A hybrid cultural-harmony algorithm for multi-objective supply chain coordination

We investigate a one-buyer, multi-vendor, coordination model with a vendor selection problem in a centralized supply chain. In the proposed model, the buyer selects one or more vendor and orders an appropriate quantity. The quantity discount mechanism is used by all vendors with the aim of coordinating the supply chain. We formulate the problem as a multi-objective mixed integer nonlinear mathematical model. Using the Global Criterion method, the proposed model is transformed into a single objective optimization problem. Since the problem is NP-hard, we propose four meta-heuristic algorithms: Particle Swarm Optimization (PSO), Scatter Search (SS), population based Harmony Search (HS-pop) and Harmony Search based Cultural Algorithm (HS-CA). The Taguchi robust tuning method is applied in order to estimate the optimum values of parameters. Then, the solution quality and computational time of the algorithms are compared.