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A stochastic programming approach to the cutting stock problem with usable leftovers

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第1期308卷 38-53页

作者： Cherri, Adriana Cristina Cherri, Luiz Henrique Oliveira, Beatriz Brito Oliveira, Jose Fernando Carravilla, Maria Antonia Univ Estadual Paulista Fac Ciencias Bauru SP Brazil Newfoundland Capital Management Sao Paulo SP Brazil Univ Porto Fac Engn INESC TEC Porto Portugal

In cutting processes, one of the strategies to reduce raw material waste is to generate leftovers that are large enough to return to stock for future use. The length of these leftovers is important since waste is expected to be minimal when cutting these objects in the future. However, in several situations, future demand is unknown and evaluating the best length for the leftovers is challenging. Furthermore, it may not be economically feasible to manage a stock of leftovers with multiple lengths that may not result in minimal waste when cut. In this paper, we approached the cutting stock problem with the possibility of generating leftovers as a two-stage stochastic program with recourse. We approximated the demand levels for the different items by employing a finite set of scenarios. Also, we modeled different decisions made before and after uncertainties were revealed. We proposed a mathematical model to represent this problem and developed a column generation approach to solve it. We ran computational experi-ments with randomly generated instances, considering a representative set of scenarios with a varying probability distribution. The results validated the efficiency of the proposed approach and allowed us to derive insights on the value of modeling and tackling uncertainty in this problem. Overall, the results showed that the cutting stock problem with usable leftovers benefits from a modeling approach based on sequential decision-making points and from explicitly considering uncertainty in the model and the solution method. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )

关键词： Cutting Usable leftovers stochastic programming Column generation

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On the safe side of stochastic programming: bounds and approximations

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2023年第6期30卷 3201-3237页

作者： Narum, Benjamin S. Maggioni, Francesca Wallace, Stein W. NHH Norwegian Sch Econ Dept Business & Management Sci Helleveien 30 N-5045 Bergen Norway Univ Bergamo Dept Management Informat & Prod Engn Viale G Marconi 5 I-24044 Dalmine BG Italy

There will always be stochastic programs that are too large or complex to be solved in their basic form. In this article, we review, discuss, and compare different ways such stochastic programs can be handled using bounds and approximations, all based on manipulations of the random variables. We are particularly interested in how methods based on different underlying ideas can be combined or possibly are the same.

关键词： stochastic programming bounds distribution approximation function approximation

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Assessing the importance of detailed forest inventory information using stochastic programming

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CANADIAN JOURNAL OF FOREST RESEARCH 2024年第12期54卷 1486-1499页

作者： Nahorna, Olha Noordermeer, Lennart Gobakken, Terje Eyvindson, Kyle Norwegian Univ Life Sci Fac Environm Sci & Nat Resource Management NMBU POB 5003 NO-1432 As Norway

Errors in forest inventory data can lead to sub-optimal management decisions and dramatic economic losses. Forest inventory approaches are typically evaluated by their levels of precision and accuracy;however, this overlooks the specific usefulness of the data in decision-making. By evaluating the value of information (VoI), we can assess the usefulness of the data for specific decision-making problems. We evaluated the VoI through stochastic programming for four airborne laser scanning-based inventory approaches. The stochastic programming model explored the trade-off between the maximal net present value and the minimal conditional value at risk of meeting specified periodic income targets. We evaluated a range of periodic targets and risk aversion preference levels. To compare the performance of the inventory approaches, we used a reference dataset that was acquired using a forest harvester with precise positioning. For a wide range of the trade-offs, inventory approaches with higher-quality information provided the best overall performance. If only one of the extreme objectives was desired, less precise inventory approaches were sufficient to produce high-quality solutions.

关键词： value of information stochastic programming uncertainty risk management forest inventory data quality

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An Uncertain Optimization Method Based on Adaptive Discrete Approximation Rejection Sampling for stochastic programming with Incomplete Knowledge of Uncertainty

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2023年第2期48卷 1399-1425页

作者： Fang, Bopeng Dong, Zhurong Zhao, Chen Liu, Zhi Wang, Jing Shenzhen Polytech Shenzhen 518055 Peoples R China Shenzhen Polytech Res Inst New Energy Vehicle Technol Shenzhen 518055 Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Peoples R China

stochastic programming has been widely used in various application scenarios and theoretical research works. However, these excellent methods depend on specific explicit probability modeling with complete knowledge of uncertainty, which is very limited in practical problem since there is usually no way to abstract complex uncertainties into the commonly used known probability models. In this paper, a novel generative model named the Adaptive Discrete Approximation Rejection Sampling is proposed for stochastic programming with incomplete knowledge of uncertainty, which can not only simulate uncertain scenarios from a complex explicit probability model that cannot meet the constraints of existing sampling methods, but also even simulate scenarios from a sample set related to uncertainty when the specific explicit probability model of uncertainty is missing or unavailable. The method is to establish the easy-to-sample proposal distribution by approximately transforming the complex hard-to-sample target probability model, to make the proposal distribution close enough to the target distribution, so as to achieve an efficient sampling while ensuring the performance of the model. On this basis, combining the Monte Carlo method and heuristic optimization, an uncertain optimization model for stochastic programming with incomplete knowledge of uncertainty is further constructed, to solve the unavailability of the existing stochastic programming methods in the absence of explicit probability model of uncertainty. Experimental results show the advantages of the proposed method in terms of applicability, adaptability, accuracy, efficiency and model performance.

关键词： stochastic programming Rejection sampling Adaptive proposal distribution Monte Carlo method Machine learning

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stochastic programming models for a fleet sizing and appointment scheduling problem with random service and travel times

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2024年 165卷

作者： Li, Shutian Shehadeh, Karmel S. Tsang, Man Yiu Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA

We propose a new stochastic mixed -integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following problems simultaneously: (i) a fleet sizing problem that determines the number of providers required to serve customers;(ii) an assignment problem that assigns customers to providers;and (iii) a sequencing and scheduling problem that decides the sequence of appointment times of customers assigned to each provider. The objective is to minimize the fixed cost of hiring providers plus the expectation of a weighted sum of customers' waiting time and providers' travel time, overtime, and idle time. We compare our proposed model with an extension of an existing model for a closely related problem in the literature, theoretically and empirically. Specifically, we show that our newly proposed model is more compact (i.e., has fewer variables and constraints) and provides a tighter linear programming relaxation. Furthermore, to handle large instances observed in other application domains, we propose two optimization -based heuristics that decompose the HFASP decision process into two steps. The first step involves determining fleet sizing and assignment decisions, and the second constructs a routing plan and a schedule for each provider. We present extensive computational results to show the size and characteristics of HFASP instances that can be solved with our proposed model, demonstrating its computational efficiency over the extension. Results also show that the proposed heuristics can quickly produce high -quality solutions to large instances with an optimality gap not exceeding 5% on tested instances. Finally, we use a case study based on a service region in Lehigh County to derive insights into the HFASP.

关键词： Fleet sizing Scheduling Routing Home services stochastic programming

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Multi-resource allocation and care sequence assignment in patient management: a stochastic programming approach

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HEALTH CARE MANAGEMENT SCIENCE 2024年第3期27卷 352-369页

作者： Yao, Xinyu Shehadeh, Karmel S. Padman, Rema Carnegie Mellon Univ Pittsburgh PA 15213 USA Lehigh Univ Bethlehem PA USA

To mitigate outpatient care delivery inefficiencies induced by resource shortages and demand heterogeneity, this paper focuses on the problem of allocating and sequencing multiple medical resources so that patients scheduled for clinical care can experience efficient and coordinated care with minimum total waiting time. We leverage highly granular location data on people and medical resources collected via Real-Time Location System technologies to identify dominant patient care pathways. A novel two-stage stochastic Mixed Integer Linear programming model is proposed to determine the optimal patient sequence based on the available resources according to the care pathways that minimize patients' expected total waiting time. The model incorporates the uncertainty in care activity duration via sample average *** employ a Monte Carlo Optimization procedure to determine the appropriate sample size to obtain solutions that provide a good trade-off between approximation accuracy and computational time. Compared to the conventional deterministic model, our proposed model would significantly reduce waiting time for patients in the clinic by 60%, on average, with acceptable computational resource requirements and time complexity. In summary, this paper proposes a computationally efficient formulation for the multi-resource allocation and care sequence assignment optimization problem under uncertainty. It uses continuous assignment decision variables without timestamp and position indices, enabling the data-driven solution of problems with real-time allocation adjustment in a dynamic outpatient environment with complex clinical coordination constraints.

关键词： Scheduling Real-time location system data Care pathway management Uncertainty in activity duration stochastic programming Operations research Operations management

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A stochastic programming model of the recycling process considering uncertainty due to processing problems

A stochastic programming model of the recycling process cons...

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International Technical Conference on Circuits/Systems, Computers, and Communications (ITC-CSCC)

作者： Suzuki, Yusei Kai, Masaya Sakakibara, Kazutoshi Takano, Ryo Matsumoto, Takuya Nakamura, Masaki Toyama Prefectural Univ Dept Informat Syst Engn Toyama Japan Toyama Prefectural Univ Grad Sch Engn Toyama Japan Toyama Prefectural Univ Dept Data Sci Toyama Japan

ISBN: (纸本)9798350379068;9798350379051

In metal recycling plants, equipment problems originating from materials are not infrequent when recycling various types of input materials. Appropriate scheduling is required while taking such uncertainties into account. In this study, the recycling process is modeled as a mixed integer programming problem and then as a two-stage stochastic programming problem that takes into account the uncertainty caused by troubles and the overtime caused by delays. Since the two-stage stochastic programming model becomes more difficult to derive the optimal solution as the problem size increases, a sampling-based solution method is used to reduce computation time by applying the integer variable values of the solution obtained by optimization in a small number of scenarios as constants to a model that includes all scenarios. The effectiveness of the model is examined through numerical experiments based on actual factory operations.

关键词： metal recycling process stochastic programming scenario sampling

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stochastic programming applications to agent route planning in adverse weather

Stochastic programming applications to agent route planning ...

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2022 International Conference on Computer, Artificial Intelligence, and Control Engineering, CAICE 2022

作者： Jian, Lv Xin Yao, Yan Zong Shandong Hi-Speed Construction Management Group Co. Ltd Shan Dong Jinan China

ISBN: (纸本)9781510655942

The agent routing process considering weather conditions is a multi-objective optimization problem constrainedly, which various optimization criteria and constraints should be considered. The quality of the given routes depends not only on the quality of the data, but also on the modelling of the optimization problem and the algorithm chosen to solve it. Because of universality of mathematical methods and the resulting decision-making challenges, the aim of this paper is to comprehensively compare the existing most advanced methods through literature review and elaborate different modelling methods, optimization algorithms and their application in agent ship route planning. © 2022 SPIE.

关键词： stochastic programming

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Resilient Supply Chain Network Planning Method with Two-Stage stochastic programming: Extension to Multiple Product Supply Chains 43rd

Resilient Supply Chain Network Planning Method with Two-Stag...

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43rd IFIP WG 5.7 International Conference on Advances in Production Management Systems (APMS)

作者： Kaihara, Toshiya Kobayashi, Hibiki Kokuryo, Daisuke Hara, Masashi Miyachi, Yuto Yamao, Dickson Hideki Sariddichainunta, Puchit Kobe Univ Grad Sch Syst Informat 1-1 Rokkodai Cho Kobe Hyogo 6578501 Japan Lion Corp 1-3-28 Kuramae Tokyo 1118644 Japan

ISBN: (纸本)9783031658969;9783031658945;9783031658938

In supply chain management, risk management is crucial to ensure a stable product supply while considering economic efficiency. It is essential to design resilient supply chains that can maintain production capacity by preparing for and responding to predictable risks. Our group has proposed strategic planning methodologies for the selection of appropriate material suppliers and the optimization of inventory levels across the supply chain, including suppliers, manufacturers, and wholesalers, with considering potential risks. We have introduced a planning method for resilient supply chain networks using two-stage stochastic programming. This paper extends the proposed method to accommodate supply chains managing multiple products, aiming for more realistic conditions. The effectiveness of the extended method is assessed through computational experiments.

关键词： Resilient supply chain network stochastic programming Inventory control Material supplier selection

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Optimal Scenario Reduction Method for stochastic programming via Probabilistic Similarity Function 36

Optimal Scenario Reduction Method for Stochastic Programming...

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36th Chinese Control and Decision Conference (CCDC)

作者： Hu, Jinxing Cao, Yimai Liu, Yumeng Huang, Zhanjun Hebei Univ Technol State Key Lab Reliabil & Intelligence Elect Equip Tianjin Peoples R China Hebei Univ Technol Coll Elect Engn Tianjin Peoples R China Northwestern Polytech Univ Coll Aeronaut Xian Peoples R China

ISBN: (纸本)9798350387780;9798350387797

In the scenario-based stochastic programming problems, the computational burden increase as the number of scenarios increases, which involves necessary scenario reduction operations. For the scenario reduction problem with high-dimensional random vector, an optimal reduction framework is presented to eliminate redundant scenarios. In this framework, the concept of probabilistic similarity function is firstly proposed to solve the problem that scenarios cannot be clearly distinguished by traditional distance-based reduction methods in the high-dimensional scenario clustering process. The relative distance under each dimension of scenarios is considered in the computation of probabilistic similarity function, which depends not only on the values of two scenario vectors but also on the overall scenario set. The proposed recursive-type reduction method aims at maximizing the probabilistic similarity between the original scenario set and reduced scenario set. The numerical results demonstrate that our method can exhibit better performance than distance-based methods and have good universality for different stochastic programming problems.

关键词： scenario reduction stochastic programming probabilistic similarity function high-dimensional scenario clustering nodes

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