Designing fuzzy supply chain network problem by mean-risk optimization method

In many practical supply chain network design (SCND) problems, the critical parameters such as customer demands, transportation costs and resource capacities are quite uncertain. The significance of uncertainty motivates us to develop a new mean-risk fuzzy optimization method for SCND problem, in which the standard semivariance is suggested to gauge the risk resulted from fuzzy uncertainty. To demonstrate the advantages of the proposed optimization method, we define a new concept about the value of fuzzy solution for our SCND problem. When the transportation costs and the demands of customers have continuous possibility distributions, we approximate the continuous fuzzy vector by a sequence of discrete fuzzy vectors. On the basis of the approximation scheme, we obtain an approximating optimization model, which is a nonlinear mixed-integer programming problem. Furthermore, we design a hybrid memetic algorithm (MA) to solve the approximating optimization problem. The designed hybrid MA incorporates the reduced variable neighborhood search to act as the local search procedure. Finally, we conduct some numerical experiments via an application example to demonstrate the effectiveness of the designed hybrid MA.