The objective function of this model is defined as the total production cost (φ); the optimal total production cost is denoted as φ * . The model determines the optimal allocations for products (d, s, f, ξ) by minimizing total production cost (2.1a) that satisfying the constraints (2.1b)-(2.1e) and capacity limits (2.1f)-(2.1g) with given cost parameters (