Variable neighborhood search based evolutionary algorithm and several approximations for balanced location–allocation design problem

This paper introduces balanced location–allocation design problem to tackle a real-world health-care application. The problem involves strategic decisions on locating a predefined number of facilities and allocating a set of customers to the facilities such that minimizes total travel, operating and congestion costs in an uncertain environment. To face more appropriately with the uncertainties, a comprehensive model which takes into account all sources of uncertainty is proposed. Moreover, in order to have a balanced use of installed capacities and/or reduce delays in servicing, congestion-related costs are defined as a power-law function of the trespassed facility’s operating capacity. The developed model is extremely hard to solve because of its inherently high combinatorial nature combined with the uncertainties and the nonlinearities associated to the congestion. Therefore, a new search mechanism based on variable neighborhood search is put forward. This algorithm employs both random and mathematical programming techniques to generate a set of initial solutions. On the other hand, to examine the quality of each move, a linear model which is scenario decomposable is extracted. The validation of the model is studied on an existing application, and the algorithm’s performance is tested on a wide range of instances taken from literature.