This paper studies operational planning in mixed charging and decentralized swapping systems under uncertainty. We consider a two-stage distributionally robust optimization (DRO) model in which ordering decisions are subject to temporally correlated disruptions, while demand remains stochastic and distributionally ambiguous. To capture this structure, we develop a joint ambiguity set through a scenario-wise construction to describe both disruption and demand uncertainties. Specifically, the distribution of disruption scenarios is modeled by an ambiguity set based on marginal disruption probabilities, and the associated worst-case disruption scenarios are characterized by exploiting the supermodularity of the second-stage value function. Conditional on each disruption scenario, demand uncertainty is modeled via a Gelbrich metric ambiguity set, which captures joint mean and covariance information and enables a closed-form reformulation of the resulting distributionally robust chance constraints. The proposed worst-case reliable operation model is tractable and can be easily solved by commercial solvers. Numerical results show that the proposed model outperforms deterministic, stochastic programming, and moment-based DRO benchmarks in both cost and service performance. It further reveals endogenous differentiation in replenishment strategies across stations with heterogeneous capacities. Out-of-sample tests show that the proposed model achieves lower and more stable costs, particularly under high disruption risk and demand variability. These results demonstrate the ability of our proposed model to effectively hedge against joint uncertainty while maintaining operational efficiency.

How should retailers and sellers distribute inventory across a large network of (potentially hundreds of) distribution centers? Motivated by the emerging challenges of inventory allocation facing volatile demand, we develop distributionally robust network inventory management policies with cross-fulfillment using a scenario-based approach that is adaptable to feature information and demand correlation. We analytically demonstrate the value of scenario modeling for a two-location newsvendor problem. The key technical development is a computationally efficient linear programming formulation for large networks, which we further incorporate into a dynamic inventory policy combined with look-ahead approximation. We validate the superior performance of the proposed policies using real-world transaction data from a leading logistics service provider and a major retailer in China. The developed policy outperforms existing data-driven approaches and can save up to 19% of operating costs over the current policy employed by the company.

Teleconsultation in China, primarily based on appointment systems, often face walk-ins who have not scheduled in advance, leading to delays for scheduled patients. To minimize waiting and overtime costs, we propose a two-stage static scheduling model for optimal patient allocation. Additionally, a dynamic update model is developed for scheduled patients, integrated with a rolling horizon optimization strategy, resulting in a Greedy-based Rolling Horizon Optimization (GRHO) approach. We introduce two insertion principles for walk-ins: GRHO and GRHO*. The SAA-VNS-Integer L-Shaped (SVILS) algorithm is employed to solve the static model, and results show that GRHO* outperforms both GRHO and SVILS. GRHO* reduces waiting time by up to 67.86

Coal-fired power plants generate substantial waste that requires green pretreatment before valorization, yet high costs and demand uncertainty discourage investment. Although government subsidies are often advocated to promote waste management, this study focuses on an implementable, enterprise-led alternative: recycler-provided pretreatment cost sharing as a contract-based mechanism within the supply chain, alongside recycler-to-plant demand information sharing. Using a game-theoretic model with demand uncertainty and quality differentiation, we compare equilibrium outcomes under four coordination regimes: no cooperation, information sharing only, subsidization only, and a combined mechanism. Results show that information transparency robustly improves coordination by enabling state-contingent pretreatment decisions and sustaining mutual profitability across diverse market conditions. Subsidization increases pretreatment by relieving the plant’s effective cost burden, but its attractiveness to the recycler is limited by direct payment costs, implying that cost-sharing requires targeted, performance-linked design. Combining the two instruments can strengthen outcomes under uncertainty but often provides limited incremental benefits beyond transparency. Policy implications emphasize prioritizing transparency infrastructure, standardized disclosure, and data governance as a baseline, while facilitating subsidy-like cost sharing selectively in contexts where quality premia and uncertainty make cost relief more likely to generate shared gains.

Problem Definition: On-demand delivery platforms increasingly distinguish themselves through faster and more reliable order fulfillment, yet the final delivery stage inside high-rise buildings can remain time-consuming and uncertain. We identify this overlooked stage as the last-100-meter vertical delivery problem and formalize it as the Elevator Delivery Problem with Deadlines (EDPD) under uncertain elevator waiting times. Elevator waiting-time data from Beijing office buildings show substantial dispersion, pronounced right tails, and systematic heterogeneity across call floors, requested travel directions, and elevator loading states. Methodology/results: To capture these empirical patterns, we use a directed network to distinguish elevator calls by call floor and requested travel direction and a scenario-wise ambiguity set to characterize each loading state with conditional moment and support information. To quantify delay risk, we propose the Flexible Essential Riskiness Index (FERI), which extends the Essential Riskiness Index (ERI) by allowing the ERI feasibility condition to be relaxed with a penalty. FERI jointly accounts for the probability and magnitude of lateness while remaining finite and informative in delay-prone instances, where ERI is inapplicable. Integrating these elements, we propose a last-100-meter vertical delivery model, derive an equivalent mixed-integer second-order cone reformulation, develop a Benders decomposition algorithm to solve the model exactly, and design a hybrid heuristic that combines a residual-capacity-based Label strategy with the Deadline and Floor strategies for real-time sequencing decisions. Managerial implications: Simulation experiments show that the Benders decomposition substantially improves tractability and that our proposed model provides more reliable out-of-sample performance than sample-average approximation under distributional misspecification. A case study using real elevator data from Weiya Building shows that the exact solution approach and the Label strategy outperform practical Floor and Deadline strategies. The results also show that reliable delivery sequences may accept additional but more predictable in-elevator riding time to avoid long and volatile waits. Mechanisms for platform--building coordination, including anticipatory elevator calling and dedicated elevator access, can further reduce vertical delivery delay risk. More broadly, this work highlights the role of vertical logistics in enabling reliable urban on-demand fulfillment.

Establishing a reliable closed-loop supply chain is crucial for companies aiming to reduce costs and enhance sustainability. Two main structures are prevalent: one diversifies risk and logistics through a specific recycling distribution center, while the other pools risk and bidirectional logistics into the co-located distribution center. In this work, we propose a hybrid structure that integrates both types of distribution centers. We formulate this reliable closed-loop supply chain network design problem into a two-stage distributionally robust optimization (DRO) model to resist facility-correlated disruptions. We demonstrate the supermodularity of the second-stage problem and reformulate it into a mixed-integer second-order cone program, making it tractable for commercial solvers. To efficiently handle large-scale, long-horizon problems, we develop a Branch-and-Benders-Cut Decomposition algorithm and introduce Supermodular Cuts specifically tailored to our model. In numerical studies, we investigate risk diversification and pooling effects within different network structures. We found that utilizing the co-located distribution center, which pools risk and bidirectional logistics in a single facility, can effectively withstand high-disruption risks. Moreover, increasing facility capacity improves the flexibility of the network in addressing disruption scenarios. Additionally, we show that our algorithm outperforms the benchmark model in terms of efficiency. Finally, we consider the problem of independent facility disruption to enhance the robustness of our results.

With increasing electricity market complexity and electricity price volatility, self-scheduling and market involvement problem has become a significant challenge for power producers. Instead of previous studies focusing solely on single-market optimization problem, we propose a self-scheduling and market involvement problem that integrates both the forward market and the spot market under price uncertainty. In our approach, the forward market determines unit commitment and electricity transaction decisions for future periods, while the spot market dictates generation scheduling and real-time electricity transaction. The objective is to maximize profit from both markets, while managing the risks associated with price uncertainty using the mean conditional value-at-risk (mean-CVaR). This risk measure captures the potential losses in profit over all spot price distributions, enabling a balance between profit maximization and risk aversion. To address electricity price uncertainty, we introduce two distributionally robust optimization (DRO) models. The first, M-DRO, utilizes the mean, support, and mean absolute deviation to define the ambiguity set, ensuring tractable and efficient optimization. The second, W-DRO, employs the 1-Wasserstein distance to capture more complex and data-driven uncertainties. A decomposition-based algorithm is proposed to solve the reformulated max-min problems. Extensive numerical experiments compare the performance of the proposed DRO models against traditional stochastic programming methods, providing key managerial insights for power producers in multi-market involvement.

On-demand delivery (ODD) platforms increasingly rely on heterogeneous courier workforces (in-house, supplementary dedicated, and crowdsourced couriers) to meet stringent time-window requirements. Among these types, crowdsourced couriers -the workforce backbone -predominantly utilize battery-swapping two-wheeled electric vehicles (TWEVs) to sustain high-frequency operations. In the face of these evolving characteristics, however, real-world operational practices reveal a critical gap: current dispatching systems often manage in-house couriers, supplementary dedicated couriers, and crowdsourced couriers through separate decision processes rather than a unified system-level mechanism, while also overlooking energy-logistics couplings, including energy-constrained order assignments, speed variations dependent on state of charge (SoC) and mandatory detours for battery swapping. Such fragmented dispatching practices and omitted energy considerations frequently lead to unexecutable plans and delivery delays. To address this, we propose an energy-aware integrated order assignment and routing model that unifies the dispatching of heterogeneous courier workforces by explicitly incorporating SoC-dependent travel speeds and battery swapping detours. To solve this computationally challenging problem, we design a nested tabu search algorithm based on a bi-level “fast search-precise evaluation” structure. The outer level conducts fast global assignment search with an incremental routing heuristic, while the inner level incrementally solves courier-level mixed-integer programming (MIP)-based routing subproblems to ensure accurate cost evaluation. Extensive experiments using real-world data demonstrate that our algorithm yields high-quality solutions efficiently, accelerating computation by 2–3 orders of magnitude over Gurobi with a 1.6% average gap, whereas traditional tabu search and adaptive large neighborhood search (ALNS) exhibit substantially larger average gaps of over 12%. Crucially, the proposed framework significantly outperforms conventional dispatching strategies that neglect energy-related constraints. Furthermore, sensitivity analyses provide managerial insights into how increasing swap-cabinet availability, expanding crowdsourced capacity, improving battery efficiency and capacity, and adjusting low-battery thresholds can enhance system efficiency. Overall, this study paves the way for sustainable and reliable urban delivery systems.

Large-scale electrification of transport encourages a fair allocation of urban charging resources to deepen the demand for energy justice. However, existing research and practices on distributional energy justice remain limited owing to the reliance on coarse data that overlook individual-level characteristics. Here, we adopt a micro-level benefit-responsibility perspective and use high-resolution data from 9,231 electric vehicle (EV) users to develop two individual-level metrics for charger allocation reassessment. We uncover in the disguise of a seemingly fair charger distribution at the macroscopic level a hidden energy injustice at the microscopic level. In Beijing, individuals residing in lower-priced housing achieve 43.24% greater carbon savings but incur 91.43% more time using urban charging services compared with those in higher-priced housing. This unattended allocation imbalance indicates that current policies insufficiently address the complexities of energy justice and carbon neutrality, underscoring the need for more nuanced strategies and revealing underlying structural causes.

As the energy landscape undergoes a profound transition with the widespread penetration of renewable energy, Virtual Power Plant (VPP) energy dispatching management emerges as a highly effective approach to manage and optimize energy scheduling. In this study, we propose a distributionally robust chance-constrained optimization framework to optimize the day-ahead bidding decisions. To effectively deal with the uncertainty associated with renewable energy generation, we establish a novel interval moment information ambiguity set, which dynamically captures the uncertain characteristics. Furthermore, we design an integrated strategy for energy storage and demand response, incorporating shedding potential contract parameters for controllable loads, thereby remarkably refining the demand-side management. On the market side, we develop a multi-market trading strategy involving both the electricity market and the ancillary service market to synergistically enhance the overall operational profitability. To efficiently tackle the chance constraint of supply-demand power balance, we employ the CVaR approximation transformation to convert the model into a tractable mixed-integer second-order programming (MISOCP) form. The results of numerical experiments prove that the proposed energy scheduling and bidding strategies increase the economic benefits by 28%, significantly reducing the peak load by 25.4% and simultaneously increasing the valley load utilization by 29.3%. Additionally, our solution method exhibits excellent applicability and computational efficiency in largescale scenarios, which markedly improves energy efficiency and reduces carbon emissions by 44.8%, thus ensuring system reliability and making a profound positive impact on environmental sustainability.

Problem definition: Distributionally robust optimization (DRO) is ubiquitous to address uncertainties inherent in operations management (OM) problems. Recently, an alternative goal-driven framework, robust satisficing (RS), is proposed. RS aims to attain a prescribed target, such as avoiding overshooting the cost budget, as much as possible under uncertainty. The goal-driven modeling philosophy fits many OM problems, yet there is a lack of direct comparisons between DRO and RS. In this paper, we uncover connections between DRO and RS. Methodology/results: Suppose both models are based on the Wasserstein metric and consider a risk-aware convex objective function affected by uncertain parameters. We demonstrate that they share the same solution family. We establish the correspondence between the radius parameter in DRO and the target parameter in RS such that the optimal solutions to the two models coincide. Inspired by the globalized distributionally robust counterpart (GDRC), we extend the analysis to GDRC and the globalized robust satisficing (GRS). We reveal that GDRC and GRS have the same solution families as DRO and RS, respectively. More importantly, we establish novel results on the equivalence of DRO, GDRC, RS, and GRS models under previously stated conditions. Managerial implications: The equivalence results help unify performance bounds of DRO and RS models. Specifically, each model now has an additional set of theoretical guarantees from the other model, and any bounds derived for one model automatically apply to other equivalent models via some parameter mapping. Despite the theoretical equivalence result, the performance of the DRO and RS models can vary depending on how the model parameters are selected. The experimental findings show how these differences emerge when transitioning from theory to practice. Additionally, the experiments provide insights for practitioners, such as how the use of cross-validation can help reflect the true model preferences, particularly when only a few validation points are set. Funding: The research of Z. Wang and L. Ran was supported by the National Natural Science Foundation of China [Grants 72272014, 91746210, and 72061127001]. Z. Wang’s research was also supported by the National Natural Science Foundation of China [Grant 72242106]. The research of M. Zhou was supported by the National Natural Science Foundation of China [Grants 72301075, and 72293564/72293560]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2023.0531 .

The integration of renewable energy and electric vehicles into the smart grid is transforming the energy landscape, and Virtual Power Plant (VPP) is at the forefront of this change, aggregating distributed energy resources to optimize supply and demand balance. In this study, we propose a two-stage distributionally robust optimization framework for day-ahead energy scheduling and real-time power scheduling in VPP energy management system. Considering the uncertainty of power deviation in renewable energy generation, we design a coordinated charging and discharging strategy which integrates electric vehicles and energy storage systems to maintain a balance between supply and demand. To efficiently solve the tri-level min-max-min optimization problem with mixed-integer recourse variables in the second stage, we develop an improved nested C&CG algorithm to make real-time decisions on energy storage, which exhibits superior computational performance. The numerical results further demonstrate the effectiveness of the optimal energy scheduling strategy and provide some valuable insights. Moreover, our strategy not only proves cost-effective but also outperforms other comparable approaches in achieving superior peak shaving and valley filling effects. By guiding VPP operators to develop a reasonable energy scheduling solution, we can effectively balance economic and environmental sustainability.

The sharing of electric vehicles and the Internet of Vehicles both positively impact societal benefits. However, the complexity, uncertainty and multi-directionality of transport-energy coupled systems greatly increase the difficulty of integrated management. This paper proposes a multi-objective robust optimization framework to solve the integrated management issue of electric vehicle sharing system operations and Internet of Vehicles energy scheduling under uncertain information, in which components such as renewable energy, microgrids, autonomous driving and their impacts are fully considered. To enhance the capability of integrated management and the synergy between supply and demand, a charging and discharging scheduling strategy that considers a converged demand response policy is proposed. Numerical analyses using real data provide valuable validation and insights. The proposed method and scheduling strategy enable the implementation of integrated management in photovoltaic microgrids and significantly improve economic and environmental benefits. Meanwhile, the microgrid system can operate in an "off-grid mode", which enables a multi-energy complementary mechanism. Additionally, electric vehicles release a great deal of scheduling flexibility through demand-side management, which combined with electric energy storage, can efficiently local consumption of photovoltaic power.

Battery swapping is experiencing a revival in the electric vehicles (EVs) industry, fueled by supportive global policies. This resurgence is entering a new development phase with the rapid progress of autonomous driving technology and the emergence of substantial new energy service platforms. Observing these features, we propose an orderly swapping strategy in which EVs carry out battery swaps at designated swapping stations in response to swapping demands, with real-time scheduling managed by the service platform. Based on this strategy, we characterize the battery swapping station location and capacity planning problem as a two-stage distributionally robust optimization model. This model presents challenges with bilinear terms involving decision variables and uncertain variables, and sums of piecewise linear functions in the second-stage problem. Notably, we demonstrate that the second-stage problem is convex concerning the uncertain variable and reveals a distinctive structure in the optimal solution of its dual problem. These model properties guide us in designing an efficient column-and-constraint generation algorithm for solving it. We also propose two alternative strategies designed for specific scenarios, reformulating them as mixed-integer second-order cone programmings. In a numerical study, we validate our algorithm's efficacy using classic transportation data and compare the performance of the three strategies with real transportation data from Beijing. Our findings indicate that the Orderly strategy surpasses the other two strategies regarding flexibility and demonstrates economies of scale as the battery swapping scale increases. This flexibility becomes more pronounced as the service rate decreases and the grid capacity increases. Furthermore, the enhanced grid capacity results in an imbalanced battery distribution and the significant technological advancement eliminates any possibility of battery shortages.

Developing doctor recommendation techniques has the potential to enhance the efficiency of telemedicine service with the increasing demand for telemedicine. We propose a novel recommendation method tailored for more sparser and more professional telemedicine contexts than online healthcare. Firstly, we construct a knowledge graph based on the expertise of physicians to extract the feature of disease relevance, so as to make up for the sparsity of data. Subsequently, coarse and fine granularity semantic feature is extracted from historical diagnostic data to calculate text similarity between doctors and patients. Then, the features of gender, age, title and scheduling activity are considered to improve model performance doctor modeling. Finally, we input the extracted features into a neural network to generate recommendation results that are both effective and interpretable. Experimental results demonstrate that, compared to traditional methods, our approach significantly improves the accuracy and robustness of telemedicine doctor recommendations. Additionally, interpretability analysis shows text similarity and disease relevance (obtained from doctors' professional expertise and consultation text) contribute mostly to the recommendation system, which reconfirms our efforts are meaningful.

This study explores the appointment scheduling problem for telemedicine consultation services within the context of telemedicine. With the objective of cost minimization, it considers uncertainties in stochastic service times and the availability of doctors. The problem is modeled using a distributionally robust optimization framework, where scenarios are depicted based on relevant uncertain events, and partial distribution information of random variables is extracted from these scenarios to construct scenario-wise ambiguity set. The model is reformulated as a mixed-integer linear programming problem, which can be directly solved using existing solvers. Numerical experiments using real data reveal that the solutions provided by this model are not overly conservative, offering reasonable scheduling solutions for different numbers of patients over a period., and with shorter solution times compared to stochastic programming models. Additionally, sensitivity analyses are conducted on model parameters, investigating the impact of fixed doctor costs and ambiguity set parameters on the results.

The combination of low-carbon electricity and electric vehicles brings considerable economic and environmen-tal benefits but also introduces challenges due to the complexity and uncertainty of system synergies in smart cities. To fully exploit the advantages of photovoltaic power generation and electric vehicles and to release the potential of electric vehicles as distributed energy storage facilities, this paper develops a multi-objective robust optimization framework that accounts for the benefits of multiple parties of smart charging and discharging systems and depicts a bounded uncertainty set based on partial statistical information from real data. The original model is scalarized and linearized using efficient methods such as max-ordering scalarization and the robust augmented weighted Tchebycheff to facilitate the solution. Moreover, a smart charging and discharging scheduling strategy based on a convergent demand response strategy is proposed to achieve better demand -side management. A case study, based on real data from Car2go and the solar radiation intensity in Portland, Oregon, shows that (1) The methodological framework effectively addresses the smart scheduling issue that considers the interests of multiple parties in complex systems with uncertainty, in contrast to conventional methods. (2) The designed convergent demand response strategy promotes photovoltaic power generation and charging demand synergy and achieves regulation effects such as peak shaving and valley filling. (3) The proposed method and strategy yield good results in multiple aspects, such as charging costs, load regulation, and clean energy utilization, while enhancing the economic and environmental benefits.

Offering time-locked free trials is a common strategy in the software industry. Pioneering studies have mainly focused on time-locked free trial strategies in monopoly markets, and acknowledged that an overall positive effect on consumers' WTP is a prerequisite for offering free trials. However, software markets are often competitive, and consumers typically follow a Bayesian learning principle. We develop a game-theoretic model to examine time-locked free trial strategies in duopoly markets with switching costs. The results show that, in the markets with small switching costs, firms pursue opposite free trial strategies when the horizontal difference between products is small, and neither offers otherwise. If the switching costs are larger than a threshold, then both firms offer free trials when the horizontal difference between products is moderate. We further demonstrate that in the presence of functionality heterogeneity between products, firms are unable to reach an equilibrium in some specific cases, and more likely to take opposite free trial strategies in equilibrium. Moreover, if the firms do choose opposite strategies, interestingly, the firm with superior product does not offer free trials when switching costs are low, and is more willing to offer as switching costs increase. Our results are robust to the inclusion of other factors in the model, such as the possibility of consumers trying only one product, correlated consumer learning across different products, consumer heterogeneity in usage time, and network effects.