Published at : 25 Jan 2024
Volume : IJtech
Vol 15, No 1 (2024)
DOI : https://doi.org/10.14716/ijtech.v15i1.5522
Iffan Maflahah | 1. Department of Industrial and System Engineering, Faculty of Industrial Technology and System Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Surabaya 60111, Indonesia, 2. Dep |
Budisantoso Wirjodirdjo | Department of Industrial and System Engineering, Faculty of Industrial Technology and System Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Surabaya 60111, Indonesia |
Putu Dana Karningsih | Department of Industrial and System Engineering, Faculty of Industrial Technology and System Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Sukolilo, Surabaya 60111, Indonesia |
Oligopoly has remained a
serious problematic market structure in the Indonesian salt supply chain, which
exterminates the bargaining power of farmers. To
eradicate the problem, a hybrid collaboration structures, i.e., vertical
collaboration (farmers with cooperatives) and horizontal collaboration (farmers
with farmers), are proposed, enabling to bring positive economic impacts to
farmers. This novel supply chain-system model follows the cooperative game
theory with Shapley's value for decision-making process. This work aimed to
evaluate the implementation of the two partnership models for the supply
chain of salt regarding their impacts on economic
benefits for farmers assessed by Shapley's value of
coalitions. The constructed model revealed that collaborative
works between salt stakeholders improved farmers’ revenue, and the optimum
benefit was achieved by farmers when their supply (?20%)
was purchased by cooperatives, while the remaining was bought by
middlemen. In this regard, the significant capacity of the
cooperative should be invigorated in various sectors, including saving and loan
services, market seekers, salt
price making, and improvement of salt quality.
Although farmers-to-farmers collaboration also bring mutual benefits,
additional attempts by cooperatives, especially for small farmers, can be
created to nurture a partnership between cooperatives and farmers, enabling
them to generate more benefits.
Cooperative game; Horizontal collaboration; Revenue; Shapley value; Vertical collaboration
Salt has become a pivotal food component for human consumption. In Indonesia, salt development is hindered by factors such as low salt quality, inadequate salt production, price uncertainty, and a complicated supply chain. The main problem of the Indonesian salt supply chain relates to inefficiency and imperfect competition market (oligopoly) (Mustofa et al., 2021). The form of the oligopoly market is likely to be dominated by one of the actors, namely middlemen. The middlemen act as collection agents, purchasers, intermediaries and retailers. Domination of the middlemen includes the ability to control the price and quality of the product (Biglaiser and Li, 2018). Farmers only act as price recipients (Chandra and Sao, 2020) because they have limited market price information, making it difficult to bargain with middlemen (Mustofa et al., 2021).
From 2016 to 2019, salt prices
ranged $0.01 to $0.06 per kilogram (Suhendi, Abdullah,
Shalihati, 2020).
Farmers should get at least $0.06 per
kilogram to cover production costs. The
government regulates prices, but it is ineffective due to the role of
intermediaries. In addition, the government needs to hold the number of salt
imports and supply chain systems by increasing productivity. This
effort is to increase income by improving the bargaining ability of farmers. The salt supply chain can be enhanced by involving
cooperatives to increase farmers' revenue (Mustofa
et al., 2021).
Research on the salt supply chain have been approached using qualitative and quantitative approaches such as margin share methods (Rinardi & Rochwulaningsih, 2017), SWOT analysis (Holis, Sayyidi, and Musoffan, 2019), system dynamics (Muhandhis et al., 2021), and SCOR approach (Purnanto, Suadi, and Ustadi, 2020). Unfortunately, those methods are unable to discuss a collaborative model of the salt supply system. This drawback can be solved by other approaches, such as game theory, which enables to overview of the collaborations aiming to increase farmer’s revenue. The method can formulate and analyze competitive situations and conflicts implicating more than one player with disparate goals (Maschler, Solan, and Zamir, 2013). Determination of options for the supply chain system for agricultural products (Prasad et al., 2019) and allocation of product supply (Bonamini et al., 2019) using the game theory. Game theory can be applied to agricultural products in various ways. For instance, it can use a single pricing strategy or a two-stage pricing strategy for products in the chain of two echelons - suppliers and retailers (Chen et al., 2018). Additionally, game theory can also be used to determine the coordination approach between farmers and traders while accounting for uncertainties like harvesting yields and demand (Behzadi et al., 2018; Gao, Yang, and Liu, 2017).
This study applies coalition game theory and transferable utility concepts using cooperative games. Coalition members are assumed to agree on the price and amount of payoff among the members (Maschler, Solan, and Zamir, 2013). The coalition in the salt supply-chain model involves a cooperative as one of the key elements in the system. In this regard, a cooperative has the functions of facilitating salt farmers to improve their revenue. Moreover, farmers, middlemen, and cooperatives have different interests. Implementing vertical (farmers with cooperative) and horizontal (farmers with farmers) collaboration systems is expected to improve the salt supply chain. Vertical collaboration is a partnership between farmers and cooperatives to reduce the role of the middlemen (Zhong et al., 2018). In addition, a horizontal collaboration between farmers and farmers is also able to increase revenue (Martins, Trienekens, and Omta, 2019). This work aimed to evaluate the implementation of horizontal and vertical collaboration models regarding their impacts on farmers' revenue based on the Shapley value obtained from the salt supply chain coalition.
1.1. Cooperative Game Theory
Shapley's value is used to determine the optimal
solution in cooperative game theory. Each
participant's final result in the game focuses on the
acquisition in the cooperative game. The
coalition is an agreement of the N player set based on the game's mathematical
model and is represented by the symbol S (Brown & Shoham, 2008). A grand coalition is an agreement of all players (n
players) without an empty coalition with a 2n possible alliance. The structure coalition is how the player forms a
coalition where a set of S = (S1, S2, ..., Sm) of the m coalition is built. Some definitions of the Shapley
value concept in cooperative game theory are as follows:
Definition 1 The
transferable utility used in coalition games (N,v) consists of: (1) a set of
N players; (2) the characteristic
function of the game v(S) is the total coalition available to all members of S
of N players, which N is the set for each player, for i = 1, 2, ..., n. The grand coalition is the N set and not the empty set for all S and T where The concept of cooperative games is a super
additive where the
acquisition of coalition results must be greater or equal to non-coalition
income (Brown & Shoham, 2008).
2.2. Model Formulation
Vertical and horizontal collaboration model is used to solve the salt supply chain problem. The stakeholders involved in this coalition are farmers, middlemen, and cooperatives (Figure 1). Farmers, as members, are obliged to sell a certain amount of salt through cooperatives.
Figure 1 The Salt Supply Chain Coalition Model
The research used six players (farmers
1, 2, 3, 4, 5, and 6). The characteristic function as
follows:
The Shapley values were
The Shapley value was determined
using a selling scenario in which salt was sold based on the farmer's minimum
obligation as cooperative members and the rest is sold through middlemen. As
cooperative members, farmers are required to sell salt for at least 10% of the
total production through the cooperative. The scenarios for selling salt from
farmers to middlemen 1, middlemen 2, middlemen 3 and cooperatives are: scenario
1 (30%, 40%, 20%, and 10%); scenario 2 (30%, 30%, 20%, and 20%); scenario 3
(25%, 25%, 25%, and 25%); Scenario 4 (40%, 20%, 10%, and 30%); Scenario 5 (10%,
30%, 20%, and 40%); and Scenario 6 (20%, 10%, 10%, and 60%).
2.3. Construction
of Shapley Value Salt Coalition Model
The model illustrates the average
contribution of six farmer coalition members {1, 2, 3, 4, 5, 6} in all possible
steps. Moreover, the player revenue is used for Shapley value calculations. The
salt supply chain channel will determine the amount of farmer revenue. Members of the salt supply chain are ith farmer (i=1,2, …,
n), jth middleman (j=1, 2. …, m), and kth cooperatives
(k=1, 2, …, h), while the salt supply and salt
price in the intermediary depend on tth time (t = 1.2,
..., l). In addition, the salt demand middlemen j at the time t (Dajt)
Middleman
revenue is obtained from the sale of salt by seeing the negotiation cost (Ca), and salt carrying capacity (G). The
formula of the middleman's revenue at time t
is shown in Equation 1.
The cooperative's revenue is revenue from procuring
salt from farmers i and benefits
distribution The membership fee of the cooperative is
There are
three types of farmer’s revenue based on a horizontal collaboration, namely:
(i) Farmers only sell salt according to the supply produced
The farmer's revenue is obtained from the salt supply through middlemen j and cooperativ
cooperative k, so the farmer i revenue at time t is explained in Equation 3.
(ii) The farmers who buy salt from other farmers
Farmers receive
revenue through middlemen j, and
cooperatives k, and part of the
profits are shared from cooperatives. However, farmers, i have to pay for a certain amount of salt purchased from other
farmers. Therefore, the formula of farmer i revenue at time
t defined
in Equation 4.
(iii) Farmers whose supply exceeds the demand of middlemen and cooperatives
Farmers'
revenue is obtained from sales through middlemen, cooperatives, and coalitions
with other farmers, so the farmer income model is described in Equation 5.
In this scenario, all farmers (Farmer 1, Farmer 2, Farmer
3, Farmer 4, Farmer 5, and Farmer 6) are responsible for meeting the demands of
three middlemen (Middlemen 1, Middlemen 2, and Middlemen 3) and the
cooperative. The supply of salt from the farmers, as well as the demand from
the middlemen and the cooperative, varies for each time period. Additionally,
the prices offered to the farmers by each middleman and the cooperative also
differ. The salt price at the market in period t (Pmt) $83.22/tons; cooperative salt price k in period t (Pbkt) $76.28/tons; salt carrying capacity (G) 9
tons; risk of selling through cooperatives benefit distribution (cooperatives and
farmers) negotiation costs from pond to
cooperatives (C) $3.12/tons; salt negotiation costs by middlemen to the market
(Ca) $6.73/tons; negotiation fee from cooperative to market (Cb) $3.12/tons;
percentage drop in salt price (r) 40%; cooperative membership fee $2.08/period.
The salt supply chain system without a coalition is the
initial scenario in which farmers sell through middlemen 1, 2, and 3 (30%, 20%,
20%) and cooperatives (20%). Based on the scenario, the total revenue of farmer
is: farmer 1, farmer 2, farmer 3, farmer 4, farmer 5, and Farmer 6 ($18,079; $27,450;
$10,346; $5,703; $47,854; $2,532).
Horizontal collaborations are used as the basis for the
coalition game scenario. A coalition carried out by farmers is expected to
provide a minimum revenue equal to or greater than not conducting a
coalition. The coalition of six farmers
in each coalition formed the functional characteristics based on Definition
1 (Table 1). Shapley's
value is the solution problem states that the concept of a coalition forms a
grand coalition in each game (Brown
& Shoham, 2008).
Table 1 Farmer supply as a base, for example, Characteristics of the v(S) function
Number Coalition
Farmer |
Farmers
Revenue v(S)
($) |
Number Coalition
Farmer |
Farmers
Revenue v(S)
($) |
Number Coalition
Farmer |
Farmers
Revenue v(S)
($) |
1 |
18,079 |
3-2-1 |
55,848 |
5-3-2-1 |
103,760 |
2 |
27,450 |
4-2-1 |
51,193 |
5-4-2-1 |
99,104 |
3 |
10,346 |
4-3-1 |
34,038 |
5-4-3-1 |
81,949 |
4 |
5,703 |
4-3-2 |
43,438 |
5-4-3-2 |
91,349 |
5 |
47,854 |
5-2-1 |
93,470 |
6-3-2-1 |
58,302 |
6 |
2,532 |
5-3-1 |
76,315 |
6-4-2-1 |
53,647 |
6-5 |
50,435 |
4-3-2-1 |
61,482 |
6-5-4-3-2-1 |
111,848 |
Shapley value ($18,092.40; $27,486.39;
$10,355.17; $5,702.19; $47,940.93; $2,617.90)
The Shapley value obtained is the
average contribution of the farmer coalition {1,2,3,4,5,6}. When one of the
players performs an S coalition, then contribute to improving the game by as
much as . Farmer's contribution 6 to the grand
coalition {6,5,4,3,2,1} is only v ({6}) = v(6) = $2,532 . The number of grand
coalition combinations is 6! - 1 = 719, producing the same value. Suppose that
the grand coalition formed from the coalition {4,2,6,1,3,5} gives the same
result as the coalition {1,2,3,4,5,6}, which is $111,848. In the farmer
coalition {4,2,6,1,3,5}: revenue
contributions from farmers 1 ($18,079); farmer 2 ($27,450); farmer 3 ($10,346);
farmer 4 ($5,703); farmer 5 ($47,854); and farmer 6 ($2,532). While the contribution of farmers from the
coalition {1,2,3,4,5,6}, namely farmers 1 ($18,079.34), farmers 2 ($27,479),
farmers 3 ($10,289.68), farmers 4 ($5,634.29); farmer 5 ($47,376.24); and
farmer 6 ($2,989.68).
There are still 5! – 2 = 118 remaining permutations in the Shapley value step present, and the results were averaged for each farmer. Thus, the imputation is as follows:
Theorem
1: Table
1 shows the characteristic function that produces the
shapley value for farmers 1, 2, 3, 4, 5, and 6 as follows: $18,092.40; $27,486.39;
$10,355.17; $5,702.19; $47,940.93; and $2,617.90. Teorema Shapley
value (super additive) i.e. the revenue of each player with coalition
system must be greater than or equal to revenue non-coalition (Brown
& Shoham, 2008).
This is evidenced by the increase in farmers' incomes with the concept of a
coalition based on Shapley values of: 100.45%, 100,386%, 100.76%, 101.22%,
100.33%, and 106.29%.
Theorem 2: The
core of the cooperative game is Shapley values based on characteristic functions
(Table 1
).
Evidence: Based on Shapley's value, the total revenue of coalition farmers 4-3 ($16,057.35), coalition farmers 4-3-1 ($34,149.75), and coalition farmers 5-4-3-1 ($82,090.68). This value is used to verify the revenue presented on Shapley's solution which is $18,092.40; $27,486.39; $10,355.17; $5,702.19; $47,940.93; and $2,617.90.
The revenue
generated by the player is higher than the revenue determined by the
characteristic function (Table 1), and an example of a verified coalition is
{1, 3, 6}. The total revenue earned by this particular coalition, as determined
by Shapley's solution, is $31,065.47,
which is the sum of the revenues earned individually by players 1, 3, and 6: $18,092.40; $10,355.17; and $ 2,617.90,
respectively. Shapley's value solution
shows the total revenue of the farmer coalition {1,3.6} is $31,065.47. This value is smaller than the characteristic function
(Table 1) which is v {1, 3, 6} = $30,857.99. It is conformity Shapley's
value concept in Definition 1, which
indicates that v(S) is the maximum value guaranteed by the S coalition by
coordinating the strategies of its members regardless of the activities of
other players (Brown
& Shoham, 2008).
The revenue of each farmer based on the scenario is shown
in Figure 2.