UPS: Small Sort Design

1. UPS: Small Sort Design Adrian Diaz Daniel Carlisle Lacey Davis

2. History • To transport packages most efficiently, UPS has developed an elaborate network of “hubs” or central sorting facilities. Each “hub” is fed by a number of local operating centers, which serve as the home base for UPS pickup and delivery. • Small packages, small enough to palm, are sorted into groups, or bags, cutting down on the handling time. Bags and small packages coming into the plant are sorted in a special area called the Small Sort Division.

3. Problem Background The current problem in the Mesquite hub is the Small Sort Design Layout. There are four different areas which the packages may be sorted into: Primary – consists of 48 bins (24 left and 24 right) Secondary One – consists of 108 bins Secondary Two – consists of 108 bins Secondary Three – consists of 72 bins

4. Problem Background • Each destination is assigned a specific bin(s) with a specified TMU (Time Measurement Unit associated with the time used to distribute a package to a particular bin) • The bins near the center have the lowest TMU values. • As packages travel from Primary to each successive Secondary, the TMU’s increase significantly.

5. Problem Overview • The current problem is that the destinations with larger volumes are not necessarily assigned to the bins with the lower TMUs, demanding more time and energy from the sorter. The system is not operating in the most efficient manner.

6. Problem Overview • Currently, the bins do not consistently serve the same destinations through all three shifts, Day, Night, and Twilight. • Destinations requiring more than one bin may be scattered, further complicating the sorters job.

7. Analysis • The bins with the same destinations need to be next to each other. • Given the maximum capacity of two hundred packages in a bin per shift, the number of bins per destination needs to be reevaluated. • Maximum: • - Two bins in Primary • - Four bins in Secondary • *Except Mesquite and Dallas which are locked at the number of bins

8. Analysis • Bins need to be serving same destination for all three shifts. • -Must take a total averaged volume for each shift, Day, Night and Twilight. • Example: Chicago (CCHIL) has the following volumes: • Day: 119 • Night: 73 • Twilight: 112 • Average Volume: 101.3

9. Model The objective function minimizes the “bin layout” cost (the total cost of summing all the averaged destination volumes times their bin(s) TMU values): Minimize ΣΣ Ai * Bj where A = destination’s average volume B = bin TMU value a = total number of destinations b = total number of bins a b i=1 j=1

10. Example Average Volumes: Dallas – 6 Houston – 5 Austin – 4 San Antonio – 3 TMU’s: The clear choice is to assign: Dallas → Bin 1 Houston → Bin 2 Austin → Bin 3 San Antonio → Bin 4 With the minimal “bin layout” cost of: 6*10 + 5*20 + 4*30 + 3*40 = 400

11. Method To solve our LP, we used AMPL, a powerful and comprehensive algebraic modeling language for linear and non-linear optimization problems. We treated the problem as an “assignment problem”

12. Main Constraints • There must be five bins assigned to Mesquite (MESTX) and eight assigned to Dallas (DALTX). They must be in the Primary Sort. • Each bin has a maximum capacity of two hundred packages per shift. (So if one destination has 350, they must have two bins) • Primary – No more than two bins per destination* • Secondary – No more than four bins per destination • *Except Dallas and Mesquite

13. Sub-problems We broke the problem in two pieces Primary Secondary solving each as a separate problem

14. Model File set O; set D; param a {i in O} default 1; param r {j in D}; param c {i in O, j in D}; var x {i in O, j in D} >= 0; minimize cost: sum {i in O, j in D} c[i,j] * x[i,j]; subject to supply {i in O}: sum {j in D} x[i,j] <= a[i]; subject to demand {j in D}: sum {i in O} x[i,j] >= r[j];

15. Output Primary Left Primary Right

16. Output Secondary One

17. Output Secondary Two

18. Interpretation • Secondary Three has been eliminated – reduces overall amount of work for the sorting process and results in extra space in the hub. • Some slight adjustments were made to place bins next to each other, although never changing any destination to a different TMU value. • New layout is much more efficient and timely.

19. Bin Layout Cost Original Layout Proposed Layout Primary: 700,066.6091 Primary: 636,736.14 Secondary: 1,061,563.316Secondary: 1,036,951.94 Total: 1,761,629.925 Total: 1,673,688.08 The proposed bin layout reduces the cost by approximately 5%.

20. Drawbacks • May take time for employees to become familiar with new layout • Cost of implementing the new layout • Model does not take into account the different volumes for the three shifts, rather works on the average

21. Conclusion • The long term benefits outweigh the short-term costs • The proposed layout results in a much more efficient and effective Small Sort division • The bin layout cost was reduced by approximately 5% • The elimination of Secondary Three provides new ways to utilize the freed sort space.