Stochastic Farm Work Scheduling Algorithm Based on Short ... - J-Stage

Research

Journal

Paper

Stochastic

of JSAM

157∼164,

61(2):

Farm Work Scheduling Algorithm Based Short Range Weather Variation (Part 1)* Development

of the Scheduling

1999

on

Algorithm

I WAYAN ASTIKA* 1, Akira SASAO* 1, Kenshi SAKAI* 1, Sakae SHIBUSAWA*

1

Abstract An algorithm for farm work scheduling named SFSW (Stochastic Farm Work Scheduling Algorithm Based on Short weather

Range Weather

Variation)

was developed

based on managing

the risk of daily

variation. The risk was evaluated by costs which were then minimized in the optimization.

Genetic algorithms

were utilized for optimization

The optimization

was established

time to do jobs by minimizing second

through

the expected

step was to decide the allocation

machinery

and incomplete

jobs. The

in order to attain flexibility.

two steps; the first step was to decide the proper costs due to the effect of daily weather,

of machinery

schedule

by minimizing

must be updated

and the

the costs of idle time of

daily in order

to extend

the

period covered by the schedule and adjust the schedule to the most recent conditions. [Keywords]farm work scheduling,genetic algorithms,optimummachineryallocation,short range weather forecast workability

of machinery

become

low2).

to other

components

ⅠIntroduction

Indirect Rain also

directly

affects

quantity

directly tion

of operations

affects

other

systems

done

mainly

occur

in farm

such

as grain

grain

may

in the

rain

because

tent.

On the

postponed may fields.

affect

in the

works

that

loss

harvested

will

harvestingg arise'.

operations

a condition,

conis

Rain

improperly.

harvesting

is done

days,

due

mills

not

will

Partly

presented

University), (Yamagata

*1東

at

April

56th

University},

Workshop

an

(Makuhari},

April

JSAM

1997,57th April

Artificial

Annual JSAM

Daily

1998,

and

If the

〓442-367-5741)JSAM Tokyo

Fuchu-shi,

3rd in

rainy

of storage

will

losses3'.

On

in the the

demand,

the

field

supply which

is to

may

costs. is a factor

long-term the

more

to avoid

days,

the

when

field

effect

scheduling of daily then

account.

Several

neglected

farm

works

or in systems

is not

dominant1'4~7).

is to optimize

the

in

of rain

operations,

to rain,

often

weather

the

arrange-

which

are sensitive

should

be taken

into

Meeting IFAC/CIGR Agriculture

factor

have

methods for handling

been

developed,

but

the weather

they

are usu-

1998

京 農 工 大 学 農 学 部(〒183-8509東

ture,

and

Intelligence

to rainy

weather

planning

greater harvesting

meet

lead to penalty

where

Meeting(Mie Annual

to

if the

postponed

in the

For example,

and duration

leading

hand,

as the jobs

early in order

the volume

increase,

ment *

happen

systems

are done

in wet

trafficability

effects

of production

other

quality

moisture

if the

machinery

In such

are sensitive

by being

hand,

are

effects

The

of its high

or in-

fields

Direct

harvesting.

decrease

other

field

but

of produc-

improperly.

a timeliness

also

in the

as operations

to be

of the

quality

components

forced

to rain,

not only the

University Saiwai-cho

Member, of Agriculture 3-5-8, Tokyo

京 都 府 中 市 幸 町3-5-8 Faculty and 183-8509

of

Agricul-

ally designed 10)12)13)

for a specific

farm work

problem

for scheduling

activities

Technology, Japan

Conventional

methods

158

adopt

Journal either

an

of the Japanese

society of agricultural

optimization1)4)5)7)or

approach6)12)13)。

machinery

Vol.61, No. 2 (1999)

heuristic

Optimization,

such

as

mathe一

matical programming, produces an optimal schedule but suffers

from rigidity

when

applied to

complex systems1°. On the other hand, heuristic approaches

are practical

but do not guarantee

optimality. The new emerging genetic algorithms (GA) are usually classified as heuristic methods, but they also perform searching processes to seek the optimum

value. With this merit, GAs

have been intensively applied to complex

studied, developed,

optimizations

and

and schedul-

Fig. 1 Formulation

of the effect of rain in SFSW

other

early

or late.

Both

choices

effects,

both

on the

quality

ing purposesls~23}. This research for general

aims to develop an algorithm

farm

work

duced risk to short The algorithm

scheduling

range

employs

low modifications

weather

with

re-

variations.

a GA in order to al-

to be made when

it is ap-

may

tioned

above,

grain

on Short Range Weather Ⅱ

Based

Variation)

Scheduling

of the jobs or on other

system.

tic Farm

Algorithm

adverse

of the

ture

Scheduling

have

days,

and quantity

plied in a specific scheduling problem. The algorithm is hereafter named SFSW (StochasWork

bright

the

other

hand,

rain

in SFSW.

There

are a number

of field

should

induces

cane

On

is done

late,

ed based on the season,

can not be fullfiled.

on the crop

growth

demands

of other

management

system,

demand

stage of the

as the peak of maturity,

of processing

or based

components such

unit

as the

of a

the

should

In

signed

risk

grain harvesting, the appropriate harvesting time is mainly determined by the peak of ma-

the

turity

verse

because

harvesting

the crop has a short optimum

period. In sugarcane

harvesting,

in

of job

costs

T,

that is, the daily demand of cane to be milled. If rain is likely to fall on T, the jobs will be performed

in the rain or will be shifted to

having both

of the

tem become

algorithm,

jobs

and

unit

T1 involves

timing

of jobs is defrom

schedule

consists

smallest

risk

on the the

system.

adverse are

harvesting

job timings

the

effects

of the all

which

rearrange

if

har-

scheduling

proper

if

arise

milling

on

the

The

The

timings

components

in deciding

T.

effects:

quantity

if the

of the

effects,

to optimally

original

hand,

also

of earlier

to do the jobs

of adverse

dry-

contrary,

losses

demand

be rearranged.

which the crops have longer harvesting periods, the demands of other components of the systhe main factors

other

the

If a planning

daily

or customers.

the

In ad-

loss arises.

as a result

vesting.

On the

before

On the

harvesting,

is stored

jobs i with their own respective appropriate timings T. Appropriate timings may be decidcrop such

enough.

late, a timeliness

In sugarcane the

mois-

rain.

earlier,

be stored

a loss.

men-

a high

in the

not mature

grain

ing, which

of the effect of

will have

as

if it is harvested

will probably the

components

harvesting,

if it is harvested

it is harvested

Fig. 1 shows the formulation

grain

the grain

content

dition,

Algorithm

In

quality

effects In the

effects

minimized

on other scheduling

are in

adand

the

treated

as

optimiza-

tion. Fig. SFSW.

2 shows In

order

the to

scheduling reduce

algorithm complexity,

of the

ASTIKA, SASAO , SAKAI, SHIBUSAWA. Stochastic FarmWorkScheduling Algorithm Basedon ShortRangeWeatherVariation (Partl( is applied

to

problem, jobs

the

are done

done,

with

on the

Rain-sensitive

while

other

implications

and quantity

of the

day depends

of the jobs. not

scheduling

implementation

on a rainy

kind

Ⅲ

a specific

159

of the

Optimization

jobs

jobs

that

are

quality

jobs decrease. and

Genetic

Algorithms

1. Deciding job timings Consider Fig.

2

Scheduling

algorithm

which

of SFSW

available scheduling

algorithm

timization;

the

timings,

and

allocation areas

the

obtained

from

tions

coverage

then

with The

expected

until

the

expected

cost

is found.

chinery

allocation,

from

as the

Even sidered

expected

In decid-

future

of the

algorithm

with

the

the

The result due

are

information,

variations

as rain.

of rainfall, it is available

amount

When

taken of the such

can not be only

Therefore,

are considered;

small

of

to idle

Detailed

a very

(1)

The performance of a schedule depends on the accuracy in allocating xij under the coming weather conditions. As shown in Fig. 2a, with the daily weather condition of either rain or bright, and the length of N days for scheduling, there are 2Npossible combinations of coming weather occurrences k. Accordingly, there are 2N possible values of cost Ck. With all 2N Ck and their respective probability of occurrence p(O)k, an expected cost E(C) is determined representing the performance of the schedule.

jobs.

of rain.

of time.

ma-

of all machines

consisting

period

is

smallest

deciding

forecasts

because

evalu-

The

variations

amount

solu-

possible

cost

for a

only two

rain or bright.

of rainfall

the scheduling

is ex-

bewhile

is generated

evaluated.

schedule

is a con-

weather

incorporated

weather

In

weather

expected

very short

all

the period. The

working

optimization

and incomplete

range

probability

daily

the allocation

is the

local

pressed with xij representing the area of the field belonging to job i to be done on day j.

result

schedule

and then

time of machinery Short

the

evaluated.

cost.

repeated

evaluation

is to decide

schedule

evaluated

is generated

done within

optimization,

and then

occurrences. is the

op-

of machinery

the

are

job

use a GA, in which

timings,

weather

first

forecasts

and a set of M jobs to be

of

optimization.

are generated

ing jobs

steps

local weather

of N days for

the

The

the

optimizations

ation

step

second

for the first

Both

two

is to decide

second

for the

the maximum

and

step

of machinery.

come inputs

straint

uses

first

a period

The occurrence k is derived probabilities

(2) of combination

multiplying

all individual

of weather

occurrences

wkj. The

probability of Wkj having value "rain" is equal to the probability of rain on that day p(R)j and the probability

of having value "bright" is

l-p(R)j.

is conalgorithm

by

probability

(3) where,

160

Journal

of the Japanese

society

of agricultural

(4) The cost Ck is the sum of the costs of each individual

job i which

depends

on job timing

j , weather occurrence on that day Wkj, job area Xij, and the sensitivity of job i to rain. The sensitivity with

of jobs to rain is represented

cilo standing

for a unit

cost for doing

job i on l days relative to Ti under weather condition o. In grain harvesting, cilo expresses the cost of the loss of quantity grain as it is harvested early harvested on rainy days.

and quality of or late and/or (5)

where,

(6)

(7) In some tion

scheduling

of cost

with

Ck may

variable

stants.

length

grain,

this

calculation,

the

process

Apart

of cost

period

unit the

For

ing unit

and

formed

cients. ous.

caused

by the

for other

loops.

the

which

can

of these

procedure. need IF-THEN This

can not

optimization

pre-defined merit

unit dry-

calculation

in conventional

of

the

be idle,

or iterative

kinds

drying

of grain,

The

a special

decrease

other

will

need

stor-

components

if the

amount

may

Here,

simulating in the

or products,

procedures

usually

grain

as costs.

need

if the

To perform

workers

be considered

paths

harvesting,

procedure the

example,

insufficient

Such

in grain

con-

is required.

arise

receives

costs also

than

is known.

cost

of the jobs

probably

system.

calcula-

procedure

rather

a special

from

of quality

a special

again

of handling

age and drying

the

cito can be determined

of storage

that

need

ci l o values

For example,

for stored

the

problems,

of using

constant

logical

machinery

Vol.61, No. 2 (1999)

The genetic algorithms may be a standard GAIS)24)or other suitable GA such as messy GA22)25). The schedule is expressed with a chromosome consisting of M x N genes in which the value of xij is expressed by the (i-1) N+ jth gene. Every time a new chromosome is generated or an old chromosome is modified with genetic operators, such as mutation or crossover, the constraints and heuristics are checked to confirm that the chromosome is valid. If the chromosome is invalid, the process is repeated until a valid chromosome is obtained. The calculation of E(C) becomes the fitness function of GA. As minimizing E(C) is the objective of the optimization, the chromosome with lowest E(C) over elapsed generations is saved as temporary solution. Every time the following generations find a better chromosome, temporary solution is replaced with this chromosome. Temporary solution is considered as optimum solution when there is no more better chromosome found. 2. Constraints and heuristics for deciding job timings The factors relating to farm works vary widely over agricultural production systems. The farm work scheduling problem in a certain production system has its own constraints characterized by specific local practices or specific personal decisions of a manager. Such constraints and heuristics play an important role in arranging the schedule. Typical constraints in farm work scheduling problems are as follows. (1) All jobs i should be completed during the working period. The sum of daily jobs xij during the working period should meet the total area Xi. (8)

be permethods coeffi-

a GA is obvi-

(2) The capacity of machinery should be enough to cover all scheduled jobs every day. Let qrij

be the working

a day, of machine

time, in fractions

of

r for doing job i on day j

ASTIKA, SASAO, SAKAI,SHIBUSAWA; Stochastic FarmWorkScheduling Algorithm BasedonShortRangeWeatherVariation (Part 1) 161

demand of other components of the system, for example, failing to provide enough cane for milling. The machinery allocation is decided for each day independently referring to the area of jobs scheduled on the corresponding day xij. Machinery allocation is expressed using fri for machine r in job i. Index day j does not exist in the expression because the allocation is done for each day independently. A machine is assumed to visit only one field in a day with the working time being either a whole day of work or no work at all,

and E(sr i) be the expected field capacity. The areas covered by all machines should be more than the scheduled areas. (9) The expected field capacity E(sri) comes from the field capacity when a machine is used on a rainy day sr i a a-rain and the field capacity machine

when the

is used on a bright day sria o=bright. (10)

The

value

machine used

of qr ij becomes

is not

on

model,

two

used

on

or more

a machine

less

a whole

jobs

two

values:

work

or no work

tively

for qrij.

1 if a

day

in a day.

is assumed

for one job in a day and the be only

than

or is In this

to be used working

whether

time

to

day

of

a whole

at all, scoring

only a

scoring respectively

1 or 0 for fri.

1 or 0 respec-

(12)

(11) The

capacity

of machinery

cover all scheduled

is enough

jobs in day j if there is at

least one set of grij allocations

that satisfies

Eqs. (8), (9), (10), and (11). This check done the

by solving simplex

to

the

method,

system

equations

multiple

choice

can be

The

expected

ered

u(υ)i

is

individual

of

E

job

estimated

expected

machines

i that

from daily

can

the

field

be

sum

covof

capacity

(13) (14) The

Chapter

idle

have to be done in a cer-

all

sri.

with

111.3.

the

of

integer

program20?, or genetic algorithms as was done for optimizing the allocation of machinery in (3) Job order The jobs usually

area

machines time

allocated

u(e)r

area

xij.

tions

of

to

job

if E(υ)i is more

Here,

the

unit

of

i have than

the

idle

time

expected scheduled is

frac-

a day.

tain order that can not be changed. For exam(15)

ple, plowing must be done before harrowing, manual sugarcane planting must be done on the same day just after furrowing

in order to

preserve soil moisture, etc. This order must be maintained in arranging the job timings. 3. Allocation The

allocation

of machinery

cost

is performed

of minimizing

idle time of machinery operators

is less than the scheduled area xij. (16)

of machinery

with the objective The

Expected incomplete area E(u)z existsif E(v)i

the costs of

and incomplete

of idle time includes and the machinery

payment

during

jobs. to

the idle

time, and the costs of incomplete

jobs include

the penalty

to fulfill the

cost for being unable

Let E(MC) be the expected total cost for idle time of machinery and incomplete jobs. Minimizing E(MC) is thus the function used to evaluate the optimization. (17) The through

machinery an

allocation

optimization

with

is

also

a GA.

decided The

chro-

162

Journal

mosome

consists

gene

of

expresses

machine yth

gene

gene

is

2

has

other

a

machine

the

value

From on

machine

will

not

The

fitness

rnin-ed

The

certain

not

set

i is

not

to

with

value

most

likely

machine

y

constraint can

do

The

schedule

not

aday

for

forecast may

the

for

Weather one

or

two

part remaining

changed

and

a

forecasts days

is

on

such

as

troubles.

tend

ahead,

the

works

machine

to but

be not

to be developed.

based

on the

also need to be

characteristics

of the

system. The most feasible parts to be changed

i or

conditions

variations

job timings or de-

Other parts of the algorithm

job

because and

by trans-

weather

problem, the procedure for determining these costs should be formulated. This is the most

check-

beginning

daily

new jobs

the

period

changes

of

particular,

at

range

model is applied to a scheduling

are the constraints

and heuristics.

More com-

plicated program coding will be required the complexity of the system increases. In deciding

entire

produce

remainder

curate

the

short

the proposed

any

schedule optimized

suitable

weather

In

the

the

creasing job quality and quantity by rain. When

whether

certain

Improvements

into costs due to changing

done

be

and Further

do

not. 4.Updating

Discussion

important

is

a

N

O.

is deter-

must

in

to

and(17)。

heuristics

daily as illustrated

to

i.

a chromosome

is updated

The core of SFSW was configured

be

there

Eqs.(13),(14),(15),(16), and

is

forming

allocate

chromosome,

the schedule

information,

ma-

not

is

and more accurate

Fig. 3.

day;f2i

allocated

job

est conditions

2

it can

gene

need

the

of

5,

a week. In order to adjust the plan to the lat-

2nd

If

sarne

yth

no

gene

constraints

ed.

job the

is

the

In

value

from

The

i.

any

to on

is

jab

be

f25=1.

xij=0,or

there

to

machine

case

Vol.61, No. 2 (1999)

r. If of

the

machinery

rth

value

that

r

if

day,

i, the

means

j obs

of

machine

example,

this

of agricultural

the

In

5.

Eq.(12),

that

which

job

i. For

5

society

of

do

allocated

to

2≠0=0.If job,

to

job

been

allocated

any

to

set

do

in

allocation

value to

chine

genes

allocated

having

allocated

Q

the

yis

the

of the Japanese

the jobs timings,

as

the chromo-

some has M x N genes. These

genes will be

full if all M jobs are done every day for N days or all xij>0. rather

This may be a very rare

than

having

the allocation

many

xij=0.

of machinery,

case

In deciding

probably

need to be used;

not all

ac-

of the machinery

for

machine may be sufficient for all jobs. A messy

only one

GA, that has variable chromosome length in which only 'potential'

genes

be appropriate

for this optimization.

smaller number

of genes, the search space can

be reduced, memory

and so the

necessary

seems

to

With

a

computer

and search time can also be reduced.

Also, weather either

are included,

rain

operations,

condition

or bright. a more

is considered

For some

specific

to be

farm

work

consideration

is

probably required, such as the amount of daily rainfall. This algorithm could be improved by considering

more specific

weather

condi-

tions. One method that could be tried is to genFig.

3 Updating

the

schedule

erate the amount of rainfall with a random number as was done by Dumont8). If the unit

ASTIKA, SASAO, SAKAI, SHIBUSAWA: Stochastic FarmWorkScheduling Algorithm Basedon ShortRangeWeatherVariation (Part 1) 163 costs

cido for a specific

available,

the

cost

amount

of rainfall

can be determined

more

are ac-

curately. VConclusion The developed er variable

SFSW

er variations

into

are then

minimized

genetic

algorithms.

was

divided

timings

incorporates

by transforming

and

into

expected

costs.

in the optimization The two

deciding

the weath-

the effects of weath-

scheduling

steps: the

deciding allocation

The

costs

by using process the

job

of ma-

chinery. References 1) Siemes, J.C.: Field machinery selection using simulation and optimization, Agricultural System Modeling and Simulation (R. M. Peart and R. B. Curry), Marcel Dekker Inc., New York, 543-566,1998 2) Audsley, E.: Use of weather uncertainty, compaction and timeliness in the selection of optimum machinery for autumn field work - a dynamic programme, J. Agric. Engng. Res., 29(2),141-149,1984 3) Ueno, M. and H. Izumi: Sugar loss due to mechanical harvesting, Int. Sugar JnL, 95, 352-355,1993 4) Astika, I. W., A. Sasao, M. Djojomartono, S. Pertiwi, H. Wiryokusumo: Optimization of Sugarcane Planting- harvesting Schedule for Dry Land Sugarcane Plantations. Journal of Japanese Society of Agricultural Machinery, 59(5),73-81, 1997 5) Ishizuka, N.: Computer aided scheduling system for farm work operation, Japanese Journal of Farm work Research, 25, 242-251,1990 6) Semenzato, R. A: Simulation study of sugarcane harvesting, Agricultural Systems, 47, 427-437, 1995 7) Corrie, W. J., D. S. Boyce: A dynamic programming method to optimize policies for the multistage harvest of crop with an extended maturity period, J. Agric. Engng. Res., 17(4),348-354, 1972 8) Dumont, A.G., D.S. Boyce: The probabilistic simulation of weather vani abler, J. Agric. Engng. Res., 19(2),131145, 1974 9) Sanders, D. W., W. F. Lalor: A method for optimizing the machine size - crop - area relationship, J. Agric. Engng. Res., 17(1),122-127,1972 10) Morey, R. V., R. M. Reart, G. L. Zachariah: Optimal harvest policies for corn and soybeans, J. Agric. Engng. Res., 17(2),139-148,1972 11) Chen, C. S.: Scheduling of planting and harvesting programmes for processing vegetables, J. Agric. Engng. Res., 19(4),415-433, 1974 12) Mc.Clendon, R. W., G. L. Barker, J. W. Jones, R. F. Colwick: Simulation of cotton harvesting to maximize return, Transaction of the ASAE, 24, 1436-1440,1981

13) Pitt, R. E.: A probability model for forage harvesting systems, Transaction of the ASAE, 25, 549-555, 1982 14) Huges, H. A., J. B. Holtman, Machinery complement selection based on time constraints. Trans. of ASAE 19 (5), 812-814, 1976 15) Rotz, C.A., H.A. Muhtar, J.R. Black: A multiple crop machinery selection algorithms, Trans. ASAE 26(6), 1644-1649, 1983 16) Annevelink, E.: Operational planning in horticulture: optimal space allocation in pot plant nurseries using heuristic techniques, J. Agric. Engng. Res., 51(3), 167177, 1992 17) Mattfield, D.C.: Evoluntionary Search and the Job Shop: Investigation on Genetic Algorithms for Production Scheduling, Physica-Verlag, Heidelberg, 1996 18) Michalewicz, Z.: Genetic Algorithms+Data Structure= Evolution Program, Springer-Verlag, Berlin, 1996 19) Savic, D. A., G. A. Wallers: Genetic Algorithms for least-cost design of water distribution networks, Journal of Water Resources Planning and Management, 123 (2), 67-77, 1997 20) Hadj-alouane, A. B., J, C. Bean: A genetic algorithm for the multiple choice integer program, Operations Research, 45(1), 92-101, 1997 21) Noguchi, N., K. Ishii, H. Terao: Autonomous vehicle by neural networks and genetics algorithms, ASAE paper No. 943054, St. Joseph, Mi., 1994 22) Halhal, D., G. A. Watlers, D. Ouazar, D. A. Savic: Water network rehabilitation with structured messy genetic algorithms, Journal of Water Resources Planning and Management, 123(3), 137-146, 1997 23) Reis, L.F.R., R. M. Porto, F. H. Chaudhry : Optimal location of control valves in pipe networks by genetic algorithm, Journal of Water Resources Planning and Management, 123(6), 317-326, 1997 24) Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, Mass., 1989 25) Goldberg D. E., K. Deb, B. Korb: Messy genetic algorithms revisited: studies in mixed size and scale, Complex Systems, 4(4), 415-444, 1990 (Received:3.Sep,1998・Question 

time 

limit:31.May,1999)

Notation

Ai :for all i Ck o

: cost when combination : unit

cost when

days relative

k occurs

job i is Cil done

on l

to its appropriate

day

T under the weather

condition

o

E(C)

: expected cost

E(e)r

: expected

E(MC)

: expected accumulation of cost due to idle time of machinery and incom-

idle time of machine

r

plete jobs E(Sri)

: expected

field capacity

of machine

r

164

Journal

of the Japanese

todojob

society of agricultural

i

u(u)i:expected

Q

area of job i that can be cov-

fri:involvement

of machine

r

:number

is not allocated to do job i :number

of jobs to be done within

Ti

:most

ui

:unit

job

:number

p(O)k

of days within the schedul-

:occurrence Lion k

weather

of

wkj

machine

rto

do

job

machine

r to

condition

do

job

i un-

o

day

for

performing

i penalty

wkj:weather

cost

for incomplete

occurrence

i:total

of done

of

day

job j in

i

com-

k

area X of丘eld

xij:area

probability of combina-

of

appropriate

bination

ing period

dayj

j of

der

on

machinery

time day

Srio:capacity

the scheduling period N

of

qrij:working

r in doing

job i;fri=1 if machine r is allocated to do job i,and fri=0if machine r

rain

probability

ion

:unit cast far idle time of machine

NI

of

p(wkj):occurrence

erect er

Vol.61, No. 2 (1999)

p(R)j:probability

area of scheduled job 2 that

can not be completed E(v)i:expected

machinery

on

field day

belonging

beionging

to

to job

job

i

i to

be

j

「研 究 論 文 」 天候 の 短 期 予 測 に基 づ く農 作 業 ス ケ ジ ュ ー リン グ

er Variation)に

に 関 す る 研 究(第1報)*

は天 気 予 測 に よ る リス ク を コ ス トで 評 価 し,こ れ

ス ケ ジ-ュ ー リ ン グ ア ル ゴ リ ズ ム の 作 成イ.ワ ヤ ン.ア ス テ ィ カ*1,笹 尾 澁 澤

彰*1,酒 井 憲 司*1,

栄*1

つ い て 報 告 す る 。SFSWの

中で

を最 小 とす る最 適 化 問題 と した 。 この 最 適 化 に は 遺 伝 的 ア ル ゴ リズ ム を用 い た 。 最 適 化 は二 段 階 で 行 っ た 。 天候 予 測 に した が っ て,第 一 段 階 は コス トを最 小 に す る作 業 時 間 を 決

要

旨

本 研 究 は 短 期 間(1週

間)の

め る。 第 二 毅 階 で は雨 天 に よ り作 業 で き な い 時 間 天 候 予 測 に基 づ い

と完 了 で き な い作 業 に よ り予 測 され る コ ス トを最

て 農 作 業 の ス ケ ジ ュー ル を作 成 しよ うとす る もの

小 に し,ま た,作 業 す る機 械 の 最 適 配 置 を決 定 す

で,天

る。 最 新 の天 気 予 測 を含 む よ うに,ス ケ ジ ュー ル

気 予 測 の リス ク を コス トと して 評 価 した 。

本 報 で は 作 成 した ス ケ ジ ュー リ ン グ ア ル ゴ リズ ム,SFSW(Stochastic ing

Algorithm

Farm Based

on

Short

Work Range

Schedul Weath-

は 毎 日更 新 され る よ うに した 。 [キーワー ド]農作業スケジュー リング,遺伝的アルゴリズム, 最適機械配置,短 期天候予測