This study introduces a novel ceiling constraint on clean energy advertisement input and examines its interaction with two carbon regulation policies—carbon tax (CT) and carbon allowance mechanism (CAM)—in shaping operational decisions. The key findings are as follows: (1) Under a low ceiling, both policies lead to identical advertisement input, yet CT results in lower profits for chain members. Under a moderate or high ceiling, CAM induces higher advertisement input than CT. (2) Regardless of the ceiling level, CAM consistently leads to higher power demand, higher total emissions, and lower conventional power prices compared to CT. (3) When the ceiling constraint is binding, raising it reduces conventional power prices, power demand, and emissions under both policies, while increasing the equilibrium values for other decision variables. Theoretical and managerial contributions: Theoretically, this study advances low-carbon operations modeling by incorporating a regulatory ceiling on advertisement input, offering a refined framework for evaluating carbon policies. It further identifies critical threshold levels (e.g., of the ceiling) that dictate the relative efficacy of CT versus CAM in promoting green input and shaping profitability. From a managerial perspective, the findings offer clear guidance; policymakers can use them to design balanced regulations, while power generators can better select operational strategies under different policy regimes.

This paper studies the participation of renewable-based microgrids in the retail market. The developed model is designed as a bi-level optimization approach. At the higher level, a distribution system operator (DSO), as the decision-maker for problem, takes part in the wholesale market to buy energy. Also, it participates in the retail market to increase its profit by selling energy to the microgrids. Moreover, at the upper level, in addition to supplying electrical energy, the provision of thermal energy to consumers is also considered, enabling the DSO to achieve greater profitability through improved efficiency. The lower level is responsible for modeling the interaction between the DSO and microgrids, where the microgrids aim to minimize their daily cost. In the proposed model, transactive energy and prices between the DSO and microgrids are the decision variables. Unlike existing models, microgrids can collaborate to convert the original non-cooperative games to hybrid cooperative and non-cooperative games. This change increases the bargaining power of microgrids and leads to a reduction in retail market prices and a decrease in microgrid operating costs. The results show that the proposed model improves operation cost and energy not supplied of microgrids by 9.09% and 33.56%, respectively.

ABSTRACT The purpose of this study was to determine the effect of bonus packs and product quality on consumer purchasing decisions at PT. Alamjaya Wirasentosa Tg. Morawa Deli Serdang, North Sumatra. The population in this study are consumers at PT. Alamjaya Wirasentosa Tg. Morawa Deli Serdang North Sumatra as many as 379 consumers for one week while the determination technique is random sampling with the withdrawal technique using the Slovin formula. So that the sample in this study amounted to 79 respondents. The sources of data in this study are primary data and secondary data. Where the primary data from observations, interviews and questionnaires. While secondary data can be from data that has been documented. While the data analysis techniques used are descriptive analysis and multiple linear regression. The results of multiple regression analysis are Y = 8.898 + 0.193X1 + 0.548X2 + e which shows that the bonus pack and product quality have a positive and significant effect on consumer purchasing decisions. While the results of the (t) test or partial test show that the bonus pack has a positive and significant effect on consumer purchasing decisions where it can be seen that the tcount value is 2.125 > ttable 1.992 and the product quality variable also has a positive and significant effect on consumer purchasing decisions where it can be seen that the tcount value is 9.425 > ttable 1992. The results of the coefficient of determination with a correlation regression value of 0.814, meaning that together the bonus pack and product quality on consumer purchasing decisions at PT. Alamjaya Wirasentosa Tg. Morawa Deli Serdang North Sumatra has contributed to a strong degree. Then the coefficient of determination (R2) is 0.653 (65.3%). So it can be said that 65.3% of the variation in the dependent variable, namely the bonus pack and product quality in the model, can explain the purchasing decision variables at PT. Alamjaya Wirasentosa while the remaining 34.7% is influenced by other variables outside the model. Keyword: Bonus Pack, Product Quality, Purchase Decision

To address the issues of high-dimensional coupling parameters easily falling into local optima and multi-objective conflicts in the beam transport of medical heavy ion accelerators, this paper proposes an improved non-dominated sorting differential evolution (NSDE) algorithm. The algorithm employs inverse learning for initialization and introduces an adaptive mechanism to adjust the mutation factor and crossover probability online, balancing exploration and exploitation. Additionally, it incorporates local enhancement based on crowding distance in particle swarm optimization (PSO) to refine non-dominated elite solutions. Large-scale experiments based on FLUKA Monte Carlo coupled simulation (nine-dimensional decision variables) have shown that the improved NSDE has increased the beam transport efficiency from the baseline of 92.42% to 99.21% (an improvement of 6.79%), while also achieving continuous improvements in key physical indicators such as the beam spot size at the end point, system power consumption, and energy retention rate. The research indicates that the proposed method exhibits significant advantages in enhancing optimization quality and maintaining robustness, making it suitable for accelerator engineering optimization that demands stringent real-time performance and multi-objective accuracy.

Abstract Perimeter control—metering inter-regional flows so that vehicular accumulation is held at a target set-point—has emerged as a cornerstone macroscopic instrument for congestion relief in urban road networks. To endow the macroscopic flow dynamics with hereditary effects, we formulate a fractional-order dynamical system (FDS) whose non-integer differentiation orders and perimeter control strategy are simultaneously treated as unknown quantities governing the temporal evolution of regional vehicle accumulations. The central objective of this study is to identify these unknown quantities. To this end, a fractional-order optimal perimeter control problem (FOPCP) constrained by the FDS is formulated to minimize the total number of vehicles remaining within the urban road network. Subsequently, an explicit numerical scheme is devised to integrate the FDS, thereby transcribing the continuous-time FOPCP into a discrete-time FOPCP. Moreover, gradient formulas for the cost functional with respect to all decision variables are rigorously derived. A hybrid solution framework—based on model predictive control, gradient-based method, and a genetic search strategy—is proposed to numerically resolve the discrete-time FOPCP. Finally, comprehensive numerical experiments are furnished to corroborate the theoretical soundness and practical efficacy of the proposed algorithm.

Aiming at the problems that multi-objective optimization algorithms are prone to fall into local optima and yield uneven solution set distributions in the magnetic circuit optimization of permanent magnet DC coreless motors for the aerospace field, an improved NSGA-Ⅲ multi-objective optimization algorithm is proposed. This algorithm incorporates a dynamic adaptive crossover and mutation mechanism, a normal distribution crossover operator, and a dynamic crowding degree operator, which effectively enhances the global search capability in high-dimensional objective spaces and the distribution uniformity of the Pareto solution set, thus solving the problems that traditional algorithms tend to fall into local optima and suffer from insufficient solution set diversity in multi-objective collaborative optimization. Taking the maximization of torque coefficient, minimization of torque ripple, and minimization of magnetic leakage coefficient of the coreless motor as the core optimization objectives, a high-precision surrogate model between the objective functions and decision variables was established based on the response surface methodology, and embedded into the improved NSGA-Ⅲ algorithm to realize the multi-objective optimization of magnetic circuit parameters. Simulation results show that after optimization, the motor torque coefficient is increased by 29%, the torque ripple is reduced by 13%, and the magnetic leakage coefficient is decreased by 37%, with comprehensive performance indicators improved significantly, indicating favorable engineering application value.

The Stackelberg game strategies are outlined for a wholesaler-retailer-consumer supply chain of an item in a finite planning schedule, where consumers’ demand is influenced by price, credit period, and inflation. As the profit of each party depends on the consumers’ demand, the retailer offers some credit period to its consumers and the wholesaler shares this burden by offering some credit period to the retailer. The retail price depends on the selling price of the wholesaler and both price are decision variables. It is also assumed that a portion of consumers are defaulters, and is increased with the length of the credit period. The model is formulated to optimise individual profits from the planning horizon following the Stackelberg game approach, where the wholesaler is the leader and the retailer is the follower. The performance of Artificial Bee Colony algorithm is enhanced by the introduction of four additional perturbation rules and their collaborative use following a Q-learning strategy. The algorithm is implemented, tested, compared with state-of-the-art algorithms, and applied in a nested way to determine the optimal policies of both players simultaneously. The model is illustrated using different numerical examples, and some managerial insights are outlined.

Emergency department crowding refers to a complex state of congestion associated with a set of performance indicators such as occupation levels, waiting times and specific scores. Among current methods to model it, an objective gap exists between forecasting machine learning methods, focusing on prediction precision and queueing and simulation methods, focusing on capturing correctly the effect of decision variables for evaluation and optimisation purposes. The objective of the present analysis is to implement and numerically validate a novel data-driven queueing methodology that can bridge this gap and to show its applicability in a simulation case study. A statistical modelling of the queueing processes, particularly patient departure rates and probabilities, is developed to cross the gap defined above. Using the data from a major emergency department of eastern France, the resultant data-driven queueing network model is validated and applied through a synchronous simulation algorithm. The model obtained considers the complex effects of patient arrivals and doctor and nurse allocations while offering an unbiased and accurate measure of long-term crowding. Its application with the case study quantifies the impact of the opening of new Unscheduled Care Services on emergency department crowding. The new data-driven queueing methodology is able to model and quantify complex crowding effects at a detailed level in an emergency department. This study shows an alternative approach successfully bridging the modelling gap by establishing a model that can effectively predict system crowding dynamics under the influence of multiple key variables.

Large-scale constrained multi-objective optimization problems (LSCMOPs) are highly challenging due to the need to optimize multiple conflicting objectives under complex constraints within a vast search space. To address this challenge, this paper proposes a multi-task optimization algorithm based on contribution-driven task design (MTO-CDTD). The algorithm constructs a multi-task optimization framework comprising one original task and multiple auxiliary tasks. Guided by an optimal contribution objective assignment strategy, each auxiliary task optimizes a subset of decision variables that contribute most to a specific objective function. A contribution-guided initialization strategy is then employed to generate high-quality initial populations for the auxiliary tasks. Furthermore, a knowledge transfer strategy based on multi-population collaboration is developed to integrate optimization information from the auxiliary tasks, thereby effectively guiding the original task in searching the large-scale decision space. Extensive experiments on three benchmark test suites—LIRCMOP, CF, and ZXH_CF—with 100, 500, and 1000 decision variables demonstrate that the proposed MTO-CDTD algorithm achieves significant advantages in solving complex LSCMOPs.

The coal mine integrated energy system dispatch problem (CMIES-DP) is a constrained multiobjective optimization problem (CMOP) with the characteristics of multiple objectives, high-dimensional decision variables, and multiple constraints, which makes it challenging for existing methods. On the one hand, existing constrained multiobjective evolutionary algorithms (CMOEAs) are prone to falling into local optima when facing problems with high-dimensional variables. On the other hand, the relationship between objectives and constraints of CMIES-DP has not been fully analyzed to guide the design of targeted solving techniques. Therefore, this article proposes a time-division-based CMOEA (TDCEA), where the characteristics of CMIES-DP are analyzed to design two main strategies. First, by analyzing the temporal relationship of objectives and constraints, CMIES-DP is decomposed into multiple subproblems with fewer variables and constraints, and these subproblems are sequentially solved to obtain better decision variables. Then, a random concatenation method is designed to combine the decision variables output from subproblems into a solution set with complete decision variables, and the new solution set will be further optimized to find feasible Pareto optimal solutions. Second, the relationship between constraints and objectives is analyzed to guide the design of evolving populations, so as to improve the search ability of the algorithm. In the experiments, the proposed algorithm is used to solve a real-world CMIES-DP case, and results demonstrate that compared with other advanced algorithms, the proposed algorithm achieves better performance regarding diversity, convergence, and distribution.

Battery electric buses (BEBs) face significant operational constraints that limit their flexibility, especially in rotating vehicles across multiple routes. This study focuses on addressing this limitation by introducing a strategic modelling approach that incorporates BEB rotation as a decision variable into an integrated planning optimization model. The proposed model jointly determines the optimal bus-to-route assignments, charging infrastructure siting and sizing, battery capacities, and charging schedules while accounting for electricity real-time pricing (RTP) rates, greenhouse gas (GHG) emissions charges, and battery degradation. Results of a real-world transit network demonstrate that enabling BEB rotation in the planning phase reduces total system costs by 37.88%, with a 12.18% reduction in capital costs and a 59.42% reduction in operational costs. Sensitivity analyses are conducted to validate the proposed model, highlighting the influence of varying key parameters, including energy consumption, infrastructure costs, charging power, electricity RTP rates, and GHG emissions charges on the optimized outcomes.

Establishing a well-planned schedule for departing and arriving aircraft is essential for satisfying the increasing demand for runway traffic, as well as ensuring the balance of runway capacity and demand. However, the existing optimal scheduling methods for departing and arriving aircraft may enhance use efficiency in the runway system for the precontrol phase of tactical planning. It may not be applicable for the flexible runway traffic configurations and the operation mode; in concrete terms, every time the runway operation mode varies, significant adaptations are mandatory to be made to the conventional model. On the other hand, the taxi-out time cost is not considered in the objective function for traditional methods, which usually leads to more taxi time. In this paper, we attempt to address the above challenges; more specifically, we propose a generalized scheduler for the combined arrival–departure scheduling for different runway operation modes in the form of a mixed integer linear program. By means of adjusting parameters, our scheduler can adapt to a wide range of operational scenarios. Meanwhile, the innovative wake separation constraints are more flexible with different aircraft types and operation modes and are linear with the decision variables. Furthermore, we have substantiated the validity of the proposed scheduler through theoretical analysis and experimental measurements.

Within a three-level engineering supply chain that includes the owner, general contractor, and subcontractor, the optimal quality control strategy of the owner under symmetric, asymmetric, and incomplete information was studied. Using the quality control level of the general contractor and subcontractors, as well as the quality supervision level of the general contractor, and the quality supervision level of the owner as decision variables, and the cost function of each party as a quadratic function, the optimal quality control strategy of the owner under symmetric and asymmetric information is derived based on the maximum value method and Lagrange multiplier method. Under incomplete information, the optimal quality control strategy of the owner is derived when the probability density function of the general contractor's quality control level and quality supervision level follows a triangular distribution. Through simulation calculations, the results under different information conditions were analyzed.

Manufacturing industries play a critical role in achieving Net Zero emission targets due to their significant contribution to greenhouse gas emissions. However, existing carbon footprint calculation practices often apply the GHG Protocol and emission factor standards independently, resulting in fragmented methodologies and limited decision-support capabilities. This study develops a carbon footprint calculation system model that integrates GHG Protocol emission scope classification with DEFRA emission conversion factors, supported by a decision-support framework for Net Zero emission planning. Using a Design Science Research (DSR) approach, the study produces a conceptual system model that structures activity data, emission scope classification, and standardized carbon calculation logic into a unified framework. The proposed model enables transparent aggregation of emissions across Scope 1, Scope 2, and Scope 3, while the decision-support framework translates calculation results into decision variables, scenario-based analysis, and Net Zero roadmap formulation. The system functions as a decision-support system that assists manufacturing organizations in interpreting carbon footprint results and supports Net Zero emission planning. The findings demonstrate that integrating standardized carbon accounting methodologies within a system-oriented design enhances methodological coherence, traceability, and strategic relevance for sustainability decision-making in the manufacturing sector.

Spatiotemporal correction of decision variables using XGBoost for multi-objective intelligent scheduling rule extraction model in reservoir-lake flood control systems

This paper presents a new integrated framework combining the Joint Replenishment Problem (JRP) with a generalized Vendor Managed Inventory (VMI) system. The model under consideration represents a three-level supply chain consisting of a supplier, manufacturer, and retailer. The model incorporates multiple product types, each produced on a dedicated machine at the manufacturer, subject to setup costs, and major and minor ordering costs. The primary objective of this research is to optimize a set of critical decision variables, including the common order interval, order frequencies for each item, backorder levels at the retailer, and production initiation times at the manufacturer for each product type, under both deterministic and stochastic demand scenarios. This analysis will provide valuable insights for improving joint replenishment operations in manufacturing. The research begins with a deterministic model fit for the particular issue area derived from the canonical JRP. Within a VMI context, the manufacturer, acting as the supply chain leader, utilizes shared information to derive initial feasible solutions. Subsequently, an optimization technique is employed, combining marginal cost-based and cumulative cost-based algorithms, while leveraging embedded discrete Markov chain decomposition method adapting Jacobi stepping method to determine steady-state probabilities. A cost function is then defined for each action state within this framework. The integration of the VMI policy into the JRP model can significantly reduce the whole cost of the supply chain, through balancing between production initiation and backorders under both the deterministic and stochastic models.

In the manufacturing sector, machine failures frequently disrupt the supply chain, leading to financial losses, particularly when downtime is prolonged. Various methods have been proposed to assess the impact of machine failures on profitability. However, the literature lacks a comprehensive approach that addresses machine failures in the context of maintaining a continuous supply chain through the implementation of an alternative production source during shortage. To bridge this gap, this study proposes an Economic Production Quantity (EPQ) model that incorporates machine failure and compares the manufacturer's profit under two scenarios: one with shortages and another with an alternative production unit compensating for the shortfall. The model aims to maximize profit by optimizing the decision variables. The proposed model is validated through numerical examples, with a detailed sensitivity analysis and managerial insights provided to support decision-making from a business perspective.

This study proposes a novel approach for optimal coordination of Directional Overcurrent Relays (DOCRs) in power distribution networks by employing the Differential Search Algorithm (DSA), complemented by a graph-theoretic network topology processor. The primary objective is to minimize relay operation time while maintaining the Coordination Time Interval (CTI) within an ideal range (0.3–0.8 seconds), thus ensuring selective and reliable protection under various fault scenarios, including those influenced by Distributed Energy Resources (DERs). The research adopts a non-linear optimization framework where the decision variables—Time Multiplier Settings (TMS), Plug Settings (PS), and time-inverse relay characteristics—are optimized. The study formulates the coordination problem under relay setting constraints, operational time limits, and CTI constraints. A detailed methodology involving fault analysis, load flow studies, selectivity constraint refinement, and relay setting computation ensures accurate coordination. DSA's performance is benchmarked against MATLAB-based Sequential Quadratic Programming (SQP) and the Seeker Algorithm across IEEE 3-bus and 8-bus test systems. The proposed method consistently achieves lower total operating times and better CTI compliance, eliminating miscoordination observed in other methods. Teaching Learning-Based Optimization (TLBO), a parameter-independent algorithm, is also integrated to improve robustness and reduce dependency on algorithm-specific tuning. Results confirm the superiority of the DSA approach in optimizing DOCR settings, ensuring protection integrity even in dynamic, DER-penetrated environments. The proposed hybrid coordination strategy, with adaptive relay characteristics, is scalable, efficient, and applicable to real-time distribution systems, demonstrating significant advancements over traditional optimization techniques.

In a random environment, the external shocks may conduct different impacts on the component. Besides, the failure process of the component can also affect the occurrence and impact of the external shock. Under the combined effect of external shocks and natural degradation, the failure process of the component follows a complex competing-risk mode. This paper proposes a mode of two-stage failure process based on delay-time mode (DTM) with multiple modes of external shocks and provides the models of the reliability, expected availability and cost rate in limited duration. An iterative algorithm combining with discretization method is proposed for approximate calculation. On this basis, a policy optimization method of preventive maintenance (PM) is proposed. Two decision variables, first inspection time and inspection interval, are determined by maximizing availability or minimizing cost rate. Finally, a numerical example of the airplane landing gear demonstrates the practicality and feasibility of our method.

Metropolitan service-placement optimization is computationally challenging under strict evaluation budgets and regulatory constraints. Existing approaches either neglect capacity constraints, producing infeasible solutions, or employ population-based metaheuristics requiring hundreds of evaluations—beyond typical municipal planning resources. We introduce a two-stage optimization framework combining Bayesian optimization with domain-informed heuristics to address this constrained, mixed discrete–continuous problem. Stage 1 optimizes continuous service area allocations via the Tree-structured Parzen Estimator with empirical gradient prioritization, reducing effective dimensionality from 81 services to 10–15 per iteration. Stage 2 converts allocations into discrete unit placements via efficiency-ranked bin packing, ensuring regulatory compliance. Evaluation across 35 benchmarks on Saint Petersburg, Russia (117–3060 decision variables), demonstrates that our method achieves 99.4% of the global optimum under a 50-evaluation budget, outperforming BIPOP-CMA-ES (98.4%), PURE-TPE (97.1%), and NSGA-II (96.5%). Optimized configurations improve equity (Gini coefficient of 0.318 → 0.241) while maintaining computational feasibility (2.7 h for 109-block districts). Open-source implementation supports reproducibility and facilitates adoption in metropolitan planning practice.