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