In the field of finance, the underwriting process is an essential step in evaluating every loan application. During this stage, the borrowers' creditworthiness and ability to repay the loan are assessed to ultimately decide whether to approve the loan application. One of the core components of underwriting is credit scoring, in which the probability of default is estimated. As such, there has been significant progress in enhancing the predictive accuracy of credit scoring models through the use of machine learning, but there still exists a need to ultimately construct an approval rule that takes into consideration additional criteria beyond the score itself. This construction process is traditionally done manually to ensure that the approval rule remains interpretable to humans. In this paper, we outline an automated system for optimizing a rule-based system for approving loan applications, which has been deployed at Hyundai Capital Services (HCS). The main challenge lay in creating a high-quality rule base that is simultaneously simple enough to be interpretable by risk analysts as well as customers, since the approval decision should be accountable. We addressed this challenge through principled submodular optimization. The deployment of our system has led to a 14% annual growth in the volume of loan services at HCS, while maintaining the target bad rate, and has resulted in the approval of customers who might have otherwise been rejected.

The bandwidth packing problem (BWP) concerns the selection of calls from a given set and the assignment of one path to each selected call. The ultimate aim of the BWP is to maximize profit while the routings of the selected calls observe the capacity constraints of the links. Here, we additionally consider queueing delays in the network, which may cause a deterioration in the quality of service to users if they exceed the acceptable limits. The integer programming formulation for the BWP with the queueing delay restriction contains a nonlinear constraint that is intrinsic to the model. We apply the Dantzig-Wolfe decomposition to this nonlinear constraint, and since the Dantzig-Wolfe decomposition has exponentially many variables, we propose the branch-and-price procedure to find optimal solutions. We also propose a generalized Dantzig-Wolfe reformulation based on the aggregation of variables, which makes our branch-and-price algorithm more competitive. Computational results on cases of randomly generated networks and some real-life telecommunication networks demonstrate that our algorithm performs well for large networks.

Abstract We consider a network design problem in which flow bifurcations are allowed. The demand data are assumed to be uncertain, and the uncertainties of demands are expressed by an uncertainty set. The goal is to install facilities on the edges at minimum cost. The solution should be able to deliver any of the demand requirements defined in the uncertainty set. We propose an exact solution algorithm based on a decomposition approach in which the problem is decomposed into two distinct problems: (1) designing edge capacities; and (2) checking the feasibility of the designed edge capacities with respect to the uncertain demand requirements. The algorithm is a special case of the Benders decomposition method. We show that the robust version of the Benders subproblem can be formulated as a linear program whose size is polynomially bounded. We also propose a simultaneous cut generation scheme to accelerate convergence of the Benders decomposition algorithm. Computational results on real‐life telecommunication problems are reported, and these demonstrate that robust solutions with very small penalties in the objective values can be obtained. © 2012 Wiley Periodicals, Inc. Networks, 2013.

We consider the routing and wavelength assignment (RWA) problem on WDM ring networks without wavelength conversion. When the physical network and required connections are given, RWA is the problem to select a suitable path and wavelength among the many possible choices for each connection such that no two paths using the same wavelength pass through the same link. We give an integer programming formulation of the problem and propose an algorithm to solve it. Although the formulation has exponentially many variables, we solve the linear programming relaxation of it by using the column generation technique. We solve the column generation problem efficiently by decomposing the problem into several subproblems. After solving the linear programming relaxation, we apply the branch-and-price procedure to get an optimal solution. We test the proposed algorithm on some randomly generated data. Test results show that the algorithm gives optimal solutions to almost all instances under the given node limit of the branch-and-bound tree.