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Optimal Biosolids Storage Site for Effective Distribution Planning

This study focuses on finding efficient storage locations for 1200 wet-tons of biosolids daily to minimize costs and distances to 3000 fields. Using multi-objective optimization, the research explores various weight combinations for Pareto optimal solutions.

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Optimal Biosolids Storage Site for Effective Distribution Planning

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  1. Optimal Location for Biosolids’ Storage Site ENCE723/Fall2004 by Prawat Sahakij

  2. Outline • Overview • Problem Description • Data • Model Formulation • Software and Method Used • Preliminary Results and Analysis • What to be done

  3. Overview • District of Columbia Water and Sewer Authority (DCWASA) • -Provides retail water and wastewater services to more than 2 million Washington metro area customers • -Produces about 1200 wet-tons of biosolids per day

  4. Overview (cont)

  5. Overview (cont)

  6. Overview (Cont) • Related Research • Statistical model for predicting odor of biosolids (S. Gabriel, S. Vilalai, C. Peot, and M. Ramirez) • MOP for processing and distributing of biosolids to reuse site (S. Gabriel, P. Sahakij, C. Peot, and M. Ramirez

  7. Problem Description • Approximately 1200 wet-ton of biosolids per day needed to be hauled to roughly 3000 fields in MD and VA

  8. Problem Description (cont) • Given the weather condition on any given day, biosolids needed be stored in the storage • Unloading and reloading biosolids causes more distributing cost

  9. Problem Description (cont) • Need to find storages that: • minimizing number of storages • minimizing total miles from each storage to each field • minimizing number of people around the storage • subject to some constraints (to be shown later) F6 F2 F3 S1 F5 S2 F1 F4

  10. Data

  11. Data (cont) • Tonnage capacity for each field • Population in a 3.1-mile radius from each field • Distance from each field to the closest highway • Distance from each field to the closest hospital • Distance from field i to field j

  12. i j o • Distance from field i to field j calculation cos(ioj)=cos(lat(i))cos(lat(j))cos(lon(j)-lon(i))+sin(lat(i))sin(lat(j)) distance(ij)=R*(ioj), with ioj in radians where, R = the radius of the earth = 6371 km or 3959 miles

  13. Model Formulation • Used only 36 selected fields in PG county • Objective function • min (numStorage, numPeople, numMile) • Constraints • Storages cannot be located within 3.1 miles from a major highway or a hospital • Cannot send biosolids to itself • Cannot be used as storages and application field at the same time (it-then constrain, binary variables)

  14. Model Formulation (cont) • Constraints (cont) • Each field could be assigned to only 1 storage • There is at least one link from each node • All storages together must hold up to 2 days production (2400 tons)

  15. Model Formulation (cont) • Problem size • Problem Statistics • 2803 ( 380 spare) rows • 2643 ( 0 spare) structural columns • 15397 ( 10600 spare) non-zero elements • Global Statistics • 2643 entities 0 sets 0 set members

  16. Software and Method Used • Software • XPRESS-MP interface with EXCEL • Multi-objective optimization method Used • Weighting method • Constraint method

  17. Preliminary Results (cont) • Weighting Method • 1st try: w1 = 1..10, w2 = 1..10, w3 = 1..10 -only one Pareto point was obtained • 2nd try: w1 = 1..10, w2 = 1..10, w3 = 901..1000 • obtained 5 more Pareto optimal points • 3rd try: w1 = 1..10, w2 = 1..10, w3 = 1000..1,000,000 (step 1000) • obtained 5 more Pareto optimal points and still running

  18. Preliminary Results (cont) • Weighting Method (cont) • Run# 1 • W1 = 1, W2 = 1, W3 = 1 • numStorage = 2 (F5,F27) • numPeople=5748.30 • numMile=108.15 • Run# 2741 • W1 = 2, W = 8, W3 = 941 • numStorage = 3 (F5,F27,F36) • numPeople=8759.79 • numMile=70.98 • Run# 2240 • W1 = 2, W = 3, W3 = 940 • numStorage = 3 (F26,F27,F35) • numPeople=8759.79 • numMile=70.98 Obj = w1*numStorage + w2*numPeople + w3*numMile

  19. Preliminary Results (cont) • Run# 2240 • W1 = 1, W = 1, W3 = 3000, numStorage = 5 (F7,F9,F10,F27,F35), numPeople=15352.19, numMile=64.74

  20. Preliminary Results (cont) • Pareto optimal solutions obtained so far

  21. Preliminary Results (cont)

  22. Preliminary Results (cont)

  23. Preliminary Results (cont)

  24. Preliminary Results (cont)

  25. Preliminary Results (cont) • What conclusions can be drawn from here? • Why did numStore and numMile seem to go in the same direction? • Why did numMile go in the opposite direction of numPeople and numStorage? • Is this really a weight driven? • Probably....YES! (look at the weight) • Need to try more grids of weight

  26. Preliminary Results (cont) • What lessons I have learned from here • Pareto optimal solutions obtained were really sensitive to grids of weight tried • In order to obtain more Pareto optimal point, should be intelligent on grids of weight used (first 1,000 runs yielded only 1 Pareto point)

  27. What to be done • Try more grids of weight • Try constraint method

  28. Question?

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