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Columbia Express

Co- Express. Columbia Express. Algorithms and heuristics used by shipping company Yoon Keun Ane Jeongwho Lee. Co- Express. Service Description. 24/7 shipping company with distribution centers across the U.S. Provides 24-hour service, 2-days shipping services

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Columbia Express

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

  2. Co- Express 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

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

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

  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. Co- Express 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

  7. Co- Express 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

  8. Co- Express 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

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

  10. Co- Express 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

  11. Co- Express 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.

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

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

  14. Co- Express TSP relaxation

  15. Co- Express 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

  16. Co- Express THANK YOU, ANY QUESTIONS?

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