upgrading uncapacitated multiple allocation p-hub‎ ‎median‎ ‎problem‎ ‎using‎ ‎benders decomposition algorithm

‎the hub location problem (hlp) is a significant problem in combinatorial optimization consisting of two main components‎: ‎location and network design‎. ‎the hlp aims to develop an optimal strategy for various applications‎, ‎such as product distribution‎, ‎urban management‎, ‎sensor network design‎, ‎computer network‎, ‎and communication network design‎. ‎additionally‎, ‎the upgrading location problem arises when modifying specific components at a cost is possible‎. ‎this paper focuses on upgrading the uncapacitated multiple allocation p-hub median problem (u-umaphmp)‎, ‎where a pre-determined budget and bound of changes are given‎. ‎the aim is to modify certain network parameters to identify the p-hub median that improves the objective function value concerning the modified parameters‎. ‎we propose a non-linear mathematical formulation for u-umaphmp to achieve this goal‎. ‎then‎, ‎we employ the mccormick technique to linearize the model‎. ‎subsequently‎, ‎we solve the linearized model using the cplex solver and the benders decomposition method‎. ‎finally‎, ‎we present experimental results to demonstrate the effectiveness of the proposed approach‎.