IEAB Cost-effectiveness Evaluation Framework for Fish Tagging:

Building a (MIP) Programming Model

Bill Jaeger, IEAB & Oregon State University

January 7, 2013

Outline of Presentation• Describe programming approach• Demo of simple model examples• More on specifics of approach

– Constraints, parameters, costs, objectives– Versatility in how the model can be used

• Practicality: we can’t include everything• Data/parameters needed (various dimensions)• Discussion – issues to explore?

– key attributes, dimensions, complementarities that should be included

• A plan, a check-list, a sign-up sheet!

A programming model• A computer algorithm:

– to optimize an objective function (max profits; min costs; etc.)

– Subject to constraints (budget limit, required level of production, water balance, laws of physics, laws of supply and demand)

• A way “to organize what we know” about a system, when there are many parts interacting simultaneously– Example: what set of crops should a farmer grow to

maximize profits.

An example: Morocco fertilizer industry

• Ingredients can arrive at one of several ports• Transported to one of several bagging stations• Shipped to markets in various cities• In quantities to satisfy market demand

• Transportation can be by road, or rail (where lines exist), or a combination of the two

• Model question: How to minimize the total cost of satisfying the demand for fertilizer in all market?

Morocco Fertilizer Distribution Problem

Question: How to sastisfy demand for fertilizer at minimum cost?Given imported ingredients from PORTS, bagged at BAGGING STATIONS and delivered to MARKET CENTERSProblem includes choices of PORTS, BAGGING STATIONS, and mode of TRANSPORTATION (road or rail)

Port Bagging stations Market centerConsumer demand

agadir agadir agadir 2200 casablanca beni-melal al-hoceima 10800 jorf-las berechid azilal 21100 kenitra bougedra beni-melal 11400 nador casablanca ben-slim 3000 safi el-ayon boulemane 24000 tanger fes casablanca 10900

marrakech el-kella 8000 meknes er-rachida 9400 nador essaouira 23000 oued-zem fes 5700 safi figuig 9700 sidi-slim ifrane 7800 taza khenifra 10100

nador 5900 ouarzazate 6400 oujda rabat 15400 safi 12400 settat 7100 tanger 3200

Fish tagging: similar to the fertilizer model in some ways

Fertilizer Fish Tagging

Market demand Detections “demanded” to generate indicators

Rail or road? PIT, CWT, Acoustic?

Ports Location of marking fish

Fertilizer typeSpecies

Fish Tagging Forum Problem

Question: How to sastisfy demand for answers to management questions at minimum cost?Given DETECTIONS from NODES of ORIGIN can be delivered by different TECHNOLOGIESChoose TECHNOLOGIES to MINIMIZE COST of generating INDICATORS of abundance and survival

Marked fish

Detected fish

Marked fish

Detected fish

Marked fish

Detected fish

Marked fish

Detected fish

Marked fish

Detected fish

Required detections:

For Chinook

CWT A to B 2,100 PIT A to C 2,500

Genetic A to D 1,000 Accoustic A to E 1,600

B to E 1,000 C to D 1,200 A to H 2,400

Indicators of survival

from:

Node A Node B Node C Node D Node E

Fish Tagging Forum Problem

Question: How to sastisfy demand for answers to management questions at minimum cost?Given DETECTIONS from NODES of ORIGIN can be delivered by different TECHNOLOGIESChoose TECHNOLOGIES to MINIMIZE COST of generating INDICATORS of abundance and survival

Marked fish

Detected fish

Marked fish

Detected fish

Marked fish

Detected fish

Marked fish

Detected fish

Marked fish

Detected fish

Required detections:

For Chinook

CWT 15,000 A to B 1,500 PIT 17,600 A to C 1,900

Genetic A to D 1,800 Accoustic 1,000 A to E 1,000

1,900 B to E 1,900 5,320 2,660 2,200 C to D 2,200

1,200 A to H 1,200

Indicators of survival

from:

Node A Node B Node C Node D Node E

So, there are sets of equations:

Objective function: {minimize costs}Subject to: {detections <= markings}

{detections iff array in place}Accounting {costs >= sum for tagging, detect.}Accounting { costs <= budgets }Accounting {index of priorities, summed up}

Other objectives: maximize priorities (given limited budget)

Other versions: maximize with all budgets, certain budgets only, maximize different versions of priority weights

General Description of the model A fish’s life cycle moves in space and time through a sequence of “nodes”: n=1, n+1, n+2, …. n+m during its life. This includes downstream, ocean, and upstream in the sequence. Tagging of fish (X) is represented as 𝑋𝑖𝑗𝑛 where species i is marked with technology j at location n. Detecting or recovering fish (Y) is represented as 𝑌𝑖𝑗𝑛 where species i are detected/recovered with technology j at location n. Expected survival for a fish species between nodes is Sn,n+1 = θ

More on general model description:

For some tag technologies detection involves recovery that can be lethal (Sj = 0), or reduce survival (Sj>0). For tags where detection does not involve recovery (touching the fish), there is no reduction in survival (Sj = 1). Indicators, I, needed to answer management questions can take several forms, such as a ratio relating detections at n to markings at n-1 or n-m.

For example, an indicator SAR, Ik = 𝐹൬𝑌𝑖𝑗(𝑛=𝑚)𝑋𝑖𝑗(𝑛=1)൰ is a function of

the ratio of fish tagged at one location and fish detected at another location

Costs and optimization:Costs for tagging will include fixed costs, F, and variable costs, V, for each tag type. TCijn = σ 𝐹𝑗𝑌+ 𝑉𝑖𝑗𝑌 +𝐹𝑗𝑋+ 𝑉𝑖𝑗𝑋𝑛 ∀ i,j,n > 0 One way to identify the optimal solution is to constrain the model to satisfy a given level of indicator data (Ik), and then minimize the costs by choosing among tag technologies. Minimize: TC s.t. Yk >= Y(Ik) A second variation will maximize the value of priority indicators W(Ik) (using subjective weights that can vary by forum), given a fixed budget.

Maximize: W(Ik) s.t. TC <= 𝑇𝐶തതതത

The nuts and bolts: Model structure and parameters need to reflect most dimensions of real world setting, but not all!

• Define a set of (most important) nodes and reaches

• Define detection/recovery requirements to answer most management questions

• Define survival rates by reach, node

• Estimate costs for each “activity” (tagging a fish, detecting a fish, installing an array, etc.)

So, now two demo models• A simple model in a spreadsheet WB:

– One species– One technology– A set of costs– A set of detection requirements

• A simple model in GAMS:– Two species– Two tag types– A network of four downstream nodes; three upstream– A set of detection requirements– A set of costs

Network Nodes for Columbia River System

OCEAN

Columbia Estuary COLR1

Columbia River COLR2

COWLR1 COWLR2

WILLR1 WILLR2 WILLR3

Columbia River COLR3

Columbia River COLR4

DESCH1

JDAR1 JDAR2

Columbia River COLR5

YAKIM1 YAKIM2

SNAKE1 SNAKE2 SNAKE3

Columbia River COLR6 GRAND1 SALR1

Columbia River COLR7 GRAND2 SALR2

Columbia River COLR8 SALMF1 SALMF2

SALR3

SALR4

We need to make reasonable choices, to build a practical model – in terms of the network of

nodes, reaches, hatcheries, release sites?

• Aim for 80% coverage? 90%?

• Start with ESA listed species?

• Aggregate model sites for each ESU?

• Issue: management questions/indicators in FTF spreadsheet are not species-specific

How to estimate # of “required” detections/recoveries?

Some possibilities:

• CSS report has “smolts arriving” at MCN, MCA, BOA, JDA, LGR, but not other locations

• Alternative: Look at data on “smolts tagged”, assume 3% SAR, and so multiply by 0.03 to estimate required “smolts arriving”

• Other approaches? • Other sources of comprehensive data?

Other model elements to decide:

• Reach/dam survival rates in river network – how to estimate?

• Locations for detection to include?• Locations for tagging to include?

– E.g., top 40 hatcheries, release sites?

• Cost data (template) – need to fill in template

91.2

91.4

BON TDAICE

91.996.689.376.6 (87.5) 94.384.5

95.193.694.289.681.2 (89.8) 86.5MCNJDA LMO LGRLGO SRTBON

JDAMCN

LMO LGO LGR

SRT

YearlingChinook salmon reach survival

2011Average

Standard errors not shown

92.8

83.9

BON TDAICE

95.594.896.085.8 (92.6) 98.677.2

96.793.091.283.874.5 (86.0) 75.5MCNJDA LMO LGRLGO SRTBON

JDAMCN

LMO LGO LGR

SRT

Steelhead reach survival

2011Average

Standard errors not shown

A table of reach survival rates will be needed

Est. Survival Rates: Chinook (species)Downstream ==> Downstream ==> Downstream ==>

To node #: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Name: SALMF2 SALMF1 SALR3 SALR2 SALR1 SNAKE4 GRAND2 GRAND1 SNAKE3 SELWY2 SELWY1 LGS SNAKE2 LGR LMN SNAKE1 IHR

From Node #: 1 SALMF22 SALMF13 SALR34 SALR25 SALR16 SNAKE47 GRAND28 GRAND19 SNAKE3 95.1 93.6 94.210 SELWY211 SELWY112 LGS13 SNAKE214 LGR15 LMN16 SNAKE117 IHR18 COLR819 COLR720 COLR621 YAKIM222 YAKIM1

Downstream

==>Dow

nstream ==>

CWT -- largest tagging locationsSpecies: Chinook Coho Steelhead Sockeye

1 2 3 4 Grand TotalPRIEST RAPIDS HATCHERY 4,752,766 4,752,766 CLEARWATER HATCHERY 2,909,332 1,067,214 3,976,546 LYONS FERRY HATCHERY 3,411,531 491,964 3,903,495 SPRING CR NFH 3,304,108 3,304,108 WELLS HATCHERY 2,501,605 254,218 412,384 3,168,207 COWLITZ SALMON HATCH 1,364,102 1,768,651 3,132,753 CLE ELUM HATCHERY 3,020,442 3,020,442 MCKENZIE HATCHERY 3,006,199 3,006,199 MAGIC VALLEY HATCH 2,967,413 2,967,413 LOOKINGGLASS HATCH 2,881,283 59,759 2,941,042 LEAVENWORTH HATCHERY 630,812 1,968,205 2,599,017 BIG CR HATCHERY 2,532,584 2,532,584 FALLERT CR HATCHERY 2,145,917 310,749 2,456,666 WINTHROP NFH 1,302,476 682,049 405,341 2,389,866 WARM SPRINGS NFH 1,804,594 1,804,594 SIMILKAMEEN HATCHERY 1,771,504 1,771,504 SAWTOOTH HATCHERY 1,207,302 401,709 1,609,011 LEWIS RIVER HATCHERY 991,295 455,762 1,447,057 DRYDEN POND 1,367,977 1,367,977 CHIWAWA HATCHERY 1,328,433 20,431 1,348,864 HAGERMAN NATIONAL FH 1,320,385 1,320,385 DWORSHAK NAT. HATCH 504,672 750,854 1,255,526 CASCADE HATCHERY 1,230,777 1,230,777 MCCALL HATCHERY 1,223,287 1,223,287 ROUND BUTTE HATCHERY 1,155,616 1,155,616 IRRIGON HATCHERY 495,506 617,643 1,113,149 WILLARD NFH 249,398 768,501 1,017,899 TURTLE ROCK HATCHERY 735,747 250,146 985,893 UMATILLA HATCHERY 677,326 303,927 981,253 TUCANNON HATCHERY 705,736 241,505 947,241 NIAGARA SPRINGS HTCH 942,523 942,523 OXBOW HATCHERY 912,662 912,662 MARION FORKS HATCH 878,696 878,696 METHOW HATCHERY 833,737 833,737 LTL WHITE SALMON NFH 742,877 742,877 WILLAMETTE HATCHERY 721,731 721,731 CLACKAMAS HATCHERY 716,629 716,629 PROSSER HATCHERY 713,763 713,763 BONNEVILLE HATCHERY 675,375 675,375 CARLTON ACCLIMATION POND 660,863 660,863 WASHOUGAL HATCHERY 370,720 265,152 635,872 PAHSIMEROI HATCHERY 587,333 587,333 DEEP R NET PENS 462,726 110,989 573,715 DEXTER PONDS (WILLAM 569,683 569,683 CHELAN FALLS HATCHERY 535,789 535,789

57,364,134 7,815,053 9,851,489 401,709 75,432,385 76% 10% 13% 1%

PIT tag instream arrays

Tagging Costs by Technology - for the Columbia River BasinFor species:

Fixed costs (facilities)

Fixed costs (equipment)Price new Life (yrs) O&M /yr Price new Life (yrs) O&M /yr

PIT TagsMarking fish (Trailer?) (Equipment)

At hatchery $2.00 5000 5000Other site

Detecting fishMainstem $0 Tributary $0 Hatchery $0 Weir $0 Hand-held $0

Caught fish $0 Carcasses $0

Data retrieval & compilation

CWTsMarking fish (Trailer?)

At hatchery $0.18 Other site $0.18

Detection (recovery)Joint with commercial harvest $90

Joint with recr. harvestHatcheryOther

Regional Mark Information System Data retrieval & compilation

Variable cost (tagging

devise, labor)

Capacity (fish/day

)Capacity

(fish/day)

Example of the kinds of “activity cost” information we need (From Dan Rawding):

• Budget Increase– 2500 PIT tags for smolts & adults ($4K/year)– 2 Handheld readers ($6K) life 10 years– Instream detector installation to replace

abundance monitoring at Hemlock Dam ($55K)– Instream detector O&M ($10K/yr)– Parr survival as part of life cycle monitoring

using 3000 PIT tags (5k/yr)– Increase for database management, analysis,

reporting ($10-20K/yr)

Checklist, sign-up sheets!• FTF work is a great resource for us;

but we need focused help from FTF participants:– Choosing the dimensions of the model– Estimating detection requirements by location, species,

population, etc.– Estimating variable and fixed costs for key “activities” (tagging,

detecting)– Survival rates– Translating management questions into gross detection numbers

between A and B, by species

– We need names, contact info, of individuals who can help with specific items; for intensive push during next three weeks