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Mathematics
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Modeling and Optimization in Supply Chain Management
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Modeling and Optimization in Supply Chain Management

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 25 December 2026 | Viewed by 5090

Special Issue Editor

Prof. Dr. Rafael Guillermo García-Cáceres

E-Mail Website
Guest Editor
School of Industrial Engineering, Universidad Pedagógica y Tecnológica de Colombia-UPTC, Sogamoso, Colombia
Interests: fuzzy front end; supplier involvement; multicriteria acceptability analysis; fuzzy multi-criteria

Special Issue Information

Dear Colleagues,

We are pleased to announce a Special Issue on “Modelling and Optimization in Supply Chain Management”, to be published in Mathematics. This Special Issue aims to explore contemporary advances in modeling and optimization techniques within supply chain management (SCM). Recognizing the increasing complexity and interconnectedness of modern supply chains, we seek contributions that address both strategic and tactical planning aspects through integrated modeling approaches.

We welcome original research and comprehensive reviews that delve into areas such as multi-echelon inventory systems, demand forecasting, production planning, distribution logistics, and risk management. Emphasis is placed on methodologies that enhance decision support systems, making them more reflective of real-world scenarios.

Submissions employing advanced mathematical models, simulation techniques, and optimization algorithms to solve practical SCM problems are particularly encouraged.

Additionally, studies that incorporate emerging technologies, such as artificial intelligence and machine learning, to improve supply chain resilience and efficiency will be highly regarded.

Through this Special Issue, we aim to bridge the gap between theoretical modeling and practical application, fostering a deeper understanding of how integrated approaches can lead to more robust and adaptable supply chains.

Prof. Dr. Rafael Guillermo García-Cáceres
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • supply chain management
  • integrated modeling
  • optimization techniques
  • strategic planning
  • tactical planning
  • decision support systems
  • inventory management
  • production planning
  • distribution logistics
  • risk management
  • simulation
  • artificial intelligence
  • machine learning
  • resilience
  • efficiency

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Published Papers (7 papers)

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Research

35 pages, 3006 KB  
Article
Analysis of a Serial Supply Network Operating Under VMI Policy with Stochastic Replenishment Times and External Demand
by Georgios Varlas, Stelios Koukoumialos, Alexandros Diamantidis, Michael Vidalis and Evangelos Ioannidis
Mathematics 2026, 14(10), 1696; https://doi.org/10.3390/math14101696 - 15 May 2026
Viewed by 126
Abstract
An algorithm based on matrix analytic methods for the exact numerical performance evaluation of a two-echelon vendor-managed inventory system with lost sales is presented in this paper. Both supply and demand uncertainties are taken into consideration. Lead times are modeled using a phase-type [...] Read more.
An algorithm based on matrix analytic methods for the exact numerical performance evaluation of a two-echelon vendor-managed inventory system with lost sales is presented in this paper. Both supply and demand uncertainties are taken into consideration. Lead times are modeled using a phase-type (Coxian) distribution with two phases, while the stochastic nature of external demand is captured with a compound Poisson distribution comprised of a pure Poisson arrival process and a discrete empirical distribution for the demand of individual customers. A computer program based on the algorithm is developed and then it is used for an extensive numerical investigation with a view to obtain insights of possible managerial importance. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
29 pages, 3673 KB  
Article
Game-Theoretic Analysis of Cooperative Advertising Decisions in Production–Retail Channels with Seasonal Demand
by Yao-Hung Hsieh, Jonas Chao-Pen Yu and Jhao-Yi Guan
Mathematics 2026, 14(4), 745; https://doi.org/10.3390/math14040745 - 23 Feb 2026
Viewed by 697
Abstract
This paper investigates cooperative advertising decisions in production–retailing channels for seasonal products under demand seasonality. We develop analytical game-theoretic models to examine how advertising cooperation influences channel coordination and profit distribution between manufacturers and retailers. Two channel structures are considered: a single-manufacturer–single-retailer channel [...] Read more.
This paper investigates cooperative advertising decisions in production–retailing channels for seasonal products under demand seasonality. We develop analytical game-theoretic models to examine how advertising cooperation influences channel coordination and profit distribution between manufacturers and retailers. Two channel structures are considered: a single-manufacturer–single-retailer channel and a single-manufacturer channel with two competing retailers. For each structure, Stackelberg and Nash equilibrium settings are analyzed and compared. Our results show that cooperative advertising can serve as an effective coordination mechanism by increasing advertising intensity and improving channel efficiency. Retailers always benefit from manufacturer-supported advertising through cost sharing and higher profitability, whereas the manufacturer’s incentive to participate depends on whether demand expansion outweighs shared advertising costs. Importantly, we demonstrate that channel leadership plays a critical role: the Stackelberg equilibrium consistently dominates the Nash equilibrium in terms of total channel profit. This study contributes to the cooperative advertising literature by explicitly incorporating demand seasonality and competing retailers, and by clarifying when cooperative advertising leads to Pareto improvements in seasonal supply chains. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
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65 pages, 4595 KB  
Article
Dual-Leverage Effects of Embeddedness and Emission Costs on ESCO Financing: Engineering-Driven Design and Dynamic Decision-Making in Low-Carbon Supply Chains
by Liurui Deng, Lingling Jiang and Shunli Gan
Mathematics 2026, 14(3), 522; https://doi.org/10.3390/math14030522 - 1 Feb 2026
Viewed by 489
Abstract
Against the backdrop of carbon quota trading policies and Energy Performance Contracting (EPC), Energy Service Companies (ESCOs) engage in supply chain emission reduction via embedded low-carbon services. However, the impact mechanism of their financing mode selection on emission reduction efficiency and economic benefits [...] Read more.
Against the backdrop of carbon quota trading policies and Energy Performance Contracting (EPC), Energy Service Companies (ESCOs) engage in supply chain emission reduction via embedded low-carbon services. However, the impact mechanism of their financing mode selection on emission reduction efficiency and economic benefits has not been fully revealed, and there is a lack of support from a systematic theoretical and engineering design framework. Therefore, this study innovatively constructs a multi-agent Stackelberg game model with bank financing, green bond financing, and internal factoring financing. We incorporate the embedding degree, emission reduction cost coefficient, and financing mode selection into a unified analysis framework. The research findings are as follows: (1) There is a significant positive linear relationship between supply chain profit and the embedding degree. In contrast, the profit of ESCOs shows an inverted “U-shaped” change trend. Moreover, there is a sustainable cooperation threshold for each of the three financing modes. (2) Green bond financing can significantly increase the overall emission reduction rate of the industrial supply chain in high-embedding-degree scenarios. However, due to emission reduction investment cost pressure, ESCOs tend to choose bank financing. (3) The dynamic change of the emission reduction investment cost coefficient will trigger a reversal effect on the financing preferences of the supply chain and ESCOs. This study unveils the internal mechanism of multi-party decision-making in the low-carbon industrial supply chain and is supported by cross-country institutional evidence and comparative case-based analysis, providing a scientific basis and engineering design guidance for optimizing ESCO financing strategies, crafting incentive contracts, and enhancing government subsidy policies. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
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25 pages, 968 KB  
Article
Profit-Oriented Tactical Planning of the Palm Oil Biodiesel Supply Chain Under Economies of Scale
by Rafael Guillermo García-Cáceres, Omar René Bernal-Rodríguez and Cesar Hernando Mesa-Mesa
Mathematics 2026, 14(3), 438; https://doi.org/10.3390/math14030438 - 27 Jan 2026
Viewed by 543
Abstract
The growing demand for sustainable energy alternatives highlights the need for decision support tools in biodiesel supply chains. This study proposes a mixed-integer programming (MIP) model for tactical planning in the palm oil biodiesel supply chain, focusing on refining, blending, and distribution. The [...] Read more.
The growing demand for sustainable energy alternatives highlights the need for decision support tools in biodiesel supply chains. This study proposes a mixed-integer programming (MIP) model for tactical planning in the palm oil biodiesel supply chain, focusing on refining, blending, and distribution. The model incorporates economies of scale, inventory, and transport constraints and is enhanced with valid inequalities (VI) and a warm-start heuristic procedure (WS) to improve computational efficiency. Computational experiments on simulated instances with up to 6273 variables and 47 million iterations demonstrated robust performance, achieving solutions within 15 min. The model also reduced time-to-first-feasible (TTFF) solutions by 60–75% and CPU times by 17–21% compared to the baseline, confirming its applicability in realistic contexts. The proposed model provides actionable insights for managers by supporting decisions on facility scaling, product allocation, and profitability under supply–demand constraints. Beyond palm oil biodiesel, the formulation and its VI + WS enhancement provide a transferable blueprint for tactical planning in other process industry and renewable energy supply chains, where (i) multi-echelon flow conservation holds and (ii) discrete operating scales couple throughput with fixed/variable cost structures, enabling fast scenario analyses under changing prices, demand, and capacities. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
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40 pages, 4871 KB  
Article
Pricing Optimization for Inventory with Integrated Storage and Credit Constraints
by Hui-Ling Yang, Chun-Tao Chang and Yao-Ting Tseng
Mathematics 2026, 14(1), 163; https://doi.org/10.3390/math14010163 - 31 Dec 2025
Viewed by 642
Abstract
Price is a pivotal determinant of market demand, as higher prices typically reduce sales while lower prices stimulate them. Thus, incorporating price-dependent demand into inventory models is both realistic and necessary. In practice, limited storage capacity often forces retailers to rent additional space, [...] Read more.
Price is a pivotal determinant of market demand, as higher prices typically reduce sales while lower prices stimulate them. Thus, incorporating price-dependent demand into inventory models is both realistic and necessary. In practice, limited storage capacity often forces retailers to rent additional space, motivating the adoption of two-warehouse systems. Trade credit also plays a critical role in supply chain management: suppliers may offer cash discounts or deferred payments to encourage larger orders, while retailers extend credit to customers to boost sales. To reduce default risk, however, retailers usually provide only partial credit. Considering the time value of money, costs and profits are assessed using discounted cash-flow analysis to account for payment delays and inflation. This study develops an integrated supplier–retailer–customer chain model that (1) incorporates price-dependent demand, (2) includes a rented warehouse for limited storage, (3) considers partial trade credit, (4) links two-level trade credit terms to order quantity, and (5) evaluates financial performance on a present-value basis. The model aims to maximize total profit by determining optimal price, replenishment cycle, and order quantity. Numerical and sensitivity analyses confirm that extending supplier credit can lower prices and improve overall profitability, offering useful insights for strategic inventory management. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
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31 pages, 1203 KB  
Article
Mathematical Modeling and Optimization of Sustainable Production–Inventory Systems Using Particle Swarm Algorithms
by Chi-Jie Lu, Chih-Te Yang, Dong-Ying Jiang and Ming-Shu Chen
Mathematics 2025, 13(24), 3912; https://doi.org/10.3390/math13243912 - 7 Dec 2025
Viewed by 651
Abstract
This research examines a multinational supply chain inventory problem involving one manufacturer and multiple retailers across a range of carbon emission combinations and an incomplete production system. It aims to identify the optimal strategies for material use, production, delivery, replenishment, and pricing to [...] Read more.
This research examines a multinational supply chain inventory problem involving one manufacturer and multiple retailers across a range of carbon emission combinations and an incomplete production system. It aims to identify the optimal strategies for material use, production, delivery, replenishment, and pricing to maximize the integrated total profits under various situations. Three particle swarm optimization techniques are used to solve all the models. Numerical examples and sensitivity analyses on parameter changes are provided. The findings indicate that in a multinational supply chain, currency appreciation in individual retailers’ countries decreases their optimal order quantities and the manufacturer’s optimal material purchase quantity, but increases the optimal quantity for other retailers. In summary, this study offers valuable guidance to enterprises and supply chain decision-makers, especially those operating in a multinational framework, aiming to effectively balance carbon reduction and profitability within the context of global trends in carbon emission reduction. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
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20 pages, 428 KB  
Article
A New Bounding Procedure for Transportation Problems with Stepwise Costs
by Jingyi Liu
Mathematics 2025, 13(22), 3709; https://doi.org/10.3390/math13223709 - 19 Nov 2025
Viewed by 757
Abstract
Transportation planning often involves not only shipment costs but also setup costs associated with deploying vehicles or transport resources. In many practical logistics operations, this setup cost does not remain constant but increases stepwise with the number of vehicles used, reflecting economies of [...] Read more.
Transportation planning often involves not only shipment costs but also setup costs associated with deploying vehicles or transport resources. In many practical logistics operations, this setup cost does not remain constant but increases stepwise with the number of vehicles used, reflecting economies of scale and scheduling thresholds. To capture this realistic feature, this study investigates the transportation problem with stepwise costs, where total costs combine shipment-dependent variable costs and vehicle activation costs. We develop a mixed-integer programming (MIP) model to represent the problem and propose an efficient algorithm based on variable-splitting reformulation and a row-and-column generation scheme. This approach dynamically introduces only the necessary variables and constraints, enabling the solution of large-scale instances that are otherwise computationally challenging. Numerical experiments show that the method produces high-quality solutions much faster than direct MIP solvers. The results highlight the model’s practical value in optimizing fleet utilization and transportation cost structures in real logistics and supply chain systems. Full article
(This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management)
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