Three-Layer Supply Chain Production/By-Production Inventory Model under Fuzzy Rough Environment

Abstract

An integrated three-layer supply chain model for production and by-production system is formulated under fuzzy-rough (Fu-Ro)-environment. At first, supplier receives 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 produce the main product in plant-1. Retailer-I has purchased this product from manufacturer of plant-1 to sale to the customers. The residue units of plant-1 have transferred to plant-2 with constant rate to manufacture another usable by-product. Retailer-II purchases this usable by-product and sales to the customers. Ideal costs of supplier, manufacturer and retailer have been taken into account. By-production of residue units of plant-1 not only minimizes the environmental pollution, but also gives some return to the manufacturer. Due to the complexity of environment, inventory holding costs, idle costs and setup costs are considered as Fu-Ro type and these are reduced to crisp ones using Fu-Ro expectation. Supply rate, production and by-production rates are assumed as decision variables. Integrated model has been developed and solved analytically in crisp and Fu-Ro environments to find the optimum value of the decision variables and corresponding individual profits of the members of the supply chain are calculated numerically and graphically. Finally, the model has been realized with a case study of sugar mill.