Risk-balanced territory design optimization for a Micro finance institution

Jesús Fabián López Pérez; Tahir Ekin; Jesus A. Jimenez; Francis A. Méndez Mediavilla

doi:10.3934/jimo.2018176

Article Contents

2020, Volume 16, Issue 2: 741-758. Doi: 10.3934/jimo.2018176

This issue Previous Article Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects Next Article Multi-objective robust cross-market mixed portfolio optimization under hierarchical risk integration

Risk-balanced territory design optimization for a Micro finance institution

1.
Universidad Autónoma de Nuevo León, Monterrey, Mexico
2.
Texas State University, San Marcos, TX 78666, USA

* Corresponding author: Tahir Ekin
* Corresponding author: Tahir Ekin

Received: July 31, 2017

Revised: June 30, 2018

Early access: December 2018

Published: February 2020

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Abstract

Micro finance institutions (MFIs) play an important role in emerging economies as part of programs that aim to reduce income inequality and poverty. A territory design that balances the risk of branches is important for the profitability and long-term sustainability of a MFI. In order to address such particular business needs, this paper proposes a novel risk-balanced territory planning model for a MFI. The proposed mixed integer programming model lets the MFI choose the location of the branches to be designated as territory centers and allocate the customers to these centers with respect to planning criteria such as the total workload, monetary amount of loans and profit allocation while balancing the territory risk. This model is solved using a branch and cut based hybrid-heuristic framework. We discuss the impact of the risk balancing and merits of the proposed model.

Keywords:

Mathematics Subject Classification: Primary: 90B50, 90C11; Secondary: 90B80, 90C90.

Citation:

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Figure 1. Illustration of branches and customers of the micro finance institution

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Figure 2. Total Cuts and Number of Disconnected BUs versus Computational Time

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Figure 3. Recenterings versus Computational Time

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Figure 4. Objective Function Values of Risk and Distance for Model 1 (bold line) and Model 2 (dashed line)

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Figure 5. Partial map of the implementation of the territory design model

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Table 1. Mathematical notation and description for sets

Set	Description
I	set of all branches
V	set of all BUs
F	set of existing (former) territory centers
K	union set of BUs that were assigned to each territory center from set F
H	set of pairs of BUs that must be assigned to different territories
$ \text{N}^i $	set of nodes which are adjacent to the $ i^{th} $ branch; $ i \in I $
C	set of unconnected BUs assigned to each branch
$ \text{N}^C $	union set of all BUs that are adjacent to any member of C

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Table 2. Mathematical notation and description for decision variables

Decision Variable	Description
$ X_{ij} \ \forall i \in I, j \in V $	set of all branches
$ Y_i \ \forall i \in I $	set of all BUs

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Table 3. Mathematical notation and description for parameters

Parameter	Description
$ d_{ij} $	Euclidean distance between nodes $ i^{th} $ branch, $ j^{th} $ BU; $ i \in I,j \in V $
$ w_1 $	Weight of the importance of similarity with the existing design
$ M_{ij} $	Binary; if $ j^{th} $ BU is assigned to $ i^{th} $ branch in the existing plan, $ i \in F $
$ w_{2i} $	Weight of the risk function for each $ i^{th} $ branch; $ i \in I $
$ PV_j $	Profit variance of $ j^{th} $ BU; $ j \in V $
$ \gamma_i $	Threshold for total profit variance of $ i^{th} $ branch; $ i \in I $
p	Number of territory centers
$ v_j^m $	Activity measure m for $ j^{th} $ BU; $ j \in V $, $ m = 1,2,3 $
$ \mu_i^m $	Target level of activity measure m for $ i^{th} $ branch; $ i \in I $, $ m = 1,2,3 $
$ t^m $	Territorial tolerance with respect to $ m^{th} $ activity measure; $ m = 1,2,3 $
$ \delta_i $	Maximum travel distance for BUs assigned to the $ i^{th} $ branch; $ i\in I $
$ g_{ib} $	Binary; indicating if ith branch is of type $ b $ or not; $ b = 1,..,5 $
$ l_b $	Lower bound for the number of branches selected of type $ b $; $ b = 1,..,5 $
$ u_b $	Upper bound for the number of branches selected of type $ b $; $ b = 1,..,5 $

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