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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.21 No.1 pp.1-19
DOI : https://doi.org/10.7232/iems.2022.21.1.001

# An Integrated Production and Distribution Planning Model in Shrimp Agroindustry Supply Chain

Lely Herlina*, Machfud, Elisa Anggraeni, Sukardi
Industrial Engineering Department, Faculty of Engineering, Universitas Sultan Ageng Tirtayasa, Banten, Indonesia, The Graduate School, Bogor Agricultural University, Bogor, Indonesia
Agroindustrial Technology, Bogor Agricultural University, Bogor, Indonesia
*Corresponding Author, E-mail: lely@untirta.ac.id
December 10, 2019 November 2, 2020 November 15, 2021

## ABSTRACT

This study discusses the integration model of production and distribution planning in the shrimp agroindustry supply chain, consisting of four echelons: shrimp suppliers, shrimp agroindustry, logistics provider companies, and buyers. The shrimp agroindustry supply chain is an essential part of the supply chain of processed product food, which transforms raw shrimp into various processed shrimp frozen products. One form of collaboration between supply chain actors is the integration of production and distribution planning activities. A model is developed to determine the flow of goods from each echelon, the number of processed shrimp products in the agroindustry, and the supplies of processed shrimp products. The bi-objective mixed-integer linear programming is proposed to describe the characteristics of the problem to minimize the total supply chain costs and maximize service level. Non-dominated sorting genetic algorithm II (NSGA-II) is designed to solve the shrimp agroindustry supply chain problem. The sample problem from the shrimp agroindustry in East Java, Indonesia, is applied to exhibit an algorithm’s efficiency. The result shows the best solution for the total supply chain is 1.75 trillion, and the service level is 1,502,264.5.

## 1. INTRODUCTION

The fishery sector is one of the mainstay sectors of the Indonesian economy, realized through the fishery agroindustry. One of the existing fisheries agro-industries is the shrimp agroindustry. For Indonesia, shrimp is one of the highly competitive export commodities. As an export commodity, shrimp agroindustry faces competition from similar businesses both from inside and outside the country.

Shrimp agroindustry cannot avoid collaboration among actors in the supply chain to deal with intense competition. Collaboration is needed to reduce uncertainty and streamline costs, and to respond quickly to market changes including changes in shrimp product demand patterns regarding product diversity, quantity, and priority deliveries. However, similar to any other agro-industrial raw materials that full of uncertainty, shrimp also has biological properties which makes it prone to environmental changes (Boonsumrej et al., 2007;Islam and Habib, 2013) and has varied harvest ages (Yu and Leung, 2005;Yu et al., 2006). This uncertainty makes raw material as a critical point in the shrimp agroindustry and contributes 80% to the production costs (Pathumnakul et al., 2007). It means that cooperation between shrimp agroindustry and shrimp suppliers is needed to guarantee raw materials, which has a vital role in winning market share.

Furthermore, to stand out in the competition, shrimp agroindustry must reduce costs, such as in production cost, in order to make it more efficient and to affect profits. However, efficient cost alone is not sufficient to win the very rapid market change. The shrimp agroindustry also has to respond quickly to it by increasing its service level. One indicator to elevate a service level is to fulfill customers’ orders at the right time with the correct quantity and the excellent quality.

Due to the competition, the requirement to streamline costs and increase service levels conduces shrimp agroindustry to collaborate with other actors along the supply chain. One form of collaboration between actors in the supply chain is the integration of planning activities by dealing with production and distribution planning as the two main optimization problems in the supply chain. According to Sawik’s research (2016), the supply of raw material is a crucial function at the supply chain operational level and production and distribution planning. Integrating these activities in a coordinated manner is very important to achieve high supply chain performance (Chen, 2010;Amorim et al., 2013a;Sawik, 2016;Rafiei et al., 2018). This is in line with Fahimnia et al. (2013), the two things which make integration of production and distribution in the supply chain critical are: 1) positively enhance profitability supply chain, 2) minimize lead time and respond quickly to market changes.

Shrimp agroindustry encounters competition from similar businesses. Because of that, shrimp agroindustry must collaborate with other actors to survive and achieve minimum costs and maximum service levels. Based on Tirkolaee et al. (2020), a company must focus on its supply chain strategy and logistics to hold out in a competitive global market to increase profits and control operation costs. Thus, the research question in this study is: How is the integration model of production and distribution planning in the supply chain of the shrimp agroindustry?

This paper’s main contribution is to develop a model of integrated production and distribution planning in the shrimp agroindustry supply chain. In this study, we consider the yield of shrimp in the production process. The conditions on the shop floor indicates that the amount of shrimp yield is very dependent on the shrimp size which later affects the final product. Mathematical models are designed with mixed-integer linear programming (MILP) to describe the characteristics of the problem, and to minimize the total supply chain costs and maximize service level. A case study in a shrimp agroindustry is solved using non-dominated sorting genetic algorithm II (NSGA-II).

This paper's presentation consists of several parts: Section 2 describes previous researches related to the integration of production and distribution planning. Section 3 is a research methodology; starting with discussing the non-dominated sorting genetic algorithm-II (NSGA-II), describing production in the shrimp agroindustry, making mathematical formulations mixed-integer linear programming (MILP), and lastly presenting the case study's data. Section 4 presents computational results and discussion. Finally, the conclusion and future research directions are stated in Section 5.

## 2. LITERATURE REVIEW

The two main optimization problems in the supply chain are production and distribution planning. Traditionally, production and distribution planning decisions often made separately (Díaz et al., 2015). The most common procedure begins with production and then continues to product distribution from manufacturers to consumers. However, globalization on the supply chain and market competitions requires the company to guarantee its resource efficiency, increase its service level for consumers, and reduce lead time and stock.

Based on the certainty value of the parameters used, the model of integrated production and distribution planning usually discusses deterministic and stochastic models. Bilgen and Ozkarahan (2007), Akkerman et al. (2009), Bilgen and Günther (2010), Rong and Grunow (2010), Ahumada and Villalobos (2011a, 2011b), Amorim et al. (2012), Farahani et al. (2012), Amorim et al. (2013b), Validi et al. (2014), Sel et al. (2015), Devapriya et al. (2017), Fu et al. (2017), Guo et al. (2017), Sakalli (2017), Wei et al. (2017), Cheng et al. (2019), and Liu et al. (2019) took up the integration model of production and distribution planning with deterministic conditions. Meanwhile, stochastic models was examined by Aliev et al. (2007), Azaron et al. (2008), Dabbene et al. (2008), Chen et al. (2009), Bilgen and Çelebi (2013), Nasiri et al. (2014), Ariafar et al. (2014), Jafarian and Bashiri (2014), Soysal et al. (2015), Ma et al. (2016), Banasik et al. (2017), Hashim et al. (2017), Rafiei et al. (2018), Nemati and Alavidoost (2018), Babazadeh and Torabi (2018), Khalifehzadeh and Fakhrzad (2018), Tirkolaee et al. (2019), and Guarnasch`elli et al. (2020). A comprehensive review of the integration of production and distribution planning was carried out by Fahimnia et al. (2013), while the Ahumada and Villalobos (2009), and Amorim et al. (2013a) reviewed the integration of production and distribution planning on perishable products. Díaz-Madroñero et al. (2015) presented a review of production and distribution planning integration at the tactical planning level.

Bilgen and Ozkarahan (2007) proposed an optimization model to solve the problem of mixing and shipping wheat in the grain supply chain. The mathematical model was proposed in mixed-integer linear programming (MILP) with the objective function is to minimize the total costs, including mixing, loading, transportation, and inventory costs. The assumption of the model system was deterministic, with model constraints covering mixing capacity, consumer demand, loading and unloading capacity, and vessel capacity. It compiled the model to determine the number of calcified products, the number of products loaded in each port, the number of products transported from each port to consumers, and the number of vessels rented each time.

Similar with Bilgen and Ozkarahan (2007), Akkerman et al. (2009), Bilgen and Günther (2010), Amorim et al. (2012), Farahani et al. (2012) and Sel et al. (2015) also modeled with a mathematical model of mixed-integer linear programming (MILP). However, the difference between these researches lies in the objective function and object of study. Akkerman et al. (2009) aimed to minimize the costs and environmental impact on ready-to-eat food. In contrast, Bilgen and Günther (2010) examined fruit juices and soft drinks to reduce production and distribution costs. One of the attractive points taken from Bilgen and Günther (2010) research is the proposed block planning for sequencing production in fast-moving consumer goods. Amorim et al. (2012) discussed the food industry to minimize total costs and maximize its freshness. Meanwhile, Farahani et al. (2012) examined food catering, aiming to reduce transportation and quality decrease. The object of the study in Sel et al. (2015) was yogurt with the objective function to bring down the total cost of the supply chain.

Quality factors lead to consideration in the research of Amorim et al. (2012) and Farahani et al. (2012). Akkerman et al. (2009) mentioned quality factors in the proposed model and included sustainability factors involving 3P dimensions (profit, people, planet). Other studies that include elements of sustainability in their studies are Validi et al. (2014) and Guo et al. (2017). Validi et al. (2014) research model which had the objective function of minimizing CO gas emissions and transportation costs throughout the supply chain. Meanwhile, Guo et al. (2017) aimed to minimize the total supply chain costs, including the cost of releasing CO2.

Rong and Grunow (2010) paid attention to food safety factors in the integration model of production and distribution planning. The study explained that traceability is something needed to respond to food safety. The integration model of production and distribution planning noticed dispersion or supply chain distribution. Supply chain dispersions are the result of decisions made for the delivery. Rong and Grunow (2010) defined supply chain dispersion that functioned as a measurement of the number of retailers served by several batches. The purpose of making this integrated model of production and distribution planning is to minimize the total cost, including dispersion, batch setup, storage, and production costs.

Ahumada and Villalobos (2011a) discussed the production and distribution planning for fresh products at the tactical decision level. Meanwhile, Ahumada and Villalobos (2011b) examined production planning and distribution at the operational level. Ahumada and Villalobos’s research objective at both the tactical and operational levels was to maximize farmers’ profits. The model formed mixed-integer linear programming (MILP) with a solution using CPlex. Devapriya et al. (2017) proposed MILP to minimize the total cost of distribution. The model solution in Devapriya et al. (2017) used genetic and memetic algorithms with limitations in this research was the capacity of production facilities. Wei et al. (2017) proposed trade-off between costs and setup time, depending on the work order.

Aliev et al. (2007) proposed the production and distribution aggregate planning model, based on fuzzy mathematical programming, and problem solving with genetic algorithms. Ariafar et al. (2014) also considered the same model for a mineral water bottling production plant. Hashim et al. (2017) discussed sustainable strategic supplier selection under a fuzzy environment based on a genetic algorithm. The proposed model used a genetic algorithm with the purpose of obtaining optimal order allocation to suppliers aimed to minimize costs, maximize quality, and increase service level. Nasiri et al. (2014) applied Lagrangian relaxation combined with a genetic algorithm for three echelon supply chains in the production-distribution planning model.

Azaron et al. (2008) developed stochastic programming in the supply chain with uncertainty. The uncertainty elements considered in this study are demand, supply, processing, transportation, and shortage cost. Dabbene et al. (2008) also adopted the stochastic model for the fresh food supply chain. They argued that in supply chain design, especially at the distribution stage, they should consider perishable nature and product variability. Dabbene et al. (2008) presented a new approach to optimize supply chains in fresh food products that manage trade-offs between logistics costs and some food quality measures in terms of consumers.

Chen et al. (2009) considered the production schedule and delivery route with time windows for a perishable product from the supplier’s perspective and formulated it in an integer non-linear programming. The Nelder-Mead method solved production scheduling and delivery route with time windows completed by the heuristic. Bilgen and Çelebi (2013) also studied the production schedule and distribution problem of the yogurt industry. They accomplished the problem by using the iterative hybrid optimization-simulation procedure.

Jafarian and Bashiri (2014) discussed dynamic supply chain configurations resulting from the development of new products. In this study, factors considered to maximize profits were product quality; inventory; and lead time consisting of transportation lead time and production lead time. Sawik (2016) designed a stochastic mix integer programming model to integrate production and distribution planning. This research focused on supplier selection, scheduling, risk of disruption in production and distribution planning, and shipping method. Guarnaschelli et al. (2020) also used stochastic programming for dairy products. They proposed two-stage stochastic mixed-integer programming with a clustering method to solve. Soysal et al. (2015) discussed vehicle loading related to distribution costs, evaluated fuel consumption, CO2 emissions, and considered service levels in the model. Ma et al. (2016) developed bi-level programming in the production and distribution planning model, a two-stage genetic algorithm with a fuzzy logic algorithm.

Banasik et al. (2017) examined the integration of production and distribution planning in the mushroom industry's closed supply chain. To predict the trade-off between economic and environmental indicators, Banasik et al. (2017) proposed a multi-objective mixed-integer linear programming. Rafiei et al. (2018) developed an integration of production and distribution planning model within four echelon supply chains to minimize the total chain cost and maximize the service level. To solve the problem, Rafiei et al. (2018) used an elastic constraint method. Concerning the uncertainty factor, Nemati and Alavidoost (2018), Babazadeh and Torabi (2018), and Khalifehzadeh and Fakhrzad (2018) developed a fuzzy mathematical model to describe uncertainty in the system. Tirkolaee et al., (2019) discussed a self-learning particle swarm optimization to minimize the total cost including fixed establishment cost, transportation cost and inventory cost.

The basic model in this study is the model of Jafarian and Bashiri (2014). However, there are differences between this study and the study of the Jafarian and Bashiri (2014). The objective of Jafarian and Bashiri (2014) is maximizing profit. Meanwhile, based on an observed object, the objective of model developed in this study is to minimize total costs and maximize service level. Another difference lies in the research article where Jafarian and Bashiri (2014) did numerical experiments on the electronic component supply chain. Meanwhile, in this proposed model, numerical experiments were carried out on the shrimp agroindustry. This industry is different from other manufacturing industries because there are perishable properties in each supply chain. Another difference is that the production process is influenced by the yield value of shrimp. The production of the final product varies depending on the yield value. The proposed model also incorporates the damage factor during the transportation process from the shrimp supplier to the agroindustry.

## 3. RESEARCH METHOD

At this stage, we describe three segments; the first is the NSGA-II algorithm; the second is production in the shrimp agroindustry; and the third is compiling an integrated model for production and distribution planning in the shrimp agroindustry supply chain.

### 3.1 Non-dominated Sorting Genetic Algorithm-II (NSGA-II)

Srinivas and Deb (1994) first introduced the nondominated sorting genetic algorithm (NSGA). NSGA is one of the most popular evolutionary algorithms in multiobjective optimization. The basis of working on the NSGA is a genetic algorithm. This algorithm is beneficial, but has high computational complexity, lacks elitism, and requires an additional parameter called the shared parameter to obtain various solution (Deb et al., 2000).

Deb et al. (2002) made a variation of the NSGA, which was later called NSGA-II (non-dominated sorting genetic algorithm-II). The NSGA-II has better performance than its predecessor. NSGA-II introduces a fast non-dominated sorting process and uses crowding distance calculations during the selection process to maintain diversity without using any additional parameters. Crowding distance states how close an individual is to their neighbors. The NSGA-II steps are as follows.

• Step 1. Parameter values initialization

The parameter values used are the probability of crossing over and mutation. The crossover parameter indicates the likelihood of crossover occurring between two chromosomes. The mutation parameter states the chance that the transformation occurs in the genes that make up chromosomes.

• Step 2. Population initialization

The population is initialized based on the scope of the problem, such as the number of objective functions, decision variables, and limits. This step carried out the chromosome assignments. A chromosome consists of genes that show all the decision variables.

• Step 3. Non-dominated list

Sort the initialized population according to non-dominance. An individual dominates another individual if at least one goal functions better than another's solutions. The non-domination arrangement aims to categorize F1, F2, …, FR fronts in the population. The first front (F1) is a non-dominant set consisting of the best solutions from the first population and up to the last front, indicating the worst solution.

• Step 4. Crowding distance list

Crowding distance compares two individuals on the same front so that the resulting solution can represent the entire Pareto-optimal solution. Its purpose is to maintain population diversity and help navigate search spaces.

Short solutions in fronts F1, F2, ..., Fj in increasing order for all k objective functions. If p = | Fj | and x (i, j) represents the ith solution and the ordered list is related to the objective function k. Set cdkx (l, k) = ~ and cdkx (p, k) = ~, and for i = 2, …., p - 1 is determined as equation 1.

$c d x x ( i , k ) = Z k ( X [ i + 1 , k ] ) − Z k ( X [ i − 1 , k ] k ) Z k m a x − Z k m i n$
(1)

Crowding distance cd (x) from solution x, obtained by adding the crowding distance of the solution for each goal, namely $c d ( x ) = ∑ k c d x ( x )$

• Step 5. Individual selection

Individual selection aims to select the best parent population. The selection process applies a tournament function based on front/rank criteria and crowding distance. The randomly selected individual then conducts a tournament based on the minimum face value; if the scores are the same, then the maximum crowding distance value is chosen.

• Step 6. Offspring generation

Generating offspring using genetic operators cross over and mutation. The cross over procedure is the process of selecting two individuals (chromosomes) from the population and combining them to form two new individuals (offspring) who have the characteristics of the parent (both parents). Cross over procedure uses the simulated binary crossover (SBX) introduced by Deb and Agrawal (1995). The SBX operator simulates the working principle of the cross over the operator on binary chromosomes. The formula used when carrying out the SBX process shown in equations 2 and 3

$b = { ( 2 + r ) 1 μ + 1 , , i f r ≤ 0 , 5 , ( 1 2 + ( 1 − r ) 1 μ + 1 , i f r > 0 , 5$
(2)

$c h i l d 1 ( j ) = 0 , 5 [ ( 1 + b ) p a r e n t 1 ( j ) + ( 1 − b ) p a r e n t 2 ( j ) ] c h i l d 2 ( j ) = 0 , 5 [ ( 1 − b ) p a r e n t 1 ( j ) + ( 1 + b ) p a r e n t 2 ( j ) ]$
(3)

With,

• r = random number between 0 and 1

• μ = crossover operator

• j = individual representations

The idea behind crossing over is that the new chromosomes may be better than their parents if the new chromosomes take on the sound characteristics of each parent.

After crossing over, only then do the mutations. Mutation is the genetic process of changing the value of one or more genes on a chromosome in a population. The mutation procedure changes the gene's value randomly by randomly selecting the parent, and the amount of the gene changes according to the range of each variable. The mutation procedure uses polynomial mutations, referring to Deb et al. (2002), with a formula as in equation 4

$b = { ( 2 + r ) 1 η + 1 , − 1 , j i k a r ≤ 0 , 5 , 1 − ( 2 * ( 1 − r ) ) 1 η + 1 , j i k a r > 0 , 5$
(4)

Child (j) = parent (j) + d

with:

• r = random number between 0 and 1

• η = mutation operator

• j = individual representations

Figure 1 shows the working principle of NSGA-II.

### 3.2 Shrimp Agroindustry Production

The raw materials used in shrimp agroindustry is fresh shrimp with a specific size. Raw materials are transported from shrimp suppliers to the shrimp agroindustry by truck or pickup truck. There are three groups of shrimp suppliers: the fish auction, intensive/semi-intensive pond, and traditional pond supplier groups.

Shrimp agroindustry produces two types of frozen shrimp product groups: 1) frozen cooked shrimp group and 2) frozen raw shrimp group. They also provide block frozen as intermediate products. The freezing processes of each product done by individual quick frozen (IQF) and semi IQF. Frozen cooked shrimp products consist of frozen cooked headless shrimp and frozen cooked peeled deveined shrimp products. The same applies to frozen raw shrimp products.

Production in shrimp agroindustry consists of sixteen activities: (1) receiving raw materials, (2) washing raw materials, (3) cutting shrimp head, (4) sorting and grading, (5) cutting, (6) peeling and deveining, (7) washing and soaking, (8) cooking, (9) cooling, (10) preparation and weighing, (11) freezing and glazing, (12) wrapping and sealing, (13) metal detection, (14) packing and labeling, (15) storing in cold storage, (16) stuffing. For frozen raw shrimp products, after the washing and soaking processes, these directly proceed to the preparation and weighing stage. Meanwhile, the cooking process of frozen cooked shrimp products is done after washing and soaking. Blocks frozen is produced after the peeling and deveining activities (Herlina et al., 2018).

The product is made based on customer orders. Some customers order large-size frozen shrimp products while others only buy small ones. Shrimp agroindustry promises to meet customer demand. The number of raw materials and block frozen stocks influence the production decision. To compete with other similar companies, it needs to do cost efficiency. Finally, after the stuffing process, frozen shrimp products are shipped to the customers.

### 3.3 Integrated Production and Distribution Planning Model for Shrimp Agroindustry Supply Chain

Shrimp agroindustry production lead time is between 1-7 days, which means that production planning is on the short planning horizon. According to Amorim et al. (2013a), integrated production and distribution planning for products with a short planning horizon is necessary. This study of integrated production and distribution planning lies on a tactical level considered four echelons in the shrimp agroindustry supply chain consisting of multi-supplier shrimp, one shrimp agroindustry, multi-logistics provider companies, and multi-buyers. There are three groups of shrimp suppliers: suppliers of fish auctions (i), intensive pond suppliers (j), and traditional pond suppliers (k). The shrimp agroindustry processes raw shrimp into two groups i.e., frozen uncooked shrimp (c1) and frozen cooked shrimp (c2). Logistics provider company (l) has a role in delivering shrimp processed products from shrimp agroindustry (A) to buyers (b).

The critical point in the supply chain of shrimp agroindustry is the supply of raw materials of fresh shrimp. Shrimp have different numbers and sizes. Shrimp size is related to the number of shrimps per kilogram. For example, the size of 41/50 means that there are 41-50 raw shrimp in one kilogram. The guarantee of raw materials is crucial in continuous production to win the market competition.

Buyers usually order based on specific sizes. The ordered pattern of buyers is uncertain each period, and shrimp agroindustry make products to fulfill buyers' requests. Order fulfillment affects buyers’ trust in shrimp agroindustry; which is one way to win market share. The other way to win the competition is efficiency costs in the supply chain.

This study has designed an integrated production and distribution planning model in the shrimp agroindustry supply chain to compete globally. The production plan refers to a calculation stating the amount of shrimp processed products that should be produced in a certain period. Simultaneously, the distribution plan shows the flow of shrimp raw material from suppliers to shrimp agroindustry and the frozen shrimp processed products from shrimp agroindustry to consumers. There is a percentage of damage during the distribution process. This damage can result in a reduced number of good quality shrimp when arriving at agroindustry. Demand quantity assumed has probability density function and has a distribution.

The integrated model of production and distribution planning in the shrimp agroindustry supply chain is formulated in bi-objective mixed-integer linear programming (MILP) to determine the trade-off between total supply chain costs and service level. The overall supply chain costs consist of raw materials procurement cost, production cost of shrimp processing, inventory cost, and damage cost. Figure 2 illustrates the shrimp agroindustry supply chain structure.

The assumptions of the developed research model are as follows:

• 1. Not fulfilling demand will result in a loss of sales.

• 2. Production capacity and frozen block supply capacity in agroindustry are limited.

• 3. The distance between the agroindustry and the logistics provider company is near, so the transportation costs and delivery lead times are ignored. The narrow range causes no quality loss in shrimp processed products during the distribution process between agroindustry and logistics provider companies.

• 4. There is no penalty fee for late delivery.

#### 3.3.1 Bi-objective Mixed-integer Linear Programming Model

A bi-objective mixed-integer linear programming model is formulated for integrating production and distribution planning in the shrimp agroindustry supply chain. The objectives of the model are minimizing total cost as well as maximizing service level. The notation for mathematical models is as follows:

Indices

• s shrimp size, sS.

• i supplier groups of fish auctions, iI.

• j intensive farm supplier groups, jJ.

• k traditional farm supplier group, kK.

• l logistics provider company, lL.

• b buyer, bB.

• c frozen shrimp products, cC (1 = frozen cooked shrimp product group, 2 = frozen raw shrimp product group).

• t time periods, tT.

Notation:

• A notation for shrimp agroindustry.

• LS notation for logistics provider company.

• B notation for buyers.

• D notation for demand.

• BF notation for block frozen.

• P notation for the purchase price of raw materials.

• N notation for capacity.

• CP notation for production costs.

• CI notation for inventory costs.

• I0 notation for initial inventory.

• θ notation for the percentage of damage to the transportation process.

• ζ notation for the percentage level of use of raw materials.

Parameters:

Demand

• $D b c s t$ the buyer demand b on frozen shrimp product c with size s in period t.

Price

• Pis price per kilogram of shrimp with size s from suppliers of fish auction i.

• Pjs price per kilogram of shrimp with size s from intensive pond suppliers j.

• Pks price per kilogram of shrimp with size s from traditional pond suppliers k

Capacity

• Nc production machine capacity for frozen shrimp products c.

• NBF production machine capacity for block frozen.

• Nl capacity of vehicles transporting processed shrimp products to logistics provider companies l.

• Nss shrimp supplier capacity.

Production costs in shrimp agroindustry

CPcs cost of production of frozen shrimp products c with size s.

CPBFs cost of production of block frozen with size s.

CPBFcs cost of production from block frozen into frozen shrimp products c with size s.

Inventory cost

• CIBFs inventory cost for block frozen with size s.

• CIcs inventory cost for frozen shrimp product c with size s.

Initial inventory

• IOBFs initial inventory block frozen with size s.

• IOcs initial inventory frozen shrimp product c with size s.

Damage during transportation

• θi percentage of shrimp damage during transportation from suppliers of fish auction i to agroindustry.

• θj percentage of shrimp damage during transportation from intensive pond suppliers j to agroindustry.

• θk percentage of shrimp damage during transportation from traditional pond suppliers k to agroindustry.

Yield

• ζBF shrimp yield for block frozen.

• ζc shrimp yield for frozen shrimp product c.

• $P c t$ percentage of shrimp supply to become product c in period t.

• $P B F t$ percentage of shrimp supply to become block frozen product in period t.

Decision variables

Inventory

• $I B F s t$ quantity of inventory block frozen with size s in period t.

• $I c s t$ quantity of inventory frozen shrimp product c with size s at the end of period t.

Flow material

• $F i s t$ quantity of shrimp with size s that supply from suppliers of fish auction i in period t.

• $F j s t$ quantity of shrimp with size s that supply from intensive pond suppliers j in period t.

• $F k s t$ quantity of shrimp with size s that supply from traditional pond suppliers k in period t.

• $G l c s t$ quantity of frozen shrimp product c with size s from agroindustry to logistic provider company l in period t.

• $G l b c s t$ quantity of frozen shrimp product c with size s from logistic provider company l to buyer b in period t.

Production in shrimp agroindustry

• $Q c s t$ quantity of frozen shrimp product c with size s that produce in period t.

• $Q B F s t$ quantity of block frozen with size s that produce in period t.

• $Q B F c s t$ quantity of block frozen that produced to be frozen shrimp product c with size s in period t.

Binary variable

• $X c s t$ binary variable if frozen shrimp product c with size s that produce in period t.

• $X B F s t$ binary variable if block frozen with size s that produce in period t.

• $X B F c s t$ binary variable if block frozen changed to be frozen shrimp product c with size s in period t.

Objective function

• Z1: Minimize total cost of supply chain

• Z1 = raw material procurement cost (OC) + production process cost (PC) + inventory cost (IC) + damage cost (DC)

- Raw material procurement cost (OC)

Raw material procurement cost (OC) is calculated as follow:

$∑ i ∑ s ∑ t P i s F i s t + ∑ j ∑ s ∑ t P j s F j s t + ∑ k ∑ s ∑ t P k s F k s t$
(5)

In Equation (5), the first part denotes price per kilogram of shrimp size s from the suppliers of fish auction I; the second shows the price per kilogram of shrimp size s from intensive pond suppliers j; and the third states price per kilogram of shrimp size s from traditional pond suppliers k.

Production process cost (PC)

$∑ s ∑ t C P B F s Q B F s t X B F s t + ∑ c ∑ s ∑ t C P B F c s Q B F c s t X B F c s t + ∑ c ∑ s ∑ t C P c s Q c s t X c s t$
(6)

Production process cost (PC) is computed as follow:

In Equation (6), the first is the cost of production of block frozen size s, the second is the cost of block frozen production into frozen shrimp products c size s, and the third is the cost of producing frozen shrimp products c size s.

Inventory cost (IC)

Inventory cost (IC) is counted as follow:

$∑ s ∑ t C I B F s I B F s t + ∑ c ∑ s ∑ t C I s I c s t$
(7)

In Equation (7), the first is inventory cost for block frozen size s, and the second is inventory cost for frozen shrimp product c size s.

Damage cost (DC)

Damage cost (DC) is calculated as follow:

$∑ i ∑ s ∑ t P i s F i s t θ i + ∑ j ∑ s ∑ t P j s F j s t θ j + ∑ k ∑ s ∑ t P k s F k s t θ k$
(8)

In Equation (8), the first denotes the cost of damage during transportation from the suppliers of fish auction i to agroindustry, the second states cost of damage during transportation from intensive pond suppliers j to agroindustry, and the third counts cost of damage during transportation from traditional pond suppliers k to agroindustry.

• Z2: Maximize service level

(9)

In equation (9), it states the amount of inventory of stock of frozen shrimp product c size s in period t divided by the number of order frozen shrimp product c size s in period t.

Subject to

Inventory

(10)

(11)

Flow

$∑ c G l b c s t ≤ D b c s t + n$
(12)

(13)

(14)

Capacity

(15)

(16)

$∑ c ∑ s G l b c s t ≤ N l ∀ l , s , t$
(17)

Supply

$∑ i F i s t + ∑ j F j s t + ∑ k F k s t ≤ N s s$
(18)

Production

(19)

(20)

Binary and integer

$I , F , G , Q ≥ 0 and integer X ∈ { 0 , 1 }$
(21)

All constraints are described from (10) – (21). Constraints (10) and (11) are inventory balance constraints in the shrimp agroindustry. It counts the quantity of inventory block frozen and inventory product at the end of the period. Constraints (12) to (14) express flow constraints of all supply chains. Constraints (15) to (17) are capacity constraints. Constraint (18) states that supply raw material from a group of suppliers. Constraints (19) and (20) represent frozen shrimp product and block frozen, respectively—production constraint considering shrimp yield and percentage of shrimp supply to become a product or block frozen. Constraint (21) shows the non-negativity of decision variables and the binary of the related decision variables.

#### 3.3.2 Data of Modelling Exercise

This section delivers the data for the shrimp agroindustry supply chain in Gresik, East Java, Indonesia. It was collected from shrimp agroindustry by interview. Shrimp agroindustry produces two groups of frozen shrimp products in various sizes, i.e., the frozen cooked product and the frozen raw product. There are two samples of demand for frozen shrimp products: ‘cooked peeled tail on’ (CPTO) and ‘peeled deveined’ (PD) with sizes 51/60, 61/70, and 71/90. Figure 3 represented demand for CPTO and PD with its size at shrimp agroindustry. Shrimp supply comes from shrimp suppliers consisting of fish auctions, intensive pond suppliers, and traditional pond suppliers. Figure 4 shows the shrimp supply from all three suppliers.

Price per kilogram of shrimp is not significantly different between the suppliers. The price difference lies in the size of the shrimp. Price for size 51/60, 61/70, and 71/90 is 65,000 IDR, 70,000 IDR and 75,000 IDR respectively. The capacity of production machines to make frozen shrimp and frozen raw shrimp is 1,200 kg/hour. To produce block frozen, the capacity of the production machine is 600 kg/hour. The capacity of trucks to transport processed shrimp products is 20,000 kg. The trucks’ capacity to transport raw shrimp from suppliers to shrimp agroindustry is 6,000 kg for big trucks and 1,500 kg for a pickup truck.

The cost for producing frozen shrimp products depends on the product group and its size. The cost for producing frozen raw shrimp products with size 51/60 is 17,145 IDR, size 61/70 is 17,459 IDR, and 71/90 is 17,790 IDR. Meanwhile, the production cost of frozen cooked shrimp products is 21,198 IDR, 21,521 IDR, and 21,828 IDR for sizes 51/60, 61/70, 71/90, respectively. The inventory cost is 1,000 IDR. Initial inventory is assumed zero.

The percentage of shrimp damage during transportation is around 2%. The shrimp yield is about 68%. The percentage of shrimp to be frozen foods or block frozen depends on the raw material inventory level.

## 4. COMPUTATIONAL RESULT AND DISCUSSION

The proposed model is implemented in the shrimp agroindustry supply chain in Gresik, East Java, Indonesia. Following steps used to apply the proposed model.

### 4.1 Determining Distribution

#### 4.1.1 Determining Distribution of Demand

Easyfit version 5.6 is used to find demand distribution. Kolmogorov-Smirnov found the goodness of fit of frozen shrimp products demands with a confidence level of 95%. Table 1 shows parameter values of delivery for each frozen shrimp product and the statistic value of Kolmogorov-Smirnov. The parameter’ value of the distribution is determined based on the minimum error value.

Determining the distribution of shrimp supply

A similar approach is used to determining the distribution of shrimp supply. Table 2 presents the parameter value of the shipping and cost of Kolmogorov-Smirnov for each shrimp supplier.

### 4.2 Chromosome Representative

A chromosome is a decision variable in a genetic algorithm. In this paper, decision variables are inventory block frozen size s in period t ($I B F s t$) inventory frozen shrimp product c size s at the end of period t ($I c s t$). Then, the quantity of shrimp size s from suppliers ($F i s t , F j s t , F k s t$), amount of frozen shrimp distributed from agroindustry to logistic provider company ($G l c s t$), the quantity of frozen shrimp product distributed to the buyer ($G l b c s t$). The quantity of frozen shrimp product ($Q c s t$), the quantity of block frozen size s that produced in period t ($Q B F s t$) the quantity of block frozen that produced to be frozen shrimp product ($Q B F c s t$), and binary variables ($X c s t , X B F s t , X B F c s t$). Figure 5 shows the chromosome representative.

Figure 5 represents a single chromosome, containing decision variables in the integrated production and distribution planning model in shrimp agroindustry supply chains. For example, IBF11 refers to the quantity of inventory block frozen with size 51/60 in period 1.

### 4.3 Non-dominated Sorting Genetic Algorithm II (NSGA-II) to Solve the bi-objective Optimization Problem

The model solution for completing mathematical formulations is carried out using the evolutionary algorithm approach using the Multi-Objective Evolutionary Algorithm (MOEA) framework with code in the Java programming language. The proposed model is solved using NSGA-II via the MOEA framework version 2.8. NSGA-II is one of the MOEA algorithms that is widely used to solve multi-objective optimization cases (Deb et al., 2000). NSGA-II has a fast non-dominated sorting process and uses more efficient calculations on the crowding distance matrix during the survival selection process.

NSGA-II was tested in a case study of the shrimp agroindustry supply chain, which had 414 variables, 174 constraints, and 23 indexes of the eight index types. The algorithm is examined with 1000, 5000, 10,000, and 20,000 generation numbers and 600 populations. At the same time, the algorithm parameters are set by default based on Hadka (2016). The NSGA-II parameters used in this study are listed in Table 3 as follows:

The NSGA II algorithm is ran using PC with processor Inter® Core™ i5-6200U CPU @ 2.30GHz 2.40 GHz, RAM 4 GB, under 64-bit Operating System.

For each crossover parameter, the candidate's initial value is 0.6. After that, an experiment is carried out by changing the value of the cross over parameter from 0.1 to 0.9. And the chosen one is 0.5. Based on the search conducted by Pareto front for the parameter cross over 0.5, it gives convergent results. Besides, if viewed from the proximity of the objective function, it offers better results. The same action is done when changing the generation value. Table 4 shows the results of the NSGA-II experiment using several generations.

Figure 6 shows finding of the Pareto front of the proposed model using NSGA II.

Figure 6 shows the Pareto solution for each generation represent the trade-off relationship between the total cost of the supply chain and service level. Increasing the number of ages will increase the computational time. The best average diversity is found in the 10,000th generation. Based on the calculation time and number of diverse solutions, this study chooses 10,000 generation numbers to complete the previously determined shrimp supply chain formulation.

Table 5 shows the integrated production and distribution planning model decisions in the shrimp agroindustry supply chain based on NSGA-II. It shows the tradeoff between the total cost of supply chain and level of demand fulfillment represented by service level. Thus, to select the best solution among the fifteen alternative decisions, a filtering/displaced ideal solution (DIS) method has been applied (Pasandideh et al., 2015).

In the DIS method, Fi is a solution for each decision, and in this study, it is based on the total cost of supply chain value (objective 1) and service level value (objective 2). In this method, select the best solution for each objective function (F*). The ideal solution is to determine the minimum value of the objective 1 and determine the maximum value of objective 2. Then the value of Fi is normalized, and the direct distance of each decision is calculated using formulas (22) and (23), respectively.

$F i N = F i * − F i F i *$
(22)

$D i r e c t d i s t a n c e = ∑ i F i N$
(23)

Finally, the best solution is a decision with minimum distance. The final results are represented in Table 6.

Table 6 shows that the best solution for the integrated production and distribution planning model in the shrimp agroindustry supply chain is decision 10th with Z1 = 1.75 trillion IDR and Z2 = 1,502,264.5. Based on the best solution, the selected chromosome for inventory, flow material, and production in shrimp agroindustry in three periods is given in Tables 7-14.

Based on the Pareto front, the value of the total supply chain cost's objective function is the most minimum of IDR 1.75trillion. Figure 7 shows the composition for each expense. Meanwhile, the service level maximization describes the shrimp agroindustry ability to meet buyer demand. Figure 8 shows the summary depiction of responsiveness.

Figure 7 shows that the most significant component is the cost of purchasing raw materials amounting to 85.55% of the total supply chain costs. As expressed by Pathumnakul et al. (2009), raw materials' cost contributed the total cost. Meanwhile, inventory cost has the most negligible impact on the entire supply chain costs.

Figure 8 shows that the percentage of fulfilled buyer's orders is 93% during the observed planning horizon, and the conditions of unfulfilled orders are 7%. It means that from all existing orders, the shrimp agroindustry can fulfill most of them.

### 4.4 Sensitivity Analysis

This section provides a sensitivity analysis of the demand parameter. The parameter are taken based on the assessment of the shrimp agroindustry. The parameter has decreased by up to 10% and an increase up to 10%. Figure 9 shows the results of the sensitivity analysis.

From Figure 9, the proposed model is sensitive to change of parameters, especially for demand.

## 5. CONCLUSION AND FUTURE RESEARCH

This study investigated the integrated production and distribution planning in the shrimp agroindustry supply chain by developing mixed-integer linear programming with bi-objective; these include minimizing total supply chain cost and maximizing service level. NSGA II was used to find the Pareto front solutions. The case study from the shrimp agroindustry is used as the validation of the model. It considered shrimp yields in the production process and damage factors during transportation from shrimp suppliers to the agroindustry. The distribution testing of demand for frozen shrimp products and supply of raw materials used the Kolmogorov-Smirnov method. The calculation results showed that NSGA-II can effectively solve integrated production and distribution planning in the shrimp agroindustry supply chain. Then, to find the best decision to minimize the total cost of the supply chain and maximize service level, the DIS method was used. The significant contributions and social impact of this paper are summarized below:

Bi-objective decision-making provided for integrated production and distribution planning model based on NSGA-II. As mentioned, this model included the yield value in production planning to produce final products and considered the damage factor during transportation from shrimp supplier to agroindustry.

• 1. An application of example problem at a shrimp agroindustry in Gresik, East Java, Indonesia, was given to verify the proposed model. DIS methods achieved the best solution through alternative solutions produced by NSGA-II. This method helped decision-maker to decide which trade-off between minimizing cost and maximizing service level.

• 2. The numerical example examined the proposed model to see the effectiveness. To see the influence of change parameters, especially demand and price, on the objective function, sensitivity analysis was used.

• 3. For social impacts, the proposed model can be used to increase cooperation between shrimp suppliers and the shrimp agroindustry.

For future research, the model can be tested on other metaheuristic algorithms with an addition of sustainability factor to the proposed model. Besides, it can still expand the objective function and model assumptions of the entire system, for example additional destination functions such as calculating the carbon footprint during the transportation process and assumptions including penalty fees due to late delivery. Moreover, it can also investigate scheduling in the shrimp agroindustry for the operation level by paying attention to order acceptance.

## ACKNOWLEDGEMENT

The authors would like to thank Indonesia Endowment Fund for Education (LPDP) for the funding, the editor (Chi-Hyuck Jun), and the anonymous referees for their very precious and valuable suggestions for improving the quality of this research.

## Figure

The working principle of NSGA-II.

Shrimp agroindustry supply chain structure

Demand for CPTO and PD with its size

Supply of shrimp commodities

The chromosome representation

Pareto front NSGA-II (a) pareto front with 1000 generations, (b) pareto front with 5000 generations, (c) pareto front with 10000 generations, (d) pareto front with 20000 generations.

Composition of total supply chain costs of shrimp agroindustry

The ability of the shrimp agroindustry to meet demand

The sensitivity analysis of demand and price of raw material parameter

## Table

Parameter values of distribution and goodness of fit of frozen shrimp products demand

Parameter values of distribution and goodness of fit of shrimp supplier

Parameter in NSGA II

The experimental result

Alternative Decision based on NSGA-II

The main result of DIS method

Inventory of block frozen for each size (kg)

Inventory of frozen shrimp product for each size (kg)

Flow of raw shrimp for each size from suppliers (kg)

Flow product from shrimp agroindustry to logistic provider company (kg)

Flow product from logistic provider company to buyer (kg)

Frozen shrimp product production

Block frozen production

Block frozen to be frozen shrimp product production

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