A Two-echelon joint continuous-discrete location model

Abstract

The problem of locating up to a given number of facilities in continuous Euclidean space that can serve as intermediate transshipment points between multiple stakeholders in a supply chain — suppliers and cus- tomers —who are distributed over the same space is considered. The first contribution is in considering the multisource Weber problem (MWP) in the presence of both source points and demand points rather than either alone. The second contribution is that the selection of intermediate facilities for further dis- crete analysis is based on a quantitative determination rather than a subjective selection process, which is typical of most popular commercial-grade mathematical programming (LP and IP) based location mod- els. While the mathematical programming approach benefits from a degree of richness in features and a sense of computational optimization, one limitation is that the candidate locations to be evaluated must be specified, often without any computational basis for them. Computational experiments on randomly generated problem instances and real case studies indicate that significant gains can be achieved with relatively little effort by expanding the boundary of analysis to include multiple suppliers and multiple customers in the analysis and design of a supply chain network. An alternating location-allocation-type heuristic method is developed that is easy to implement. The third contribution is the development of two different lower bounding procedures that demonstrate the high quality of this obtained heuristic solution.