11/6/1007 MIT Field Intelligence Lab 1 · L 0.35 1.5729 1.5842 1.6001 1.6249 1.6533 0.40 1.7094...

11/6/1007 1MIT Field Intelligence Lab

HARVEST RISK: AN INTRODUCTION TO QUANTITATIVE MODELING AND OPTIMIZATION IN QUANTITATIVE MODELING AND OPTIMIZATION IN

AGRICULTURE

INFORMS ANNUAL MEETING, SEATTLENOVEMBER 6, 2007

Edmund W. SchusterResearch Engineer

MIT Field Intelligence Lab

Stuart J. AllenProfessor Emeritus

Penn State Erie – The Behrend College


WHAT I WILL DISCUSS TODAYSCUSS O

• An introduction to agriculture and FIL

• A case study of quantitative risk modeling in agriculture

• Some ideas about sensing and new approaches to sampling, and the future of agriculture


INTRODUCTION - AGRICULTUREO UC O G CU U

• Agriculture began about 12,000 years ago

• Several types of risks exist – weather, pests, price

• Initial ideas on risk reduction– prevention of risk (e.g. irrigation)– dispersion of risk (by diversification of risky activities such as the cultivation of different

varieties of crops)– control of risk– insurance against risk.

Maatman, A., C. Schweigman, A. Ruijs, M. H. van Der Vlerk, “Modeling Farmers’ Response to U t i R i f ll i B ki F A St h ti P i A h ” O ti R h 50 3 Uncertain Rainfall in Burkina Faso: A Stochastic Programming Approach,” Operations Research 50:3 (2002), pp. 399–414.

• For an agricultural cooperative, the harvest involves an important business g p passet (Welch Foods, grapes = $70 million in inventory)

11/6/1007 MIT Field Intelligence Lab 4

INTRODUCTION – MIT FIELD INTELLIGENCE LAB(AGRICULTURAL SYSTEMS PRODUCTIVITY)(AGRICULTURAL SYSTEMS PRODUCTIVITY)

• Under the leadership of Prof. Sanjay Sarma, Dept. of Mechanical Engineering

– New research group (six people)

• Computers, data, and mathematical models will play an important role in agricultural productivity, offering an alternative to genetic advances in plants.

• Opportunities exist to apply the principles of manufacturing systems engineering to agriculture.g g g

• It is critical that agriculture respond to global climate change.


INTRODUCTION – MIT FIELD INTELLIGENCE LAB (CONTINUED)LAB (CONTINUED)

• Global competition will prompt the need for higher productivity in U.S. agriculture.

• America’s drive for energy independence will include a role for gy pagriculture.

• The study of supply chain management spanning from the farm to end The study of supply chain management, spanning from the farm to end customer, represents a significant opportunity.


INTRODUCTION – THE CONCORD GRAPEO UC O CO CO G

• A flavorful and aromatic variety - purple in color– Developed by Ephraim Wales Bull (1849)– Small fresh market– Used for juices, jams, jellies, and concentrate

• Major growing areas– Western New York, northern Ohio, and northern Pennsylvania (all three near Lake

Erie) western Michigan and south central WashingtonErie), western Michigan, and south-central Washington

• The role of agricultural cooperatives– Growing processing packaging distribution and marketingGrowing, processing, packaging, distribution and marketing– Vertical integration– Welch Foods, Inc. - (1869)


REFERENCES – HARVEST RISK MODELC S S S O

Allen, S.J. and E.W. Schuster, “Controlling the Risk for an Agricultural Harvest,” Manufacturing & Service Operations Management 6:3 (2004): pp 225 – 236.

Allen, S.J. and E.W. Schuster, “Managing the Risk for the Grape Harvest at Welch’s,” Production and Inventory Management Journal 41:3 (2000): pp 31 – 36.

Schuster, E.W. and S.J. Allen, “Raw Material Management at Welch’s,” Interfaces 28:5 (1998): pp. 13 - 24.

Schuster, E.W., S.J. Allen, and M.P. D’Itri, “Capacitated Materials Requirements Planning and its Application in the Process Industries,” Journal of Logistics Management 21:1 (2000): pp. , g g ( ) pp169 – 189.


INTRODUCTION – HARVEST OPERATIONSO UC O S O O S

• A single processing plant for a grape-growing region– Hundreds of growers deliver grapes from the surrounding area

• Mechanical harvestingg– Cost of the machine is high ($200k)

• Limited ability to increase or decrease the harvest rateLimited ability to increase or decrease the harvest rate

• Bayesian analysis is not appropriate


INTRODUCTION - MICROCLIMATESO UC O C OC S

• All fruits are susceptible to cold weather

• Low temperatures during harvest cause the grapes to fall from the vine– 28 degrees F. is the critical temperatureg p

• Some growing areas are located close to large bodies of water that act as a heat sink

• Harvest is a race against time

• Sometimes the crop is very large


PURPOSE OF THE “HARVEST MODEL”U OS O S O

• Balance the growers desire to harvest all grapes before a hard frost (28 degrees F.) verses capital expenditures required for maximum through-put rate

Hi t i ll W l h’ d fi d l gth f h t t l th th gh• Historically, Welch’s used a fixed-length of harvest to plan the through-put rate

– The consensus: a “30 day harvest”– In general, there are many heuristics in agriculture - some are correct g , y g– Divide crop forecast by 30 to get R (the rate to harvest, no risk)– All capital equipment investment assumed a 30 day harvest

• The fixed-length of harvest method did not consider the risk of a hard freeze or uncertain start dates

– Variability of growing areas, dependent on location


THE ELEMENTS OF UNCERTAINTYS O U C

H = crop size in tons, a random variable

L = length of harvest season in days, a random variable

R = pressing rate in tons per day, the decision variable

From these variables two sets of expressions can be defined; oneset each for the amount of crop loss (ACL) and the excess harvest rateset each for the amount of crop loss (ACL) and the excess harvest rate(EHR).


THE ELEMENTS OF UNCERTAINTY (CONTINUED)(CONTINUED)

H-RL if H RLACL (1)

0 if H RL>⎧

= ⎨ ≤⎩0 if H RL≤⎩

0 if H RL≥⎧0 if H RLEHR (2)

RL-H if H < RL≥⎧

= ⎨⎩


HARVEST MODEL DEVELOPMENTS O O

• S.J. Allen is the primary architect

• L is not correlated with harvest size, H– .14 correlation with significance of 53%g– Statistically independent

• A joint density function can be formed as the product of two marginal distributions.

• Form a total cost function for ACL and EHR (each is an expected value)Form a total cost function for ACL and EHR (each is an expected value)

• Minimize the function to find R*


COSTSCOS S

• Underage Cost (CH, dollars per ton): This reflects the cost of harvesting too slowly, therefore foregoing sales for grapes left in the field at the end of the harvest season.

O g C t (C d ll t ) Thi fl t th t f h ti g • Overage Cost (CR, dollars per ton): This reflects the cost of harvesting too fast, therefore committing an excessive amount of resources to the harvesting effort.

• Observation – a grain famer in W. Ohio once told me, “Why would I want to spend money to hire people to help me with the harvest, or purchase a larger combine, just to get done early?”g g

• I believe there are a number of opportunities in agriculture to optimize capacity


DEFINITION OF “POLICY”O O O C

• Take 100% of the crop, 85% of the time– Allen, S.J. and E.W. Schuster, “Managing the Risk for the Grape Harvest at Welch’s,”

Production and Inventory Management Journal 41:3 (2000): pp 31 – 36

– Allen, S.J. and E.W. Schuster, “Controlling the Risk for an Agricultural Harvest,” Manufacturing & Service Operations Management 6:3 (2004): pp 225 236 Manufacturing & Service Operations Management 6:3 (2004): pp 225 – 236.

• First Model (1996 – 2000) focus on policy “specification”• Second Model (2000 – current) focus on optimization of CH and CR

• Implies a harvest rate (R) required to meet the policy (first model)

• By defining a “statistical” policy for receiving grapes we can make trade-offs By defining a statistical policy for receiving grapes we can make trade offs between harvest capacity and investment in equipment

• We calculated a “loss function” and found the 85% policy to be optimal


CALCULATION OF R* UNDER DIFFERENT SCENARIOS (SECOND MODEL)SCENARIOS (SECOND MODEL)

KL and KH are the COV for L and H kH

0 05 0 1 0 15 0 2 0 250.05 0.1 0.15 0.2 0.25

0.25 1.3350 1.3564 1.3828 1.4195 1.4620

0.30 1.3880 1.4019 1.4291 1.4618 1.5004

kL 0.35 1.4306 1.4449 1.4662 1.4954 1.5305

0.40 1.4586 1.4732 1.4879 1.5167 1.5489

0.45 1.4713 1.4860 1.5008 1.5239 1.5532Optimal r for CR/(CR+CH)=0 1


CR/(CR+CH)=0.1

DETERMINATION OF THE PERCENT RECOVERY FOR A SPECIFIC R* (SECOND MODEL)( )

kH

0 05 0 1 0 15 0 2 0 250.05 0.1 0.15 0.2 0.25

0.25 97.16 97.08 96.95 96.79 96.61

0.30 95.96 95.91 95.80 95.65 95.48

kL 0.35 94.52 94.46 94.35 94.21 94.04

0.40 92.75 92.71 92.56 92.44 92.27

0.45 90.67 90.63 90.49 90.35 90.18


FINDING R UNDER CONDITIONS OF AN IMPOSED HARVEST POLICY (FOR R 85% SECOND MODEL)HARVEST POLICY (FOR R = 85%, SECOND MODEL)

kH

0.05 0.1 0.15 0.2 0.25

0.25 1.3547 1.3682 1.3927 1.4225 1.4573

0.30 1.4570 1.4684 1.4883 1.5144 1.5458

kL 0.35 1.5729 1.5842 1.6001 1.6249 1.6533

0.40 1.7094 1.7265 1.7371 1.7545 1.7837


0.45 1.8716 1.8903 1.9002 1.9192 1.9384

DATA REQUIRED FOR THE HARVEST MODELQU O S O

• Harvest Size - we use the average of the Long Range Plan (LRP) for Concord, for each growing area

• Historical analysis shows the harvest size to be normally distributedy y


DATA (CONTINUED)(CO U )

• We use the “start date” and “end date” provided by National Co-op to calculate the length of season, L

• We assume the distribution of the season length to be normal (based g (on observations of histograms)

ONLY DATA AVAILABLE POINT ESTIMATE OF TEMPERATURE• ONLY DATA AVAILABLE – POINT ESTIMATE OF TEMPERATURE

• THE ROLE OF TEMPERATURE SENSORS IN THE FIELD


SENSORSS SO S

“the number of deployed sensors will dwarf the number of personal computers by a thousand fold in 2010”

Ferguson, G., S. Mathur and B. Shah (2005), “Evolving From Information to Insight,” Sloan Management Review 46:2, p. 52.


DROP SENSORS (PROF. SANJAY SARMA)O S SO S ( O S J S )

• The initial applications of sensors in agriculture commonly involve two deployment approaches

– fixed where the sensor is mounted in the field– moving where the sensor is attached to a piece of farm machinery such as a

har esterharvester

• A third approach exists where sensors are dropped into areas of interestThis method is a way to optimize the deployment of sensors – This method is a way to optimize the deployment of sensors.

– To determine drop locations, remote sensing of various types serves an important role in narrowing down the area of interest

– Measure pollen count or temperatures

Deshpande, A. and S.E. Sarma, “Error Tolerant Distributions For Sampling,” American Control Conference (2008), forthcoming.


THREE RISK MODEL – L, H, AND DEMANDS O , ,

Demand-D

Region 1

Region 2Region 5 D=QY

D=RL

Region 3 Yield-Y

Y=RL/Q

Region 4

Length-L


THE SEA OF DATAS O

40% to 60% annual increase in data

What are you going to do with all your Data?


RFID APPLICATIONS IN AGRICULTUREC O S G CU U


THE FUTUREU U

The integration of marketing science, engineering technology, and supply chain management.

Supply chains that sense and respond to the physical world, and included an assessment of riskand included an assessment of risk.

Thi i I lli I f f This requires an Intelligent Infrastructure for management, control, automation and interaction.


FINAL NOTE: RECENT RESEARCH

Turvey, C.G., A. Weersink, and S-H. C. Chiang, “Pricing Weather y g gInsurance with a Random Strike Price: The Ontario Ice-Wine Harvest,” American Journal of Agricultural Economics 88:3 (2006): pp 696 – 709(2006): pp. 696 – 709.


Ed d W S hEdmund W. SchusterField Intelligence LabMassachusetts Institute of Technology77 Massachusetts Avenue 35 13577 Massachusetts Avenue, 35-135Cambridge, MA [email protected] ed-w infowww.ed w.info(c) 603-759-5786

Stuart J. AllenMarysville, [email protected]


11/6/1007 MIT Field Intelligence Lab 1 · L 0.35 1.5729 1.5842 1.6001 1.6249 1.6533 0.40 1.7094...

Documents

Transcript of 11/6/1007 MIT Field Intelligence Lab 1 · L 0.35 1.5729 1.5842 1.6001 1.6249 1.6533 0.40 1.7094...