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A decomposition algorithm for multi-item production planning with independent random demand

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2025年第2期32卷 1002-1032页

作者： Kafiabad, Shayan Tavakoli Zanjani, Masoumeh Kazemi Nourelfath, Mustapha Interuniv Res Ctr Enterprise Networks Logist & Tra Montreal PQ Canada Concordia Univ Dept Mech & Ind Engn Montreal PQ Canada Laval Univ Dept Mech Engn Quebec City PQ Canada

Production planning in a multiproduct setting where the demands for different items are independent random variables that are also featured with a dynamic behavior over the planning horizon is a challenging task. With a particular focus on maintenance facilities, this study proposes a multistage stochastic programming (MSP) model for operations planning under independent random demand of faulty components in the modular-structured devices (e.g., gas turbines) received for repair and overhaul services. A Lagrangian relaxation-based decomposition heuristic is also developed to efficiently solve the problem for real-size instances. This heuristic relies on decomposing the MSP model into submodels corresponding to component STs and coordinating them via a subgradient algorithm to obtain a high-quality feasible solution. Our numerical experiments conducted on a range of problem instances endorse the significant value of incorporating demand uncertainty and the effectiveness of the proposed solution methodology in overcoming computational complexity.

关键词： production planning multistage stochastic programming random demand scenario tree Lagrangian relaxation

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How a dedicated postdischarge unit can reduce hospital congestion and costs

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DECISION SCIENCES 2025年第1期56卷 93-115页

作者： Khatami, Maryam Stauffer, Jon M. Lawley, Mark A. Univ North Texas G Brint Ryan Coll Business Dept Informat Technol & Decis Sci Denton TX 76203 USA Texas A&M Univ Mays Business Sch Dept Informat & Operat Management College Stn TX USA Texas A&M Univ Dept Ind & Syst Engn College Stn TX USA

Depending on the patient's condition, up to 60% of inpatients are discharged to post-acute care facilities (PACFs). These patients may experience several days of nonmedical inpatient stay until the hospital finds a facility that fits their needs, contributing to overcrowding in upstream units. This article studies the feasibility of creating a "postdischarge unit" (PDU) for medically ready-for-discharge patients who experience transfer delays, to improve access to inpatient beds. We use a multistage stochastic program, solved with a dual dynamic programming algorithm, to address the PDU size and capacity question. The random variable is the number of bed requests from upstream units (e.g., emergency department). Our numerical analysis, using data from a large hospital, shows that a PDU can reduce costs and significantly reduce the number of patients waiting for transfer to PACFs that are occupying inpatient beds, as long as the percentage of these patients in the hospital is more than 4%. Compared to current practice in our partner hospital, a PDU could increase access to inpatient beds by up to 13% and result in 2%-21% cost savings. Results show that PDU capacity in hospitals with a larger number of patients waiting for transfer is more sensitive to variation in PDU renovation and operational costs. In addition to using fewer medical staff, a PDU can improve discharge transitions to lower levels of care and more efficiently utilize social workers and physical therapists assisting these patients.

关键词： discharge planning healthcare operations multistage stochastic programming OR in health services patient flow

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Integrated Optimization Scheduling Model for Ship Outfitting Production with Endogenous Uncertainties

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哈尔滨工程大学学报(英文版) 2025年第1期24卷 194-209页

作者： Lijun Liu Pu Cao Yajing zhou Zhixin Long Zuhua Jiang College of Mechanical&Electrical Engineering Shaanxi University of Science&TechnologyXi’an 710021China School of management Hefei University of TechnologyHefei 230009China School of Mechanical Engineering Shanghai Jiao Tong UniversityShanghai 200240China

Ship outfitting is a key process in *** and high-quality ship outfitting is a top priority for modern *** activities are conducted at different stations of *** outfitting plan is one of the crucial issues in *** this paper,production scheduling and material ordering with endogenous uncertainty of the outfitting process are *** uncertain factors in outfitting equipment production are usually decision-related,which leads to difficulties in addressing uncertainties in the outfitting production workshops before production is conducted according to *** uncertainty is regarded as endogenous uncertainty and can be treated as non-anticipativity constraints in the *** address this problem,a stochastic two-stage programming model with endogenous uncertainty is established to optimize the outfitting job scheduling and raw material ordering process.A practical case of the shipyard of China Merchants Heavy Industry Co.,*** used to evaluate the performance of the proposed *** results are achieved at the lowest expected total cost as the complete kit rate of outfitting equipment is improved and emergency replenishment is reduced.

关键词： Ship outfitting Production scheduling Purchase planning Endogenous uncertainty multistage stochastic programming

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Data-Driven multistage Distribuionally Robust programming to Hydrothermal Economic Dispatch With Renewable Energy Sources

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2024年第4期15卷 2322-2335页

作者： Zhang, Xiaosheng Ding, Tao Xiao, Yang Zhang, Hongji Liu, Jinbo Wang, Yishen Xi An Jiao Tong Univ Sch Elect Engn Xian 710049 Peoples R China Natl Power Dispatching & Control Ctr Beijing 100032 Peoples R China State Grid Smart Grid Res Inst Co Ltd Beijing 102209 Peoples R China

The multistage solution is very important to achieve optimal hydrothermal economic dispatch considering the uncertainty of renewable energy sources. In data-driven settings, only some historical trajectories are available and the probability distribution is unknown. A data-driven scheme for multistage stochastic hydrothermal economic dispatch with Markovian uncertainties is proposed in this paper. Then a data-driven distributionally robust stochastic dual dynamic programming (DDR-SDDP) is proposed to tackle the corresponding computational intractability, where the conditional probability distributions are estimated by using kernel regression. The out-of-sample performances are improved by distributionally robust optimization on a Wasserstein distance-based ambiguity set. Furthermore, a scenario aggregation method is designed to reduce the computational burden. Numerical results for a practical regional power system in China are presented and analyzed to verify the effectiveness of the proposed method.

关键词： Economic dispatch renewable energy data-driven multistage stochastic programming data-driven distributionally robust dual stochastic dual dynamic programming Economic dispatch renewable energy data-driven multistage stochastic programming data-driven distributionally robust dual stochastic dual dynamic programming

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BOUNDS AND APPROXIMATIONS FOR multistage stochastic PROGRAMS

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SIAM JOURNAL ON OPTIMIZATION 2016年第1期26卷 831-855页

作者： Maggioni, Francesca Pflug, Georg Ch. Univ Bergamo Dept Management Econ & Quantitat Methods Via Caniana 2 I-24127 Bergamo Italy Univ Vienna Dept Stat & Operat Res Laxenburg Austria Univ Vienna IIASA Laxenburg Austria

Consider (typically large) multistage stochastic programs, which are defined on scenario trees as the basic data structure. It is well known that the computational complexity of the solution depends on the size of the tree, which itself increases typically exponentially fast with its height, i.e., the number of decision stages. For this reason approximations which replace the problem by a simpler one and allow bounding the optimal value are of great importance. In this paper we study several methods to obtain lower and upper bounds for multistage stochastic programs and we demonstrate their use in a multistage inventory problem.

关键词： multistage stochastic programming bounds refinement chain expected value problem

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An interval multistage joint-probabilistic chance-constrained programming model with left-hand-side randomness for crop area planning under uncertainty

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JOURNAL OF CLEANER PRODUCTION 2017年第Nov.20期167卷 1276-1289页

作者： Zhang, Chenglong Li, Mo Guo, Ping China Agr Univ Ctr Agr Water Res China Tsinghuadong St 17 Beijing 100083 Peoples R China

The characteristics of the agricultural water management system is its great complexity and uncertainty as well as dynamic variations in the system components, which results in dynamic characteristics in optimizing the agricultural water allocation and crop area planning. In this study, an interval multistage joint-probabilistic left-hand-side chance-constrained programming (IMJLCP) model is developed for crop area planning in response to these issues. This method is derived from incorporating the techniques of multistage stochastic programming and joint-probabilistic left-hand-side chance-constrained programming within a general interval optimization framework. It can address uncertainties presented as both discrete intervals and probability distributions, and also reflect dynamic characteristics of the system conditions. Moreover, it can reflect randomness in the left-hand-side of the constraints and examine the reliability level of satisfying constraints at both joint and individual probabilities. The developed method is applied to a case study of dynamic agricultural water management and irrigated crop area planning in different growth stages in the middle reaches Of Heihe River Basin, taking ground water and surface water use into account. Six scenarios with different joint (i.e. p = 0.01, 0.05 and 0.1) and individual probabilities (i.e. same and increasing) of the irrigation quota are examined, and a multilayered scenario tree will be provided for a dynamic analysis in a planning horizon. The results indicate that different levels of constraints violation reflect the attitudes of managers to economic benefit and risk. Furthermore, it can help managers to identify desired decision alternatives in intra- and inter-seasonal water allocation among different crops in different subareas. This application makes it highly feasible to enhance the efficiency of irrigation water and ensure sustainable use of water resources, especially for the arid regions dominated by a

关键词： Crop area planning Agricultural irrigation multistage stochastic programming Left-hand-side chance-constrained programming Joint probabilistic programming Uncertainty

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Sampling Scenario Set Partition Dual Bounds for multistage stochastic Programs

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INFORMS JOURNAL ON COMPUTING 2020年第1期32卷 145-163页

作者： Bakir, Ilke Boland, Natashia Dandurand, Brian Erera, Alan Univ Groningen Dept Operat NL-9712 CP Groningen Netherlands Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA RMIT Univ Dept Math Sci Melbourne Vic 3000 Australia

We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. There has been recent interest in dual bounds for such problems, of two types. One, known as expected group subproblem objective (EGSO) bounds, require solution of a group subproblem, which optimizes over a subset of the scenarios, for all subsets of the scenario set that have a given cardinality. Increasing the subset cardinality in the group subproblem improves bound quality, (EGSO bounds form a hierarchy), but the number of group subproblems required to compute the bound increases very rapidly. Another is based on partitions of the scenario set into subsets. Combining the values of the group subproblems for all subsets in a partition yields a partition bound. In this paper, we consider partitions into subsets of (nearly) equal cardinality. We show that the expected value of the partition bound over all such partitions also forms a hierarchy. To make use of these bounds in practice, we propose random sampling of partitions and suggest two enhancements to the approach: sampling partitions that align with the multistage scenario tree structure and use of an auxiliary optimization problem to discover new best bounds based on the values of group subproblems already computed. We establish the effectiveness of these ideas with computational experiments on benchmark problems. Finally, we give a heuristic to save computational effort by ceasing computation of a partition partway through if it appears unpromising.

关键词： stochastic programming multistage stochastic programming bounds dual decomposition

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A successive convex approximation method for multistage workforce capacity planning problem with turnover

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第1期188卷 29-48页

作者： Song, Haiqing Huang, Huei-Chuen Natl Univ Singapore Dept Ind & Syst Engn Singapore 119260 Singapore Sun Yat Sen Univ Lingnan Coll Guangzhou 510275 Peoples R China

Workforce capacity planning in human resource management is a critical and essential component of the services supply chain management. In this paper, we consider the planning problem of transferring, hiring, or firing employees among different departments or branches of an organization under an environment of uncertain workforce demands and turnover, with the objective of minimizing the expected cost over a finite planning horizon. We model the problem as a multistage stochastic program and propose a successive convex approximation method which solves the problem in stages and iteratively. An advantage of the method is that it can handle problems of large size where normally solving the problems by equivalent deterministic linear programs is considered to be computationally infeasible. Numerical experiments indicate that solutions obtained by the proposed method have expected costs near optimal. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multistage workforce capacity planning multistage stochastic programming successive convex approximation method

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multistage stochastic capacity planning of partially upgraded bitumen production with hybrid solution method

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OPTIMIZATION AND ENGINEERING 2019年第4期20卷 1193-1226页

作者： Shahandeh, Hossein Nasab, Farough Motamed Li, Zukui Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 1H9 Canada

Partial upgrading technologies have received a great amount of attention as a promising and economic solution for Canadian oil sands bitumen processing. In this paper, the optimal planning of capital and expansion capacities for partial upgrading of bitumen is studied. We propose a multistage stochastic planning model with consideration of various sources of uncertainties. The main challenge of the stochastic model is the presence of terms in which an uncertain parameter is multiplied by an adjustable dynamic decision variable. To solve the problem, two hybrid methods are proposed: in method 1, the uncertain parameter is modeled with an uncertainty set and the dynamic variable is modeled as scenario dependent variables;in method 2, the uncertain parameter is modeled with samples and the dynamic variable is modeled using the decision rule-based approximation. Finally, results obtained from both hybrid models are compared based on different criteria: (1) computational time, (2) solution performance, and (3) solutions for representative scenarios.

关键词： Partial upgrading Canadian bitumen Capacity and expansion planning multistage stochastic programming Robust optimization

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A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

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CANADIAN JOURNAL OF FOREST RESEARCH 2016年第2期46卷 234-248页

作者： Belval, Erin J. Wei, Yu Bevers, Michael Colorado State Univ Dept Forest & Rangeland Stewardship Ft Collins CO 80523 USA USDA Forest Serv Rocky Mt Res Stn Ft Collins CO 80526 USA

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of "suppression nodes", which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

关键词： multistage stochastic programming wildfire growth wildfire suppression uncertain fire weather

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