The Development of the Optimal Harvesting Model of an Offshore Fishery Supply Chain Based on a Single Vessel
Abstract
:1. Introduction
 To develop a model of supply chain based on profit maximization;
 To identify the crucial player in the offshore fishery supply chain;
 To provide decisionmakers with a solution based on the determining parameters in the offshore fishery supply chain.
1.1. Literature Review of Supply Chain
1.2. Offshore Fishery Supply Chain Model
1.3. Previous Studies
2. Materials and Methods
2.1. Review Methodology
2.2. Bat Algorithm
 All bats use echolocation to sense distance and ${x}_{i}$, the location of a bat, and encode the position as a solution to the optimization problem under consideration.
 Bats fly with velocity ${v}_{i}$ at position ${x}_{i}$ with a frequency ${f}_{min}$, varying wavelength $\mathsf{\lambda}$ and loudness ${A}_{0}$ to search for prey randomly. They automatically adjust the wavelength (or frequency) of their emitted pulses and regularly the rate of pulse emission$\mathrm{r}\in \left[0,1\right]$, based on the proximity of the prey source.
 The loudness ranges from a large (positive) ${A}_{0}$ to a minimum value (constant) ${A}_{min}$ as assumed in this study.
2.3. Bat Algorithm Structure
 Initialization of bat population: The search space is assumed as a region that contains many preys in it. The algorithm attempts to find the highquality or best position in the search space. Since the locations of the prey source are unknown, the initial population is randomly generated from realvalued vectors with dimension d and number N, by taking into account lower and upper boundaries. Then, the prey source located within the population are evaluated.$${x}_{ij}={x}_{min}+\phi \left({x}_{max}{x}_{min}\right)$$
 Generation of frequency, velocity, and new solution: The movements could be influenced by the evaluated fitness values of all bats. For each bat $\left(i\right)$, its position $\left({x}_{i}\right)$ and velocity $\left({v}_{i}\right)$ in a ddimensional search space should be defined. ${x}_{i}$ and ${v}_{i}$ should be updated subsequently in the iterative process. The rules for updating the position and velocities of a bat $\left(i\right)$ are given below:$${f}_{i}={f}_{min}+\left({f}_{max}{f}_{min}\right)\beta ,$$$${v}_{i}^{t}={v}_{i}^{t1}+\left({x}_{i}^{t}{x}_{*}\right){f}_{i},$$$${v}_{i}^{t}{x}_{i}^{t}={x}_{i}^{t1}+{v}_{i}^{t}$$
 Local search capability of the algorithm: In order to improve the local search capability of the algorithm, once a solution is selected among the current best solution, a new solution will be generated locally using a random fly for each bat.$${x}_{new}={x}_{old}+\mathsf{\u2107}{A}^{t},$$
 Loudness and pulse emission rate: The loudness ${A}_{i}$and the rate ${r}_{i}$ of pulse emission have to be updated according to the iteration processing. When a bat approaches its prey, the loudness A and the pulse emission rate r will be updated. Pulse emission rate r is increased as loudness A is decreased with respect to Equations (6) and (7) respectively.$${A}_{i}^{t+1}=\alpha {A}_{i}^{t},$$$${r}_{i}^{t+1}={r}_{i}^{0}\left[1\mathrm{exp}\left(\gamma t\right)\right],$$
2.4. Formulation of the Optimization Problem
2.5. Disaggregate Inventory Constraints
 (1)
 For raw material suppliers (mclayer1),
 (2)
 For wholesalers (mclayers 2),
 (3)
 For product manufacturers (mclayer 3),
 (4)
 For retailers (mclayer 4),
3. Experimental and Numerical Results
3.1. Parameter Setting
3.2. Analysis of Numerical Results
3.3. Sensitivity Analysis of Cost Allocation
4. Discussion
4.1. Theoretical Implication
4.2. Managerial Implication
4.3. Political and Academic Implications
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
 Ma, Q.; Wang, W.; Peng, Y.; Song, X. A twostage stochastic optimization model for port cold storage capacity allocation considering pelagic fishery yield uncertainties. Eng. Optim. 2018, 50, 1926–1940. [Google Scholar] [CrossRef]
 Macusi, E.D.; Morales, I.D.G.; Macusi, E.S.; Pancho, A.; Digal, L.N. Impact of closed fishing season on supply, catch, price, and the fisheries market chain. Mar. Policy 2022, 138, 105008. [Google Scholar] [CrossRef]
 Flynn, B.B.; Koufteros, X.; Lu, G. On theory in supply chain uncertainty and its implications for supply chain integration. J. Supply Chain Manag. 2016, 52, 3–27. [Google Scholar] [CrossRef] [Green Version]
 Tliche, Y.; Taghipour, A.; CanelDepitre, B. An improved forecasting approach to reduce inventory levels in decentralized supply chains. Eur. J. Oper. Res. 2020, 287, 511–527. [Google Scholar] [CrossRef]
 Aragão, G.M.; SaraleguiDíez, P.; Villasante, S.; LópezLópez, L.; Aguilera, E.; Moranta, J. The carbon footprint of the hake supply chain in Spain: Accounting for fisheries, international transportation and domestic distribution. J. Clean. Prod. 2022, 360, 131979. [Google Scholar] [CrossRef]
 Asioli, D.; Boecker, A.; Canavari, M. On the linkages between traceability levels and expected and actual traceability costs and benefits in the Italian fishery supply chain. Food Control 2014, 46, 10–17. [Google Scholar] [CrossRef]
 Rosales, R.M.; Pomeroy, R.; Calabio, I.J.; Batong, M.; Cedo, K.; Escara, N.; Facunla, V.; Gulayan, A.; Narvadez, M.; Sarahadil, M.; et al. Value chain analysis and smallscale fisheries management. Mar. Policy 2017, 83, 11–21. [Google Scholar] [CrossRef]
 Fister, I., Jr.; Fister, D.; Yang, X.S. A hybrid bat algorithm. Elektroteh. Vestn. 2013, 80, 1–7. [Google Scholar] [CrossRef]
 Zebari, A.Y.; Almufti, S.M.; Abdulrahman, C.M. Bat algorithm (BA): Review, applications and modifications. Int. J. Sci. World 2020, 8, 1–7. [Google Scholar] [CrossRef]
 Goyal, S.K. An integrated inventory model for a single suppliersingle customer problem. Int. J. Prod. Res. 1977, 15, 107–111. [Google Scholar] [CrossRef]
 Majumder, A.; Jaggi, C.K.; Sarkar, B. A multiretailer supply chain model with backorder and variable production cost. RAIRO Oper. Res. 2018, 52, 943–954. [Google Scholar] [CrossRef] [Green Version]
 Guan, R.; Zhao, X. Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies. Comput. Oper. Res. 2011, 38, 1294–1304. [Google Scholar] [CrossRef]
 Theiben, S.; Spinler, S.; Huchzermeier, A. Reducing the carbon footprint within fastmoving consumer goods supply chains through collaboration: The manufacturers’ perspective. J. Supply Chain Manag. 2014, 50, 44–61. [Google Scholar] [CrossRef]
 Sibanda, P.H.; Pooe, D. Enhancing supply chain performance through supply chain practices. J. Transp. Supply Chain Manag. 2018, 12, a400. [Google Scholar] [CrossRef]
 Swierczek, A. The role of manufacturer in supply chain transformation from intransitive into transitive triads: Implications for the network rent. Int. J. Supply Chain. Manag. 2019, 24, 445–468. [Google Scholar] [CrossRef]
 Desiderio, E.; GarcíaHerrero, L.; Hall, D.; Segrè, A.; Vittuari, M. Social sustainability tools, and indicators for the food supply chain: A systematic literature review. Sustain. Prod. Consum. 2022, 30, 527–540. [Google Scholar] [CrossRef]
 Karray, S.; MartínHerrán, G. The impact of a store brand introduction in a supply chain with competing manufacturers: The strategies role of pricing and advertising decision timing. Int. J. Prod. Econ. 2022, 244, 108378. [Google Scholar] [CrossRef]
 Sarkar, B. A productioninventory model with probabilistic deterioration in twoechelon supply chain management. Appl. Math. Model. 2013, 37, 3138–3151. [Google Scholar] [CrossRef]
 Soysal, M.; BloemhofRuwaard, J.M.; Van Der Vorst, J.G. Modelling food logistics networks with emission considerations: The case of an international beef supply chain. Int. J. Prod. Econ. 2014, 152, 57–70. [Google Scholar] [CrossRef]
 Ahumada, O.; Villalobos, J.R. Operational model for planning the harvest and distribution of perishable agricultural products. Int. J. Prod. Econ. 2011, 133, 677–687. [Google Scholar] [CrossRef]
 Jaber, M.Y.; Zanoni, S.; Zavanella, L.E. Economic order quantity models for imperfect items with buy and repair options. Int. J. Prod. Econ. 2014, 155, 126–131. [Google Scholar] [CrossRef]
 CárdenasBarrón, L.E.; Chung, K.J.; TreviñoGarza, G. Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris. Int. J. Prod. Econ. 2014, 155, 1–7. [Google Scholar] [CrossRef]
 Yang, S.; Xiao, Y.; Zheng, Y.; Liu, Y. The green supply chain design and marketing strategy for perishable food is based on temperature control. Sustainability 2017, 9, 1511. [Google Scholar] [CrossRef] [Green Version]
 Bányai, T.; Illés, B.; Gubán, M.; Gubán, Á.; Schenk, F.; Bányai, Á. Optimization of JustInSequence Supply: A Flower Pollination AlgorithmBased Approach. Sustainability 2019, 11, 3850. [Google Scholar] [CrossRef] [Green Version]
 Chen, H.K.; Hsueh, C.F.; Chang, M.S. Production scheduling and vehicle routing with time windows for perishable food products. Comput. Oper. Res. 2009, 36, 2311–2319. [Google Scholar] [CrossRef]
 Song, X.; Ma, Q.; Wang, W.; Peng, Y. Capacitiesbased distantwater fishery cold chain network design considering yield uncertainty and demand dynamics. In Proceedings of the 2017 International Conference on Progress in Informatics and Computing (PIC), Nanjing, China, 15–17 December 2017. [Google Scholar]
 Liu, Z.; Qu, S.; Goh, M.; Wu, Z.; Huang, R.; Ma, G. Twostage meanrisk stochastic optimization model for port cold storage capacity under pelagic fishery yield uncertainty. Phys. A Stat. Mech. Appl. 2020, 541, 123338. [Google Scholar] [CrossRef]
 Gandomi, A.H.; Yang, X.S.; Alavi, A.H.; Talatahari, S. Bat algorithm for constrained optimization tasks. Neural. Comput. Appl. 2013, 22, 1239–1255. [Google Scholar] [CrossRef]
 Yılmaz, S.; Küçüksille, E.U. A new modification approach on bat algorithm for solving optimization problems. Appl. Soft Comput. 2015, 28, 259–275. [Google Scholar] [CrossRef]
 De Jesús Rubio, J. Bat algorithm based control to decrease the control energy consumption and modified bat algorithm based control to increase the trajectory tracking accuracy in robots. Neural Netw. 2023, 161, 437–448. [Google Scholar] [CrossRef]
 Essa, K.S.; Diab, Z.E. Gravity data inversion applying a metaheuristic Bat algorithm for various ore and mineral models. J. Geodyn. 2023, 155, 101953. [Google Scholar] [CrossRef]
 Sharma, P.; Sharma, K. Fetal state health monitoring using novel Enhanced Binary Bat Algorithm. Comput. Electr. Eng. 2022, 101, 108035. [Google Scholar] [CrossRef]
 Mihoubi, M.; Rahmoun, A.; Lorenz, P.; Lasla, N. An effective bat algorithm for node localization in distributed wireless sensor network. Secur. Priv. 2018, 1, e7. [Google Scholar] [CrossRef] [Green Version]
 Acampora, G.; Chiatto, A.; Vitiello, A. Genetic algorithms as classical optimizer for the Quantum Approximate Optimization Algorithm. Appl. Soft Comput. 2023, 142, 110296. [Google Scholar] [CrossRef]
 Piotrowski, A.P.; Napiorkowski, J.J.; Piotrowska, A.E. Partical Swarm Optimization or Differential Evolution—A comparison. Eng. Appl. Artif. Intell. 2023, 121, 106008. [Google Scholar] [CrossRef]
 Zhou, X.; Gui, W.; Heidari, A.A.; Cai, Z.; Liang, G.; Chen, H. Random following ant colony optimization: Continuous and binary variants for global optimization and feature selection. Appl. Soft Comput. 2023, 144, 110513. [Google Scholar] [CrossRef]
 VuHuu, T.; PhamVan, S.; Pham, Q.H.; CuongLe, T. An improved bat algorithm for optimization design of truss structures. Structures 2023, 47, 2240–2258. [Google Scholar] [CrossRef]
 Yang, X.S. A New Metaheuristic BatInspired Algorithm. In Nature Inspired Cooperative Strategies for Optimization (NICSO 2010); González, J.R., Pelta, D.A., Cruz, C., Terrazas, G., Krasnogor, N., Eds.; Springer: Berlin/Heidelberg, Germany, 2010; Volume 284. [Google Scholar]
Reference  Assumptions  Methods 

Macusi et al. [2]  The study assumes that shrimp aquaculture is facing the need to increase production to meet growing food demand, particularly in the Philippines where there has been a shift from milkfish to prawn due to market demand. It acknowledges the positive and negative impacts of intensification on the environment and socioeconomic aspects.  The study utilizes the PRISMA method to review and assess the challenges faced by the shrimp aquaculture industry, including environmental issues like farm management, marine pollution, disease outbreaks, and social, economic, and climate change impacts. 
Flynn et al. [3]  The study assumes the existence of three types of supply chain uncertainty, namely, microlevel, mesolevel, and macrolevel, and hypothesizes that these uncertainties coexist and interact with each other, while also positing that supply chain integration, centralization, formalization, and flatness influence the dimensions of uncertainty, which are tested using hierarchical regression analysis.  A hierarchical regression analysis based on data collected from 339 manufacturing plants. 
Tliche et al. [4]  The study assumes that utilizing a downstream demand inference (DDI) strategy with various forecasting methods, including the proposed weighted moving average, can effectively address information disclosure issues in decentralized supply chains and improve supply performance metrics, while formalizing the manufacturer’s forecast optimization problem.  A comprehensive approach encompassing downstream demand inference (DDI) strategy, various forecasting methods, analysis of demand processes, evaluation of supply performance metrics, formalization of the manufacturer’s forecast optimization problem, and application of Newton’s method for solution. 
Aragão et al. [5]  The study assumes that greenhouse gas emissions are crucial for climate change mitigation, and that emission assessments are typically excluded from the management of capture fisheries. It also assumes that hake is an important food in Spain and aims to estimate the carbon footprint of the hake seafood chain by analyzing its extraction, transport, and distribution.  The analysis of the hake seafood chain in Spain, which includes the extraction (fishing), international transport, and domestic distribution within Spanish territory. The data is obtained from various sources, such as vessels’ logbook records for hake landings, the official database of seafood trade flows, and the Food Consumption Panel data. 
Desiderio et al. [16]  The study assumes that achieving sustainable production and consumption in food systems requires considering the entire supply chain and the social dimensions that are often overlooked compared to environmental and economic aspects. It acknowledges the lack of consensus and measurement methods regarding social sustainability in food supply chains.  The study reviews 101 papers and gray literature documents to identify the current state of measuring social sustainability using various tools and indicators. The analysis focuses on five stages of the food supply chain (production, processing, wholesale, retail, and consumer) and four stakeholders (farmers, workers, consumers, and society). 
Karray and MartínHerrán [17]  This research assumes that the introduction of a store brand in a supply chain with competing national brands can have significant impacts on the profitability of different supply chain members, particularly the national brand manufacturers. The study focuses on analyzing the effects of manufacturers’ decision timing choices regarding pricing and advertising on the competition between national and store brands.  A gametheoretic model is developed, considering different decision timing scenarios. 
Metaheuristic Algorithms  Characteristics 

Bat Algorithm [9,33] 

Genetic Algorithm [34] 

Particle Swarm Optimization [35] 

Ant Colony Optimization [36] 

LayerMc  Parameter  Unit Revenues (kg/US)  

Lower Bound  Upper Bound  
m1 → (raw materials) → m2  ${r}_{m1,m2}^{raw}\left(t\right)$  2.74  4.79 
m1 → (raw materials) → m3  ${r}_{m1,m3}^{raw}\left(t\right)$  2.74  4.79 
m2 → (raw materials) → m3  ${r}_{m2,m3}^{raw}\left(t\right)$  1.35  2.33 
m2 → (products) → m4  ${r}_{m2,m4}\left(t\right)$  2.39  5.17 
m2 → (products) → m5  ${r}_{m2,m5}\left(t\right)$  4.24  5.46 
m3 → (products) → m4  ${r}_{m3,m4}\left(t\right)$  1.94  3.35 
m3 → (products) → m5  ${r}_{m3,m5}\left(t\right)$  2.43  4.2 
m4 → (products) → m5  ${r}_{m4,m5}\left(t\right)$  4.26  6.47 
LayerMc  Parameter  Unit Revenues (kg/US)  

Lower Bound  Upper Bound  
m1: raw material suppliers  ${c}_{m1}^{in{v}^{raw}}\left(t\right)$  0.3  0.5 
${c}_{m1}^{lab}\left(t\right)$    30  
m2: wholesalers  ${c}_{m1,m2}^{pr{o}^{raw}}\left(t\right)$  2.37  4.16 
${c}_{m2}^{Fz}\left(t\right)$  0.88  1.12  
${c}_{m2}^{DEP}\left(t\right)$    100  
${c}_{m2}^{MT}\left(t\right)$    250  
${c}_{m2}^{in{v}^{raw}}\left(t\right)$  0.3  0.5  
${c}_{m2}^{inv}\left(t\right)$  0.3  0.5  
${c}_{m1,m2}^{tp}\left(t\right)$  0.25  0.5  
${c}_{m2}^{lab}\left(t\right)$    25  
m3: manufacturer  ${c}_{m1,m3}^{pr{o}^{raw}}\left(t\right)$  2.38  4.16 
${c}_{m2,m3}^{pr{o}^{raw}}\left(t\right)$  1.35  2.33  
${c}_{m3}^{man}\left(t\right)$    0.94  
${c}_{m3}^{Fz}\left(t\right)$  0.88  1.12  
${c}_{m3}^{DEP}\left(t\right)$    1000  
${c}_{m3}^{MT}\left(t\right)$    500  
${c}_{m3}^{in{v}^{raw}}\left(t\right)$  0.3  0.5  
${c}_{m3}^{inv}\left(t\right)$  0.38  0.61  
${c}_{m1,m3}^{tp}\left(t\right)$  0.25  0.5  
${c}_{m2,m3}^{tp}\left(t\right)$  0.25  0.5  
${c}_{m2}^{lab}\left(t\right)$    30  
m4: retailers  ${c}_{m2,m4}^{pro}\left(t\right)$  2.72  4.14 
${c}_{m3,m4}^{pro}\left(t\right)$  2.74  4.79  
${c}_{m4}^{Fz}\left(t\right)$  0.88  1.12  
${c}_{m4}^{DEP}\left(t\right)$    100  
${c}_{m4}^{MT}\left(t\right)$    100  
${c}_{m4}^{inv}\left(t\right)$  0.5  1.00  
${c}_{m2,m4}^{tp}\left(t\right)$  0.35  0.6  
${c}_{m3,m4}^{tp}\left(t\right)$  0.35  0.6  
${c}_{m4}^{lab}\left(t\right)$    15  
m5: customers  ${c}_{m2,m5}^{tp}\left(t\right)$  0.35  0.6 
${c}_{m3,m5}^{tp}\left(t\right)$  0.35  0.6  
${c}_{m5,m5}^{tp}\left(t\right)$  0.35  0.6 
 
${\Psi}_{m1}^{in{v}^{raw}}$  ${\Psi}_{m2}^{in{v}^{raw}}$  ${\Psi}_{m2}^{inv}$  ${\Psi}_{m3}^{in{v}^{raw}}$  ${\Psi}_{m3}^{inv}$  ${\Psi}_{m4}^{inv}$ 
5000  2000  1000  2000  3000  1000 
 
${\alpha}_{1}$  ${\alpha}_{2}$  ${\alpha}_{3}$  $\beta $  $\sigma $  
0.18  0.3  0.18  0.18  0.14  
 
 
$\mathcal{L}$  $\mathcal{K}{\mathcal{L}}_{1}$  $\mathcal{K}{\mathcal{L}}_{2}$  $\mathcal{K}{\mathcal{L}}_{3}$  
1000  596.43  466.23  589.77 
Evaluation Criterion  Net Profit (USD) 

Operation Alternative  
Nonlinear programming  41,850 
Bat Algorithm approach (80 bats)  41,515 
Evaluation Criterion  Net Profit (USD) 

Operation Alternative  
Scene 1 (Raise inventory of m2)  66,290 
Scene 2 (Raise inventory of m3)  68,240 
The optimal method  41,515 
Scene 1  Scene 2  

Raise Inventory of m2 (USD)  Raise Inventory of m3 (USD)  
Aggregate revenue  157,940  168,230  
Aggregate cost  
Procurement cost  34,550  35,940  
Manufactured cost  22,220  26,340  
Inventory cost  14,830  16,160  
Transportation cost  16,300  17,800  
Aggregate profit  66,290  68,240 
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. 
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Yang, M.F.; Kao, S.L.; Sujanto, R.Y. The Development of the Optimal Harvesting Model of an Offshore Fishery Supply Chain Based on a Single Vessel. J. Mar. Sci. Eng. 2023, 11, 1593. https://doi.org/10.3390/jmse11081593
Yang MF, Kao SL, Sujanto RY. The Development of the Optimal Harvesting Model of an Offshore Fishery Supply Chain Based on a Single Vessel. Journal of Marine Science and Engineering. 2023; 11(8):1593. https://doi.org/10.3390/jmse11081593
Chicago/Turabian StyleYang, MingFeng, ShengLong Kao, and Raditia Yudistira Sujanto. 2023. "The Development of the Optimal Harvesting Model of an Offshore Fishery Supply Chain Based on a Single Vessel" Journal of Marine Science and Engineering 11, no. 8: 1593. https://doi.org/10.3390/jmse11081593