Optimal-transport satisficing with applications to capacitated hub location

Abstract

We present a coherent satisficing criterion for evaluating the attractiveness of strategic decisions under uncertainty. Specifically, we define a satisficing criterion using the optimal-transport measure, termed as Optimal-Transport Satisficing (OTS), to evaluate the random cost saving (that equals cost target minus cost) associated with a strategic decision. We apply this criterion to the capacitated hub location problem under demand and cost uncertainty, a problem that minimizes a setting up cost of selected hubs and a shipping cost. We seek the optimal strategic decision by maximizing OTS, termed as the Optimal-Transport satisficing model, whose solution shares the finite sample performance guarantee as in distributionally robust optimization. Methodologically, we show that the Optimal-Transport satisficing model possesses a compact (regularization) form for the cost uncertainty. Computationally, we propose a column-and-constraint generation based bisection search algorithm for solving the model under demand and cost uncertainty. Numerical experiments demonstrate the attractiveness and competitiveness of our proposed model.