Benders Decomposition Method on Adjustable Robust Counterpart Optimization Model for Internet Shopping Online Problem

In this paper, the implementation of the Benders decomposition method to solve the Adjustable Robust Counterpart for Internet Shopping Online Problem (ARC-ISOP) is discussed. Since the ARC-ISOP is a mixed-integer linear programming (MILP) model, the discussion begins by identifying the linear variables in the form of continuous variables and nonlinear variables in the form of integer variables. In terms of Benders decomposition, the ARC-ISOP model can be solved by partitioning them into smaller subproblems (the master problem and inner problem), which makes it easier for computational calculations. Pseudo-codes in Python programming language are presented in this paper. An example case is presented for the ARC-ISOP to determine the optimal total cost (including product price and shipping cost) and delivery time. Numerical simulations were carried out using Python programming language with case studies in the form of five products purchased from six shops.