Regression and extrapolation guided optimization for production–distribution with ship–buy–exchange options

The production–distribution problem relates to the location of manufacturing plants and warehouses, and to the distribution of multiple commodities from plants to warehouses and from warehouses to customers. Motivated by industrial practices, we extend herein the problem by considering ship–buy–exchange options. Given the complexity of the studied problems, the branch-and-bound method embedded in commercial solvers cannot obtain favorable solutions for medium- and large-sized instances. Herein, we propose a new regression and extrapolation guided optimization method for the solution of these problems. This method obtains the solution values related to the Lagrangian and uncapacitated relaxation problems and performs a regression analysis with these identified solutions and the optimal values to generate the optimal solution patterns. The generated knowledge pertaining to these optimal patterns is extended from small- to large-sized problems using the extrapolation and quadratic regression approaches. When solving large-sized problems, the method employs the extrapolated knowledge in a local search procedure to fix some of the variables and combines an optimization method to solve the reduced-sized problems. We compare this optimization method with other existent methods in the literature. The computational results indicate that with the use of the same computational resources, our optimization method can identify supply chain decisions at lower costs.