1. 一个简单的分布式配送模型 谢金星 清华大学数学科学系 Tel: 010-62787812

2. 简要提纲
分布式配送的基本概念
简单的数学模型
求解与分析
扩展：带时间窗口的情形 小结

3. Centralized Warehousing (CW) vs. Distributed Distribution (DD)
CW: The components for a product is stocked together in a central warehouse, and orders are integrated at that warehouse.
DD: The components for a product is stocked separately, near their manufacturing sites or landing points, and orders integration occurs at one of many non-stocking merge centers distributed over the region, using a merge-in-transit process (e.g. Use 40 merge centers to cover USA)
“DD” first introduced by L.R. Kopczak (Stanford) in 1995.

4. References
Li J. and Xie J., "Performance Analysis of Distributed-Distribution System Under Uniform Distribution of Transportation Time", OR Transactions, Vol. 7, No.1, 2003, (in Chinese)
Li J. and Xie J., "Performance Analysis of Distributed-Distribution System With Time Window Under Uniform Distribution of Transportation Time", Systems Engineering: Theory & Practice, Vol.22, No.3, 2002, (in Chinese)
Li J. and Xie J., "Performance Analysis of Distributed-Distribution System Under Normal Distribution of Transportation Time", Control Theory & Applications, Vol.20, No.3, 2003, (in Chinese)

5. Distributed distribution: Example

6. A simple model for two components
Transportation time: fi – fixed part (assumed to be 0)
Xi – i.i.d., Uniform on [0, a]
Holding cost h1 <= h2

7. A simple model for two components
TM: A customer requests a delivery in TM from now on
: Expected service level (order filled before needed)
Problem: When to transport part 1 and 2, respectively?
Decision variable: (t, T ) (Noticing h1 <= h2)
We can assume T + t <= TM, T <= a (why?)

8. A simple model for two components
Objective: holding cost in the merge center f (T )

9. A simple model for two components
Constraints: service level
g (t, T )

10. The model

11. Solving the model
f(T) is convex in T, the unconstrained minimum point is
For the service level,
t = TM - T

12. Equivalent model

13. Solving the model Step 1: Calculate Step 2: Calculate
Step 3: Optimal T* = min (T0*, T1*).

14. Discussion Min Max Application:
For given TM and , can you accept the order?
If no, how to negotiate with the customer?

15. Generalization: time window (JIT)
But the analytical expression for g(t,T) is more complicated

16. Summary Thanks you! CW vs. DD A simple model and solving procedure
Discussion and applications
Generalized to the case with time window
Other generalizations?
More components?
More constraints?
More cost considerations? ……
Thanks you!