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A stochastic mixed integer programming Framework for Underground Mining Production Scheduling Optimization Considering Grade Uncertainty

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IEEE ACCESS 2020年 8卷 24495-24505页

作者： Huang, Shuwei Li, Guoqing Ben-Awuah, Eugene Afum, Bright Oppong Hu, Nailian Univ Sci & Technol Beijing Sch Civil & Resource Engn Beijing 100083 Peoples R China Laurentian Univ Bharti Sch Engn MOL Sudbury ON P3E 2C6 Canada

Conventional mine planning approaches use an estimated orebody model as input to generate optimal production schedules. The smoothing effect of some geostatistical estimation methods cause most of the mine plans and production forecasts to be unrealistic and incomplete. With the development of simulation methods, the risks from grade uncertainty in ore reserves can be measured and managed through a set of equally probable orebody realizations. In order to incorporate grade uncertainty into the strategic mine plan, a stochastic mixed integer programming (SMIP) formulation is presented to optimize an underground cut-and-fill mining production schedule. The objective function of the SMIP model is to maximize the net present value (NPV) of the mining project and minimize the risk of deviation from the production targets. To demonstrate the applicability of the SMIP model, a case study on a cut-and-fill underground gold mining operation is implemented.

关键词： Production schedule optimization mining industry stochastic mixed integer programming grade uncertainty underground mining

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A study of progressive hedging for stochastic integer programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2023年第3期86卷 989-1034页

作者： Christiansen, Jeffrey Dandurand, Brian Eberhard, Andrew Oliveira, Fabricio RMIT Univ Math & Stat 124 La Trobe St Melbourne Vic 3000 Australia Aalto Univ Math & Syst Anal Otakaari 1 Espoo 02150 Uusimaa Finland

Motivated by recent literature demonstrating the surprising effectiveness of the heuristic application of progressive hedging (PH) to stochastic mixed-integer programming (SMIP) problems, we provide theoretical support for the inclusion of integer variables, bridging the gap between theory and practice. We provide greater insight into the following observed phenomena of PH as applied to SMIP where optimal or at least feasible convergence is observed. We provide an analysis of a modified PH algorithm from a different viewpoint, drawing on the interleaving of (split) proximal-point methods (including PH), Gauss-Seidel methods, and the utilisation of variational analysis tools. Through this analysis, we show that under mild conditions, convergence to a feasible solution should be expected. In terms of convergence analysis, we provide two main contributions. First, we contribute insight into the convergence of proximal-point-like methods in the presence of integer variables via the introduction of the notion of persistent local minima. Secondly, we contribute an enhanced Gauss-Seidel convergence analysis that accommodates the variation of the objective function under mild assumptions. We provide a practical implementation of a modified PH and demonstrate its convergent behaviour with computational experiments in line with the provided analysis.

关键词： stochastic mixed integer programming Progressive hedging Variational analysis Gauss-Seidel methods

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A stochastic optimisation approach to maintain supply chain viability under the ripple effect

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2023年第8期61卷 2452-2469页

作者： Sawik, Tadeusz Reykjavik Univ Dept Engn Reykjavik Iceland AGH Univ Sci & Technol Dept Operat Res Krakow Poland Reykjavik Univ Dept Engn IS-101 Reykjavik Iceland AGH Univ Sci & Technol Dept Operat Res PL-30059 Krakow Poland

This paper presents a novel quantitative approach and stochastic quadratic optimisation model to maintain supply chain viability under the ripple effect. Instead of viability kernel commonly used in the viability theory, this paper establishes the boundaries on acceptable production states for which the production can be continued under the ripple effect, with no severe losses. For a given implementable portfolio of controls, the boundaries on acceptable production trajectories associated with the two conflicting objectives, cost and customer service level are determined. The decision maker selects a viable production trajectory in-between the two boundary trajectories: the cost-optimal and the service-optimal. The selection depends on the decision maker preference, represented by a chosen weight factor in the optimised quadratic objective function that minimises weighted deviations from the cost-optimal and from the service-optimal production schedules under the ripple effect. The findings indicate that for the extreme values of the weight factor, the viable production trajectory is inclined toward the corresponding boundary trajectory and remains in-between the two boundaries, when both objectives are equally important. Keeping production trajectory in-between the two boundaries makes the supply chain more resilient to disruption risks, while the supply chain resilience diminishes as the production trajectory approaches a boundary trajectory. Then a more severe disruption may push the production outside the viability region and cause greater losses.

关键词： Supply chain risk management supply chain viability supply chain resilience ripple effect stochastic mixed integer programming

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A stochastic data envelopment analysis approach for multi-criteria ABC inventory classification

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2022年第6期39卷 415-429页

作者： Tavassoli, Mohammad Saen, Reza Farzipoor Univ Isfahan Dept Management Esfahan Iran Sultan Qaboos Univ Coll Econ & Polit Sci Dept Operat Management & Business Stat Muscat Oman

One of the common methods for classifying inventory items is ABC classification approach. In many cases, the data might be stochastic. In the current study, using stochastic data envelopment analysis model, we present a new approach to categorize inventory items given stochastic data and nature of criteria. Then, a new stochastic mixed integer programming model is proposed to forecast classes of the new inventory items. The proposed stochastic mixed integer programming model does not impose subjective judgment on the classification of inventory items and can be used for multi-group classification. The developed approach can classify inventory items and forecast the class of new items with both qualitative and quantitative criteria. The applicability of developed stochastic data envelopment analysis and stochastic mixed integer programming models is demonstrated by a case study.

关键词： Inventory classification stochastic data envelopment analysis stochastic discriminant analysis stochastic mixed integer programming

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Models and Algorithms for Data-Driven Scheduling

Models and Algorithms for Data-Driven Scheduling

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作者： Fan, Zhengyang George Mason University

学位级别：Ph.D., Doctor of Philosophy

The dissertation examines the problem of machine scheduling in an uncertain environment. To address this challenge, the study employs both traditional operations research (OR) techniques and modern prescriptive analytics methodologies. The traditional OR approaches utilized in the study include stochastic programming and distributionally robust optimization (DRO). Three research works were conducted that focus on modeling and solution perspectives for different types of stochastic scheduling problems: Decomposition Algorithm for stochastic Parallel Machine Scheduling Problem with Sequence Dependent Setups Distributionally Robust Single Machine Scheduling Under Wasserstein Ambiguity Copula-Based Wasserstein Distributionally Robust Optimization with Application in Machine Scheduling and Portfolio Optimization In addition to the traditional OR techniques, the study also employs modern prescriptive analytics methods that integrate machine learning and decision-making. One research work was conducted that focus on building an integrated system for prediction and optimization: Flight and Maintenance Scheduling for Military Aircraft Fleet: A Data-Driven Approach Overall, the dissertation aims to explore the effectiveness of both traditional OR and modern prescriptive analytics approaches in handling uncertainty in scheduling problems. The results of this research could have practical implications for industries such as manufacturing, logistics, and transportation, where scheduling plays a critical role in operational efficiency.

关键词： Decomposition Algorithm Deep learning Distributionally robust optimization Machine scheduling stochastic mixed integer programming

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stochastic Optimization Model for Short-term Planning of Tanker Water Supply Systems in Urban Areas 13th

Stochastic Optimization Model for Short-term Planning of Tan...

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13th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems (DYCOPS)

作者： Maheshwari, A. Misra, S. Gudi, R. Subbiah, S. Laspidou, C. Indian Inst Technol Jodhpur Rajasthan India Indian Inst Technol Tirupati Andhra Pradesh India Indian Inst Technol Bombay Maharashtra India Indian Inst Technol Guwahati Gauhati 781039 Assam India Univ Thessaly Volos Greece

Tanker-based water distribution systems are amongst one of the most prevalent methods to supply water in many developing countries facing water crisis and intermittent piped water supply. These tanker water supply systems need tighter coordination between the water sources, treatment facilities, consumers and tanker suppliers to efficiently manage timely delivery and quality water. Furthermore, accounting for the uncertain nature of customer demands while making the planning decisions would not only aid in achieving minimum operational cost but is also important in reducing the water wastage. This paper proposes a two-stage stochastic recourse programming model for an optimal planning and scheduling of tanker water supply system under daily demand uncertainty. The main objective is to supply water to maximum number of consumers with minimum total operating costs. A solution strategy combining Sample Average Approximation (SAA) and Monte-Carlo Simulation (MCS) methods, to generate an equivalent deterministic MILP (mixed integer programming problem) model with multiple scenarios of demand uncertainty realization, is adopted for problem solving. The proposed model is applied to an example tanker water supply system and the benefits of two-stage stochastic modelling in making agile decisions incorporating the effect of uncertainties are illustrated. The results also demonstrate the efficacy of adopting stochastic programming models and methods in such real-world application cases. Copyright (c) 2022 The Authors. This is an open access article under the CC BY-NC-ND license(https://***/licenses/by-nc-nd/4.0/)

关键词： Uncertainty Urban water management stochastic mixed integer programming Water tankers Two stage recourse model

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Modular supply chain optimization considering demand uncertainty to manage risk

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AICHE JOURNAL 2021年第11期67卷 e17367-e17367页

作者： Bhosekar, Atharv Badejo, Oluwadare Ierapetritou, Marianthi GAMS Dev Corp Fairfax VA USA Univ Delaware Dept Chem & Biomol Engn 150 Acad St Newark DE 19716 USA

Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. In this work, the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.

关键词： feasibility analysis machine learning modular manufacturing stochastic mixed integer programming supply chain optimization

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A two-period model for selection of resilient multi-tier supply portfolio

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2020年第19期58卷 6043-6060页

作者： Sawik, Tadeusz AGH Univ Sci & Technol Dept Operat Res Krakow Poland

A two-period decision-making model is developed for selection of resilient supply portfolio in a multi-tier supply chain under disruption risks. The planning horizon is divided into two aggregate periods: before and after the disruption. The resilience of the supply chain is achieved by selection ahead of time primary supply portfolio and by pre-positioning of risk mitigation inventory of parts at different tiers that will hedge against all disruption scenarios. Simultaneously, recovery and transshipment portfolios are determined for each disruption scenario and decisions on usage the pre-positioned inventory are made to minimise expected cost or maximise expected service level. Some properties of optimal solutions, derived from the proposed model provide additional managerial insights. The findings also indicate that the developed portfolio approach with an embedded network flow structure leads to computationally efficient stochastic mixed integer program with a strong LP relaxation.

关键词： Supply chain risk management multi-tier supply chain portfolio approach stochastic mixed integer programming

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stochastic Optimization Model for Short-term Planning of Tanker Water Supply Systems in Urban Areas

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IFAC-PapersOnLine 2022年第7期55卷 464-469页

作者： A. Maheshwari S. Misra R. Gudi S. Subbiah C. Laspidou Indian Institute of Technology Jodhpur India Indian Institute of Technology Tirupati India Indian Institute of Technology Bombay India Indian Institute of Technology Guwahati Guwahati Assam 781039 India University of Thessaly Greece

关键词： Uncertainty Urban water management stochastic mixed integer programming Water tankers Two stage recourse model

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Joint stochastic short-term production scheduling and fleet management optimization for mining complexes

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OPTIMIZATION AND ENGINEERING 2020年第4期21卷 1717-1743页

作者： Both, Christian Dimitrakopoulos, Roussos McGill Univ Dept Min & Mat Engn COSMO Stochast Mine Planning Lab FDA Bldg3450 Univ St Montreal PQ H3A 0E8 Canada

This article presents a novel stochastic optimization model that simultaneously optimizes the short-term extraction sequence, shovel relocation, scheduling of a heterogeneous hauling fleet, and downstream allocation of extracted materials in open-pit mining complexes. The proposed stochastic optimization formulation considers geological uncertainty in addition to uncertainty related to equipment performances and truck cycle times. The method is applied at a real-world mining complex, stressing the benefits of optimizing the short-term production schedule and fleet management simultaneously. Compared to a conventional two-step approach, where the production schedule is optimized first before optimizing the allocation of the mining fleet, the costs generated by shovel movements are reduced by 56% and lost production due to shovel relocation is cut by 54%. Furthermore, the required number of trucks shows a more balanced profile, reducing total truck operational costs by 3.1% over an annual planning horizon, as well as the required haulage capacity in the most haulage-intense periods by 25%. A metaheuristic solution method is utilized to solve the large optimization problem in a reasonable timespan.

关键词： Short-term mine planning Production scheduling Fleet management stochastic mixed integer programming Metaheuristics

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