Robust uncapacitated multiple allocation hub location problem under demand uncertainty: minimization of cost deviations

Subject Areas : Mathematical Optimization

Aleksejs Lozkins ¹ (Department of Mathematical Game Theory and Statistical Decisions, Saint Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, Russian Federation, 199034|Department of Mathematical optimization and Modeling, Ltd. BIA-Technologies, 94, Moskovskiy avenue, St. Petersburg, Russian Federation, 196084)
Mikhail Krasilnikov ² (Department of Mathematical optimization and Modeling, Ltd. BIA-Technologies, 94, Moskovskiy avenue, St. Petersburg, Russian Federation, 196084)
Vladimir Bure ³ (Department of Mathematical Game Theory and Statistical Decisions, Saint Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, Russian Federation, 199034)

Received: 2020-10-09 Accepted : 2020-10-09 Published : 2020-09-01

Keywords: Benders decomposition, Pareto, Stochastic programming, optimal cuts, Hub location problem, Absolute deviation · Robust solution,

Abstract :

The hub location–allocation problem under uncertainty is a real-world task arising in the areas such as public and freight transportation and telecommunication systems. In many applications, the demand is considered as inexact because of the forecasting inaccuracies or human’s unpredictability. This study addresses the robust uncapacitated multiple allocation hub location problem with a set of demand scenarios. The problem is formulated as a nonlinear stochastic optimization problem to minimize the hub installation costs, expected transportation costs and expected absolute deviation of transportation costs. To eliminate the nonlinearity, the equivalent linear problem is introduced. The expected absolute deviation is the robustness measure to derive the solution close to each scenario. The robust hub location is assumed to deliver the least costs difference across the scenarios. The number of scenarios increases size and complexity of the task. Therefore, the classical and improved Benders decomposition algorithms are applied to achieve the best computational performance. The numerical experiment on CAB and AP dataset presents the difference of resulting hub networks in stochastic and robust formulations. Furthermore, performance of two Benders decomposition strategies in comparison with Gurobi solver is assessed and discussed.

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