MULTI-CRITERIA ANALYSIS

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Bahan kajian MK Perencanaan Lingkungan,
soemarno desember 2011
MULTI-CRITERIA ANALYSIS PENGELOLAAN DAERAH
ALIRAN SUNGAI
MULTIPLE GOALS PROGRAMMING
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http//www.kswraps.org/planning
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Goal Programming Goal programming is a branch of
multiple objective programming, which in turn is
a branch of multi-criteria decision analysis
(MCDA), also known as multiple-criteria decision
making (MCDM). It can be thought of as an
extension or generalisation of linear programming
to handle multiple, normally conflicting
objective measures (ukuran/dimensi dari tujuan).
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http//www.fao.org/docrep/007/y5...0e0d.htm
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Beberapa macam tujuan yang tidak saling menenggang
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Each of these measures is given a goal or target
value to be achieved. Unwanted deviations from
this set of target values are then minimised in
an achievement function. This can be a vector or
a weighted sum dependent on the goal programming
variant used. As satisfaction of the target is
deemed to satisfy the decision maker(s), an
underlying satisficing philosophy is assumed.
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Variants The initial goal programming
formulations ordered the unwanted deviations into
a number of priority levels, with the
minimisation of a deviation in a higher priority
level being of infinitely more importance than
any deviations in lower priority levels.
(penetapan prioritas goals) This is known as
Lexicographic or pre-emptive Goal Programming.
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Lexicographic goal programming Ignizio gives an
algorithm showing how a lexicographic goal
programme can be solved as a series of linear
programmes. Lexicographic goal programming
should be used when there exists a clear priority
ordering amongst the goals to be achieved.
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If the decision maker is more interested in
direct comparisons of the objectives then
Weighted Goal Programming should be used.
(penetapan bobot untuk masing-masing goal) In
this case all the unwanted deviations are
multiplied by weights, reflecting their relative
importance, and added together as a single sum to
form the achievement function.
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It is important to recognise that deviations
measured in different units cannot be summed
directly due to the phenomenon of
incommensurability. Hence each unwanted
deviation is multiplied by a normalisation
constant to allow direct comparison.
(normalisasi dilakukan untuk dapat
membandingkan simpangan ketidak-tercapaian goals)
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Popular choices for normalisation constants are
the goal target value of the corresponding
objective (hence turning all deviations into
percentages) or the range of the
corresponding objective (between the best and the
worst possible values, hence mapping all
deviations onto a zero-one range) .
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For decision makers more interested in obtaining
a balance between the competing objectives,
Chebyshev Goal Programming should be used.
Introduced by Flavell in 1976 9, this variant
seeks to minimise the maximum unwanted deviation,
rather than the sum of deviations.
(MEMINIMUMKAN SIMPANGAN DARI KENDALA TUJUAN
TERTENTU YANG TIDAK DIINGINKAN) This utilises the
Chebyshev distance metric, which emphasizes
justice and balance rather than ruthless
optimisation.
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Kekuatan dan Kelemahan A major strength of
goal programming is its simplicity and ease of
use. This accounts for the large number of goal
programming applications in many and diverse
fields . As weighted and Chebyshev goal
programmes can be solved by widely available
linear programming computer packages, finding a
solution tool is not difficult in most cases.
Lexicographic goal programmes can be solved as a
series of linear programming models, as described
by Ignizio and Cavalier .
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Goal programming Goal programming can hence
handle relatively large numbers of variables,
constraints and objectives. A debated weakness
is the ability of goal programming to produce
solutions that are not Pareto efficient. This
violates a fundamental concept of decision
theory, that is no rational decision maker will
knowingly choose a solution that is not Pareto
efficient.
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Analytic Hierarchy Process However, techniques
are available to detect when this occurs and
project the solution onto the Pareto efficient
solution in an appropriate manner. The setting
of appropriate weights in the goal programming
model is another area that has caused debate,
with some authors suggesting the use of the
Analytic Hierarchy Process or interactive methods
for this purpose.
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Pengembangan wilayah aliran sungai
SISTEM PERTANIAN BERWAWASAN LINGKUNGAN Pembanguna
n pertanian, menimbulkan dampak lingkungan
(DAL) 1. Kebutuhan manusia atas barang dan
jasa Beragam sumberdaya input Gangguan
lingkungan 2. Pertumbuhan penduduk
Kegiatan ekonomi pd kondisi lingkungan rawan 3.
Pengembangan teknologi ---------------- DAL 4.
Mekanisme pasar ------------- Mengabaikan biaya
sosial 5. Peningkatan produksi --- LIMBAH ---
Kualitas Lingkn 6. DAS ------------- Ekosistem
Pertanian yang Tipikal
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http//www.sfei.org/wetlands/Rep...ject.pdf of
the Arkansas Watershed
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KONFIGURASI DAS Ecological yield Debit air,
sedimen Economic yield Bio-economic yield,
ton/ha Cash income, rp/ha Employment,
HOK/th/ha Sub DAS
I
III II
IV

V


VI
VII
X VIII


x6 X2 x4 X1
x5 IX
X3
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http//www.kars.ku.edu/research/...ability/ Waters
hed Classification System
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Pengembangan wilayah aliran sungai
MGP Multiple Goal Programming Teknik
pemrograman matematika untuk menyelesaikan
maslaah pengambilan keputusan yang mempunyai
beberapa tujuan yang tidak dapat dipenuhi secara
serempak Tahapan Problem identification Tahapan
Problem solving Identifikasi Masalah 1.
Diagram lingkar sebab-akibat (causal loop
diagram) 1.1. Semua peubah yang berperan 1.2.
Pengaruh peubah thd yang lain tanda
panah 1.3. Sifat pengaruh/ akibat . tanda
atau 2. Diagram Kotak Hitam Input
SISTEM Output
Proses-proses
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Pengembangan wilayah aliran sungai
DAS -------------------- Aktivitas manusia 1.
Konstruksi fisik (X1) 2. Pertambangan (X2) 3.
Pertanian (X3) 4. Perikanan (X4) 5. Peternakan
(X5) 6. Perkebunan (X6) 7. Kehutanan (X7) 8.
Lainnya (Xi) Dampak
Negatif Model Perencanaan 1. Model Optimasi
--------untuk mencapai tujuan yg ditetapkan 2.
Model Non-Optimasi 1. Tunggal (single) 2.
Ganda (Multiple)
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CAUSAL LOOP Model Perencanaan DAS
Evapo- Transpirasi
Intersepsi Transpirasi


Bahan Organik
Fisika Tanah
Biomasa Vegetasi
Dispersi agregat
Retensi Air
Infiltrasi
Penutupan Vegetasi
KAT

EROSI
Run-off
Perkolasi

Konservasi
Fluktuasi debit sungai
DEBIT
Lahan pertanian
Intensifikasi Usahatani
Produktivitas lahan
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Diagram Kotak Hitam Model DAS
Geomorfologi
Sistem DAS Hidrologi Erosi
Hidrologi Sedimentasi
Produksi Prod. Lahan
Input tak terkontrol Iklim
Output
Landuse optimum
Input terkontrol landuse
Parameter DAS
Pengelolaan Konservasi Intensifikasi
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Pengembangan wilayah aliran sungai

• Pemecahan masalah
• 1. Analisis Optimasi Landuse Model MGP
• Landuse optimal Kombinasi optimum dari
  berbagai jenis landuse
• Variabel Luasan sutu jenis landuse
• Ciri utama MGP
• Sasaran yg ingin dicapai diberi urutan prioritas,
  
• setidaknya dalam sekala ORDINAL
• 2. Pemenuhan sasaran dilakukan berdasarkan
  prioritas. Sasaran dengan prioritas lebih rendah
  baru diperhatikan bila sasaran dg prioritas lebih
  tinggi telah terpenuhi
• 3. Sasaran tidak perlu harus terpenuhi, tetapi
  diusahakan sedekat mungkin.

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Model Umum MGP a. Fungsi Tujuan Minimumkan
Fungsi Tujuan Z S Pk S ( w-ki.di-
wki .di ) b. Fungsi Kendala Kendala Riil
S S akj Xj atau Ck Kendala
Sasaran S S eij Xj di- - di bi Xj,
di-, di 0 Dimana i 1 ..m j 1
.. n k 1.. p
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Pengembangan wilayah aliran sungai
Keterangan Xj Peubah keputusan ke-j atau
kegiatan sub-tujuan eij Koefisien Xj pada
kendala sasaran ke-i akj Koefisien Xj pada
kendala sasaran ke-k Ck Nilai kendala riil
ke-k, Jumlah sumberdaya ke-k yang tersedia bi
Target sasaran ke-i (RHS) di- Kekurangan dari
sasaran ke i (simpangan negatif) Pk Faktor
prioritas ordinal ke k di Kelebihan dari
sasaran ke i Wki- bobot bagi di- pada prioritas
Pk Wki Bobot bagi di pada prioritas Pk
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Peubah dan Parameter Peubah (Xi) X1 Luas
hutan (ha) X2 Luas tanaman tahunan lahan
kering (ha) X3 Luas tanaman pangan lahan
kering (ha) X4 Luas padi sawah (ha) X5 Luas
alang-alang (ha) X6 Luas pemukiman
(ha). Parameter (Sasaran RHS) a1 s/d a10
Debit /limpasan permukaan bulanan sub DAS ke 1
s/d 10 (m3) a11 s/d a20 Kehilangan tanah
tolerable pd sub DAS ke 1 s/d 10 (mm/th) a21
s/d a30 Sediment Delivery Ratio (SDR) pada sub
DAS ke 1 s/d 10 a31 s/d a40 Trapping
efficiency (TE) pada sub DAS ke-1 s/d 10
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Pengembangan wilayah aliran sungai
Parameter a41 Produktivitas hutan a42
Produktivitas kebun tanaman tahunan , kw/ha a43
Produktivitas tegal tranaman pangan, kw/ha a44
Produktivitas padi sawah , kw/ha a45 a54
Pendapatan petani sub DAS ke 1 s/d ke 10,
rp/ha/th a55 Rasio min. luas hutan dg luas DAS
yg diinginkan a56 Rasio minimum luas kebun
dengan luas DAS a57 Rasio minimum luas tegalan
dengan luas DAS a58 Rasio minimum luas sawah
dengan luas DAS a59 Rasio minimum luas
alang-alang dngan luas DAS a60 Rasio minimum
luas pemukiman dngan luas DAS
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Pengembangan wilayah aliran sungai

• Fungsi Kendala Model Urutan Prioritas
• 1. Kendala luas landuse
• 2. p1 Kendala sasaran debit atau runoff
• 3. p2 Kendala sasaran toleransi erosi
• 4. p3 Kendala sasaran sedimentasi minimum
• p3 Kendala sasaran produksi usahatani
• p4 Kendala sasaran total income petani
• (p1 prioritas tinggi, p4 prioritas rendah)
• Fungsi Tujuan Model
• Z p1 S dk- p2 S dk p3 S dk p4 S
  dk-

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Fungsi Kendala Kendala riil luas lahan DAS
10 Sub DAS 1. Luas Hutan (X1) e1X1.1 e2
X1.2 .. e10X1.10 d1- X1 2. Luas
Kebun (X2) e1X2.1 e2 X2.2 .. e10X2.10
d2- X2 3. Luas Tegalan (X3) e1X3.1 e2 X3.2
.. e10X3.10 d3- X3 . Dst 6. Luas
Permukiman (X6) e1X6.1 e2 X6.2 .. e10
X6.10 d6- X6 7. Kendala sasaran Debit
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Kendala sasaran Debit atau run off 7. Sub DAS
1 e17 X17 e67 X67 d7- a1 8. Sub
DAS 2 e18 X18 e68 X68 d8-
a2 dst.. 16. Sub DAS 10 e1.16 X1.16
e6.16 X6.16 d16- a10 X1.7 luas
lahan pada sub DAS 1 X1.16 luas lahan pada sub
DAS 10 X6.7 luas permukiman pada sub DAS 1 Dst.
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Fungsi kendala riil / sasaran 1. X1.1 X2.1
X3.1 X4.1 X5.1 X6.1 Ck1
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ANALISIS HIDROLOGIS A. HIDROLOGI Model Q
a. Qmaks (1-ekt ) Peubah yg ditetapkan /
dipilih 1. Laju transpirasi Dimana 2.
Besaran intersepsi Q Peubah yang
ditetapkan (1-4) 3. Laju evaporasi dari
tanah Qmaks NIlai maksimum dari Q
4. Laju evaporasi permukaan air bebas a
Faktor koreksi bagi Q t Peubah bebas k
Konstante e Bilangan alam
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b. EROSI Model A R.K.L.S.C.P. A
Kehilangan tanah, ton/ha/th R Faktor erosivitas
hujan K Faktor reodibilitas tanah Dst Tolera
nsi erosi tanah Tolerable Soil Loss TSL
(SDE x SDF) / T SDE Kedalaman efektif tanah,
mm SDF Faktor kedalaman tanah.
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c. TINGKAT SEDIMENTASI Sedimen Potensial
(Erosi aktual) x SDR Sedimen Erosi Aktual yang
masuk ke sungai SDR ---------------------------
----------------------------- Volume sedimen di
lahan d. PRODUKTIVITAS LAHAN 1. Usahatani
Sawah 2. Usahatani Tegalan 3. Usahatani
Kebun 4. Produksi Hutan e. INCOME PETANI ?
TP - TC ? Income usahatani TP Total
produksi TC Total biaya produksi