1. Columbia Express Algorithms and heuristics used by shipping company Yoon Keun Ane Jeongwho Lee Co- Express

2. Service Description 24/7 shipping company with distribution centers across the U.S. Provides 24-hour service, 2-days shipping services If late, the company refunds shipping fees to the customers Co- Express

3. Company Objective & Constraints Objective : minimize overall costs including shipping costs and penalty costs Constraints – Deadlines – Carrier Capacity Co- Express

4. How to approach the problem 3 stages of the problem 1.Package Center to Main Dist. Center - Package Shipment Schedule (Knapsack) 2.MDC to Local Dist. Centers - Minimizing Carrier Cost (Bin-Packing) 3.LDC to Final Destination - Minimizing Delivery Cost (TSP) Co- Express

5. Co- Express Problem Delineation One MDC Many customers Local distribution centers at each zone (zones divided by customer population) Optimization done by each zone

6. I. Shipment Schedule to MDC 1. Package received at Columbia 2. Package scheduled by deadline to be send to MDC  Use the following integer programming to maximize the total weight of jobs that finish before their deadlines Co- Express CO- Express

7. Integer Programming Cj = shipping cost based on weight, distance and deadline Wj= Physical weight of the package This problem is NP-complete problem also called knapsack problem, and can be solved by dynamic programming Co- Express

8. II. MDC to LDC Purpose : Minimize number of trucks according to its size Motivation : No need to use huge trucks nor many trucks going from MDC to LDC Solution: “Bin-packing” Problem : Maximize utilization space in each container Co- Express

9. Graphical Interpretation Co- Express Figure 1Figure 2 We need to minimize the size of empty space which is shown by white spaces in figure 2

10. Column Generation Method CGM is used to solve bin-packing Dual variables from original LP is used to create new column of constraints that will give a better solution than orig. LP Repetition of above steps will lead to finding the optimal pattern Formulation used most frequently nowadays Co- Express

11. Bin Packing Approx. First Fit Label bins as 1, 2, 3,... Objects are considered for packing in the order 1, 2, 3,... Pack object i in bin j where j is the least index such that bin j can contain object i. Best Fit The same as FF, except that when object i is to be packed, find the bin which after accommodating object i will have the least amount of space left. Co- Express

12. III. Local Delivery Purpose: Minimize the total distance traveled by local delivery trucks Well-known NP-hard Traveling Salesman Problem Co- Express

13. Solving TSP TSP can be solved using various methods ex) Algorithm 4.4.4.5 TSP relaxation Dynamic Programming We adopted TSP relaxation method to arrive at near-optimal solution Co- Express

14. TSP relaxation Solve Relaxation t o TSP ->get vecto r X* Check to see if x* violate s any sub-tour inequality (do this by solving min-c ut problem). If not stop If so, add the sub-tour ineq. To TSP relax Co- Express

15. Limitations & Future Research Stochastic demand and processing time Hard deadline was not considered when solving II & III Minimizing cost at distribution intsct Application to real-life data Co- Express

16. Co- Express THANK YOU, ANY QUESTIONS?