Fishing Fleet Operations Model: Monthly Planning for Maximizing Profit

1. Sjávarútvegur og reiknilíkön Páll Jensson Háskóli Íslands

2. Heimildir Sigvaldason, H. et al. 1969: "A Simulation Model of a Trawler as a Raw Material Supplier for Freezing Plants in Iceland", Techn. Report, Univ. of Iceland (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 Vessel Design and Operation", Dr. Ing. Thesis, NTH Trondheim, Norway (in Norwegian). 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.

3. Heimildir Jensson, 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 Product Mix 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.

4. Nokkur reiknilíkön í sjávarútvegi • Hermilíkan af loðnuveiðum • Útgerðaráætlun • Samhæfing veiða og vinnslu • Bestun veiða og vinnslu frystitogara • Bestun flokkunar og ráðstöfunar hráefnis

5. 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

6. 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

7. 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.

8. 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.

9. 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)

10. 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

11. Model: • Max tfr Sfrt Yfrt - tvg Cvgt Xvgt + f Hf (Z-f - Z+f ) + tf 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

12. Model: • TotalQuotaf : tvg 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

13. Co-ordination of Fishingand 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.

14. Data coefficients: • Cf,v,t = expected catch of fish species f brought on land by vessel v if it lands it’s catch on day t. • Pv,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). • Rf,t = net revenue per kg raw material processed of fish species f on day t.

15. Data coefficients: • XMINf,t and XMAXf,t = bounds on production rates for • fish species f on day t. • IMAXf,t = upper bounds on inventories of raw material, mainly due to freshness requirements.

16. 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). • If,t = inventory of fish species f at the end of day t.

17. The model:  1 all t = 1 all v

18. 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

19. 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

20. 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).

21. Decision variables: • X(j) : Quantity produced of final product j (tons of product) • T : Time allocated for processing (hours)

22. 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

23. Bestun flokkunar og ráðstöfunar hráefnis • Vísar: • v : Vinnsluleið • i : Númer stærðarflokks hráefnis. i = 1…20 • n : Númer afurðar innan vinnsluleiðar. n = 1…6

24. 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).

25. 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

26. 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.

27. Breytur: • Xvi : Magn flaka í stærðarflokki i sem ráðstafa skal í vinnsluleið v

28. Model: vXvi/NvPi*R Xvi0