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Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 224))

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Abbreviations

Simulation optimization problem general form:

Minimize F(x) (Objective function)

\( \mathrm{Subject}\ \mathrm{t}\mathrm{o}\kern-2pt :\kern0.75em Ax\le b\kern4.35em \left(\mathrm{Constraints}\ \mathrm{o}\mathrm{n}\ \mathrm{input}\ \mathrm{variables}\right) \)

\( {g}_l\le G(x)\le {g}_u\kern1em \left(\mathrm{Constraints}\ \mathrm{on}\ \mathrm{output}\ \mathrm{measures}\right) \)

\( l\le x\le u\kern3.35em \left(\mathrm{Bounds}\right) \)

where F(x) and G(x) represent output performance measures obtained from the simulation. The constraints represented by inequality Ax ≤ b, and both the coefficient matrix A and the right-hand-side values corresponding to vector b are known. The constraints represented by inequalities of the form g l ≤ G(x) ≤ g u impose simple upper and/or lower bound requirements on an simulation output function G(x) that can be linear or nonlinear. The values of the bounds g l and g u are known constants. The vector x is the decision variable that includes continuous and discrete values. All decision variables x are bounded. Each evaluation of F(x) and G(x) requires an execution of a simulation of the system.

B f :

Final body weight of a fish (kg)

B i :

Body weight of a fish (kg) in growing phase i

c :

Number of netcages

c i :

Number of netcages in growing phase i e.g., c 1, c 2, c 3 = 4, 8, 16 stands for 4 netcages in the first growing phase 8 netcages in the second growing phase, and 16 netcages in the third phase

D :

Fish biomass stocking density (kg/m3)

D i :

Biomass in growing phase i

DOE:

Design of experiment (Kleijnen 2008)

MR:

Mortality rate. The number of fish at each phase: N i+1 = N i  × (1 − MR). Survival rate = 1 − MR

N, c 1, c 2, c 3, S 1, S 2, S 3, P 1, P 2, P 3 :

The decision parameters

N f :

Final number of fish in a batch

N i :

Number of fish in a batch in growing phase i

P :

Number of sub-batches formed from a batch

RSM:

Response surface methodology (Kleijnen 2008)

S :

Growth period in a netcage (years)

S.T.:

“Subject to the constraints.” This term refers to extrema with constraints in mathematical optimization

Si :

Growth period in growing phase i

T :

Fish age (days in sea)

V :

Culture volume (m3)

V i :

Culture volume in growing phase i a culture volume is a manmade water tank pond or netcage, made of plastic, concrete, soil, etc. (inland aquaculture) or made of a net and located in the sea (marine fish farming), lakes, rivers, seaports, or offshores, e.g., in Ashdod harbor 18 netcages of 2,900 m3 each and 11 netcages of 2,000 m3 each can fit along the breakwater. Total number of netcages is 29

y(t):

Fish body weight on any given day

λ and μ :

Fish arrival and departure rates, respectively (batches/year)

ρ :

Expected utilization of a netcage

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Acknowledgements

Many thanks go to the fish farmers Mr. Nir Tzohari and Dubi Helman (Ardag) who collected the data and actively seeks out professional management tools. Thanks to Dudi Gada (Ardag) and Roni (Ardag) who participated in the scenario running events and the brainstorming at the face-validity meeting in Newe Yaar.

This study was also financed by grants no. 459-4255-05 and 459-0265-06 from the Israel Ministry of Agriculture’s chief scientist fund. This chapter is contribution no. 705/06 from the Institute of Agricultural Engineering, ARO. Israel.

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Halachmi, I. (2015). Simulation Optimization: Applications in Fish Farming—Theory vs. Practices. In: Plà-Aragonés, L. (eds) Handbook of Operations Research in Agriculture and the Agri-Food Industry. International Series in Operations Research & Management Science, vol 224. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2483-7_9

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