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Market proliferation and the impact of locational complexity on network restructuring

J. M. Pinar-Pérez, D. Ruiz-Hernández, M. B. C. Menezes

TL;DR

This paper defines locational complexity via pars-complexity, an entropy-based measure of supply chain structure, and embeds it into a non-linear K-Median extension called the $K$-MedianPlex problem. The authors decompose the complexity impact into an intrinsic cost and an ignore-cost, offering a framework to explain why network restructuring often fails to reduce total costs. They propose three practical strategies—network rebalancing, network rationalisation, and network reduction—to mitigate complexity, and evaluate them through extensive numerical experiments, showing that substantial profitability gains typically require reducing market share or abandoning unprofitable markets. The findings underscore that incorporating complexity costs into network design is crucial, and they suggest organizational approaches (e.g., autonomous units) as potential remedies for absorbing complexity costs. The work advances measurement and optimization of locational complexity and lays out open research avenues for non-linear, combinatorial network design under complexity constraints.

Abstract

This manuscript investigates the problem of locational complexity, a type of complexity that emanates from a companys territorial strategy. Using an entropy-based measure for supply chain structural complexity ( pars-complexity), we develop a theoretical framework for analysing the effects of locational complexity on the profitability of service/manufacturing networks. The proposed model is used to shed light on the reasons why network restructuring strategies may result ineffective at reducing complexity-related costs. Our contribution is three-fold. First, we develop a novel mathematical formulation of a facility location problem that integrates the pars-complexity measure in the decision process. Second, using this model, we propose a decomposition of the penalties imposed by locational complexity into (a) an intrinsic cost of structural complexity; and (b) an avoidable cost of ignoring such complexity in the decision process. Such a decomposition is a valuable tool for identifying more effective measures for tackling locational complexity, moreover, it has allowed us to provide an explanation to the so-called addiction to growth within the locational context. Finally, we propose three alternative strategies that attempt to mimic different approaches used in practice by companies that have engaged in network restructuring processes. The impact of those approaches is evaluated through extensive numerical experiments. Our experimental results suggest that network restructuring efforts that are not accompanied by a substantial reduction on the target market of the company, fail at reducing complexity-related costs and, therefore, have a limited impact on the companys profitability.

Market proliferation and the impact of locational complexity on network restructuring

TL;DR

This paper defines locational complexity via pars-complexity, an entropy-based measure of supply chain structure, and embeds it into a non-linear K-Median extension called the -MedianPlex problem. The authors decompose the complexity impact into an intrinsic cost and an ignore-cost, offering a framework to explain why network restructuring often fails to reduce total costs. They propose three practical strategies—network rebalancing, network rationalisation, and network reduction—to mitigate complexity, and evaluate them through extensive numerical experiments, showing that substantial profitability gains typically require reducing market share or abandoning unprofitable markets. The findings underscore that incorporating complexity costs into network design is crucial, and they suggest organizational approaches (e.g., autonomous units) as potential remedies for absorbing complexity costs. The work advances measurement and optimization of locational complexity and lays out open research avenues for non-linear, combinatorial network design under complexity constraints.

Abstract

This manuscript investigates the problem of locational complexity, a type of complexity that emanates from a companys territorial strategy. Using an entropy-based measure for supply chain structural complexity ( pars-complexity), we develop a theoretical framework for analysing the effects of locational complexity on the profitability of service/manufacturing networks. The proposed model is used to shed light on the reasons why network restructuring strategies may result ineffective at reducing complexity-related costs. Our contribution is three-fold. First, we develop a novel mathematical formulation of a facility location problem that integrates the pars-complexity measure in the decision process. Second, using this model, we propose a decomposition of the penalties imposed by locational complexity into (a) an intrinsic cost of structural complexity; and (b) an avoidable cost of ignoring such complexity in the decision process. Such a decomposition is a valuable tool for identifying more effective measures for tackling locational complexity, moreover, it has allowed us to provide an explanation to the so-called addiction to growth within the locational context. Finally, we propose three alternative strategies that attempt to mimic different approaches used in practice by companies that have engaged in network restructuring processes. The impact of those approaches is evaluated through extensive numerical experiments. Our experimental results suggest that network restructuring efforts that are not accompanied by a substantial reduction on the target market of the company, fail at reducing complexity-related costs and, therefore, have a limited impact on the companys profitability.
Paper Structure (24 sections, 1 theorem, 14 equations, 9 figures, 9 tables)

This paper contains 24 sections, 1 theorem, 14 equations, 9 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Problem formulation
  4. Pars-Complexity
  5. Gross profit and the effect of complexity
  6. The $K$-MedianPlex Problem
  7. Assessing the impact of complexity
  8. The cost of complexity
  9. The addiction to growth
  10. Restructuring and complexity
  11. Addressing locational complexity
  12. Network rebalancing
  13. Network rationalisation
  14. Network reduction
  15. Numerical experiments
  16. ...and 9 more sections

Key Result

Proposition 1

Consider systems $\mathcal{L}^1$ and $\mathcal{L}^2$. If $\sum_{\ell=1}^L H_\ell = \sum_{m=1}^M G_m$ and $\oplus_{\ell=1}^K \left(\mathbf{p}^1_{\ell}\mathbf{q}^{1,\ell}\right)= \oplus_{m=1}^M \left(\mathbf{p}^2_{\left(m\right)}\mathbf{q}^{2,m}\right)$, i.e. the contribution of each retailer to the t

Figures (9)

  • Figure 1: Operating profit, revenue and stores of two retailers.
  • Figure 2: Operating costs (left-hand-side axis) and number of branches (right-hand-side axis) of two banking institutions.
  • Figure 3: Two alternative configurations of a distribution network with 14 demand nodes and (a) three facilities; or (b) two facilities.
  • Figure 4: Cost of Complexity
  • Figure 5: Addiction to growth in network design.
  • ...and 4 more figures

Theorems & Definitions (1)

  • Proposition 1