近年來餐飲業面臨競爭激烈和獲利空間縮減等問題，加上COVID-19疫情影響，促使業者積極尋求創新服務模式。本研究提出一個嶄新的多車輛同步配送及回收服務之途程問題，不同於傳統車輛途程問題，本研究同時考量：(1)正向物流與逆向物流的整合，實現餐點配送與餐具回收的雙向服務；(2)軟時間窗限制，允許適度的服務時間彈性；(3)車輛容量限制，確保配送效率最佳化。
在理論建構方面，本研究以層空網路架構為基礎，建立整數規劃模型。此架構能有效描述車輛在不同時空層次的移動軌跡，使模型更精確反映實際運作情況。為克服NP-Hard問題的計算複雜性，本研究開發三種創新演算法：(1)貪婪類演算法—整合工作路線、單點互換及2-opt路徑交換三種策略，實現多層次最佳化；(2)貪婪類模擬退火演算法—結合貪婪策略與模擬退火架構，通過溫度參數動態調整搜尋空間，平衡探索與利用；(3)數學演算法—在模擬退火框架下融合整數規劃邏輯，分別處理工作分配與服務時刻最佳化，提升解的品質。
實驗結果顯示演算法效能具顯著優勢：在小規模網路(5個客戶)中，整數規劃模型能在最長27秒內求得最佳解；中規模網路(6-9個客戶)採用貪婪類模擬退火演算法，求解時間可從數千秒大幅縮短至100秒以內，同時維持良好的解品質；大規模網路(20-25個客戶)則以數學演算法表現最佳，相較於整數規劃模型花費7200秒的求解效果，數學演算法在某些測資只需花其1/6的時間即可改善2.79倍的解品質。特別是在考慮軟時間窗限制的情況下，本研究提出的演算法展現出優異的適應性與穩定性。
研究成果不僅可為餐飲業提供實用的配送路徑最佳化工具，更為環保永續經營提供具體方案。透過同步配送與回收機制，有效降低一次性餐具使用，實現經濟效益與環保目標的雙贏。實驗結果亦證實，本研究所提出的解決方案能因應不同規模的實務需求，在效率與解品質之間取得良好平衡。

This study addresses a novel multi-vehicle routing problem with synchronized delivery and collection services, incorporating soft time window and capacity constraints. The research develops an integer programming model based on the level-space network structure to optimize vehicle routing for food delivery and tableware collection services.
To overcome the computational complexity of this NP-hard problem, three innovative algorithms are proposed: (1) greedy algorithms incorporating route construction, single-point exchange, and 2-opt path exchange strategies; (2) greedy simulated annealing algorithm combining greedy strategies with simulated annealing framework; and (3) matheuristic algorithm integrating integer programming logic with simulated annealing structure.
Numerical experiments demonstrate superior algorithmic performance: for small networks (5 customers), the integer programming model obtains optimal solutions within 27 seconds. In medium networks (6-9 customers), the greedy simulated annealing algorithm dramatically reduces computation time from thousands to under 100 seconds while maintaining solution quality. For large networks (20-25 customers), the matheuristic algorithm excels by achieving 2.79 times better solution quality while requiring only one-sixth of the computation time compared to the integer programming model's 7200-second solutions. Notably, the proposed algorithms exhibit exceptional adaptability and stability when considering soft time window constraints.
The research contributes both theoretical insights to the vehicle routing problem and practical value to the food delivery industry, offering an environmentally sustainable solution through synchronized delivery and collection services.

中文文獻
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