Abstract
In the aftermath of the Great Recession of the first decade of this century, we have witnessed an important increase in the number of bank mergers and acquisitions. One of the most important problems faced after a merger is the reduction of the branch network, eliminating redundant branches and adapting the capacity of the resulting network in order to accommodate the demand. This problem becomes even more complex when the uncertainty in the way that the market will react to the restructuring is considered. In this work, we present a stochastic capacitated branch restructuring problem, formulated as a two-stage recourse stochastic programming model. It takes into account the size of the shuttered branches, the existence of competitors, and the uncertainty in the demand’s response. We propose three alternative versions of our formulation that model different ways in which the different stages of the restructuring may be carried out. The model’s performance is tested on 25 alternative settings designed on an extension of Swain’s network. The results show that the banks may obtain important benefits if the necessary changes in the service capacity are carried out after the information about the market’s reaction is available.
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Notes
A unit of waiting area space is typically considered to be equal to 2 m\(^2\), and the size of a batch (the number of customers that can be accommodated in such area) varies between 4 and 6 individuals.
Notice that the physical service capacity, \(\overline{a}_i\), is usually a legal safety constraint; the architectural features of the building impose a natural limit, \(e_i\), on any potential increase in the branch’s waiting area. On the other hand, the virtual service capacity, \(\overline{b}_i\), is related to the number of employees working on the branch and it is fixed by the institution.
Here and in the next version, we use the notational convention that variables which are directly determined by scenario \(\omega \) are expressed as \(f\left( \omega \right) \); whereas variables affected by the scenario only through a third \(f\left( \omega \right) \) variable, are expressed as \(f^\omega \).
Church and Meadows (1979) showed that, if the set of nodes in a network is augmented by a set of points which lie on the links of the initial nodes, called network intersection points, then the solution to a covering problem, in which the set of candidate points is restricted to this augmented set, will contain the same number of facilities than the problem where the planner is allowed to locate the facilities anywhere in the network. An equivalent result was found for the p-median problem in Church and Meadows (1977).
All these values were calibrated based on real data and respect the underlying proportions between the different figures.
Notice that this will not always be the case as the first stage changes in service capacities, conducted in versions 1 and 3, can lead to different closing decisions.
Notice that, even though there seems to be an exception for branches 4 and 17, the actual Manhattan distance between those branches is larger than \(d^r\).
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Acknowledgments
The authors acknowledge with gratitude Prof. Laureano Escudero for his fruitful contribution in early stages of this article.
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Ruiz-Hernández, D., Delgado-Gómez, D. The stochastic capacitated branch restructuring problem. Ann Oper Res 246, 77–100 (2016). https://doi.org/10.1007/s10479-014-1730-3
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DOI: https://doi.org/10.1007/s10479-014-1730-3