A capacitated facility location model with bidirectional flows. Articles uri icon

publication date

  • February 2015

start page

  • 114

end page

  • 129


  • 1


  • 49

International Standard Serial Number (ISSN)

  • 0041-1655

Electronic International Standard Serial Number (EISSN)

  • 1526-5447


  • Supply chains with returned products are receiving increasing attention in the operations management community. The present paper studies a capacitated facility location model with bidirectional flows and a marginal value of time for returned products. The distribution system consists of a single supplier that provides one new product to a set of distribution centers (DCs), which then ships to the final retailers. While at the retailers' site, products can be shipped back to the supplier for reprocessing. Each DC is capacitated and handles stocks of new and/or returned products. The model is a nonlinear mixed-integer program that optimizes DC location and allocation between retailers and DCs. We show that it can be converted to a conic quadratic program that can be efficiently solved. Some valid inequalities are added to the program to improve computational efficiency. We conclude by reporting numerical experiments that reveal some interesting properties of the model.


  • Business
  • Economics


  • capacitated facility location model; conic quadratic programming; valid inequalities; closed-loop supply chain