With the growing global focus on low-carbon development and the accelerating transition toward electric vehicles as a central strategy for reducing transport emissions, this study examines the strategic interactions between electric vehicle and fuel vehicle manufacturers under alternative government subsidy regimes, using game models. Three subsidy scenarios are considered: no subsidy, a fixed lump-sum subsidy, and a quantity subsidy. The findings show that fixed subsidies do not enhance perceived value. Moreover, we prove that subsidies can lead to an inefficient allocation of resources when the investment coefficient is low, as they fail to achieve objectives such as driving technological innovation or supporting sustainable industry development. Quantity subsidies, by contrast, offer greater flexibility and can shift the game equilibrium by adjusting subsidy intensity, thereby fostering mutually beneficial outcomes. The cost differential between electric and fuel vehicles also plays a critical role: subsidy policies prove effective only when this differential falls within a moderate range. Through analytical and numerical analyses, the study yields managerial insights and policy recommendations for the automotive industry.

Abstract. Let G = (V (G),E(G)) be a simple, finite graph. The central operator C(G) of G is obtained by subdividing each edge of G exactly once and adding an edge between every pair of nonadjacent vertices of G. Let D ⊆ V (G), and let B(D) denote the set of neighbors of D in V (G) \ D. The differential ∂(D) of D is defined as ∂(D):= |B(D)| − |D|. The maximum value of ∂(D) over all subsets D ⊆ V (G) is the differential of G, denoted by ∂(G). A set D is called a differential set of G if ∂(D) = ∂(G). In this paper, we establish bounds for ∂(C(G)) in terms of several classical graph invariants and investigate structural properties of differential sets in C(G). Furthermore, we determine the exact value of ∂(C(G)) for certain well-known families of graphs.

Due to data source and forecast competency differences, an increasing number of enterprises in hybrid platform supply chains implement forecast signal sharing to eliminate information asymmetry. Existing studies mostly examine vertical-sharing incentive of the platform retailer with suppliers, while neglecting horizontal sharing among suppliers. This paper explores the optimal bi-direction signal-sharing strategy including vertical sharing of platform retailer and horizontal sharing between two suppliers adopting reselling channel and agency channel respectively to improve supply chain performance. By analyzing the established Bayesian Stackelberg game models, the study finds that the two types of suppliers are always willing to implement horizontal sharing, while the vertical sharing strategy of platform retailers depends on channel competition and signal correlation. Specially, when channel competition intensity and signal correlations are sufficiently high, the platform retailer would like to share signal only with the supplier adopting reselling channel, which is different from previous studies. Moreover, it is found that horizontal sharing weakens the vertical-sharing incentive of the platform retailer and reduces the benefits of vertical sharing for two suppliers. This paper enriches the existing literature by combining the research on horizontal and vertical sharing within the context of hybrid-channel platform supply chains, and systematically clarifies the impacts of channel competition and signal correlation on the optimal strategy. Some managerial insights and practical schemes derived from findings may guide enterprises in making decisions on effective bi-direction information cooperation to improve supply chain performance.

In this paper, we explore a parallel batch scheduling problem, focusing on scenarios where jobs, equal in duration, differ in release dates and sizes, and are processed on uniform machines with varied batch capacities. The objective function to be minimized is makespan, i.e., the maximum completion time of all the jobs. We present two exact algorithms tailored for a scenario characterized by jobs whose sizes are sequentially divisible. Addressing the general context where this divisibility does not hold, we introduce a 2-approximation algorithm which is considered the best achievable in some sense, since improving the approximation ratio superior to 2 is improbable without resolving the P versus NP problem.

The Alon-Tarsi number of a graph G AT(G) defined as the smallest integer k admitting an Alon-Tarsi orientation with maximum out-degree at most k-1, satisfies the fundamental inequalities χl(G)≤AT(G)≤d(G)+1, where χl(G) and d(G) denote the list chromatic number and degeneracy respectively. Notably, for planar graphs without k-cycles where k∈{5,6}, the 3-degeneracy implies AT(G)≤4, and our main result extends this by proving AT(G)≤ 4 for planar graphs without 4-cycles adjacent to 3-cycles, thereby improving previous results from [JCTB 1999] and [Discrete Math. 2016].

In this paper, we propose an analytical solution to the problem of Generalized Mutual Exclusion Constraints (GMECs) in a Network of Timed Event Graphs (NTEGs). The contribution of the paper lies in the development of a method to design control laws that satisfy these constraints across different place paths in the graphs. Using Min-Plus dioid algebra, we employ algebraic techniques to express GMECs as weighted inequalities. The solution involves translating the constraints into Min-Plus linear equations that describe the behavior of NTEGs. We provide sufficient conditions for the existence of causal control laws, considering both the initial marking of the NTEGs and the parameters of the GMECs. To demonstrate the practical application of the approach, we include a case study that illustrates the effectiveness of the proposed control strategy.

This study investigates the blockchain platform joining strategy of third-party remanufacturers (TPRs) in authorized remanufacturing. We develop a tripartite game-theoretic model involving an original equipment manufacturer (OEM), a TPR, and a retailer to analyze the interaction between remanufacturing authorization strategies and blockchain platform joining decisions. Our findings reveal that the OEM's authorization strategy depends collectively on the production cost of new products, the fixed authorization fee, blockchain platform joining cost, consumer privacy concern cost, and the value discount multiplier. The OEM prefers the fixed authorization fee strategy only when most parameters reach high levels while the value discount multiplier remains relatively low. The TPR tends to join the retailer's blockchain platform when the joining cost and privacy concern cost are low. Notably, even when these costs are elevated, the TPR can still benefit from joining if the new product cost and the value discount multiplier are sufficiently high. A tripartite-win scenario emerges exclusively under a high new product cost combined with the TPR's decision not to join the retailer's blockchain platform. These results delineate the applicability boundaries of blockchain technology in remanufacturing supply chains and provide theoretical guidance for enterprises in coordinating digital transformation with authorization strategy decisions.

This study investigates the start-up firm’s optimal decision in multi-round equity and debt portfolio crowdfunding financing and the design of risk-sharing mechanism. A crowdfunding platform serves as an intermediary between a start-up firm with limited initial capital and external investors seeking debt and equity investments. When the funding target is not met, the crowdfunding platform provides loans to bridge the start-up firm’s capital gap, which also gives chance to adjust its capital structure. Firstly, a decision-making model is established to derive optimal financing strategies for a startup firm and a crowdfunding platform, while also derived the financing ratio between equity and debt crowdfunding channels. A numerical analysis further examines how key parameters—such as fundraising rate and loan interest rate—affect the startup’s capital structure. More importantly, a novel debt-to-equity swap arrangement (DTE) is proposed for sharing debt risk between the start-up firm and the platform. The findings reveal that startup firms primarily rely on equity crowdfunding when the fundraising rate is moderate, while the low fundraising rate leads to a single equity crowdfunding approach. Similarly, the high loan interest rate drive startup firms to favor equity crowdfunding, whereas low rates may prompt platform to discontinue loans, leaving startup firms to rely solely on equity financing. Additionally, the DTE facilitates coordination among parties requires balanced adjustments from platforms (moderate commission rates), startup firm (capital structure optimization), and investors (appropriate success rates) to ensure effective risk-sharing and profit distribution.

Since the ports are the backbone of international trade they need to be managed efficiently. This study addresses to analyze the operational and financial efficiency of the selected privatized ports that have been belonged to TCDD (Republic of Türkiye State Railways). For this purpose, EATWOS (Efficiency Analysis Technique with Output Satisfying) method is employed, and the weights of the inputs and outputs are determined using LOPCOW (Logarithmic Percentage Change-Driven Objective Weighting), MEREC (Method Based on the Removal Effects of Criteria), and CRITIC (Criteria Importance Through Intercriteria Correlation) methods. After obtaining the weights from these objective methods, the comprehensive weights are calculated using TPOP (Technique of Precise Order Preference) method. Finally, Spearman’s rank-order correlation shows that there is no relationship between the operational and financial efficiency of the ports. The number of studies that address both operational and financial efficiency of ports is limited, and this study distinguishes itself by investigating the relationship between both efficiency types.

This work delves into implementing two models of uncertainty theory, namely the Expected Value Model (EVM) and the Optimistic Value Model (OVM), to address the complexities of the Multi-Objective Travelling Salesman Problem (MOTSP) and the Multi-Objective Solid Travelling Salesman Problem (MOSTSP). The study con- siders the impact of carbon emissions in these models. It employs a newly developed Aspiration Level-based Multi-Objective Quasi Oppositional Jaya (AL-based MOQO Jaya) algorithm for solving problems based on real-world data from the city of Surat for 10 and 50 nodes. The significant advantage of using the AL-based MOQO Jaya algorithm is it does not require any algorithm-specific parameters. Hence, it can solve different optimization problems irrespective of parameter setting. The average run time of AL-based MOQO Jaya for the EVM model is 1.1952 sec, and for the OVM model is 1.0554 sec with ten nodes. For 50 nodes, the average run time for the EVM model is 1.5595 sec, and for OVM, it is 1.4764 sec, which is relatively lesser compared to CPLEX, FPT, HGA, and Rao algorithms for both MOTSP and MOSTSP. Further, the AL-based MOQO Jaya algorithm dominates the solutions obtained by other established techniques. The study concludes solutions obtained through the AL-based MOQO Jaya algorithm are more efficient and provide a viable alternative for decision-makers.