A column generation heuristic for districting the price of a financial product

Abstract

This paper studies a districting problem that arises in the context of financial product pricing. The challenge lies in partitioning a set of small geographical regions into a set of larger territories. In each territory, the customers will share a common price. These territories need to be contiguous, contain enough customers and be as homogeneous as possible in terms of customer value. To address this problem, we present a column generation-based heuristic where the subproblem generates contiguous territories taken into account a nonlinear objective function. Computational results indicate that the territories produced by this heuristic are about 35% more homogeneous than those previously used in practice. The developed algorithm has been transferred to a financial firm and is now used to help craft more competitive financial products.

Optimisation and Static Equilibrium of Three-Dimensional LEGO Constructions

“…Instead of using the traditional branch-and-bound method for solving the problem, it imposes heuristic branching decisions that are permanent. This method of branching was used by, e.g., de Fréminville et al [11]. Each step in the branching heuristic is a part of breaking the symmetry in the decision variables.…”

“…The objective function heavily penalises this variable, such that the variable only activates if no other possibility exists. Constraints ( 10)- (11) state that each brick placement variable x b is a real number between 0 and 1. Constraints ( 12)-( 13) state that each voxel variable o v is a real number between 0 and 1.…”

A branch-and-price algorithm for the scheduling of customer visits in the context of multi-period service territory design

“…The authors incorporate some heuristic elements to increase computational efficiency, e.g., simplified contiguity constraints and distance-based variable fixing. de Fréminville et al (2015) deal with a special single-period districting problem which they call the financial product districting problem. In this problem, customers must be partitioned into territories such that the expected customer-dependent cost price of a financial product is relatively the same for all customers that belong to the same territory.…”