Linear Optimization Model for fish processing production ... · 265 million ISK Direct contribution to the GDP 12% Total TAC in thousand tons 1.047 1.0 Exports of fish products is

Linear Optimization Model for fish processing production planning

Elín Helga Jónsdóttir

Thesis of 30 ECTS credits

Master of Science (M.Sc.) in Engineering

Management

January 2017

ii


by


Thesis of 30 ECTS credits submitted to the School of Science and Engineering

at Reykjavík University in partial fulfillment of the requirements for the degree of

Master of Science (M.Sc.) in Engineering Management

January 2017

Research Thesis Committee:

Páll Jensson, Supervisor PhD, Professor, School of Science and Engineering at Reykjavík University, Iceland. Hlynur Stefánsson, Co-supervisor Associate Professor, School of Science and Engineering at Reykjavík University, Iceland. Sæmundur Elíasson, Examiner MSc in Mechanical Engineering and PhD candidate at University of Iceland.

iv

Copyright


January 2017

vi

Optimization Linear Model for fish processing

production planning


January 2017

Abstract

The fishing industry feature a fast paced and ever-changing environment wherein recent years major developments of high-tech equipment’s have occurred in the processing sector resulting in a wider range of product possibilities as well as increasing production capacity. This paper attempts to show that optimization model and sensitivity analysis can be beneficial as a decision making tool for production manager in this fast paced environment. The paper proposes a linear optimization model that can be used as a decision aid for one-day production planning. The Net Profit Contribution is maximized subject to raw material requirements, machine time requirements, orders, and contracts. The model was tested and validated using real data from a typical processing day at a vertically integrated fishery in Iceland.

Keywords: Linear programming, Product mix, Production planning, Fish processing

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Línulegt bestunarlíkan fyrir áætlanagerð í fiskvinnslu


Janúar 2017

Útdráttur Sjávarútvegur einkennist af hröðu og síbreytilegu umhverfi þar sem mikil þróun hátæknibúnaðs hefur átt sér stað undanfarin ár og áratugi í fiskvinnslunni, sem skilað hefur aukinni afkastagetu tækja og auknu vöruúrvali. Í þessari ritgerð er gerð tilraun til þess að sýna fram á notagildi bestunar og næmnigreiningar við ákvörðunartöku í framleiðslu fiskvinnslu. Línulegt bestunarlíkan fyrir daglega áætlanagerð í fiskvinnslu er sett fram og sýnt er fram á notkunarmöguleika líkansins til aðstoðar við ákvörðunartöku. Framlegð fiskvinnslunnar er hámörkuð með tilliti til hráefnis, véltíma, pantana og samninga. Líkanið var prófað í íslensku sjávarútvegsfyrirtæki og var byggt á raungögnum frá dæmigerðum vinnsludegi.

Lykilorð: Línuleg bestun, afurðarsamsetning, áætlanagerð, fiskvinnsla

x



Thesis of 30 ECTS credits submitted to the School of Science and Engineering at Reykjavík University in partial fulfillment of

the requirements for the degree of Master of Science (M.Sc.) in Engineering Management

January 2017

Student:


Supervisors:

Superior A. Páll Jensson

Superior B. Hlynur Stefánsson

Examiner:

Examiner. Sæmundur Elíasson

xii

The undersigned hereby grants permission to the Reykjavík University Library to reproduce single copies of this Thesis entitled Linear Optimization Model for fish processing production planning and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the Thesis, and except as herein before provided, neither the Thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author’s prior written permission.

date

Elín Helga Jónsdóttir Master of Science

xiv

I dedicate this thesis to my parents, Jón and Þóra.

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Acknowledgements

I would like to thank my supervisors, Dr. Páll Jensson and Dr. Hlynur Stefánsson, for their valuable insights and comments on the development of the model. Special thanks to Dr. Páll Jensson for coming along with me on repeated visits to Vísir hf. Also I would like to acknowledge their valuable comments and suggestions when reviewing the paper.

The author would like to express gratitude to Vísir hf. for being a part of this study. Special thanks to Jóhann Helgason, Ómar Enoksson and Sveinn Guðjónsson for their time and effort in assisting me, and for allowing me to visit and contact them as much as I needed during the study. Thanks to Finnbogi Alfreðsson for his support and for bringing me in contact with Vísir hf. I am incredibly thankful for my favorite study partner, Björg, and would like to thank her for her moral support and valuable collaboration throughout our engineering studies. Last but not least I would like to thank my friends and family for being always on my team and supporting me in everything do.

Inngangur

Í þessu MSc verkefni tóku leiðbeinendur í upphafi verkefnis þá ákvörðun að nemandinn

skyldi skila MSc ritgerð á formi tímaritsgreinar, sem líta mætti á sem drög að

birtingarhæfri grein. Stefnt verður á birtingu í tímaritum Elsevier; Fisheries Research eða

Food Engineering.

Markmið verkefnisins var að setja fram línulegt bestunarlíkan af daglegri

framleiðsluskipulagningu í fiskvinnslu. Líkanið er hugsað sem hjálpartæki fyrir

framleiðslustjóra til að ákvarða afurðasamsetningu dagsins eða með öðrum orðum val á

vinnsluleiðum. Einnig skyldi það geta svarað ýmsum spurningum m.a. með því að birta

skuggaverð og fórnarkostnað (reduced cost).

Haft var samband við sjávarútvegsfyrirtækið Vísir hf í Grindavík og sýndu þeir verkefninu

strax áhuga og veittu góðfúslega aðgang að gögnum. Einnig tóku þeir þátt í að sannreyna

bestunarlíkanið að líkanþróun lokinni.

Nemandi byggði sína vinnu á fyrri rannsóknum sem birtar hafa verið (sjá umfjöllun um

fræði (e. Literature review). Nemandinn vann sjálfur alla vinnuna við verkefnið en

meðhöfundar þjónuðu hlutverki leiðbeinanda.

* Corresponding author. Tel.: +354-698-7566.

E-mail address: [email protected] xxxx-xxxx/$ – see front matter © 2013 xxxxxxxx. Hosting by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.rgo.2013.10.012


Elín Helga Jónsdóttira, Páll Jenssonb, Hlynur Stefánssonb a,bDepartment of Engineering Management, Reykjavík University, Iceland

A R T I C L E I N F O

Article history: Received Received Accepted Keywords: Linear programming Product mix Fish processing Production planning

A B S T R A C T

The fishing industry feature a fast paced and ever-changing environment wherein recent years major developments of high-tech equipment’s have occurred in the processing sector resulting in a wider range of product possibilities as well as increasing production capacity. This study attempts to show that optimization model and sensitivity analysis can be beneficial as a decision making tool for production manager in this fast paced environment. The paper proposes a linear optimization model that can be used as a decision aid for one-day production planning. The Net Profit Contribution is maximized subject to raw material requirements, machine time requirements, orders, and contracts. The model was tested and validated using real data from a typical processing day at a vertically integrated fishery in Iceland.

1. Introduction

The total world catch from marine waters in 2014 was around 81.5 million tons wherein 82.1% of the total catch was divided between 25 countries. Iceland is one of the 25 major producers with a total catch around 1.3 million tons setting Iceland as the 19th largest fishing nation in the world (Food and Agriculture Organization of the United Nations, 2016). The Icelandic fishing industry has been of major importance to the Icelandic economy for many decades. Fig. 1 provides a summary of key figures in the Icelandic fishing industry in 2015. The world’s fish consumption has increased rapidly in the last two decades. The increase can be attributed to growth in aquaculture production, which has also boosted the world fish supply in 2014 to 20 kg per capita. However, the state of world’s marine fish stocks has not improved overall which is a big concern (FAO, 2016). It is necessary to promote a balanced approach when fishing so that fish stocks will not be diminished. In order to ensure responsible fisheries in Iceland, a fishery management system called Individual Transferable Quota system (ITQ) was introduced in 1984 (Samtök fyrirtækja í sjávarútvegi, n.d). This system indicates how much the fisheries industry can catch of each species over each fishing year set from Sept 1 to Aug 31 the following year (Skrifstofa Alþingis, n.d). Before a new fishing year, the Minister of

Fisheries and Agriculture decides, in consultation with the Icelandic Marine Research Institute, the total allowable catch (TAC). Each Icelandic fishery owns a proportion of the TAC for every fish species that is assigned to each of their vessels (Fiskistofa, n.d.) In recent years, the TAC has been around 1.1 to 1.4 million tons (Fiskistofa, n.d.). There exists an auction market in Iceland, since 1987, where the raw material is on auction to balance supply and demand. It is possible to buy and sell all species of fish on the market. Wherein cod is the most sold

Fig. 1. Overview of key figures in the Icelandic fishing industry in 2015 (Deloitte, 2016).

Total value of exported seafood

265 million ISK

Direct contribution to the GDP

12%

Total TAC in thousand tons

1.047

1.0 Exports of fish

products is 42 %

of the total export products

Number of Icelandic companies in

fisheries 1.739

Workforce in the fish industry is

5% of the total workforce

2

species on the market accounting for about 40% of the total fish sold on the market in the first nine months of 2016 (Reiknistofa fiskmarkaða, 2016). Advances in technology have affected many industries and the fishing industry is no exception. Significant changes have occurred in fish processing where advanced machines and software are now used to control everything from sorting raw material to packaging the final product. This has led to a faster pace when doing business. Today, customers of the fisheries can place an order for fresh fish and have it delivered to them at the end of the day. This fast pace requires fast decisions; therefore, it might be useful to have a decision tool to aid production managers in making these decisions. Furthermore the collection and availability of reliable data has greatly increased in recent years, which makes it feasible to develop decision tools based on advanced Operations Research methods. Up to this time, much research has been done regarding fisheries management where the research focus has been on fish biology and bio-economics. Planning and operational aspects of this industry have not been as widely researched (Gunn, Miller & Newbold, 1991). This study addresses planning challenges in the processing aspect of the fishing industry, in particular, aspects centered around production planning and its effect on the business. The objective of this study is to develop an optimization model that can be used as a decision tool to aid production managers in determining how to best allocate raw material for processing to fulfill demand and maximize profit. It is the aim that the model could enable managers to take more conscious decisions concerning their business in an environment characterized by a fast pace. A vertically integrated fishery in Iceland was analyzed in this study where the fish processing sector was studied and an LP model was developed with real data and tested it in real time. The fishery under study is one of the leading fisheries companies in Iceland, operating five vessels and two processing facilities. Processing takes place in two buildings where salted products are processed separately from fresh and frozen products. Their advanced processing plants and experience enables them to offer a variety of premium products to customers around the world. The company have worked in close co-operation with the Icelandic company Marel Ltd, a provider of advanced food processing systems worldwide. Marel has as of now provided almost all the processing equipment in the freezing plants operated by the company under study. In 2015, the company took in use a new machine, FleXicut invented by Marel, used in the freezing plants when processing cod and haddock, however it is also used when processing catfish, ling and redfish. According to the CEO of the fishery under study, is FleXicut the biggest step towards automation in fish processing that has been introduced in many years (Marel, 2015). FleXicut had a big impact on how the model, introduced in this study, was structured one reason being it offers many different cutting patterns, examples can be seen in Fig 2. With the emergence of FleXicut two steps in whitefish processing have been combined: namely to locate and remove pinbones and to further cut the fillets into portions. The machine locates pinbones by taking an X-ray of the fillets and removes pinbones with eater-jet cuts. FleXicut further divides the fillets with twin blades. Each fillet is assessed, by size and weight, seeking the highest value cuts after predefined specifications from customer and or production managers (Marel, n.d). The benefits of being

able to offer wide range of small proportion of the fillets is aligned with the development of customer requirements. Also, the cuts performed by FleXicut delivers more consistent and accurate products than products hand-cut by different employees. The remainder of the study is organized into several sections as follows: Section 2 outlines key results of several studies done in this field. Section 3 discusses key aspects of the fish value chain. Section 4 introduces the model and mathematical formulations are set up and explained. Section 5 shows the experimental results of the model. Finally, Section 6 concludes the study.

2. Literature review

This section presents an overview of operations research projects that have been conducted in the fishing industry in Iceland and internationally. Literature on the fishing industry can be divided into three sections (Randhawa & Bjarnason, 1995): Fish stocks and harvesting, fish processing, and fish marketing. In this section, the emphasis is on key results of studies involving the fish processing sector. Operations research studies in Iceland have mostly focused on the fishing industry, and according to Ólafsson (1995), the first research was conducted in 1966. The project introduced a computer simulation model of fishing and landing of herring.

Among the first researchers designing an LP model for production planning in fish processing were Mikalsen and Vassdal (1981). Their model covered a one-year period, subdivided into five periods. The intention was to attempt to improve profitability in the Norwegian fish processing industry. Jensson (1988) developed an LP model for fish processing that maximizes net profit contribution over a five days’ period. Focus was among other things on making the model user-friendly since it was to be used and tested by the production manager in real time in a freezing plant in Reykjavík. The model proved to aid production managers with their daily production planning as well as being sufficiently close to the real situation. In addition to Jensson’s study in 1988, developed Jensson and Maack (1997), a similar LP model where they introduce how duality theory can

Fig. 2. Examples of the many possible fillet cutting patterns that FleXicut offers (Marel, n.d).

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be used and set up graphically to help with daily decision-making in fish processing. In their study, the problem was characterized by two bottlenecks; manpower and raw material. They showed how to calculate the net profit contribution per unit of the bottleneck and how such information can aid production managers when deciding overwork or to sell or buy raw material. Gunn, Millar, & Newbolt (1991) analyzed how to coordinate fishing and fish processing in Canada. A major LP model was designed that demonstrated what should be caught and what products should be produced to satisfy market demand. Gunn et al, proposed that such an extensive LP model could be useful when dealing with tactical planning in large fishing enterprises. Another study on how to integrate fishing and fish processing is from Randhawa and Bjarnason (1995). Their approach was to develop a simulation model and LP optimization model that worked together to optimize net revenue and to be used as decision aid for production planning. The simulation model analyzed trawler operations that then generated information to the LP model, that is used to determine labor requirements, inventory levels and production levels. The results obtained from this research indicated that the system could be very useful for decision aid for production planning in fisheries. Most of the above studies were carried out some decades ago. Since then, technology in fish processing has developed rapidly. Automated machines have replaced labor in some work centers, which has led to significant changes in the production planning. This study takes into account these changes where machines are more automated than before and account for the machines as bottlenecks rather than the manpower. A great effort has been devoted to studies about decision making tools when catching and processing Icelandic cod. Several studies have been utilized the same data set, on fillet yield, gaping and parasites, collected from 2002 to 2006. Along with a collective data sets these studies share a common objective to increase the value of seafood along with optimizing productivity and profit in Icelandic fisheries. Based on this data set Margeirsson (2003) concluded that further analysis of the data would be valuable as well as to collect more data. Guðmundsson et al., 2006 developed a multicommodity flow network model and an LP model using the data set mentioned above and some estimated data when needed. His focus was to evaluate how seasons and catching areas in the Icelandic ocean affect the quality of the fish. This was carried out by dividing the ocean around Iceland into 13 areas as well as dividing the year into quarters. Quality features under investigation affecting the profitability of the fish were mainly fillet yield, gaping and nematodes. Other factors affecting profitability were examined, like buying leased quota, different product mix as well as product price. In addition, Guðmundsdóttir (2007) made a mixed integer linear programming model (MIP) for scheduling a seasonal divided aggregated plan. The results from Margeirsson (2008) indicates that catching cod in certain seasons and areas can increase profit. These results were obtained using statistical modeling and optimization model. Statistical analysis showed that quality factors affect the fish depending on catching condition, storage and different properties of the cod. This information was then used

as input to the optimization model. Margeirsson et al., (2010) utilized the same data set as well as collecting more data on new catching grounds. The findings obtained from this study showed a strong correlation between variables for profitability in the fish industry and catching ground, catch method and age of raw material when processed. Ólafsson et al., 2013 developed optimization models both for long- and short-term planning. For the long-term planning, a linear optimization model was developed that described a vertically integrated fisheries company. A mixed integer linear optimization model was developed for short-term vessel trip planning. The models were tested and validated at a fishery in Iceland with good results. Bakhrankova, Midthun, & Uggen (2014) made an integral stochastic model based on a case study in Northern Norway that combines fishing fleet operations with plant processing. The model addresses uncertainties in raw material and market prices with restrictions on fish quality and shelf-life. The main objective of this study was to explore how super chilled products would affect the efficiency of the planning process. Bakhrankova et al., 2014 came to the conclusion that in order to increase profit it is essential to take into consideration uncertainties in raw material quantities.

3. Fish processing value chain

This section discusses the value chain of fish, broken down into three parts: raw material, processing and market. Each step will be described briefly; the process can be shown in Fig. 3. This study focuses on optimization in the processing sector of the value chain, nonetheless it is important to grasp the overall process because comprehension of the value chain as a whole can enable opportunities for improvement in one part of the chain leading to changes in prior or following activities. An example of this could be if improvement in raw material handling is identified and fixed, it might result in improvement in processing and even lead to a positive effect in the market. Activities of the value chain can vary depending on fish species and whether the company is vertically or horizontally integrated. The difference between these strategies is that vertical integration is when a company runs all activities of the value chain, from acquiring raw material to providing finished goods to the consumer. While partnership relationship, horizontally integrated, adds value to the chain by being a part of one or more activities in the chain. The value chain discussed in this section is in correspondence with the company under study which is vertically integrated and acquires raw material by catching.

Processing Market

Material flow

Order flow

Pushing

Pulling

Raw material

Fig. 3. Value chain of fish (Margeirsson, 2008), (Jensen, Nielsen & Larsen, 2009).

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3.1 Raw material

The fishing industry operates in a challenging environment where there is much uncertainty even on a daily basis. One cause of uncertainty is that fishermen are essentially hunters who seek wild fish in the sea (Jensen et al., 2009) where there is uncertainty of how much they will catch. Some catching areas are known to be off-limits, because of parasites or other undesirable attributes or fish species (Margeirsson, 2008). In fact, the fishermen are never sure of the quality of the fish nor what fish species can be expected in each haul. After each haul, the mixed catch should be sorted on board into different species and sizes in order to accelerate processing. The importance of raw material handling throughout the process is worth mentioning. Unnecessary transportation and correct handling (gutting, bleeding, cooling etc.) of material should be minimized since it can lower the quality of the finished product.

3.2 Processing

It is important that the raw material is processed as soon as possible after the catch is landed where fresh fish is processed first as its quality decreases with time. Fish processing involves splitting raw material, the fish, into several products like fillets and further into loins and other various portions of the fish. This disassembly process differs from an assembly process, where traditional products are made from parts on stock and also from food production, where the raw material is produced, grown and manufactured (Jensen et al., 2009). Bill of materials (BOM) is often used in assembly processing, it provides a recipe of required components, on stock, for the final product. On the other hand, the structure of fish processing can be described with a reverse bill of material (Jensen et al., 2009), where each raw material is split into various products, as shown in Fig. 4. (Cardós & Miralles). Production plans are primarily determined based on the supply of fish, raw material properties, and the age of the fish when it arrives at the processing plants. Also, the capacity of the processing plants plays a big role when determine the product mix produced. Pressure on what will be processed each time usually comes from the market where contracts are made beforehand and orders are received with short notice particularly for fresh products.

3.3 Market

The traditional market involves distribution and sales where the final product is delivered to the customer. The market is constantly changing, depending on customer requirements and other market variables, making the value chain change alongside with it. The market may have a different impact on how raw material flows through the value chain, as shown in

Fig. 3, where orders flow is in the opposite direction of the material flow. This can be explained by pushing and pulling effects on and from the market. Wherein pushing means that products are pushed to the market, the product might not exactly be based on customer preferences (see Fig.3). In which case, the process/value chain begins in the first step of the chain, raw material, allowing flexibility in processing. On the other hand, pulling means that the customer requests a specific product. Resulting in the value chain beginning at the end of the chain, the market, is putting pressure on the first two steps in the chain. (Margeirsson, 2008). It has been shown that each activity in this simple fish processing value chain, described above, depends on the others (Margeirsson, 2008). This gives an insight into the importance of a good production plan when reacting in this rapidly changing environment.

4 Mathematical Model

The model presented here is a linear programming model where the decision variables determine how much raw material is allocated to each product combination that we call “processing allocation”, within the constraints of available machine time, raw material and other constraints including constraints concerning customer orders and sales contracts. Each processing allocation can contain many different combinations of products, especially in the fresh and frozen production. The model will be formulated here as a decision aid for one-day production planning, later an extension will be discussed. The development of a model like this is an iteration process that stops when the model is considered to be close enough to describe the processes observed, and yet practical and tractable. In the process of constructing this model repeated visits were made to the processing plants observing the “real life” situation and collecting data and information about the processing. The model is based on data provided from an Icelandic fishery, however, information about products has been modified because of confidentiality reasons. Below is a table listing the indices of the model, the decision variables, and the coefficients or data. In the tables, rkg refers to kg of raw material and pkg to kg of product.

Table 1. Indices used in the mathematical model

Indices Definition

f Raw material, species and size, here cod of size 2,5 rkg to 7,5 rkg.

(f=1)

p Processing allocation, each fish or fillet is produced to give a certain product combination, according to the reverse bill of material RBOM, see below.

(p=1,..30)

w Work center, machine bottlenecks in the processing line.

(w=1,..4)

k Products, division of the fish or fillets into products.

(k=1,..47)

Rawmaterial+

Product+ Product1 . . . . . . . .

Fig. 4. Reverse bill of material (Cardós & Miralles).

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Table 2. Decision variables used in the mathematical model.

Decision variable

Definition Unit

𝑥34 Raw material f allocated to processing allocation p.

[pkg]

Table 3. Coefficients or data used in the mathematical model.

Coefficients Definition Unit

𝐼𝑛𝑝𝑢𝑡3 The amount of available raw material of species and size f available for processing.

[rkg]

𝐶34 Net Profit Contribution of processing allocation p from raw material f.

[kr/pkg]

𝑀< Available machine time in work center w. [min/day]

𝑚3< Required machine minutes for raw material f in work center w.

[min/rkg]

𝐷𝑒𝑚𝑎𝑛𝑑B Demand (orders) for product k in the fresh and frozen production.

[pkg]

𝑆𝑐𝑜𝑛𝑡𝑟B Minimum production of product k according to sales contracts in the salted production.

[pkg]

𝑅𝐵𝑂𝑀34B The proportion of raw material f processed as processing allocation p that produces product k.

[%]

𝑌34 Yield (kg product/ kg raw material) of raw material f in processing allocation p.

pkg/rkg

RawS Raw material forced to be allocated to salted production.

rkg

RawF Raw material forced to be allocated to fresh and frozen production.

rkg

The calculation of the Net Profit Contribution for each processing allocation is based upon an idea presented by Jensson & Maack (1997). They argued that the Net Profit Contribution for each product in a daily production plan should be calculated as sales price minus only a few relevant variable costs, in this case packing cost and estimated inventory cost. Labor- and raw material cost does not fall under variable cost in daily production since the raw material has already been bought (sunk cost) and employees are on fixed salaries and will get paid regardless of the product mix produced. The objective is to maximize Net Profit Contribution, calculated as described above, by finding the optimal production plan for one day.

(1)

The capacity in the processing plants is limited by the available machine time and raw material. Constraint (2) is for the machine time, four machines are considered as bottlenecks, in salted production it is an Advant freezer and a feeding machine. In fresh and or frozen production is it the FleXicut machine described above and a Gyro freezer.

(2)

The required raw material constraint depends on the yield of each processing allocation and the available raw material each day.

(3)

Constraints (4) and (5) enables production mangers to decide the minimum production on products according to customer order or sales contracts.

(4)

(5)

Constraints (6) and (7) are used to allow the possibility to ensure some amount of raw material to be allocated for processing to either salted or fresh and frozen production.

(6)

(7)

4.1 Implementation

The model was implemented using the MPL modeling language (MPL Modeling System. (n.d.)) and solved with the CLPEX solver. Excel was used as a database with a connection to MPL and the solution output was displayed both in MPL and exported back to Excel. In the underlying database there is information regarding each processing allocation including the division into each product and corresponding sales price, raw material yield, packing cost and estimated inventory cost. The model consists of 30 variables and 54 constrains. The daily input data consists of the following:

• Daily input of available raw material, Inputf • Processing allocation of raw material to salted production or

fresh and frozen production, RawS and RawF. • Market restrictions for a certain product, Demandk and Scontrk. • Exchanges rate update.

To ensure that the model functioned properly, many different input condition were tested wherein the corresponding reactions were analyzed and the model adjusted when and if needed. Eventually, the model was tested and validated with production managers of the company under study; they decided the input conditions based on a typical processing day and concluded that the results of the model were as they expected.

Max C fpx fpf∑

mfwx fp ≤p∑

f∑ Mw

RBOMfpkx fpp=1

11

∑f∑ ≥Demandk

RBOMfpkx fpp=12

30

∑f∑ ≥ Scontrk

x fpYfp

≥p=1

11

∑ RawFf∑

x fpYfp

≥p=12

30

∑ RawSf∑

x fp ≥0

x fpYfp

≤ Input fp∑

6

5. Case study

The results of a case study will be analyzed in this section to illustrate the usability of optimization and sensitivity analysis in the production management of a fish processing facility. Among questions, that the model presented here can provide answers to and would be beneficial for the production manager to get quick estimate to, are: 1. Which processing allocation should the company produce today to

maximize Net Profit Contribution?

2. When is it desirable for the company to increase capacity and what should they be willing to pay for it?

3. Is it advisable to work overtime?

4. What is the desirable price for the company to buy additional raw material from the market?

5. How much higher price would the company have to require in order to produce a certain product or processing allocation?

Questions such as these are among the many questions production managers have to ask themselves every day. These questions will be answered with the following case study.

5.1 Analysis

As mentioned before, the company is vertically integrated producing variety of fish products; salted, fresh and frozen. The raw material in this case study is assumed to be one fish species, cod, in the same size category, f=1, allocated to few possible processing allocations during one-day planning period. The objective is to maximize the Net Profit Contribution for one-day planning period. In the case when the model is allowed to run unrestricted, with 90 tons of available raw material, then the model yields a Net Profit Contribution of around 39 million ISK (1 EURO=118,8 mbl.is 12 des 2016). Allocating, 55 tons to processing allocation 3 in the fresh and frozen production and 35 tons to processing allocation 1 in the salted production. Our case study is based on the input conditions tested with the production mangers of the company under study. They decided the input conditions based on a typical processing day. It was decided to force 22,2% of the available raw material, 90 tons, to be allocated to salted production. And the following market restrictions were present for this particular processing day; orders requesting products 1,3,5 and 17 in the fresh and frozen production and there were sales contracts that need to be fulfilled in the salted production, products 31,37 and 40. The Net Profit Contribution in this case resulted in a decrease, from the previous example, and returned approximately 37 million ISK. An examination of the results of the model using sensitivity report revealed that two of the machine constraints, the FleXicut and the Gyro freezer, were tight along with the raw material constraint. Table 4 provides answers to questions 2, 3 and 4, listed above, giving information on if it’s advisable to work overtime and how much the Net Profit Contribution would increase if one additional machine minute or raw material (rkg) is added to their capacity. In this particular example, the Net Profit Contribution would increase by 2.163 ISK or 2.867 ISK if one extra minute is added to either the FleXicut or Gyro freezer capacity.

Question 4 can be answered based on the capacity of the machine constraints since labor cost is not taken into account when calculating the Net Profit Contribution. Therefore, if the company decides to work overtime for one hour they need to be willing to pay labor cost that is less than 129.780 ISK for the hour. The shadow price for the raw material constraint, 421 ISK, in table 4 gives the desirable price for the company to buy one extra kilo of raw material and answers question 4. Table 4. Machine and raw material capacity constraints.

Constraint Slack Shadow Price

Raw Material 0 421

FleXicut 0 2.163

Feeding 121,7 0

Advant Freezer 360 0

Gyro Freezer 0 2.867

The effect orders and sales contracts have on the model is that it forces the model to allocate raw material to product combinations, i.e. processing allocations, that include those products. The allocation of raw material to processing allocation, for the case described above, can be seen in table 5 for fresh and frozen production and table 6 for salted production, the numbers that are bolded are the products that have been requested to be produced by order or sales contracts. Table 5 and 6 provides answers to question 1.

Table 5. Processing allocation within the fresh and frozen production, bolded products have been requested to be produced.

Processing allocation

Products

1 1,5,18,27

2 3,5,16,19,23

3 4,7,12,13,22

5 5,7,12,15,17,28

10 1,5,17,19,21

Table 6. Processing allocation within the salted production, bolded products have been requested to be produced.


Products

1 29

3 31

9 37 12 40

Processing allocations that are not in the optimal solution have a corresponding opportunity cost (reduced cost) giving information on how much the sales price needs to increase for the processing allocation to be produced in the optimal solution. Information required for question 5 are in tables 7 and 8 showing examples of how much the sales price of

7

processing allocations, 4 and 11 in the freezing plants and 2 and 13 in the salted plants need to increase in order for the company to produce them. Table 7. Example of opportunity cost for processing allocations in fresh and frozen production.


Opportunity cost

4 89,4

11 31,4

Table 8. Example of opportunity cost for processing allocations in salted production.


Opportunity cost

2 29,75

13 32,7

6. Conclusion

Production planning in the fisheries industry differs from the traditional production planning in the way that it is a case of a reverse BOM where the raw material is split into various products having many possible product structures. Automation that has been introduced in the last years and decades offers many different fillet cutting patterns and thus a wide range of products. Managers in fish processing operate in a fast pace environment where customer requirements and technical equipment’s change frequently. Customers are demanding products, a smaller proportion of the fish (ready to eat fish), that did not exist, as products, some years ago. Machines have more throughput than ever and are more automatic than before, this development will lead to further automation. In this fast pace and ever-changing environment where decisions need to be made quickly while being aware of increasing profitability, potential benefits of optimization solutions should not be overlooked. In this study, an LP model was developed and tested with different operating conditions to determine the effect it had on the Net Profit Contribution. The model presented here is an attempt to show the possibilities that this or similar model can provide to the production management in fisheries industry. The approach of using optimization and sensitivity analysis while deciding daily production planning can aid to make more conscious decisions and be more aware of the effects their decisions, regarding the product mix produced, have on the company’s profit. The model was tested and validated at a fisheries company in Iceland based on a typical production day giving realistic results. Possible future work would include extending the model to cover a period longer than one day by adding a inventory variables along with estimating the expected catch and state of the raw material before it is landed. That in addition to extending the product range along with possible processing allocations to the model would be realistic next steps. It is proposed here that optimization model similar to what is presented in this study could become a part of the developments and future updates of automative machines like the FleXicut.

Acknowledgements

Financial support from the Samtök fyrirtækja í Sjávarútvegi (SFS) is gratefully acknowledged.

REFERENCES

Bakhrankova, K., Midthun, K. T., & Uggen, K. T. (2014). Stochastic optimization of operational production planning for fisheries. Fisheries Research, 157, 147-153.

Cardós, M., & Miralles, C. Can heuristic planning algorithm for the discrete manufacturing industry with reverse BOM and alternative structures. 19th International Conference on Production Research. Retrieved November 10, 2016 from http://www.icpr19.cl/mswl/Papers/002.pdf

Deloitte. (2016). Sjávarútvegurinn: Gagnagrunnur og lykiltölur 2016. Retrieved November 12, 2016 from

https://www2.deloitte.com/content/dam/Deloitte/is/Documents/consumer-business/sjavarutvegsbaeklingur%202016.PDF

Fiskistofa. (2016, October 17). Aflahlutdeildir stærstu útgerðanna. Retrieved November 01, 2016, from http://www.fiskistofa.is/umfiskistofu/frettir/nr/1510

Fiskistofa. (n.d). Um fiskveiðistjórn. Retrieved November 29, 2016, from http://www.fiskistofa.is/fiskveidistjorn/stjornfiskveida/

Food and Agriculture Organization of the United Nations. (2016). The state of world fisheries and aquaculture. Retrieved 13 October, 2016 from http://www.fao.org/3/a-i5798e.pdf.

Guðmundsdóttir, GH (2007). Scheduling for maximum profit in the Icelandic cod industry. M.Sc. Thesis, Faculty of Engineering, University of Iceland.

Guðmundsson R., Jensson, P., Margeirsson S., Arason S. (2006b). Ákvarðanataka og bestun í sjávarútvegi. Rf skýrsla 27-06. http://www.matis.is/media/matis/utgafa/Skyrsla_27-06.pdf.

Gunn, EA,. Millar, HH, & Newbold, SM (1991). Planning harvesting and marketing activities for Integrated fishing firms under an enterprise allocation scheme. European Journal of Operational Research, 55 (2), 243-259.

Íslenski sjávarklasinn, Vigfússon, B,. Gestsson, HM,. Sigfússon, Þ. (2016). Efnahagsleg umsvif og afkoma 2015. Retrieved September 20, 2016 from http://www.sjavarklasinn.is/wp-content/uploads/2016/09/Sjavarklasinn-Efnahagsleg-umsvif-og-afkoma-20151.pdf.

Jensen, T. K., Nielsen, J., Larsen, E. P., & Clausen, J. (2009). The fishing industry-toward supply chain modelling. DTU Management.

Jensson, P. (1988). Daily production planning in fish processing firms. European Journal of Operational Research, 36 (3), 410-415.

Jensson, P., & Maack, PK. (1997). The Practical use of duality in product mix optimization. Yearbook VFÍ/TFÍ, 237-246.

Marel. (2015, April 17). Product Variety with FleXicut. Retrieved November 1, 2016, from http://marel.com/fish-processing/news/product-variety-with-flexicut/3306

Marel. (n.d.). FleXicut. Pinbone detection & removal with filet portioning. Retrieved November 1, 2016, from https://marel.com/files/pdf/flexicut-leaflet.pdf?ind=fish

Margeirsson, S. (2008). Processing forecast of cod. Decision making in the cod industry based on recording and analysis of value chain data. Ph. D. Thesis, faculty of Engineering, University of Iceland.

Margeirsson, S., Hrafnkelsson, B., Jónsson, G. R., Jensson, P., & Arason, S. (2010). Decision making in the cod industry based on recording and analysis of value chain data. Journal of food engineering, 99(2), 151-158.

Mikalsen, B., & Vassdal, T. (1981). A short term production planning model in fish processing. In Applied operations research in fishing (pp. 223-232). Springer US.

MPL Modeling System. (n.d.). Retrieved December 12, 2016, from http://www.maximalsoftware.com/mpl/

Olafsson, A., Jensson, P., Margeirsson, S., Asgeirsson, E.I., Stefansson, H., Gudmundsson, R. and Arason, S. (2013). Quantitative Methods for

8

Decision Support in the Icelandic Fishing Industry. Natural Resource Modeling, 26(3), 365-384.

Olafsson, S. (1995). A review of OR practice in Iceland. European Journal of Operational Research, 87 (3), 456-460.

Randhawa, S. U., & Bjarnason, E. T. (1995). A decision aid for coordinating fishing and fish processing. European Journal of Operational Research,81(1), 62-75.

Reiknistofa fiskmarkaða (RSF). (2016). Metsala í ágúst og september - Metár. Retrieved Oktober 29, 2016, from https://rsf.is/frettir/240-metsala-i-agust-og-september-metar.

Samtök fyrirtækja í sjávarútvegi. (n.d). The ITQ. Retrieved September 18, 2016 from http://www.sfs.is/english/more/the-itq

Skrifstofa Alþingis. (n.d). I. kafli. Almenn ákvæði. Retriveded Septemer 18, 2016 from http://www.althingi.is/lagas/145a/2006116.html

Appendix A

TITLE

Visir;

OPTIONS

ExcelWorkbook="Model3.xlsx"{Workbooktogetthedatafrom}

ExcelSheetName="Model"{Sheetintheworkbookwherethedatais}

INDEX

p:=(A1_F,A2_F,A3_F,A4_F,A5_F,A6_F,A7_F,A8_F,A9_F,A10_F,A11_F,A1_S,A2_S,A3_S,A4_S,A5_S,A6_S,A7_S,A8_S,A9_S,A10_S,A11_S,A12_S,A13_S,A14_S,A15_S,A16_S,A17_S,A18_S,A19_S); {Thenumberofprocessingallocationproduced}

k=(Product_1_F,Product_2_F,Product_3_F,Product_4_F,Product_5_F,Product_6_F,Product_7_F,Product_8_F,Product_9_F,Product_10_F,Product_11_F,Product_12_F,Product_13_F,Product_14_F,Product_15_F,Product_16_F,Product_17_F,Product_18_F,Product_19_F,Product_20_F,Product_21_F,Product_22_F,Product_23_F,Product_24_F,Product_25_F,Product_26_F,Product_27_F,Product_28_F,Product_29_S,Product_30_S,Product_31_S,Product_32_S,Product_33_S,Product_34_S,Product_35_S,Product_36_S,Product_37_S,Product_38_S,Product_39_S,Product_40_S,Product_41_S,Product_42_S,Product_43_S,Product_44_S,Product_45_S,Product_46_S,Product_47_S){ThenumberofproductsproducedatVisir}

DATA

Profit[p]:=EXCELRANGE("Framlegð");{NetProfitContribution}

RawMat[p]:=EXCELRANGE("Hráefni_þörf");{RawMatrequirment}

Flexicut[p]:=EXCELRANGE("Flex");{Flexicut}

Feeding[p]:=EXCELRANGE("Feed");{Feeding}

Advant[p]:=EXCELRANGE("Adva");{Advania}

Gyro[p]:=EXCELRANGE("Gyro");{Gyrofreezes}

Fish:=EXCELRANGE("Fiskur"); {AvailableRawmaterialinput}

FlexDay:=EXCELRANGE("FleXicut_available");{AvailablemachineminutesFlexicut}

FeedDay:=EXCELRANGE("Innmötun_available");{AvailablemachineminutesFeeding}

AdvaDay:=EXCELRANGE("Advant_frystir_available");{AvailablemachineminutesAdvantfreezer}

GyroDay:=EXCELRANGE("Gyro_frystir_available");{AvailablemachineminutesGyrofreezer}

Orders[k]:=EXCELRANGE("pantanir_samningar"); {Ordersandcontractsmadeforproductk}

RBOM[k,p]:=EXCELRANGE("ReverseBOM");{Productkproducedinproductcompositionp}

Yield[p]:=EXCELRANGE("Nýt"); {Yieldofproductcomposistionp}

AlloRawF:=EXCELRANGE("Hráefni_þvingað_i_ferskt");{Rawmaterialforcedtobeallocatedtofreshandfrozenproduction}

AlloRawS:=EXCELRANGE("Hráefni_þvingað_i_salt"); {Rawmaterialforcedtobeallocatedtosaltedproduction}

VARIABLES

Produced[p]->PrEXPORTTOEXCELRANGE("Framleitt");{Whatprocessingallocationshouldweproduce}

MODEL

MAXTotalProfit=SUM(p:Profit[p]*Produced[p]);

SUBJECTTO

RawM:sum(p:RawMat*Produced)<Fish; {Rawmaterialconstrain}

Flex:sum(p:Flexicut*Produced)<FlexDay; {MachineconstrainFlexicut}

Feed:sum(p:Feeding*Produced/Yield)<FeedDay; {MachineconstrainFeeding}

Adva:sum(p:Advant*Produced)<AdvaDay; {MachineconstrainAdvantfreezer}

GyrF:sum(p:Gyro*Produced)<GyroDay; {MachineconstrainAdvantfreezer}

Orde[k]:sum(p:RBOM*Produced/Yield)>Orders[k];{OrderandContractconstrainforproductk}

RawF:sum(p=1..11:Produced/Yield)>AlloRawF;{Rawmaterialallocatedtofreshandfrozenproduction}

RawS:sum(p=12..30:Produced/Yield)>AlloRawS; {Rawmaterialallocatedtosaltedproduction}

END

Afurðar-samsetning

NR: Afurð Magn

Þyngd.afurðar(akg)

Heildarþyngd(akg)

Áætlskipting

(akg/hkg)

Ferskt/

Frosið NýtingAfur.Verð(kr/akg)

Umb-kost

(kr/akg)

Áætl.Birgðak(kr/kg)

Virði(kr/akg)

Hráef-þörf

(hkg/akg)

Vélar.þörf(vmin/akg)

Frystiþörf(min/akg)

A1_F Gyro AdvantHnakki Product1 1 0,25 0,25 14% 0,07 Ferskt 49% 1.250 24 177 0,295Hnakki Product5 2 0,2 0,4 23% 0,11 Ferskt 49% 1.250 24 283 0,472Bakflak Product27 1 0,6 0,6 35% 0,17 Frosið 49% 694 24 1,2 232 0,708 0,02Biti Product18 2 0,1 0,2 12% 0,06 Frosið 49% 726 24 1,2 81 0,236 0,01Þunnildi 1 0,17 0,17 10% 0,05 Ferskt 49% 298 29 0,201Marningur 1 0,11 0,11 6% 0,03 Frosið 49% 184 2,3 12 0,130

1,73 100% 0,49 814 2,041 0,013 0,02 0A2_FHnakki Product3 1 0,65 0,65 36% 0,18 Ferskt 49% 1250 24 443 0,737Hnakki Product5 1 0,2 0,2 11% 0,05 Ferskt 49% 1250 24 136 0,227Biti Product16 2 0,15 0,3 17% 0,08 Frosið 49% 740 24 1,2 119 0,340 0,01Biti Product19 1 0,115 0,115 6% 0,03 Frosið 49% 739 24 1,2 46 0,130 0Sporður Product23 1 0,095 0,095 5% 0,03 Frosið 49% 675 24 1,2 34 0,108 0Þunnildi 1 0,29 0,29 16% 0,08 Ferskt 49% 298 48 0,329Marningur 1 0,15 0,15 8% 0,04 Frosið 49% 184 2,3 15 0,170

1,8 100% 0,49 49% 841 2,041 0,013 0,01 0A3_FHnakki Product4 1 0,6 0,6 45% 0,219 Ferskt 49% 1333 24 584 0,910Biti Product12 2 0,145 0,29 22% 0,11 Ferskt 49% 952 24 200 0,440Biti Product13 1 0,035 0,035 3% 0,01 Frosið 49% 682 24 9,2 17 0,053 0Sporður Product22 1 0,08 0,08 6% 0,03 Frosið 49% 675 24 1,2 39 0,121 0Þunnildi 1 0,19 0,19 14% 0,07 Ferskt 49% 298 42 0,288Marningur 1 0,15 0,15 11% 0,05 Frosið 49% 184 2,3 20 0,228

AppendixB

1,345 100% 0,49 49% 902 2,041 0,013 0 0A4_FJ-cut Product10 1 1,25 1,25 76% 0,37 Ferskt 49% 1000,8 24 738 1,541Þunnildi 1 0,255 0,255 15% 0,08 Ferskt 49% 297,5 46 0,314Marningur 1 0,15 0,15 9% 0,04 Frosið 49% 184,5 2,3 17 0,185

1,655 100% 0,49 800 2,041 0,013 0 0A5_FHnakki Product5 2 0,2 0,4 22% 0,11 Ferskt 49% 1250 24 268 0,446Hnakki Product7 1 0,15 0,15 11% 0,05 Ferskt 49% 1190 24 130 0,228Bakflak Product28 1 0,2 0,2 11% 0,05 Frosið 49% 694 24 1,2 73 0,223 0,01Biti Product15 2 0,14 0,28 15% 0,07 Frosið 49% 740 24 1,2 109 0,312 0,01Biti Product12 2 0,145 0,29 16% 0,08 Ferskt 49% 952 24 147 0,323Biti Product17 2 0,1 0,2 11% 0,05 Frosið 49% 690 24 1,2 73 0,223 0,01Þunnildi 1 0,2 0,2 11% 0,05 Ferskt 49% 298 33 0,223Marningur 1 0,11 0,11 6% 0,03 Frosið 49% 184 2,3 11 0,123

1,83 103% 0,5 844 2,101 0,013 0,02 0A6_FHnakki Product3 1 0,55 0,55 39% 0,19 Ferskt 49% 1.250 24 475,7 0,792Biti Product17 1 0,095 0,095 7% 0,03 Frosið 49% 690 24 1,2 44,6 0,137 0Biti Product20 2 0,08 0,16 11% 0,06 Frosið 49% 635 24 1,2 68,9 0,230 0,01Biti Product14 2 0,065 0,13 9% 0,04 Frosið 49% 516 24 9,2 44,4 0,187 0Sporður Product22 1 0,07 0,07 5% 0,02 Frosið 49% 675 24 1,2 32,1 0,101 0Þunnildi 1 0,292 0,292 21% 0,1 Ferskt 49% 298 61,3 0,421Marningur 1 0,12 0,12 8% 0,04 Frosið 49% 184 2,3 15,4 0,173

1,417 100% 0,49 49% 742,5 2,041 0,013 0,02 0A7_FHnakki Product6 1 0,4 0,4 22% 0,11 Ferskt 49% 1.339 24 291 0,451Hnakki Product2 2 0,175 0,35 19% 0,09 Ferskt 49% 1.095 24 207 0,395Biti Product19 2 0,115 0,23 13% 0,06 Frosið 49% 739 24 1,2 91 0,259 0,01Biti Product14 2 0,06 0,12 7% 0,03 Frosið 49% 516 24 9,2 32 0,135 0

Biti Product20 2 0,065 0,13 7% 0,04 Frosið 49% 635 24 1,2 44 0,147 0Bakflak Product26 1 0,16 0,16 9% 0,04 Frosið 49% 694 24 1,2 59 0,180 0Þunnildi 1 0,27 0,27 15% 0,07 Ferskt 49% 298 44 0,304Marningur 1 0,15 0,15 8% 0,04 Frosið 49% 184 2,3 15 0,169

1,81 100% 0,49 783 2,041 0,013 0,02 0A8_FHnakki Product8 1 0,35 0,35 19% 0,1 Ferskt 49% 1.261 24 241 0,398Hnakki Product9 1 0,2 0,2 11% 0,05 Frosið 49% 847 24 4,6154 91 0,227 0,0056Biti Product18 2 0,11 0,22 12% 0,06 Frosið 49% 726 24 1,1538 86 0,250 0,01Biti Product17 2 0,1 0,2 11% 0,05 Frosið 49% 690 24 1,1538 74 0,227 0,01Biti Product16 2 0,15 0,3 17% 0,08 Frosið 49% 740 24 1,1538 120 0,341 0,01Bakflak Product25 1 0,085 0,085 5% 0,02 Frosið 49% 655 24 1,1538 30 0,097 0Þunnildi 1 0,27 0,27 15% 0,07 Ferskt 49% 298 45 0,307Marningur 1 0,17 0,17 9% 0,05 Frosið 49% 184 2,3 17 0,193

1,795 100% 0,49 704 2,041 0,013 0,02 0,0056A9_FJ-cut Product11 1 0,85 0,85 71% 0,35 Ferskt 49% 1000,8 24 692 1,446 0,2223Þunnildi 1 0,2 0,2 17% 0,08 Ferskt 49% 297,5 50 0,340Marningur 1 0,15 0,15 13% 0,06 Frosið 49% 184,5 2,3 23 0,255

1,2 100% 0,49 764 2,041 0,013 0 0,2223A10_FHnakki Product1 2 0,25 0,5 34% 0,169 Ferskt 49% 1.250 24 422 0,7028Hnakki Product5 1 0,2 0,2 14% 0,067 Ferskt 49% 1.250 24 169 0,2811Biti Product19 1 0,115 0,115 8% 0,039 Frosið 49% 739 24 1,1538 57 0,1616 0Biti Product17 2 0,1 0,2 14% 0,067 Frosið 49% 690 24 1,1538 92 0,2811 0,01Sporður Product21 1 0,067 0,067 5% 0,023 Frosið 49% 516 24 4,6154 23 0,0942 0Þunnildi 1 0,22 0,22 15% 0,074 Ferskt 49% 298 45 0,3092Marningur 1 0,15 0,15 10% 0,051 Frosið 49% 184 2,3077 19 0,2108

1,452 825 2,0408 ##### 0,01A11_F

Hnakki Product4 1 0,6 0,6 43% 0,211 Ferskt 49% 1.333 24 564,62976 0,8803Hnakki Product2 1 0,175 0,175 13% 0,062 Ferskt 49% 1.095 24 134,74119 0,2568Biti Product19 1 0,115 0,115 8% 0,041 Frosið 49% 739 24 1,1538 59,032464 0,1687 0Biti Product20 2 0,065 0,13 9% 0,046 Frosið 49% 635 24 1,1538 57,05665 0,1907 0Sporður Product24 1 0,011 0,011 1% 0,004 Frosið 49% 675 24 1,1538 5,1384167 0,0161 0Þunnildi 1 0,2 0,2 14% 0,070 Ferskt 49% 298 42,774982 0,2934Marningur 1 0,16 0,16 12% 0,056 Frosið 49% 184 21,216391 0,2347

1,391 884,58986 2,0408 ##### 0,01

Saltað/Frosið

Þyngd.afurðar(akg)

Heildarþyngd(akg)

Nýt-ing

Áætlskipting

Þyngdafurðarm.v

hkg(akg/hkg)

Afur-Verð(kr/akg)

Umb-kost

(kr/akg)

Áætl-Birgða(kr/kg)

Framlegð(kr/akg)

Hráef-þörf

(hkg/akg)Vélar.þörf(vmin/hkg)

Frystiþörf(min/akg)

A1_SSaltað 4 25 57% 100% 0,57 809,20 29,18 40 740,02 1,75439 0,005432 0

A2_SSaltað 4 25 57% 100% 0,57 779,45 29,18 40 710,27 1,75439 0,005432 0

A3_SSaltað 3 25 57% 100% 0,57 773,50 29,18 40 704,32 1,75439 0,005432 0

A4_SSaltað 3 25 57% 100% 0,57 720 29,18 40 651 1,75439 0,005432 0

A5_SSaltað 2,5 25 57% 100% 0,57 719,95 18,54 15 686,41 1,75439 0,005432 0

A6_SSaltað 2,5 25 57% 100% 0,57 720 18,54 15 686 1,75439 0,005432 0

A7_SSaltað 1,5 25 57% 100% 0,57 702,10 18,54 10 673,56 1,75439 0,005432 0

A8_S

Processingallocation#

Appendix C

Product35

Product29

Product30

Product31

Product32

Product33

Product34

Saltað 1,5 25 57% 100% 0,57 660 18,54 10 632 1,75439 0,005432 0

A9_SSaltað 1 15 57% 100% 0,57 658 30,23 5 623 1,75439 0,005432 0

A10_SSaltað 1 25 57% 100% 0,57 631 18,54 5 607 1,75439 0,005432 0

A11_SSaltað 1 25 57% 100% 0,57 649 18,54 5 625 1,75439 0,005432 0

A12_SSaltað 1,4 25 43% 100% 0,43 1.006 29,18 15 961 2,32558 0,0072 0

A13_SSaltað 1,3 25 43% 100% 0,43 982 18,54 15 948 2,32558 0,0072 0

A14_SFrosið 2,2 550 68% 100% 0,68 524 11 10 502 1,47059 0,004553 0,0857143

A15_SFrosið 2,2 550 68% 100% 0,68 530 11 10 508 1,47059 0,004553 0,0857143

A16_SFrosið 2 550 68% 100% 0,68 524 11 10 502 1,47059 0,004553 0,0857143

A17_SFrosið 2 550 68% 100% 0,68 530 11 10 508 1,47059 0,004553 0,0857143

Product41

Product42

Product43

Product44

Product45

Product36

Product37

Product38

Product39

Product40

A18_SFrosið 1,25 11 68% 100% 0,68 595 8,20 5 582 1,47059 0,004553 0,0857143

A19_SFrosið 1,25 11 68% 100% 0,68 559 8,20 5 546 1,47059 0,004553 0,0857143Product47

Product46

School of Science and Engineering Reykjavík University Menntavegur 1 101 Reykjavík, Iceland Tel. +354 599 6200 Fax +354 599 6201 www.ru.is