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Sjávarútvegur og reiknilíkön
Páll JenssonHáskóli Íslands
HeimildirSigvaldason, H. et al. 1969: "A Simulation Model of a Trawler as a RawMaterial Supplier for Freezing Plants in Iceland", Techn. Report, Univ. ofIceland (in Icelandic). Jensson, P. 1981: "A Simulation Model of the Capelin Fishery in Iceland", in Applied Operations Research in Fishing, ed. K. B. Haley, Plenum Press. Digernes, T. 1982: "An Analytical Approach to Evaluating Fishing VesselDesign and Operation", Dr. Ing. Thesis, NTH Trondheim, Norway (inNorwegian). Jensson, P. 1988: "Daily Production Planning in Fish Processing Firms". European Journal of Operations Research, Vol. 36, No. 3. Jensson, P. 1991: “Co-ordinating Fishing and Fish Processing”. Working paper, Dept. of Agriculture and Resource Economics, Oregon State Univ.
HeimildirJensson, P. & Arnarson, I. 1991: “Simulation Model of Factory Trawler Operations”. Working paper, Dept. of Agriculture and Resource Economics, Oregon State Univ. Randhawa, S.U. & Bjarnason, E.Th. 1995: “A Decision Aid for Co-ordinating Fishing and Fish Processing”. European Journal of Operations Research, Vol. 81. Jensson, P. & Maack, P.K. 1996: “The Practical use of Duality in ProductMix Optimization”. Árbók VFÍ/TFÍ. Jensson, P. & Snæland, P. 1997: “Bestun við vinnslustjórnun í bitavinnslu”.Árbók VFÍ/TFÍ. Gunnarsson, H. 1998: “Hámörkun afurðaverðmætis í botnfiskvinnslu”. CSc-ritgerð Verkfræðideild HÍ.
Nokkur reiknilíkön í sjávarútvegi Hermilíkan af loðnuveiðum Útgerðaráætlun Samhæfing veiða og vinnslu Bestun veiða og vinnslu
frystitogara Bestun flokkunar og
ráðstöfunar hráefnis
Fishing Fleet Operations Model Purpose: To plan on monthly basis the operations of
a fishing fleet over a year, and the allocation of the catch to sales and processing, in order to maximize the net profit contribution of a fishing company
Indices: v = vessel t = time period (usually month) g = grounds, or type of fishing or
gear (including staying idle in harbour)
f = fish species r = raw material allocation, i.e.
landing the catch to own processing plant, or to be sold on a fish market
Data: Rfgt = ratio of species f on grounds g in t (%). Evg = catch rate (tons/day) for v on g. Qf = quota of fish species f, tons. HImax f = bounds on hired-in quota of species f,
tons. HOmax f = bounds on hired-out quota of species
f, tons. VQminvf , VQmaxvf = bounds on quotas, tons. RBmaxft = bounds on raw material bought of
species f in period t, tons.
Data: RSmaxft = bounds on raw material sold of
species f in period t, tons. Sfrt = value added to catch in processing
kr/ton, i.e. sales value – variable cost (except raw material cost) of fish species f in month t when allocated to r
Cvgt = cost of operating vessel v on grounds g (or using gear g) in period t, kr/day. This includes crew share, gear cost, fuel and maintenance. When a vessel stays in harbour it carries only the fixed part of the cost.
Data: Hf = price of hired quota, kr/ton Pft = expected price of raw material of
species f on fish market in period t, kr/ton Dvt = available operating days for vessel v in t DGmaxvg = bounds on gear use or ground
days for each vessel, days. RAminrt , RAmaxrt = bounds on raw material
allocation r in period t, including bounds on catch landed to own processing, or sold on a fish market (tons/period)
Variables: Xvgt = number of days for vessel v in
month t on grounds g Yfrt = quantity (tons/period) of fish
species f allocated to r in month t Z+
f , Z-f = quota of fish species f (tons)
hired in/out. T+
ft , T-ft = raw material (tons/period) of
species f traded in/out on fish market in period t
Model: Max tfr Sfrt Yfrt - tvg Cvgt Xvgt + f Hf
(Z-f - Z
+f ) + tf Pft (T
-ft - T
+ft)
FishingDaysvt :g Xvgt Dvt , vt
GearUsevg : t Xvgt DGmaxvg , vg
Catchft : r Yfrt = v g Rfgt Evg Xvgt + T+ft -
T-ft , ft
RawMatBoughtft : T+ft RBmaxft , ft
RawMat Soldft : T-ft RSmaxft , ft
Model: TotalQuotaf : tvg Rfgt Evg Xvgt Qf + Z+
f - Z-
f, f
QoutaHiredIn f :Z+
f HImax f , f
QoutaHiredOut f : Z-f HOmax f , f
VQvf : VQminvf t g Rfgt Evg Xvgt VQmaxvf , vf
Allocationrt : RAminrt f Yfrt RAmaxrt, rt
Yfrt , Xvgt , Z+
f , Z-f , T
+ft , T
-ft 0
Co-ordination of Fishing and Fish Processing The model proposed here is a
combination of a short term inventory/production model and an assignment model, assigning vessels to landing days and simultaneously taking care of the inventories of raw material at the plants.
Data coefficients: C f,v,t = expected catch of fish species f
brought on land by vessel v if it lands it’s catch on day t.
P v,t = a profit measure for vessel v landing on day t (shortening a trip by one day should be reflected in a lower profit measure one day earlier).
R f,t = net revenue per kg raw material processed of fish species f on day t.
Data coefficients: XMIN f,t and XMAX f,t = bounds
on production rates for fish species f on day t. IMAX f,t = upper bounds on
inventories of raw material, mainly due to freshness requirements.
Variables: Y v,t = 1 if vessel v lands it’s
catch on day t, 0 else. X f,t = quantity of fish species f
processed on day t (kg raw material).
I f,t = inventory of fish species f at the end of day t.
The model:
t v f
tfXtfRtvYtvPMax ),(),(),(),(
1 all t v
tvY ,
= 1 all v t
tvY ,
v
tftftvtvftf XIYCI ,,,,,,1
tftf IMAXI ,,0
tftftf XMAXXXMIN ,,,
Decision Support System for a Factory Trawler Product Mix Optimization Model: The model maximizes the sales
value of the products minus the opportunity cost of time, with respect to limited manpower, raw material, filleting and freezer capacity
Coefficients: P(j) : Sales Price for product j (IKR/ton) W(j) : Work Requirement for product j
(man hours/ton) R(j) : Raw Material Requirement for
product j, i.e. the reciprocal of the yield coverage (tons of fish/ton product)
F(j) : Filleting Machine Time Requirement for product j (machine hours/ton). This is zero for whole frozen fish
Coefficients: EVT : Expected “Value of Time” (IKR/hour) MEN : Crew size on shift working in
processing RAW : Raw Material, i.e. catch of last haul
(tons of fish) FIL : No of Filleting Machines FRC : Freezer Capacity (tons of
products/hour) ETT : Expected Trawl Time for next haul,
here simply equal to the trawl time of last haul (hours).
Decision variables: X(j) : Quantity produced of final
product j (tons of product) T : Time allocated for processing
(hours)
Product Mix Optimization Model: max z = SUM(j: P(j) * X(j) ) - EVT * T Manpower: SUM(j: W(j) * X(j) ) <= MEN*T Raw. Mat : SUM(j: R(j) * X(j) ) <= RAW Filleting: SUM(j: F(j) * X(j) ) <= FIL * T Freezing: SUM(j: X(j) ) <= FRC * T Time: T >= ETT X(j) >= 0
Bestun flokkunar og ráðstöfunar hráefnis Vísar: v : Vinnsluleið i : Númer stærðarflokks
hráefnis. i = 1…20 n : Númer afurðar innan
vinnsluleiðar. n = 1…6
Fastar: Pi : Hlutfall hráefnis sem fellur í
stærðarflokk i (%) Nv :Flakanýting hráefnis í vinnsluleið v (%). T :Hráefnisverð (Kr./kg) R :Hámarks hráefnismagn til umráða (Kg) R :Lágmarks hráefnismagn sem þarf að
vinna úr (Kg) Liv :Tákn um það hvort leyfilegt sé að
ráðstafa hráefni í stærðarflokki i til vinnsluleiðar v. ( 1 ef leyfilegt, 0 annars).
Fastar: Bv :Meðal breytilegur kostnaður við
framleiðslu afurða úr vinnsluleið v (Kr/kg afurða). Getur t.d. verið áætlaður umbúða- og birgðahaldskostnaður.
Av :Afköst mannafla í vinnsluleið v (Kg/klst hráefni)
Dv :Efri framleiðsluskorður í vinnsluleið v (Kg/afurða)
Dv :Neðri framleiðsluskorður í vinnsluleið v (Kg/afurða)
M :Manntímar til umráða
Fastar: Cnv: Verð afurða n innan
vinnsluleiðar v Unv: Umbúðakostnaður afurðar n
innan vinnsluleiðar v fnvi : Hlutfall hvers kg flaka
sem til fellur í afurð n í vinnsluleið v og þyngdarbili i.
Breytur: Xvi : Magn flaka í stærðarflokki
i sem ráðstafa skal í vinnsluleið v
Model:
v i n vvnvinvnvvi N
TBfUCXMax
i
vvi DX i
vvi DX
vivivi NRPLX v i v
vi RN
X
v i v
vi MANv
XvXvi/Nv Pi*R
Xvi 0
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