Mathematics

Background: Agricultural logistics in arid, geographically dispersed areas require complex trade-offs among efficiency, equity, and robustness under uncertainty. Standard multi-objective vehicle routing problem (VRP) formulations, which primarily focus on cost or environmental parameters, do not explicitly account for social equity or transparency in decision-making. However, existing work seldom combines the objective of social equity as an endogenous optimization objective with robustness and interpretability within a unified mathematical framework. Methods: In this paper, we present a systems engineering decision-support framework informed by a multi-objective mixed-integer linear programming formulation for agricultural logistics planning. Economic, environmental, operational, and social equity goals are combined through ε-constraint to create trade-offs that can be interpreted at the policy level. We assess robustness against demand and travel-time uncertainty using the Bertsimas–Sim framework. A staged activation strategy separates conceptual model completeness from numerical implementation, and sensitivity analyses are conducted by perturbing vital operational parameters. Results: An illustrative situation in Northern Chile shows that this framework produces stable decision regimes and clear trade-offs in practice. The results show that meaningful improvements in workload balance and service equity can be achieved with negligible changes in operational efficiency. As we have learned in sensitivity experiments, assignment structures and qualitative trade-off patterns are robust under realistic parameter variations, and structural changes occur only beyond known threshold regimes. Conclusions: The major contribution of this work is the formulation of a systems engineering framework that extends traditional multi-objective VRP formulations and integrates social equity, robustness, and decision transparency as core design principles. Instead of focusing only on numerical optimization performance, the framework encourages auditable planning decisions in the face of uncertainty. The numerical analysis results are for a proof-of-concept scale only; however, the framework can be extended to larger agricultural networks using decomposition and/or hybrid solutions.

Cross-border e-commerce, as a vital form of digital trade, is emerging as a new engine for corporate internationalization. This study employs China’s cross-border e-commerce pilot zones (established since 2015) as a quasi-natural experiment to investigate their causal effects on Chinese cities’ outward foreign direct investment (OFDI) and the underlying mechanisms. Distinct from previous trade-focused studies, this paper innovatively adopts a greenfield investment perspective. By integrating the Global Greenfield Investment Database (2010–2022) with the China City Statistical Yearbook, we constructed a greenfield OFDI dataset spanning the city–destination–target industry dimensions. Based on this dataset, this study employs a time-varying DID approach combined with PSM-DID, parallel trend tests, and placebo tests to empirically analyze how cross-border e-commerce development influences OFDI and its underlying mechanisms. The findings reveal that establishing cross-border e-commerce pilot zones boosts local outward investment by approximately 18.8%. A binary marginal decomposition analysis indicates that this effect primarily manifests through the extensive margin—significantly driving investment into new destination markets. Additionally, the mechanism operates by reducing information search costs and enhancing factor allocation efficiency. Furthermore, the outward investment promotion effect of cross-border e-commerce pilot zones is more pronounced in samples where the destination is a developed country, the target industry is high-tech, and the origin is eastern China. This study not only expands the dimensions for assessing the economic effects of cross-border e-commerce but also provides concrete empirical evidence for governments to optimize digital trade policy arrangements and for enterprises to leverage digital tools to overcome the “Liability of Foreignness” and achieve internationalization.

This paper develops a unified fractional version of the Hermite–Hadamard inequality and Bullen-type inequalities for convex functions defined on discrete time scales. By employing generalized fractional difference operators, the obtained result encompasses and extends previously known discrete formulations, including both the classical case and higher-order variants. Furthermore, we investigate the approximation accuracy of the introduced fractional mean operator. Specifically, we establish explicit error bounds for Lipschitz functions and for functions with convex differences, providing a more comprehensive analysis of the discrete fractional setting.