考慮需求內生性、設施提升及網路效應之競爭性設施選址

Abstract

本研究針對具有設施提升及網絡效應的競爭性設施選址問題，提出了一種新穎的解決方案，結合了貪婪演算法、四捨五入演算法和基因演算法。我們通過重構數學模型，使問題在不失一般性的情況下去除了空間限制，讓模型更加簡化和易於處理。此外，我們開發了一種精巧的四捨五入演算法，以提高解決方案的品質。我們在 72 種場景下進行了廣泛的數值實驗，每種場景包含 20 個實例，評估了我們的方法在不同候選位置質量、有效需求函數配置、候選設施規模、服務類型選擇以及是否考慮外部網絡效益下的表現。

結果表明，在高質量候選設施場景中，我們的綜合解決方案表現穩健，能夠實現接近最佳的解決方案，並優於基準算法。在低質量候選設施場景中，我們的方法顯著優於基準，證明了其對候選位置質量的有效性和不敏感性。此外，我們發現四捨五入算法是最耗時的部分，這表明未來的工作應該優化計算效率與解決方案質量之間的權衡。

這些結果強調了我們綜合方法在解決具有網絡效應的競爭性設施選址問題中的穩健性和有效性。未來的研究應重點解決隨著服務類型數量增加而導致的組合爆炸問題，並進一步優化演算法效率，以提升解決方案的性能。

This paper addresses the competitive facility location problem with network effects involving decorations by introducing a novel solution approach that integrates greedy, rounding, and genetic algorithms. We reformulate the problem to eliminate spatial constraints, simplifying the problem without loss of generality and making it more tractable. Additionally, we develop a sophisticated rounding algorithm to enhance solution quality. Extensive numerical experiments were conducted across 72 scenarios, each comprising 20 instances, to evaluate our approach under different candidate location qualities, configurations of the effective demand function, varying scales of candidate facilities, service type choices, and the presence or absence of external network benefits.

Our results demonstrate that, in high-quality candidate location scenarios, our integrated solution approach performs robustly, achieving near-optimal solutions and outperforming benchmark algorithms. In low-quality candidate location scenarios, our approach significantly outperforms benchmarks, proving its effectiveness and insensitivity to candidate location quality. Additionally, we identify the rounding algorithm as the most time-consuming component, suggesting future work to optimize the trade-off between computational efficiency and solution quality.

The findings highlight the robustness and efficacy of our integrated approach in solving the competitive facility location problem with network effects. Future research should focus on addressing the exponential growth of service type combinations and optimizing algorithmic efficiency to further enhance solution performance.