A bi‐objective supply chain design problem with uncertainty

We consider the design of a two‐echelon production distribution network with multiple manufacturing plants, customers and a set of candidate distribution centers. The main contribution of the study is to extend the existing literature by incorporating the demand uncertainty of customers within the distribution center location and transportation mode allocation decisions, as well as providing a network design satisfying the both economical and service quality objectives of the decision maker within two levels supply network setting. We formulate the problem as two stage integer recourse problem to find a set of optimal network configuration and assignment of transportation modes and the respective flows in order to minimize total cost and total service time, simultaneously. We develop a stochastic optimization model under demand uncertainty, where the inherent risk is modeled by scenarios. Finally, we propose solution methods for our stochastic optimization problem based on L‐shaped algorithm within an ϵ‐optimality framework and present numerical results demonstrating the computational effectiveness.