A Fuzzy Multi-objective Optimization Model in Sustainable Supply Chain Network Design Considering Financial Flow
الموضوعات : Fuzzy Optimization and Modeling JournalSeyed Hesamoddin Motevalli 1 , Adel Pourghader Chobar 2 , Maryam Ebrahimi 3 , Raheleh Alamiparvin 4
1 - Department of Future Studies, Eyvanekey University, Semnan, Iran
2 - Department of industrial engineering, Qazvin branch, Islamic Azad University, Qazvin, Iran
3 - Department of Information Technology Management, Islamic Azad University, Electronic Branch, Tehran, Iran
4 - Department of Industrial Engineering, Bonab Branch, Islamic Azad University, Bonab, Iran
الکلمات المفتاحية: Fuzzy Rule-based, Master Planning, Financial Flow, Goal Pprogramming, Fuzzy Multi-objective Solution Methods,
ملخص المقالة :
Integrated and coordinated planning of the main functions of the supply chain (procurement, production and distribution) often leads to economic efficiency and, as a result, more profit for the entire supply chain. On the other hand, the financial flow and the flow of goods and information are crucial and influential flows in any supply chain. In this paper, the main contribution is to integrated planning of procurement, production and distribution for a multi-product supply chain in order to maximize the producer's profit and also minimize the deviations of the producer's financial indicators by considering both the physical and financial flow. In this regard, the studded supply chain includes several suppliers, one producer and several customers. One of the prominent features of the proposed model is the use of mathematical programming to model the financial flow and achieve the producer's financial goals. Since the presented model is a bi-objective one, two fuzzy multi-objective interactive methods, Selim and Ozkarahan (SO) and Torabi and Hassini (TH) can adjust the degree of satisfaction of the objective functions have been applied. Next, the model is optimized using the goal programming method. Finally, the numerical results in optimizing the proposed fuzzy model show the proposed model's efficiency and the high quality of performance and applicability of the proposed model. The core achievement in the numerical results is that the total value of the distribution in the two models is equal. However, the SO method obtains more unbalanced solutions when the decision maker pays more attention to the first objective function.
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A Fuzzy Multi-objective Optimization Model in Sustainable Supply Chain Network Design Considering Financial Flow
Seyed Hesamoddin Motevallia, Adel Pourghader Chobarb,*, Maryam Ebrahimic, Raheleh Alamiparvind
aDepartment of Future Studies, Shomal University, Amol, Iran
bDepartment of Industrial Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
cDepartment of Information Technology Management, Islamic Azad University, Electronic Branch, Tehran, Iran
dDepartment of Industrial Engineering, Bonab Branch, Islamic Azad University, Bonab, Iran
A R T I C L E I N F O |
| A B S T R A C T The integrated and coordinated planning of the primary functions within the supply chain, including procurement, production, and distribution, often results in enhanced economic efficiency and, consequently, increased profitability for the entire supply chain. Conversely, the financial flow, as well as the flow of goods and information, are pivotal and influential elements within any supply chain. This paper aims to make a significant contribution by integrating the planning of procurement, production, and distribution within a multi-product supply chain to maximize the producer's profit while minimizing deviations in the producer's financial indicators, taking into account both the physical and financial flow. The studied supply chain encompasses multiple suppliers, a single producer, and numerous customers. As the presented mathematical programming model is bi-objective, two fuzzy multi-objective interactive methods, Selim and Ozkarahan (SO) and Torabi and Hassini (TH), have been employed to adjust the degree of satisfaction of the objective functions. Subsequently, the model is optimized using the goal programming method. The numerical results of optimizing the proposed fuzzy model demonstrate the efficiency, high-quality performance, and applicability of the model. A key finding in the numerical results is that the total value of the distribution in the two models is equal. However, the SO method yields more unbalanced solutions when the decision maker prioritizes the first objective function.
|
Article history: Received 17 December 2023 Revised 20 April 2024 Accepted 14 March 2024 Available 20 April 2024 | ||
Keywords: Fuzzy Rule-based Master Planning Financial Flow Goal Pprogramming Fuzzy Multi-objective Solution Methods
|
1. Introduction
In today's business landscape, traditional management practices characterized by limited integration in their processes have lost their effectiveness, giving way to new integrated approaches. This shift towards integration is also evident in supply chain management, as the industry seeks to address its challenges through an integrated approach for managing the flow of materials, goods, information, and finance, while also adapting to dynamic environmental conditions [14]. Supply chain management encompasses a collection of methods aimed at effectively integrating suppliers, manufacturers, warehouses, and stores. The management of inventories plays a crucial role in the success or failure of the chain, making the coordination of inventory levels throughout the supply chain a significant concern [1]. The primary objective of supply chain management is to efficiently control the flow of materials between suppliers, warehouses, and customers in order to minimize the total cost of the supply chain [3,17]. A substantial portion of the research in this field has focused on developing optimization models for integrating various activities such as purchasing, production, and distribution. The central concept of this approach involves the simultaneous optimization of decision variables across different activities, a departure from the traditional sequential optimization method [24].
In the realm of supply chain management, one of the primary challenges lies in the master planning of the supply chain. Master planning is tasked with determining the quantities of supply, production, and distribution for facilities at various levels of the supply chain over a medium-term period [33]. Historically, these activities were managed independently or sequentially, leading to excessive inventory and subpar chain performance. However, in today's competitive environment, the development of an effective tactical plan capable of integrating supply, production, and distribution plans within an efficient framework is crucial [11]. Financial flows, alongside goods and information flows, are fundamental components within all supply chains. Given the significant impact of financial performance on the overall supply chain performance, managing financial flows is critical [21]. While many successful integrated models have been proposed for tactical supply chain planning, most have overlooked decisions related to revenue, marketing activities, capital planning, and other financial aspects of the firm [11].
Financial factors play a pivotal role in influencing the planning of procurement, production, and distribution within the supply chain. Global financial factors such as exchange rates, customs, and insurance costs greatly influence the tactical decisions of the supply chain. Therefore, it is imperative to consider these factors in the master planning of the supply chain. Integrating financial factors into tactical supply chain models allows for a systematic assessment of the impact of production decisions on financial operations and facilitates the selection of an optimal combination of financial and production decisions, ultimately creating a competitive advantage for the company [9,5]. Hence, it is crucial to consider financial flow in supply chain models, particularly in scenarios involving capital-intensive activities, as financial operations complement production operations.
Financial operations are indeed crucial as they ensure the necessary financial resources for production and distribution activities [15]. Furthermore, financial resources are essential for investing in new production processes, equipment, innovative products, and expanding into new markets. Public sources of financing encompass loans from financial institutions and funds raised through the issuance of equity shares, with or without an initial public offering. To attract capital from these investment groups, companies must maintain a clear and satisfactory financial situation [29]. Evaluating a company's future investment and creditworthiness involves a process based on statistical and comparative analysis of financial statements [20]. Additionally, the analysis of financial statements allows financial institutions to assess companies operating in the same industries using specific criteria [35].
The primary objective of this research is to establish financial indicators for designing a sustainable supply chain. To achieve this, a multi-echelon and multi-product mathematical model is proposed to maximize profit and minimize deviations of financial indicators from their desired limits. Furthermore, the research integrates and coordinates procurement, production, distribution, and financial decisions (such as investment, debt, equity, etc.) based on operational resource constraints and financial limitations arising from factors such as exchange rates, value-added tax, income tax, and insurance, optimizing these aspects effectively.
The rest of the paper is organized as follows. In Section 2, an overview of the theoretical foundations of the subject is provided. In Section 3, the definition of the problem and the assumptions, the mathematical model by considering the financial and physical flow, as well as the description of the proposed solution method are provided. In Section 4, the numerical results of the model are analyzed. Finally, Section 5 is devoted to conclusions and suggestions.
2. Research Background
Several research items have been conducted regarding the simultaneous optimization of production and distribution. Moreover, master planning for production units is a fundamental issue that can affect the distribution of products. In this regard, the most important relevant research works are examined in this section. Moreover, the application of financial metrics in production and distribution planning is assessed.
Cohen & Sangwon [8] attempted to optimize the flow of materials, products, and product production mix within a supply chain network with a fixed structure by introducing a mixed spherical model. Chandra & Fisher [7] introduced a model titled "coordinated production and distribution planning," where the demand for each product in a period for each retailer is known. The objective function of this model aims to minimize the total cost, encompassing setup costs, production costs, transportation of manufactured products to retailers, and inventory costs. Pirkul & Jayarama [27] presented an integrated model of the mixed integer programming type, with an objective function seeking to minimize the costs of the entire chain, including establishment, operations and warehouses, variable production and distribution costs, transportation costs of raw materials from sellers to production centers, and transportation costs of finished products to customers. Patterson & Kim [25] introduced an integrated production-distribution model of probabilistic type, aiming to minimize costs related to production and distribution in the model's objective function, with constraints related to facility demand and capacity. Sabri & Benita [30] presented an integrated multi-objective model for strategic and operational planning in the supply chain, seeking to minimize chain costs at the strategic level and determine raw material purchase amounts and distribution at the operational level using economic scale formulas. Peng et al. [26] introduced a hierarchical model with strategic and tactical levels, focusing on purchasing, production, and distribution planning, with the outputs of the strategic level model serving as inputs for the tactical level model.
Although many researchers have emphasized the importance of financial flow in the supply chain, little research has been done in this field. The research items that have been done in the field of financial flow in the supply chain can be divided into two groups. The first group is those who have considered financial flow items as variables that model financial operations and are optimized like other supply chain planning variables. The second group is those who have considered the financial flow-related items as parameters in the constraints and objective function.
In the first group, Romero et al. [28] introduced a multi-cycle mathematical planning model that integrates planning and scheduling, while also considering financial flow and budget management in the chemical industry. Badell et al. [4] presented a mixed integer programming model for master planning and scheduling, taking into account financial flow and budget in the chemical industry. Burke et al. [6] developed a mixed-integer linear programming (MILP) model for a multi-level, multi-product chemical supply chain that optimizes planning, scheduling, financial flow, and budget variables simultaneously. The model, designed for multiple periods, aims to change the company's equity. Ge et al. [10] presented a two-level optimization model for the optimal design of a batch storage network, where production decisions in each activity are coordinated with financial operations resulting from the financial flow.
In the second group, Melo et al. [22] introduced a limited capacity dynamic location model for multi-product facilitation. The proposed MILP model simulates supply chain operational decisions while considering capital constraints. Vafadar et al. [34] presented a MILP model for the optimal configuration of the production and distribution network. The model aims to minimize the cost of the network according to financial constraints related to the exchange rate and customs fees. Hammami et al. [14] presented a supply chain network design model, which is a multi-product, multi-level, and multi-factory MILP model considering transfer price, supplier deployment cost, and cost allocation. Thevenin et al. [32] introduced a stochastic linear programming model for supply chain planning, similar to an asset and debt management model. The model includes constraints related to financial flow management and debt to maximize the expected value of net cash in the planning horizon.
Compared to other related works, the main contribution and novelty of this research is the simultaneous modeling of financial and physical flow in the supply chain. Moreover, the marginal contributions of this research are as follows:
· Optimizing a master planning model aims to maximize the producer's profit and minimize the deviations of the financial indicators from the optimal limits.
· Realization of the supply chain profit by considering different Financial parameters.
· Implementation of goal programming to handle all objective functions simultaneously.
· Presenting a new solution method approach for multi-objective models by combining mathematical programming and Selim and Ozkarahan (SO) and Torabi and Hassini (TH) approaches
It should be noted that using the fuzzy multi-objective TH and SO approaches, along with goal programming, enables the decision maker to make the final decision by choosing the appropriate solution based on the degree of satisfaction and priority of each objective function. Moreover, this approach is able to produce efficient, balanced and unbalanced solutions according to the decision-maker's preference.
3. Research Methodology
Figure 1 shows the structure of the chain investigated in this research. In this supply chain, a manufacturer produces different products using different raw materials that are provided by a set of suppliers located in foreign countries. Final products are delivered to different customers based on their demands. The manufacturer can order from a limited number of potential suppliers in each period. Therefore, the manufacturer considers factors such as the selling price of raw materials, exchange rates, customs duties, transportation costs, and transportation insurance of purchased materials to allocate orders to suppliers.
The proposed model makes decisions related to the amount of purchase of raw materials, the amount of production, the level of inventory of raw materials and finished products, and the amount of distribution of finished products under the limitation of financial and operational resources with the aim of maximizing the company's profit and minimizing the deviations of financial indicators from their desired limits. One of the prominent features of the proposed model is financial flow modeling with the help of goal programming.
The purpose of this research is to determine the best medium-term (less than one year) multi-period program with the goals of maximizing profits and minimizing the deviations of financial indicators from their optimal limits (defined by decision-makers) by considering operational and financial limitations in a joint and integrated manner for the following issues:
· Supply plan: the purchase amount of each material from each supplier in each period
· Production plan: the amount of production of each final product in each period
· Distribution schedule: the number of each final product to be delivered in each period
· Financial management: determining the amount of investment, the amount of equity, the amount of debt, the number of accounts receivable, the amount of cash, etc., in each period.
Figure 1. Structure of the investigated supply chain
The assumptions used in modeling the problem are as follows:
1. The supply chain is global, and raw material suppliers are based in other countries.
2. The facility capacity is limited at the producer level.
3. Each of the considered suppliers has the ability to supply all raw materials.
4. Suppliers do not have a supply limit and are able to produce the entire amount ordered.
5. The logistics network is multi-product.
6. The presented model is multi-period.
7. The number and location of customers, suppliers and production center is fixed and known in advance.
8. The production center has a safety stock (SS) of raw materials and finished products.
9. The transportation time between the components of the supply chain is considered insignificant.
10. Customers' demands must be answered at the end of each period, and it is not possible to fulfill them in subsequent periods.
11. Inventory of raw materials and manufactured products are transferred from one period to the next.
12. In each period, the amount of total assets is equal to the amount of total liabilities.
13. Total liabilities in each period are equal to the amount of short-term debt, long-term debt and equity in each period.
14. Current assets in each period are equal to the sum of cash, accounts receivable and inventory value in each period.
15. The total debt rate in each period is lower than the maximum optimal rate.
16. The turnover rate of fixed assets in each period is higher than the minimum optimal rate.
17. The ratio of current assets to short-term liabilities is greater than the minimum desired value in each period.
18. The company's profit margin rate is higher than the minimum desired rate.
19. The money coverage rate in each period is higher than the minimum optimal rate.
20. The return rate of assets in each period is higher than the minimum desired rate.
21. The rate of return of shareholders' assets in each period is higher than the minimum optimal rate.
22. The turnover ratio of accounts receivable in each period is higher than the minimum desired value.
3.1. Problem formulation
Indexes:
| K: index of final products | ||
J: Index of suppliers | L: index of customers | ||
T: Index of time periods | N: Index of financial metrics | ||
| Customer l's demand for product k in period t |
| The minimum amount of production of product k in period t that is economical. |
| The maximum production capacity of product k in period t |
| The amount of material i needed to produce each unit of product k |
| The amount of volume required to store each unit of material i purchased |
| The amount of volume needed to store each product unit k |
| Storage capacity (by volume) of the manufacturer's receiving warehouse |
| The storage capacity (in terms of volume) of the warehouse of the shipped goods |
| The purchase price of each unit of raw material i from supplier j in period t |
| The cost of maintaining each unit of material i in period t |
| Variable production cost of each unit of product k in period t |
| The cost of keeping each unit of product k in the production center in period t |
| The confidence reserve of product k in period t |
| Safety stock of raw material i in period t |
| Cost of ordering one unit from supplier j in period t |
|
|
| Cash rate at the end of period t |
| Depreciation rate at the end of period t |
| The cost of transporting each unit of product k from the production center to the customer l at the end of period t |
| The lower limit of the turnover rate of fixed assets at the end of period t |
| The selling price of each unit of product k at the end of period t |
| The upper limit of the long-term debt rate at the end of period t |
| Customs duty rate at the end of period t |
| Long-term interest rate at the end of period t |
| The lower bound of the money cover rate at the end of period t |
| The lower limit of the profit margin rate at the end of period t |
| Exchange rate at the end of period t |
| Minimum rate of return (return) of assets at the end of period t |
| The cost of transporting each unit of raw material i from supplier j to the production center during period t |
| The lower limit of the rate of return of shareholders' equity at the end of period t |
| Short-term interest rate at the end of period t |
| Import value-added tax rate at the end of period t |
| The upper limit of the total debt rate at the end of period t |
| The amount of investment for fixed assets during the period t |
| Income tax rate at the end of period t |
| Customs duty rate at the end of period t |
| The lower limit of the instantaneous ratio at the end of period t |
| The upper limit of the debt-to-equity rate at the end of period t |
| The lower limit of the accounts receivable turnover ratio at the end of period t |
| Transport insurance per unit of raw material i at the end of period t in dollars |
| The amount of material i purchased from supplier j in period t |
| The amount of downward deviation of financial index type n in period t |
| The production amount of product k under in period t |
| The amount of upward deviation of financial index type n in period t |
| Quantity of product k shipped to customer l in period t |
| The amount of cash available at the end of period t |
| The final inventory level of material i in the production center in period t |
| Depreciation at the end of period t |
| The final inventory level of product k at the production center in period t |
| The amount of income before paying interest and taxes at the end of period t |
| 1 if supplier j is given an order in period t, 0 otherwise |
| Total shareholders' capital at the end of the period |
| Fixed assets at the end of period t |
| Accounts receivable at the end of period t |
| Interest paid at the end of period t |
| Short-term liabilities at the end of period t |
| Inventory value at the end of period t |
| Long-term liabilities at the end of period t |
| Net sales at the end of period t |
| Taxable income during period t |
| New shares at the end of period t |
| Taxable operating income during period t |
| New shareholders' capital during period t |
| Current assets at the end of period t Accounts receivable at the end of period t |
| Net operating income after tax at the end of period t |
|
|
| (1) | |
| (2) | |
| (3) | |
(4) |
|
Moreover, the net sales value is calculated according to Eq. (5).
(5) |
|
In addition, the amount of depreciation at the end of each period is obtained based on Eq. (6).
(6) |
|
The total cost of logistics includes the total cost of purchase, production and distribution and is obtained according to Eq. (7).
(7) |
|
The total purchase cost includes ordering costs (
), the cost of purchasing raw materials (
), cost of transporting raw materials from the supplier to the manufacturer (
), transportation insurance for raw materials (
), maintaining inventory of raw materials (
, and customs fees (
, which can be estimated using Eqs. (8)-(16).
(8) |
| |
(9) |
| |
(10) |
| |
(11) |
| |
(12) |
| |
(13) |
| |
(14) |
| |
(15) |
| |
(16) |
| |
(17) |
|
The total cost of production (
) is equal to the sum of the variable costs of production (except the costs of raw materials) and the costs of maintaining the final inventory in the factory, which is calculated according to Eq. (18).
(18) |
|
The cost of distribution (
) is equal to the cost of transportation, which is calculated in Eq. (19).
(19) |
|
Second objective function: Minimizing the deviations of financial indicators from the desired limits. Because the final performance of the supply chain is affected by financial performance, financial flow management is very important. The study of financial flows is usually focused on the analysis of financial ratios. Financial ratios are indicators that analyze the company's financial position. For the optimization of financial indicators, goal programming (GP) has been used. For this purpose, the optimal limit of each index is determined according to the existing standards, and then, according to the goal programming, an attempt has been made to minimize the deviations of the financial indicators of the company's production center from the optimal limits.
The objective function related to the minimization of the deviations of the producer's financial indicators from the optimal limits is defined in the form of Eq. (20).
(20) |
|
3.1.2. Constraints of the Model
Inventory level constraints: The constraints of adjusting the inventory level in the factory are summarized as Eqs. (21)-(27).
(21) |
|
(22) |
|
(23) |
|
(24) |
|
(25) |
|
(26) |
|
(27) |
|
(28) |
|
Eq. (29) shows the minimum acceptable order quantity from the customer that is economically viable.
(29) |
|
(30) |
|
(31) |
|
(32) |
|
(33) |
|
(34) |
|
The operating income in each period is obtained from Eq. (35).
(35) |
|
Eq. (36) states that total liabilities must be equal to total assets.
(36) |
|
This Equation shows that the sum of fixed assets (
) and current assets (
) should be equal to the sum of total liabilities, which includes: long-term liabilities (
), short-term liabilities (
) and equity (
).
The amount of current assets in each period is obtained from Eq. (37).
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