Mathematics

Editorial

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5 pages, 149 KiB

Open AccessEditorial

Preface to the Special Issue “Mathematical Modelling and Optimization of Service Supply Chain”

by Yong He

Mathematics 2024, 12(14), 2292; https://doi.org/10.3390/math12142292 - 22 Jul 2024

Viewed by 736

Abstract

In recent years, as the world economy has grown, increasingly, service-oriented systems play a more significant role in the supply chain [...] Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

Research

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24 pages, 1396 KiB

Open AccessArticle

Multi-Objective Green Closed-Loop Supply Chain Management with Bundling Strategy, Perishable Products, and Quality Deterioration

by Golnaz Hooshmand Pakdel, Yong He and Sina Hooshmand Pakdel

Mathematics 2024, 12(5), 737; https://doi.org/10.3390/math12050737 - 29 Feb 2024

Viewed by 1028

Abstract

This study presents a four-objective mathematical model to improve closed-loop supply chain (CLSC) management. The aim of this research is to reduce the costs of the entire chain, risk, emission of pollutants, and time to deliver the product to the customer in uncertain [...] Read more.

This study presents a four-objective mathematical model to improve closed-loop supply chain (CLSC) management. The aim of this research is to reduce the costs of the entire chain, risk, emission of pollutants, and time to deliver the product to the customer in uncertain demand condition. In this paper, the NSGAII algorithm is used to solve the model. In this algorithm, among the answers of each generation, a number of them are selected using the two-run tournament selection method. In the binary selection method, the answers are randomly selected from the population, and then a comparison is made between these two answers, and whichever is better is finally selected. The selection criteria in NSGA-II are, firstly, the rank, and secondly, the crowding distance related to the answer. Also, the performance of the NSGA-II algorithm on the same model and data has been compared with the MOPSO algorithm. In the proposed algorithm, if it encounters an impossible solution, it exits the local mode and solves the problem in global conditions. The results show that the proposed method strikes a better balance between discovery and efficiency criteria and avoids falling into local optima. Therefore, in addition to its effectiveness in discovering optimal answers, the genetic-based method has high speed and subsequently, high convergence and diversity rates compared to the particle swarm method. Also, compared to previous methods in the green closed-loop supply chain, the proposed method is better than the modified genetic algorithm, reducing the costs of the chain by about 2.38%. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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21 pages, 1895 KiB

Open AccessArticle

Self-Built or Third-Party Blockchain Traceability Strategy in a Dual-Channel Supply Chain Considering Consumers’ Traceability Awareness

by Yuling Sun, Xiaomei Song, Xiang Fang and Jian Guo

Mathematics 2023, 11(20), 4312; https://doi.org/10.3390/math11204312 - 16 Oct 2023

Cited by 1 | Viewed by 1375

Abstract

Blockchain is widely used in the manufacturing industry. This paper establishes a dual-channel supply chain composed of a manufacturer and an e-retailer. A monopoly manufacturer conducts indirect online selling through retailers as well as direct offline selling. The manufacturer chooses to adopt a [...] Read more.

Blockchain is widely used in the manufacturing industry. This paper establishes a dual-channel supply chain composed of a manufacturer and an e-retailer. A monopoly manufacturer conducts indirect online selling through retailers as well as direct offline selling. The manufacturer chooses to adopt a self-built blockchain traceability system (SBT) or a third-party blockchain traceability system (TBT). Game analysis is developed to depict the pricing decision for the manufacturer and e-retailer. The optimal pricing decisions of the supply chain between manufacturer and e-retailer for different blockchain traceability strategies are obtained. We explore the influence of consumers’ traceability awareness on the decisions of dual-channel supply chain members when adopting different blockchain traceability strategies. The main results show that when the fee paid to the blockchain service provider is low, the manufacturer will prefer to adopt TBT. Moreover, we prove that consumers’ traceability awareness, the cost of adopting TBT, the blockchain traceability technology level, and the research and development cost factor of blockchain technology could affect the decisions of supply chain members. Finally, some management suggestions are provided. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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30 pages, 2623 KiB

Open AccessArticle

Robust Bi-Level Optimization for Maritime Emergency Materials Distribution in Uncertain Decision-Making Environments

by Cong Wang, Zhongxiu Peng and Wenqing Xu

Mathematics 2023, 11(19), 4140; https://doi.org/10.3390/math11194140 - 30 Sep 2023

Cited by 3 | Viewed by 1480

Abstract

Maritime emergency materials distribution is a key aspect of maritime emergency responses. To effectively deal with the challenges brought by the uncertainty of the maritime transport environment, the multi-agent joint decision-making location-routing problem of maritime emergency materials distribution (MEMD-LRP) under an uncertain decision-making [...] Read more.

Maritime emergency materials distribution is a key aspect of maritime emergency responses. To effectively deal with the challenges brought by the uncertainty of the maritime transport environment, the multi-agent joint decision-making location-routing problem of maritime emergency materials distribution (MEMD-LRP) under an uncertain decision-making environment is studied. First, two robust bi-level optimization models of MEMD-LRP are constructed based on the effect of the uncertainty of the ship’s sailing time and demand of emergency materials at the accident point, respectively, on the premise of considering the rescue time window and priority of emergency materials distribution. Secondly, with the help of robust optimization theory and duality theory, the robust optimization models are transformed into robust equivalent models that are easy to solve. Finally, a hybrid algorithm based on the ant colony and tabu search (ACO-TS) algorithm solves multiple sets of numerical cases based on the case design of the Bohai Sea area, and analyzes the influence of uncertain parameters on the decision making of MEMD-LRP. The study of MEMD-LRP under uncertain decision-making environments using bi-level programming and robust optimization methods can help decision makers at different levels of the maritime emergency logistics system formulate emergency material reserve locations and emergency material distribution schemes that can effectively deal with the uncertainty in maritime emergencies. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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18 pages, 784 KiB

Open AccessArticle

Strategy Analysis of Fresh Agricultural Enterprises in a Competitive Circumstance: The Impact of Blockchain and Consumer Traceability Preferences

by Yuling Sun, Xiaomei Song, Yihao Jiang and Jian Guo

Mathematics 2023, 11(5), 1090; https://doi.org/10.3390/math11051090 - 22 Feb 2023

Cited by 4 | Viewed by 1792

Abstract

Blockchain technology allows fresh agricultural enterprises to share records stored on the chain, and the technology can benefit information management systems, such as decentralization and transparency. This study uses game theory to examine a blockchain introduction strategy for fresh agricultural enterprises in a [...] Read more.

Blockchain technology allows fresh agricultural enterprises to share records stored on the chain, and the technology can benefit information management systems, such as decentralization and transparency. This study uses game theory to examine a blockchain introduction strategy for fresh agricultural enterprises in a competitive environment, considering consumer traceability preferences. We establish a pricing decision model in traditional and blockchain traceability modes and identify optimal solutions. Additionally, we analyze the impact of the blockchain introduction strategy, consumer preferences, and blockchain influence factor on optimal pricing decisions. The results indicate that the introduction of blockchain could improve the profits of enterprises under certain conditions. Moreover, consumer traceability preferences and the blockchain influence factor could significantly affect the blockchain introduction strategy. We also discover that when the blockchain influence factor meets a certain range, introducing blockchain technique in the traceability system could shift demand from traditional enterprises to blockchain enterprises. The total market demand for blockchain enterprises under the blockchain traceability mode will increase, whereas that of traditional enterprises under the blockchain traceability mode will decrease. Both consumer traceability preferences and the blockchain influence factor could significantly affect optimal pricing. Finally, some management suggestions are provided for the traceability of fresh agricultural enterprises based on the research conclusions. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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23 pages, 2880 KiB

Open AccessArticle

Decisions for a Retailer-Led Low-Carbon Supply Chain Considering Altruistic Preference under Carbon Quota Policy

by Xiao Zhou and Xiancong Wu

Mathematics 2023, 11(4), 911; https://doi.org/10.3390/math11040911 - 10 Feb 2023

Cited by 6 | Viewed by 1799

Abstract

With the release of the national energy-saving emission reduction policy and the improvement of consumers’ awareness of environmental protection, the demand for low-carbon products is growing rapidly. In a retailer-led low-carbon supply chain, the increased cost of carbon emission reduction puts manufacturers at [...] Read more.

With the release of the national energy-saving emission reduction policy and the improvement of consumers’ awareness of environmental protection, the demand for low-carbon products is growing rapidly. In a retailer-led low-carbon supply chain, the increased cost of carbon emission reduction puts manufacturers at a disadvantage. Under the carbon quota policy, to improve manufacturers’ profits as well as enhance carbon emission reduction, this paper studies the players’ decisions in a low-carbon supply chain consisting of one dominant retailer and one manufacturer. To maintain the supply chain’s stability and sustainability, the dominant retailer tends to employ altruistic preference policies towards the manufacturer. The optimal decision, carbon emission reduction and supply chain profit are compared and analyzed under three decision models: (i) centralized decision, (ii) decentralized decision without altruistic preference and (iii) decentralized decision with altruistic preference. The results indicate that the carbon emission reduction rate, market demand and profit in the centralized model are higher than in the decentralized model. The retailer’s altruistic preference is beneficial to the improvement of carbon emission reduction, market demand and the profit of the manufacturer and the supply chain. Under certain conditions, carbon trading can effectively reduce the cost pressure of manufacturers and improve the level of carbon emission reduction and the overall profit of the supply chain. These results will guide low-carbon supply chain decision-making and provide insight into the research of irrational behaviors in supply chain decision-making under carbon policies. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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35 pages, 738 KiB

Open AccessArticle

Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements

by Yonit Barron

Mathematics 2023, 11(4), 864; https://doi.org/10.3390/math11040864 - 8 Feb 2023

Cited by 4 | Viewed by 1551

Abstract

We study an inventory control problem with two storage facilities: a primary warehouse (PW) of limited capacity M, and a subsidiary one (SW) of sufficiently large capacity. Two types of customers are considered: individual customers arriving at (positive and negative) linear rates [...] Read more.

We study an inventory control problem with two storage facilities: a primary warehouse (PW) of limited capacity M, and a subsidiary one (SW) of sufficiently large capacity. Two types of customers are considered: individual customers arriving at (positive and negative) linear rates governed by a Markov chain, and retailers arriving according to a Markov arrival process and bringing a (positive and negative) random number of items. The PW is managed according to a triple-parameter band policy

(M, S, s),

0 \leq s < S \leq M,

under a lost sales assumption. Under this policy, as soon as the stock level at the PW falls below s, a refilling to S is performed by a distributor after a random lead-time. However, if the stock exceeds level S when the distributor arrives, no refilling is carried out, and only maintenance services are performed. Items that exceed level M are transferred to the SW at a negligible amount of time for those used in related products. Our cost structure includes a fixed order cost, a variable cost for each item supplied by the distributor, a cost for the additional maintenance, a salvage payment for each transferred item from the PW to the SW, and a loss cost for each unsatisfied item due to demands. We seek to determine the optimal thresholds that minimize the expected overall cost under the discounted criterion. Applying first-passage time results, we present a simple set of equations that provide managers with a useful and an efficient tool to derive the optimal thresholds. Sensitivity analysis and fruitful conclusions along with future scope of research directions are provided. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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26 pages, 378 KiB

Open AccessArticle

Are State-Owned Enterprises Equally Reliable Information Suppliers? An Examination of the Impacts of State Ownership on Earnings Management Strategies of Chinese Enterprises

by Shan Lu, Peng Wu, Lei Gao and Richard Gifford

Mathematics 2023, 11(4), 814; https://doi.org/10.3390/math11040814 - 5 Feb 2023

Cited by 2 | Viewed by 1794

Abstract

Earnings management refers to a company’s use of either accounting techniques (accrual-based earnings management) or real economic activities (real earnings management) to manipulate reported earnings and mislead users of financial information. It often indicates serious ethical issues in a company’s management, which will [...] Read more.

Earnings management refers to a company’s use of either accounting techniques (accrual-based earnings management) or real economic activities (real earnings management) to manipulate reported earnings and mislead users of financial information. It often indicates serious ethical issues in a company’s management, which will affect the reliability and sustainability of a firm’s services in the supply chain. Using A-share listed Chinese firms on the Shanghai and Shenzhen Stock Exchanges, we investigated the impacts of state ownership on management’s decision to select real or accrual-based earnings management strategies. We found that state-owned enterprises (SOEs) tend to favor real earnings management over accrual-based earnings management more than non-SOEs. Furthermore, those SOEs that are controlled by the central government engage in real earnings management more often than those controlled by local governments. We also examined whether media attention and litigation interact with state ownership to affect earnings management. We found that SOEs, especially central SOEs, with a high level of media attention or an incidence of litigation, are more likely to use real earnings management. Our research can assist firms in making better decisions in selecting business partners and service suppliers in an emerging market through the assessment of management integrity. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

16 pages, 1983 KiB

Open AccessArticle

Optimal Decision-Making of Retailer-Led Dual-Channel Green Supply Chain with Fairness Concerns under Government Subsidies

by Lei Song, Qi Xin, Huilin Chen, Lutao Liao and Zheyi Chen

Mathematics 2023, 11(2), 284; https://doi.org/10.3390/math11020284 - 5 Jan 2023

Cited by 10 | Viewed by 2239

Abstract

Green innovation is the inevitable trend in the development of the supply chain, and thus the government adopts subsidy policies for the relevant enterprises to enhance their enthusiasm for green development. In view of the manufacturers’ fairness concerns in the dual-channel green supply [...] Read more.

Green innovation is the inevitable trend in the development of the supply chain, and thus the government adopts subsidy policies for the relevant enterprises to enhance their enthusiasm for green development. In view of the manufacturers’ fairness concerns in the dual-channel green supply chain that is composed of manufacturers and retailers, we propose a novel Stackelberg game model led by retailers and analyze the impact of manufacturers’ fairness concerns on the decision-making of manufacturers and retailers in the dual-channel green supply chain under government subsidies. The results show that only the wholesale price of products, manufacturers’ profits, and retailers’ profits are affected by manufacturer’s fair concerns. When manufacturer has fair concerns, product greenness and profits of supply chain members rise with the increase in government subsidies. The results can offer an effective reference for the dual-channel supply chain members with fairness concerns to make optimal decisions under government subsidies. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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19 pages, 778 KiB

Open AccessArticle

Using Four Metaheuristic Algorithms to Reduce Supplier Disruption Risk in a Mathematical Inventory Model for Supplying Spare Parts

by Komeyl Baghizadeh, Nafiseh Ebadi, Dominik Zimon and Luay Jum’a

Mathematics 2023, 11(1), 42; https://doi.org/10.3390/math11010042 - 22 Dec 2022

Cited by 8 | Viewed by 4705

Abstract

Due to the unexpected breakdowns that can happen in various components of a production system, failure to reach production targets and interruptions in the process of production are not surprising. Since this issue remains for manufactured products, this halting results in the loss [...] Read more.

Due to the unexpected breakdowns that can happen in various components of a production system, failure to reach production targets and interruptions in the process of production are not surprising. Since this issue remains for manufactured products, this halting results in the loss of profitability or demand. In this study, to address a number of challenges associated with the management of crucial spare parts inventory, a mathematical model is suggested for the determination of the optimal quantity of orders, in the case of an unpredicted supplier failure. Hence, a production system that has various types of equipment with crucial components is assumed, in which the crucial components are substituted with spare parts in the event of a breakdown. This study’s inventory model was developed for crucial spare parts based on the Markov chain process model for the case of supplier disruption. Moreover, for optimum ordering policies, re-ordering points, and cost values of the system, four metaheuristic algorithms were utilized that include Grey Wolf Optimizer (GWO), Genetic Algorithm (GA), Moth–Flame Optimization (MFO) Algorithm, and Differential Evolution (DE) Algorithm. Based on the results, reliable suppliers cannot meet all of the demands; therefore, we should sometimes count on unreliable suppliers to reduce unmet demand. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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21 pages, 4219 KiB

Open AccessArticle

Strategic Licensing of Green Technologies to a Brown Rival: A Game Theoretical Analysis

by Liu Liu, Ying Yuan, Xiaoya Wang and Hongfu Huang

Mathematics 2022, 10(23), 4433; https://doi.org/10.3390/math10234433 - 24 Nov 2022

Cited by 2 | Viewed by 1447

Abstract

This paper studies a green manufacturer’s strategic licensing of its green technology to a brown rival under the consideration of the green manufacturer’s environmental concerns. Consumers in the market have green awareness. Adopting the green technology not only helps manufacturers to reduce carbon [...] Read more.

This paper studies a green manufacturer’s strategic licensing of its green technology to a brown rival under the consideration of the green manufacturer’s environmental concerns. Consumers in the market have green awareness. Adopting the green technology not only helps manufacturers to reduce carbon emissions, but also to increase market sizes. The green manufacturer can choose from three technology licensing strategies, i.e., no licensing (N), royalty licensing (R) or fixed-fee licensing (F). The equilibrium licensing strategy can be derived by comparing the respective payoff after adopting the three strategies. It is found that the green manufacturer should choose fixed-fee licensing strategy when the market size expansion effect is strong, and the competition intensity is moderate; otherwise, the green manufacturer should choose royalty licensing strategy. Furthermore, it is found that when the green manufacturer is more concerned about environmental impacts, it will be more willing to choose fixed-fee licensing strategy, rather than royalty licensing strategy. Through numerical tests, some interesting results are also found. For example, the brown manufacturer might be hurt even if the cost reduction effect of technology licensing is relatively stronger. Moreover, it is found that consumer surplus and social welfare nonmonotonically change with the substitution level. In summary, this research tries to provide some guidelines to the industry and the society on better managing green technology diffusions. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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12 pages, 369 KiB

Open AccessArticle

Queueing-Inventory System for Two Commodities with Optional Demands of Customers and MAP Arrivals

by N. Anbazhagan, Gyanendra Prasad Joshi, R. Suganya, S. Amutha, V. Vinitha and Bhanu Shrestha

Mathematics 2022, 10(11), 1801; https://doi.org/10.3390/math10111801 - 25 May 2022

Cited by 5 | Viewed by 1623

Abstract

This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second item or service (they [...] Read more.

This research analyses the performance of a perishable queueing-inventory system for two commodities with optional customers demands. We assume in the article that all customers who come to the system can only purchase the first item or the second item or service (they do not purchase both items). This is the original aspect of the paper. We show the significance of the impact of optional demands on the system’s performance, which is the purpose of the paper. In this system, customers arrive, using the Markovian arrival process (MAP), to a demand for a single unit. The system is composed of a waiting hall with a limited capacity of F. The arriving customer observes the waiting hall is filled to capacity or the stock stage is zero, and they decide to leave the system. In the steady-state case, the joint probability distribution for the first commodity, the second commodity, and the number of customers in the system are computed using matrix geometric methods. We evaluate diverse system performance measures. Finally, we provide a numerical illustration of the optimal value for diverse parameters of the system, which highlights the results and implications of the article. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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17 pages, 2291 KiB

Open AccessArticle

Can a Restaurant Benefit from Joining an Online Take-Out Platform?

by Peng Zhang, Sisi Ju and Hongfu Huang

Mathematics 2022, 10(9), 1392; https://doi.org/10.3390/math10091392 - 21 Apr 2022

Cited by 7 | Viewed by 2263

Abstract

In this paper, we study a restaurant’s take-out model choice and the coordination of an online take-out supply chain. To this end, we first derive the restaurant’s optimal price and/or platform’s commission rate under the restaurant’s three possible take-out models: do not provide [...] Read more.

In this paper, we study a restaurant’s take-out model choice and the coordination of an online take-out supply chain. To this end, we first derive the restaurant’s optimal price and/or platform’s commission rate under the restaurant’s three possible take-out models: do not provide online take-out service (NTO model), provide take-out service by joining an online take-out platform (TOF model), or provide online take-out service by itself (TOH model). We investigate the restaurant’s optimal take-out model choice. We then derive the optimal decisions of price and the take-out model under centralization, and study the online take-out supply chain coordination problem. We find that, first, the restaurant may not always benefit from providing online take-out service. It will be beneficial only if the incremental demand generated by take-out service is high. Second, under the centralized supply chain, the TOF model is always better than the TOH model. Meanwhile, when the incremental demand is high, the restaurant should choose the TOF model; otherwise, the NTO model is better. Third, we find that the restaurant’s take-out price and model choice decisions under a decentralized supply chain are both inconsistent with that under the centralized supply chain. Last, we design a sales reward contract which can achieve the price and model choice coordination as well as win-win outcomes for all supply chain members. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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23 pages, 20801 KiB

Open AccessArticle

Research on Location-Routing Problem of Maritime Emergency Materials Distribution Based on Bi-Level Programming

by Zhongxiu Peng, Cong Wang, Wenqing Xu and Jinsong Zhang

Mathematics 2022, 10(8), 1243; https://doi.org/10.3390/math10081243 - 10 Apr 2022

Cited by 17 | Viewed by 2641

Abstract

To solve the location-routing problem of maritime emergency materials distribution (MEMD-LRP) of multi-agent joint decision, a bi-level programming model of MEMD-LRP is constructed. The model is established on the premise of considering the rescue time window and emergency materials distribution priority, aiming at [...] Read more.

To solve the location-routing problem of maritime emergency materials distribution (MEMD-LRP) of multi-agent joint decision, a bi-level programming model of MEMD-LRP is constructed. The model is established on the premise of considering the rescue time window and emergency materials distribution priority, aiming at the strong regional characteristics of maritime accidents, strong timeliness of maritime rescue, great difficulty of rescue, high cost of rescue, and so on. From the point of view of the emergency management department, the upper level makes the location decision to minimize the construction cost of the shore-based emergency materials reserves and the time satisfaction loss cost of the accident point. From the point of view of the commercial rescue unit, the lower level plans the routes by minimizing the cost of emergency material distribution, ship transportation, ship dispatch, and time penalty. A hybrid algorithm of the ant colony and tabu search is designed to solve the model, and an example is designed and analyzed based on the case of the Bohai Sea to verify the effectiveness of the model and algorithm. Modeling and algorithm design based on bi-level programming can help decision-makers at different levels in maritime emergency logistics systems to make more scientific and reasonable decisions to improve the service capability of the maritime emergency logistics system. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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Review

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19 pages, 1287 KiB

Open AccessReview

Mathematical Modeling and Optimization of Platform Service Supply Chains: A Literature Review

by Xiaotong Guo and Yong He

Mathematics 2022, 10(22), 4307; https://doi.org/10.3390/math10224307 - 17 Nov 2022

Cited by 7 | Viewed by 2738

Abstract

With the increasing importance of the platform service supply chain (PSSC) in creating economic value, academic research is paying more and more attention to it. The current literature’s research topics and problems cover broad areas. This review adopts bibliometric analysis and thematic analysis [...] Read more.

With the increasing importance of the platform service supply chain (PSSC) in creating economic value, academic research is paying more and more attention to it. The current literature’s research topics and problems cover broad areas. This review adopts bibliometric analysis and thematic analysis to review the related literature systematically and comprehensively. We divided the literature about PSSC into six groups according to the literature’s research topic and research question. Each literature’s research problem and research method are categorized and summarized. Our review results demonstrate that the supply chain’s members’ operational decisions and the supply chain’s coordination are two main types of research questions. Pricing decisions have received the most attention. In terms of the research method, game models are the most common method used in research to achieve the optimization of the PSSC. Full article

(This article belongs to the Special Issue Mathematical Modelling and Optimization of Service Supply Chain)

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