Multistage Decision Research Articles

Optimization scheme design in production process based on multi-stage decision-making

This paper studies the control of defective rate in the electronic industry chain, designs a small sample binomial distribution sampling detection scheme to verify the supplier 's defective rate statement and optimize the detection cost. Based on the defective rate, the linear programming and dynamic programming / decision tree model are used to optimize the multi-stage production process, including parts inspection, finished product inspection and unqualified product treatment, so as to maximize the profit of the enterprise. A phased optimization strategy is proposed for complex multi-process situations. Finally, according to the sampling test results, the defect rate estimation is adjusted, the problem model is re-optimized, and the cost control reference scheme is provided.

UNIFY: A unified policy designing framework for solving integrated Constrained Optimization and Machine Learning problems

The integration of Machine Learning (ML) and Constrained Optimization (CO) techniques has recently gained significant interest. While pure CO methods struggle with scalability and robustness, and ML methods like constrained Reinforcement Learning (RL) face difficulties with combinatorial decision spaces and hard constraints, a hybrid approach shows promise. However, multi-stage decision-making under uncertainty remains challenging for current methods, which often rely on restrictive assumptions or specialized algorithms. This paper introduces unify, a versatile framework for tackling a wide range of problems, including multi-stage decision-making under uncertainty, using standard ML and CO components. unify integrates a CO problem with an unconstrained ML model through parameters controlled by the ML model, guiding the decision process. This ensures feasible decisions, minimal costs over time, and robustness to uncertainty. In the empirical evaluation, unify demonstrates its capability to address problems typically handled by Decision Focused Learning, Constrained RL, and Stochastic Optimization. While not always outperforming specialized methods, unify’s flexibility offers broader applicability and maintainability. The paper includes the method’s formalization and empirical evaluation through case studies in energy management and production scheduling, concluding with future research directions.

A stochastic ridesharing user equilibrium model with origin-destination-based ride-matching strategy

Ridesharing, as an emerging mode of modern urban transportation, has gained widespread popularity due to its ability to improve convenience and reduce the expenses in daily travel. To capture its impact on the network-wide traffic flow pattern, this paper develops a new variational inequality (VI) formulation for modeling the stochastic ridesharing user equilibrium (SRUE) problem considering an origin–destination (O-D) -based ride-matching strategy. The proposed SRUE problem is formulated based on a hierarchical logit choice model to depict the multi-stage decision-making (i.e., role choice, ride-matching, and route choice) of the ridesharing travelers. The SRUE model also reflects a two-sided market equilibrium considering the interaction effect between the ridesharing market and the road traffic equilibrium market. The logit choice model captures the ride-matching problem between the drivers and the passengers traveling on the same/different O-D pairs. Moreover, the lower- and upper-bound constraints for a ridesharing driver picking up passengers are established at the O-D level. For solving the SRUE model with O-D-based ride-matching constraints, the Lagrangian dual method (LDM) is adopted by incorporating the Barzilai-Borwein (BB) step size to update the dual variables, which accelerates the convergence of the LDM. Three numerical examples are conducted to illustrate the features of the proposed SRUE model and demonstrate the performance of the solution algorithm.

A generalized outcome-adaptive sequential multiple assignment randomized trial design.

A dynamic treatment regime (DTR) is a mathematical representation of a multistage decision process. When applied to sequential treatment selection in medical settings, DTRs are useful for identifying optimal therapies for chronic diseases such as AIDs, mental illnesses, substance abuse, and many cancers. Sequential multiple assignment randomized trials (SMARTs) provide a useful framework for constructing DTRs and providing unbiased between-DTR comparisons. A limitation of SMARTs is that they ignore data from past patients that may be useful for reducing the probability of exposing new patients to inferior treatments. In practice, this may result in decreased treatment adherence or dropouts. To address this problem, we propose a generalized outcome-adaptive (GO) SMART design that adaptively unbalances stage-specific randomization probabilities in favor of treatments observed to be more effective in previous patients. To correct for bias induced by outcome adaptive randomization, we propose G-estimators and inverse-probability-weighted estimators of DTR effects embedded in a GO-SMART and show analytically that they are consistent. We report simulation results showing that, compared to a SMART, Response-Adaptive SMART and SMART with adaptive randomization, a GO-SMART design treats significantly more patients with the optimal DTR and achieves a larger number of total responses while maintaining similar or better statistical power.

Post-disaster repair optimization method for traction power supply system of electrified railways based on train operation loss

The traction power supply system (TPSS) is the critical facility that provides power to electrified railways. However, TPSS is highly susceptible to extreme events. Therefore, it is essential to develop reasonable post-disaster repair strategies to mitigate losses. In this context, this paper proposes a post-disaster repair optimization method for TPSS based on train operation loss. The hazard characterization and equipment fragility analysis are introduced to simulate post-disaster fault scenarios of TPSSs. By analyzing the changes in component states during the repair process, the component state transition model based on the multi-stage decision process is established and the state transition relationship is derived. According to the component state and TPSS topology, the model for evaluating the power supply state of the traction network is constructed. On this basis, the indicator of train operation loss is defined, which is used as the objective to formulate the post-disaster repair optimization model of TPSSs. The case study using real-world high-speed railway data demonstrates that, compared to traditional repair strategies, the proposed method effectively reduces the restoration time of TPSS and significantly decreases train operation loss. This method can provide maintenance personnel with theoretical bases for formulating post-disaster repair strategies.

Healthcare Waste Management through Multi-Stage Decision-Making for Sustainability Enhancement

The possible threats that healthcare waste management (HWM) poses to the environment and public health are making it more and more crucial for medical facility administrators to be worried about it. This is in line with the global trend towards firms giving sustainability more of a priority. Many organizations, including the World Health Organization (WHO) and other organizations, as well as national and state laws, have mandated the proper disposal of infectious and hazardous healthcare waste. To effectively address the complex problem of selecting the best treatment option for HWM, a multi-criteria decision-making (MCDM) procedure must be used. The alternative ranking order method accounting for two-step normalization (AROMAN) methodology is provided in the context of q-rung orthopair fuzzy environment. This method comprises two steps of normalization and is based on the criteria importance through intercriteria correlation (CRITIC) paradigm. Whereas the AROMAN methodology uses vector and linear normalization techniques to improve the accuracy of the data for further computations, the CRITIC method assesses the intercriteria correlations and scores the significance of each criterion. The ranking from the proposed method is Al5>Al4>Al3>Al1>Al2. The study’s conclusions indicate that recycling (Al5) is the best option since it lessens trash production, aids in resource recovery, and protects the environment. Using this method helps decision makers deal with subjectivity and ambiguity more skillfully, promotes consistency and transparency in decision making, and streamlines the process of choosing the best waste management system. Sustainable waste management practices have been implemented in the biomedical industry with some success. The proposed technique is a helpful tool for legislators and practitioners seeking to improve waste management systems.

A Dynamic Programming Approach to the Collision Avoidance of Autonomous Ships

The advancement of autonomous capabilities in maritime navigation has gained significant attention, with a trajectory moving from decision support systems to full autonomy. This push towards autonomy has led to extensive research focusing on collision avoidance, a critical aspect of safe navigation. Among the various possible approaches, dynamic programming is a promising tool for optimizing collision avoidance maneuvers. This paper presents a DP formulation for the collision avoidance of autonomous vessels. We set up the problem framework, formulate it as a multi-stage decision process, define cost functions and constraints focusing on the actual requirements a marine maneuver must comply with, and propose a solution algorithm leveraging parallel computing. Additionally, we present a greedy approximation to reduce algorithm complexity. We put the proposed algorithms to the test in realistic navigation scenarios and also develop an extensive test on a large set of randomly generated scenarios, comparing them with the RRT* algorithm using performance metrics proposed in the literature. The results show the potential benefits of an autonomous navigation or decision support framework.

Research on Multi-Stage Post-Occupancy Evaluation Framework of Community Comprehensive Elderly Care Service Facilities under the Public-Private Partnership Mode—A Case Study of China

The key to whether elderly individuals in the community can enjoy their later years peacefully lies in the service capabilities of community comprehensive elderly care service facilities (CCECSF) under the Public-Private Partnership (PPP) mode. To maintain a high level of service capability in community comprehensive elderly care service facilities under PPP mode, scientific evaluation of the effectiveness of these facilities is equally crucial. This article first constructs a post-occupancy evaluation index system of community comprehensive elderly care service facilities under PPP mode that includes three evaluation attributes and fifteen evaluation criteria based on the Chinese culture and lifestyle habits. Regarding the issue of direct users being unable to directly participate in evaluations, the uncertainty in evaluation information, and the volatility of evaluation results, a multi-stage post-occupancy evaluation model is constructed based on probabilistic linguistic term set, TOPSIS model and multi-stage decision theory. The above post-occupancy evaluation index system and evaluation model together constitute a multi-stage post-occupancy evaluation framework for community comprehensive elderly care service facilities under PPP mode. The outcomes of the case study indicate that the post-occupancy evaluation index system can offer a scientifically guided approach for evaluating the service level of community comprehensive elderly care service facilities under the PPP mode; meanwhile, the multi-stage evaluation model can enable direct user participation in the post-evaluation of facility usage and improve the robustness and reduce the fluctuation of the evaluation results, so as to improve the scientificity of the evaluation results.

Modeling heterogeneous and adaptive homeowners’ decision-making for green retrofit

Green retrofitting (GR) of existing residential buildings is widely acknowledged as a potential solution for addressing climate and energy challenges. However, the realization of GR potential depends on homeowners’ decision-making, as they play a pivotal role in initiating GR and are the primary users of retrofitted homes. Previous studies have explored homeowners’ GR decisions from various perspectives. The majority of these studies may have encountered limitations, such as the use of static analysis methods, homogeneity assumptions, and oversimplified decision processes. These limitations can potentially hinder a comprehensive understanding of homeowners’ GR adoption, indicating the need for further research. To address this research gap, this study develops a decision-making model for homeowners that incorporates multiple dimensions: heterogeneity (e.g., individual attributes and GR motivations), a multi-stage decision process (needs-utility-willingness-adoption), and dynamic adaptability (both at individual and overall networks). The proposed model is empirically validated through Python simulations based on a case study in China. The findings of this study reveal the critical roles of GR needs, perceived (actual) utility, and perceived behavioral control in homeowners’ adoption of GR. Moreover, this study highlights the significance of coordinating homeowners’ overall perceived utility with the specific sub-utility associated with their motivations. Furthermore, empirical evidence underscores the influence of social factors on GR adoption and emphasizes the existence of gaps across different stages of the decision-making process. Drawing from these research findings, policy implications are proposed for promoting housing GR. This research contributes to the advancement of decision models for building GR and provides valuable insights for policymakers to promote housing GR.

GOALNET: Interleaving Neural Goal Predicate Inference with Classical Planning for Generalization in Robot Instruction Following

Our goal is to enable a robot to learn how to sequence its actions to perform high-level tasks specified as natural language instructions, given successful demonstrations from a human partner. Our novel neuro-symbolic solution GOALNET builds an iterative two-step approach that interleaves (i) inferring next subgoal predicate implied by the language instruction, for a given world state, and (ii) synthesizing a feasible subgoal-reaching plan from that state. The agent executes the plan, and the two steps are repeated. GOALNET combines (i) learning, where dense representations are acquired for language instruction and the world state via a neural network prediction model, enabling generalization to novel settings and (ii) planning, where the cause-effect modeling by a classical planner eschews irrelevant predicates, facilitating multi-stage decision making in large domains. GOALNET obtains 78% improvement in the goal reaching rate in comparison to several state-of-the-art approaches on benchmark data with multi-stage instructions. Further, GOALNET can generalize to novel instructions for scenes with unseen objects. Source code available at https://github. com/reail-iitd/goalnet.

Multiobjective Lipschitz Bandits under Lexicographic Ordering

This paper studies the multiobjective bandit problem under lexicographic ordering, wherein the learner aims to simultaneously maximize ? objectives hierarchically. The only existing algorithm for this problem considers the multi-armed bandit model, and its regret bound is O((KT)^(2/3)) under a metric called priority-based regret. However, this bound is suboptimal, as the lower bound for single objective multi-armed bandits is Omega(KlogT). Moreover, this bound becomes vacuous when the arm number K is infinite. To address these limitations, we investigate the multiobjective Lipschitz bandit model, which allows for an infinite arm set. Utilizing a newly designed multi-stage decision-making strategy, we develop an improved algorithm that achieves a general regret bound of O(T^((d_z^i+1)/(d_z^i+2))) for the i-th objective, where d_z^i is the zooming dimension for the i-th objective, with i in {1,2,...,m}. This bound matches the lower bound of the single objective Lipschitz bandit problem in terms of T, indicating that our algorithm is almost optimal. Numerical experiments confirm the effectiveness of our algorithm.

Project Investment Decision Under Uncertain Information

With the change of environment and market, the current investment project decision is facing a more complex environment, the competition of enterprises intensifies, the decision complexity increases, and the demand for scientific decision is increasing. The advantage of multi-attribute decision making in investment project decision is increasingly prominent. This paper studies the application of multi-attribute decision making under triangular fuzzy uncertainty information in investment decision making. Considering the decision makers' risk aversion and preference attitude in multi-stage decision making process, a dynamic reference point setting method based on stage development characteristics is proposed. Considering that the attribute value and attribute value will produce compensation in the decision-making process, the attribute value difference formula is constructed to reduce the decision-making bias, and on this basis, an improved TODIM method is proposed. The triangular fuzzy number uncertainty information is introduced to evaluate the attributes of each scheme in each decision stage, and the information is aggregated by the aggregation operator. Combining the dynamic multi-attribute decision model, the practical problem is solved. The practicability and feasibility of this method are demonstrated by the example analysis and method comparison.

Q-Rung orthopair fuzzy dynamic aggregation operators with time sequence preference for dynamic decision-making.

The q-rung orthopair fuzzy set (q-ROPFS) is a kind of fuzzy framework that is capable of introducing significantly more fuzzy information than other fuzzy frameworks. The concept of combining information and aggregating it plays a significant part in the multi-criteria decision-making method. However, this new branch has recently attracted scholars from several domains. The goal of this study is to introduce some dynamic q-rung orthopair fuzzy aggregation operators (AOs) for solving multi-period decision-making issues in which all decision information is given by decision makers in the form of "q-rung orthopair fuzzy numbers" (q-ROPFNs) spanning diverse time periods. Einstein AOs are used to provide seamless information fusion, taking this advantage we proposed two new AOs namely, "dynamic q-rung orthopair fuzzy Einstein weighted averaging (DQROPFEWA) operator and dynamic q-rung orthopair fuzzy Einstein weighted geometric (DQROPFEWG) operator". Several attractive features of these AOs are addressed in depth. Additionally, we develop a method for addressing multi-period decision-making problems by using ideal solutions. To demonstrate the suggested approach's use, a numerical example is provided for calculating the impact of "coronavirus disease" 2019 (COVID-19) on everyday living. Finally, a comparison of the proposed and existing studies is performed to establish the efficacy of the proposed method. The given AOs and decision-making technique have broad use in real-world multi-stage decision analysis and dynamic decision analysis.

Distributionally Robust Multiperiod Inventory Model for Omnichannel Retailing Considering Buy-Online, Pickup-in-Store and Out-of-Stock, Home-Delivery Services

This article proposes the distributionally robust multiperiod inventory model incorporating the buy-online-pickup-in-store (BOPIS) and out-of-stock-home-delivery-service (OSHDS), which are the representative services of omnichannel retailing. Under this omnichannel system, the retailer operates both online and brick-and-mortar (B&M) stores simultaneously, which allow interactive flows of customer demands and desired products. The BOPIS allows customers who buy products through the online store to pick them up in the B&M store. Meanwhile, the OSHDS allows customers who find the product they want out of stock in a B&M store to receive it later, through express delivery from the online store. To capture the correlated uncertain demands of the BOPIS and OSHDS, we adopt a factor-based demand model that is affinely dependent on predefined uncertain factors. To handle a multistage decision process under uncertain demands, we utilize a rule-based approximation and distributionally robust bound to derive a tractable formulation. Computational results achieved in this article offer some insights that BOPIS and OSHDS play a role in providing retailer with flexibility, which could handle unsatisfied demands efficiently.

Multi-Stage Decision Rules for Power Generation & Storage Investments With Performance Guarantees

We develop multi-stage linear decision rules (LDRs) for dynamic power system generation and energy storage investment planning under uncertainty and propose their chance-constrained optimization with performance guarantees. First, the optimized LDRs guarantee operational and carbon policy feasibility of the resulting dynamic investment plan even when the planning uncertainty distribution is ambiguous. Second, the optimized LDRs internalize the tolerance of the system planner towards the stochasticity (variance) of uncertain investment outcomes. They can eventually produce a quasi-deterministic investment plan, which is insensitive to uncertainty (as in deterministic planning) but robust to its realizations (as in stochastic planning). Last, we certify the performance of the optimized LDRs with the bound on their sub-optimality due to their linear functional form. Using this bound, we guarantee that the preference of LDRs over less restrictive – yet poorly scalable – scenario-based optimization does not lead to financial losses exceeding this bound. We use a testbed of the U.S. Southeast power system to reveal the trade-offs between the cost, stochasticity, and feasibility of LDR-based investments. We also conclude that the LDR sub-optimality depends on the amount of uncertainty and the tightness of chance constraints on operational, investment and policy variables.

Exploration of Digital Transformation Path of Ideological education in Colleges and Universities with the Help of Digital Technology

Abstract With the development of information technology and the advancement of education informatization, the use of mathematical modeling and extensive data analysis technology makes the realization of precision education possible. In this paper, we study the problem of precise teaching intervention from the perspective of multi-stage decision-making, introduce a reinforcement learning algorithm, portray the process attributes and temporal characteristics of teaching, use a Q-learning algorithm to construct a general framework for precise teaching intervention, and through the empirical study of Ideologicalcs teaching in colleges and universities, we show the specific application of this framework in teaching practice and analyze the digital transformation path of the Ideologicalcs education in colleges and universities. The results show that under precise teaching intervention, the students’ pre-post test scores of each Ideologicalcs behavioral characteristic index are significantly different at the 0.05 level. This study helps improve students’ learning effectiveness and provides support for teachers to conduct precise ideological teaching.

New similarity measures and TOPSIS method for multi stage decision analysis with cubic intuitionistic fuzzy information

This research work proposes a novel approach for multi stage decision analysis (MSDA) using innovative concepts of cubic intuitionistic fuzzy set (CIFS) theory. The paper introduces CIF-technique for order preference by similarity to ideal solution (TOPSIS) as a robust method for MSDA problems, particularly for the diagnosis of epilepsy disorders. To achieve this goal, new similarity measures (SMs) are developed for CIFS, including the Cosine angle between two vectors, a new distance measure, and the Cosine function, presented as three different types of Cosine similarity measures. The proposed CIF-TOPSIS approach is found to be suitable for precise value performance ratings and is expected to be a viable approach for case studies in the diagnosis of epilepsy disorders. The efficiency and reliability of the proposed MSDA methods is efficiently carried through numerical examples and comparative analysis.

Carbon-neutral potential analysis of urban power grid: A multi-stage decision model based on RF-DEMATEL and RF-MARCOS

Carbon-neutral potential analysis of urban power grid: A multi-stage decision model based on RF-DEMATEL and RF-MARCOS

MRI-based automated multitask deep learning system to evaluate supraspinatus tendon injuries.

To establish an automated, multitask, MRI-based deep learning system for the detailed evaluation of supraspinatus tendon (SST) injuries. According to arthroscopy findings, 3087 patients were divided into normal, degenerative, and tear groups (groups 0-2). Group 2 was further divided into bursal-side, articular-side, intratendinous, and full-thickness tear groups (groups 2.1-2.4), and external validation was performed with 573 patients. Visual geometry group network 16 (VGG16) was used for preliminary image screening. Then, the rotator cuff multitask learning (RC-MTL) model performed multitask classification (classifiers 1-4). A multistage decision model produced the final output. Model performance was evaluated by receiver operating characteristic (ROC) curve analysis and calculation of related parameters. McNemar's test was used to compare the differences in the diagnostic effects between radiologists and the model. The intraclass correlation coefficient (ICC) was used to assess the radiologists' reliability. p < 0.05 indicated statistical significance. In the in-group dataset, the area under the ROC curve (AUC) of VGG16 was 0.92, and the average AUCs of RC-MTL classifiers 1-4 were 0.99, 0.98, 0.97, and 0.97, respectively. The average AUC of the automated multitask deep learning system for groups 0-2.4 was 0.98 and 0.97 in the in-group and out-group datasets, respectively. The ICCs of the radiologists were 0.97-0.99. The automated multitask deep learning system outperformed the radiologists in classifying groups 0-2.4 in both the in-group and out-group datasets (p < 0.001). The MRI-based automated multitask deep learning system performed well in diagnosing SST injuries and is comparable to experienced radiologists. Our study established an automated multitask deep learning system to evaluate supraspinatus tendon (SST) injuries and further determine the location of SST tears. The model can potentially improve radiologists' diagnostic efficiency, reduce diagnostic variability, and accurately assess SST injuries. • A detailed classification of supraspinatus tendon tears can help clinical decision-making. • Deep learning enables the detailed classification of supraspinatus tendon injuries. • The proposed automated multitask deep learning system is comparable to radiologists.

Global Trajectory Optimization of Multispacecraft Successive Rendezvous Using Multitree Search

This paper investigates the global optimization of multispacecraft successive rendezvous trajectories, which is divided here into three subproblems: target assignment, sequence optimization, and rendezvous time optimization. A method consisting of two novel algorithms is proposed to solve these subproblems. First, a multitree search framework is developed to assign multiple targets to each spacecraft and simultaneously optimize the rendezvous sequence for every single spacecraft. Specifically, a novel algorithm of local search combined with beam search is proposed. Second, this paper converts the rendezvous time optimization problem into a multistage decision problem. Based on a critical rendezvous-epoch-dependent characteristic found in this subproblem, the number of state variables is thereby reduced. A novel dual dynamic programming algorithm is proposed and combined with dynamic programming to solve for the globally optimal rendezvous epochs efficiently. Global optimality is guaranteed by Bellman’s principle of optimality, which is the first time in such a problem to our knowledge. The proposed method achieves state-of-the-art performance in several typical fuel-optimal scenarios of active debris removal. This open-sourced method is non-database-dependent and contains only one design stage, which is expected to be adopted in other successive rendezvous missions.