purchases usable by-product and sales to the customers. Ideal costs of suppliers, manufacturer and retailers have been taken into account. Due to complexity of market situation, all inventory holding costs are considered as uncertain variables and these are reduced to crisp ones using uncertain theory. Supply rate, production rate and by-production rates are assumed as decision variables. Integrated model has been developed and solved analytically in crisp and uncertain environments to find the optimum value of the decision variables. Finally corresponding individual profits are calculated through numerical and graphical methods.