مساله پوشش هاب تک تخصیصی بر روی شبکه ستاره‌ای؛ مدل‌بندی، خطی‌سازی و یافتن کران مناسب برای آن‌

The present study evaluates two problems of single allocation hub-covering problem with star structure including two problems of maximal p-hub covering and hub covering by considering the flow transfer costs. The star structure is as there is a central hub with definite location and other hubs are connected directly to the central hub. In the first problem, the goal is selection of p-hub locations and allocation of each customer to at most one hub as total transferred demand between customers is maximum. The purpose of the second problem is minimizing the sum of constant costs of construction of hubs and flow transfer costs between the network nodes as complete covering is created in the network. In two problems, connection of customers to hub centers and connection of hubs to the central hub is as the source to destination distance by considering discount factor to connect hub and central hub is lower or equal to the predefined value. After presenting the math model in two problems, linearization is performed, and then Lagrangian relaxation is applied to find suitable bounds. In addition, in the second problem, valid inequalities equal to two constraints of problem are presented. Finally, the results of solution of linear, non-linear models and using Lagrangian relaxation are evaluated and compared. The evaluation of these results on CAB data set shows that the linear models are better than non-linear models in terms of optimal value of objective function and implementation time. Based on the results, the bounds of Lagrangian relaxation are closer to the optimal solution of problems.