Bi-objective location-allocation-inventory-network design in a two-echelon supply chain using de novo programming, NSGA-II and NRGA

This paper proposes a bi-objective integrated model for supplier location-allocation, capacity allocation and supplier selection and order allocation problems in a two echelon supply chain. The goals of the proposed model are to: 1) select the best supplier(s); 2) locate the selected supplier(s) in the best location(s); 3) determine the optimal capacity of selected supplier(s); 4) allocate the customer(s) to supplier(s); 5) allocate customer's order (order interval). In the first step we proposed a single-objective model to minimise the total costs consist of inventory related costs (purchasing, inventory replenishment, holding and shortage (backordering) costs), transportation costs (fixed and variable costs) and fixed establishment costs. In the second stage we used de novo programming to determine the optimal capacity of selected supplier(s). Therefore, we consider a second objective function to minimise the total costs related to capacity of selected supplier(s) (variable establishment cost). We used NRGA and NSGA-II algorithms to solve the proposed bi-objective mix-integer nonlinear model. At the end, we propose various test problems to show the performance of the proposed methodology. To show which meta-heuristic algorithm is better we used t-test and the simple additive weighting (SAW) method.