Search Results (24)

This paper presents a two-stage stochastic programming model for the joint optimization of fleet deployment and sailing speed in liner shipping under fuel price volatility and carbon tax uncertainty. The integrated framework addresses strategic fleet planning by determining optimal fleet composition in the first stage, while the second stage optimizes operational decisions, including vessel assignment to routes and sailing speeds on individual voyage legs, after observing stochastic parameter realizations. The model incorporates nonlinear fuel consumption functions that are approximated using piecewise linearization techniques, with the resulting formulation being solved using the Sample Average Approximation (SAA) method. To enhance computational tractability, we employ big-M methods to linearize mixed-integer terms and introduce auxiliary variables to handle nonlinear relationships in both the objective function and constraints. The proposed model provides shipping companies with a comprehensive decision-support tool that effectively captures the complex interdependencies between long-term strategic fleet planning and short-term operational speed optimization. Numerical experiments demonstrate the model’s effectiveness in generating optimal solutions that balance economic objectives with environmental considerations under uncertain market conditions, highlighting its practical value for resilient shipping operations in volatile fuel and carbon pricing environments. Full article

The global cruise industry has demonstrated remarkable growth, with modern ships functioning as large-scale floating resorts. Effective food provisioning is a critical operational function that directly impacts both cost efficiency and passenger satisfaction. This task is characterized by massive consumption scales and high demand uncertainty. To address these challenges, this paper develops a two-stage stochastic optimization model for cruise ship food provisioning. The first-stage decisions involve procurement quantities made before the voyage under demand uncertainty, subject to the volumetric constraints of different storage types. The second-stage decisions determine the optimal substitution plan after the actual demand is realized, mitigating shortages by utilizing alternative available items. Solving stochastic programs with continuous distributions is computationally challenging. Therefore, we employ the sample average approximation (SAA) method to obtain tractable solutions, complemented by a full statistical evaluation of solution quality. Numerical experiments using real-world data confirm that a scenario size of 80 achieves an optimal balance with an optimality gap of 0.78%. Sensitivity analysis demonstrates the model’s robust performance and provides valuable managerial insights: higher shortage penalty coefficients significantly reduce stockouts; two-way substitution structures enhance system flexibility; appropriate salvage value accounting reduces total costs; and implementing a service level constraint of ${\lambda }_i=0.80$ optimally balances operational resilience with economic efficiency. These findings support the development of more resilient and cost-effective provisioning strategies, offering cruise operators a practical decision-support tool for managing food provisioning under uncertainty. Full article

This paper presents a Monte Carlo simulation-based approach for solving stochastic two-stage bond portfolio optimization problems. The main objective is to optimize the cost of the bond portfolio while making decisions on bond purchases, holdings, and sales under random market conditions such as interest rate fluctuations and liabilities. The proposed algorithm identifies the number of randomly generated scenarios required to convert the stochastic problem into a deterministic one, subsequently solving it as a Mixed-Integer Linear Program. The practical relevance of this research is shown through an application of the proposed method to a real-world bond market. The results indicate that the proposed approach successfully minimizes costs and meets liabilities, providing a robust solution for bond portfolio optimization. Full article

When using optical remote sensing methods for Kelvin wake imaging, the imaging is affected by sea-surface stochastic fluctuation, imaging noise, and weak reflectivity contrast, resulting in weak wake image signals. In order to better obtain wake optical remote sensing images, this article proposes a multi-objective parameter stochastic optimization method for a time-delayed integration optical remote sensing imaging system. By constructing the wake imaging mechanism framework integrating a hydrodynamic model, rough sea surface probability and statistics model, and Time-Delay Integration Charge-Coupled Device (TDI-CCD) imaging link model, a stochastic multi-objective optimization model with constraints is established. The multi-objective function of this model is specifically defined as follows: maximizing the digital number difference between the crest and trough of Kelvin wakes in imaging results, maximizing the F number, minimizing the integration stages, and minimizing the quantization bits. Meanwhile, a two-stage solution method based on sample average approximation (SAA), branch and bound method (B&B), and the complex method is designed. The model can be used to obtain optimized design results for remote sensing imaging parameters, providing theoretical and methodological support for the design of remote sensing imaging systems. Numerical simulation results show that the optimized parameter combination can achieve clear imaging of the Kelvin wake, and the core indicators meet the design requirements. Full article

The rapid growth of e-commerce has intensified the need for efficient last-mile delivery, making unmanned aerial vehicles (UAVs) a promising solution. However, despite their potential, practical deployment remains limited by how to effectively plan depot locations and UAV fleet sizes under stochastic customer demands with probabilistic same-day modifications. Existing approaches often address the strategic and operational decisions separately, leading to inefficiencies and infeasible solutions in practice. This study develops a unified two-stage decision framework integrating strategic depot location and UAV fleet allocation with operational assignment and scheduling. Three strategic models are considered: a deterministic model, a stochastic model solved via Sample Average Approximation (SAA), and a robust optimization model. Operational decisions assign UAV trips to realized requests while respecting time-slot and UAV availability constraints. Deterministic and SAA models are solved directly as integer programs, whereas the robust model is tackled via a logic-based Benders decomposition framework, with all approaches evaluated through simulation. The results show that the robust model provides overly conservative solutions, resulting in higher costs; the deterministic model minimizes cost but risks service failures; and the SAA approach balances cost and service across demand scenarios. The findings demonstrate the value of jointly considering strategic and operational decisions in UAV delivery design and provide practical guidance for UAV logistics operators. The proposed framework helps firms select appropriate planning models that align with their risk tolerance and service reliability goals, thereby improving the feasibility and competitiveness of UAV-based delivery systems. Full article

Patient unpunctuality substantially complicates appointment scheduling in integrated telemedicine–traditional outpatient systems. The current research frequently ignores behavioral distinctions between telemedicine patients and outpatients, while neglecting to measure the intangible burden on physicians from service mode switches. To address these gaps, this study incorporates patient heterogeneity and introduces two novel cost metrics. Specifically, we implement penalties for service-mode switching and penalties for consecutive telemedicine sessions. We develop a Stochastic Mixed-Integer Programming (SMIP) model. This stochastic model is transformed into a deterministic Mixed-Integer Linear Programming (MILP) formulation via Sample Average Approximation (SAA). Linearization techniques enhance computational efficiency. In numerical experiments, the dual-penalty model yields balanced schedules with moderate patient mix, reducing physician overtime by 62.5% and service mode switches by 55% compared to baseline approaches. Sensitivity analysis confirms that narrowing outpatient unpunctuality ranges significantly reduces patient waiting and overtime, while raising telemedicine patient proportions bolsters system stability at the cost of increased physician idle time. These insights offer actionable guidance for healthcare institutions managing integrated online–offline services. Full article

The ship fleet deployment problem plays a critical role in maritime logistics management, requiring shipping companies to determine optimal vessel configurations for cargo transportation. This problem inherently contains stochastic elements due to the random nature of cargo demand fluctuations. While the Sample Average Approximation (SAA) method has been widely adopted to address this uncertainty through empirical distributions derived from historical observations, its effectiveness is constrained by data scarcity in practical scenarios. To overcome this limitation, we propose a novel Sample Distribution Approximation (SDA) framework that employs estimated probability distributions, rather than relying solely on empirical data. We implement a leave-one-out cross-validation mechanism to optimize distribution estimation accuracy. Through comprehensive computational experiments, using decision cost as the primary evaluation metric, our results demonstrate that SDA achieves superior performance compared to the conventional SAA method. This advantage is particularly pronounced in realistic operational conditions, where historical demand observations range from 15 to 25 data points, or fleet configurations involve two to six candidate vessel types. The proposed methodology provides shipping operators with enhanced decision-making capabilities under uncertainty, especially valuable in data-constrained environments. Full article

Commercial aircraft manufacturers often face order uncertainty in particular situations, such as quantity or demand change, or lack of confirmed customer options. As a countermeasure, aircraft manufacturers can adopt a two-stage strategy to produce batch General-Configuration Aircraft (GCA), so as to maintain continuous aircraft production. Nevertheless, additional work on disassembling and re-assembling must be performed, to convert the GCA into specific configurations specified later by the customer. Thus, an appropriate GCA that leads to a minimal overall manufacturing workload is essential. In this paper, a Sample Average Approximation (SAA) model for GCA optimization is proposed, to obtain a robust GCA whose prediction results can help minimize the total production time. Compared with the empirical method, the proposed SAA approach significantly accelerates the production operation and is adaptive to various scenarios. The robustness of the SAA approach was evaluated, and the results prove that the general configuration obtained by the SAA approach has sustainable variances in the manufacturing workload. Full article

With the increasing integration of stochastic sources and loads, ensuring the flexibility of AC/DC hybrid distribution networks has become a pressing challenge. This paper aims to enhance the operational flexibility of AC/DC hybrid distribution networks by proposing a flexibility-oriented optimization framework that addresses the growing uncertainties. Notably, a comprehensive evaluation method for operational flexibility assessment is first established. Based on this, this paper further proposes a flexibility-oriented operation optimization model using the distributionally robust chance-constrained (DRCC) method. A customized solution method utilizing second-order cone relaxation and sample average approximation (SAA) is also introduced. The results of case studies indicate that the flexibility of AC/DC hybrid distribution networks is enhanced through sharing energy storage among multiple feeders, adaptive reactive power regulation using soft open points (SOPs) and static var compensators (SVCs), and power transfer between feeders via SOPs. Full article

In the context of flight test planning, numerous uncertainties exist, encompassing aircraft status, number of flights, and weather conditions, among others. These uncertainties ultimately manifest significantly in the actual number of flight sorties executed, rendering high significance to engineering problems related to the execution of flight test missions. However, there is a dearth of research in this specific aspect. To address this gap, this paper proposes an opportunity-constrained integer programming model tailored to the unique characteristics of the problem. To handle the uncertainties, Sample Average Approximation (SAA) is employed to perform oversampling of the uncertain parameters, followed by the Adaptive Large Neighborhood Search (ALNS) algorithm to solve for the optimal solution and objective function value. Results from numerical experiments conducted at varying scales and validated with diverse sampling distributions demonstrate the effectiveness and robustness of the proposed methodology. By decoding the generated execution sequences, comprehensive mission planning schemes can be derived. This approach yields sequences that exhibit commendable feasibility and robustness for the flight test planning problem with sorties uncertainty (FTPPSU), offering valuable support for the efficient execution of future flight test missions. Full article

This paper undertakes a revisit of the sunk cost fallacy, which refers to the tendency of people to persist investing resources into something, even if it is destined to have no good outcome. We emphasize that the utilities associated with different alternatives are not static for decision makers, which is exactly opposite to the traditional perspective. This paper argues that the utility of an option may change due to the choice of another option, suggesting that decisions considered irrational by the traditional analytical method, i.e., sunk cost fallacy, may be rational. We propose a novel analytical method for decision making with sunk cost when considering the utility change and validate the effectiveness of this method through mathematical modeling and computational experiments. This paper mathematically describes such decision-making problems, analyzing the impact of changes in the utilities across different alternatives on decision making with a real-world example. Furthermore, we develop a two-stage stochastic optimization model for such decision-making problems and employ the sample average approximation (SAA) method to solve them. The results from computational experiments indicate that some decisions traditionally considered irrational are, in fact, rational when the utility of an option changes as a result of choosing another option. This paper, therefore, highlights the significance of incorporating utility changes into the decision-making process and stands as a valuable addition to the literature, offering a refreshed and effective decision-making method for improved decision making. Full article

The global supply chain is facing huge uncertainties due to potential emergencies, and the disruption of any link may threaten the security of the supply chain. This paper considers a disruption scenario in which supply disruption and distribution center failure occur simultaneously from the point of view of the manufacturer. A resilient supply chain optimization model is developed based on a combination of proactive and reactive defense strategies, including manufacturer’s raw material mitigation inventory, preference for temporary distribution center locations, and product design changes, with the objective of obtaining maximum expected profit. The proposed stochastic planning model with demand uncertainty is approximated as a mixed integer linear programming model using Latin hypercube sampling (LHS), sample average approximation (SAA), and scenario reduction (SR) methods. In addition, an improved genetic algorithm (GA) is also developed to determine the approximate optimal solution. The algorithm ensures the feasibility of the solution and improves the solving efficiency through specific heuristic repair strategies. Numerical experiments are conducted to verify the application and advantages of the proposed disruption recovery model and approach. The experimental results show that the proposed resilient supply chain optimization model can effectively reduce the recovery cost of manufacturers after disruption, and the proposed approach performs well in dealing with related problems. Full article

This paper critically examines the weighted sample average approximation (wSAA) framework, a widely used approach in prescriptive analytics for managing uncertain optimization problems featuring non-linear objectives. Our research pinpoints a key deficiency of the wSAA framework: when data samples are limited, the minimum relative regret—the discrepancy between the expected optimal profit realized by an oracle aware of the genuine distribution, and the maximum expected out-of-sample profit garnered by the data-driven policy, normalized by the former profit—can approach towards one. To validate this assertion, we scrutinize two distinct contextual stochastic optimization problems—the production decision-making problem and the ship maintenance optimization problem—within the wSAA framework. Our study exposes a potential deficiency of the wSAA framework: its decision performance markedly deviates from the full-information optimal solution under limited data samples. This finding offers valuable insights to both researchers and practitioners employing the wSAA framework. Full article

One-stage stochastic linear complementarity problem (SLCP) is a special case of a multi-stage stochastic linear complementarity problem, which has important applications in economic engineering and operations management. In this paper, we establish asymptotic analysis results of a sample-average approximation (SAA) estimator for the SLCP. The asymptotic normality analysis results for the stochastic-constrained optimization problem are extended to the SLCP model and then the conditions, which ensure the convergence in distribution of the sample-average approximation estimator for the SLCP to multivariate normal with zero mean vector and a covariance matrix, are obtained. The results obtained are finally applied for estimating the confidence region of a solution for the SLCP. Full article

Due to the high randomness and volatility of renewable energy sources such as wind energy, the traditional thermal unit commitment (UC) model is no longer applicable. In this paper, in order to reduce the possible negative effects of an inaccurate wind energy forecast, the chance-constrained programming (CCP) method is used to study the UC problem with uncertainty wind power generation, and chance constraints such as power balance and spinning reserve are satisfied with a predetermined probability. In order to effectively solve the CCP problem, first, we used the sample average approximation (SAA) method to transform the chance constraints into deterministic constraints and to obtain a mixed-integer quadratic programming (MIQP) model. Then, the quadratic terms were incorporated into the constraints by introducing some auxiliary variables, and some second-order cone constraints were formed by combining them with the output characteristics of thermal unit; therefore, a tighter mixed-integer second-order cone programming (MISOCP) formulation was obtained. Finally, we applied this method to some systems including 10 to 100 thermal units and 1 to 2 wind units, and we invoked MOSEK in MATLAB to solve the MISOCP formulation. The numerical results obtained within 24 h confirm that not only is the MISOCP formulation a successful reformulation that can achieve better suboptimal solutions, but it is also a suitable method for solving the large-scale uncertain UC problem. In addition, for systems of up to 40 units within 24 h that do not consider wind power and pollution emissions, the numerical results were compared with those of previously published methods, showing that the MISOCP formulation is very promising, given its excellent performance. Full article