Optimal Location for Biosolids Storage Site ENCE 723Fall

Optimal Location for Biosolids’ Storage Site ENCE 723/Fall 2004 by Prawat 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 wettons of biosolids per day

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) F 6 F 2 S 1 F 3 S 2 F 5 F 1 F 4

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 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 o 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 (num. Storage, num. People, num. Mile) • 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 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 – 1 st try: w 1 = 1. . 10, w 2 = 1. . 10, w 3 = 1. . 10 -only one Pareto point was obtained - 2 nd try: w 1 = 1. . 10, w 2 = 1. . 10, w 3 = 901. . 1000 - obtained 5 more Pareto optimal points - 3 rd try: w 1 = 1. . 10, w 2 = 1. . 10, w 3 = 1000. . 1, 000 (step 1000) - obtained 5 more Pareto optimal points and still running

Preliminary Results (cont) • Weighting Method (cont) • Run# 1 – W 1 = 1, W 2 = 1, W 3 = 1 – num. Storage = 2 (F 5, F 27) – num. People=5748. 30 – num. Mile=108. 15 • Run# 2741 – W 1 = 2, W = 8, W 3 = 941 – num. Storage = 3 (F 5, F 27, F 36) – num. People=8759. 79 – num. Mile=70. 98 • Run# 2240 – W 1 = 2, W = 3, W 3 = 940 – num. Storage = 3 (F 26, F 27, F 35) – num. People=8759. 79 – num. Mile=70. 98 Obj = w 1*num. Storage + w 2*num. People + w 3*num. Mile

Preliminary Results (cont) • Run# 2240 – W 1 = 1, W 3 = 3000, num. Storage = 5 (F 7, F 9, F 10, F 27, F 35), num. People=15352. 19, num. Mile=64. 74

Preliminary Results (cont) • Pareto optimal solutions obtained so far run# w 1 w 2 w 3 num. Stor age 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 num. People num. Mile

Preliminary Results (cont)

Preliminary Results (cont) • What conclusions can be drawn from here? – Why did num. Store and num. Mile seem to go in the same direction? – Why did num. Mile go in the opposite direction of num. People and num. Storage? – 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?