Optimal Location for Biosolids’ Storage Site

ENCE723/Fall2004

byPrawat Sahakij

Outline

• Overview

• Problem Description

• Data

• Model Formulation

• Software and Method Used

• Preliminary Results and Analysis

• What to be done

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

Overview (cont)

Overview (cont)

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

Problem Description

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

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

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)

F2

F3

F1

F6

F4

F5

S1

S2

Data

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

• Distance from field i to field j calculation

o

i j 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

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)

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)

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

Software and Method Used

• Software– XPRESS-MP interface with EXCEL

• Multi-objective optimization method Used– Weighting method – Constraint method

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

Preliminary Results (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

Obj = w1*numStorage + w2*numPeople + w3*numMile

• Run# 2240– W1 = 2, W = 3, W3 = 940

– numStorage = 3 (F26,F27,F35)– numPeople=8759.79

– numMile=70.98

•Weighting Method (cont)

Preliminary Results (cont)• Run# 2240

– W1 = 1, W = 1, W3 = 3000, numStorage = 5 (F7,F9,F10,F27,F35), numPeople=15352.19, numMile=64.74

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

run# w1 w2 w3numStor

age numPeople numMile

1 1 1 1 2 5748.30 108.15

1001 1 1 901 3 9019.26 68.53

1501 1 6 901 3 8900.01 69.26

2240 2 3 940 3 8995.93 68.89

2741 2 8 941 3 8759.79 70.98

4035 4 1 935 3 8940.12 69.22

11002 1 1 2000 4 12434.57 65.97

11003 1 1 3000-13000 5 15352.19 64.74

11014 1 1 14000-19000 6 18589.90 64.50

11020 1 1 20000 7 21601.39 64.34

12021 1 1 21000-->running 8 24318.69 64.21

Preliminary Results (cont)

Preliminary Results (cont)

Preliminary Results (cont)

Preliminary Results (cont)

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

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)

What to be done

• Try more grids of weight

• Try constraint method

Question?