We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production ac...
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We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and develop a branch-and-cut algorithm in order to solve the resulting mixed-integer linear program to optimality. This algorithm relies on a new set of tree inequalities obtained by combining valid inequalities previously known for each individual scenario of the scenario tree. These inequalities are used within a cutting-plane generation procedure based on a heuristic resolution of the corresponding separation problem. Computational experiments carried out on randomly generated instances show that the proposed branch-and-cut algorithm performs well as compared to the use of a stand-alone mathematical solver. Finally, rolling horizon simulations are carried out to assess the practical performance of the multi-stagestochastic planning model with respect to a deterministic model and a two-stagestochastic planning model. (C) 2019 Elsevier Ltd. All rights reserved.
We consider a long-term engine maintenance planning problem for an aircraft fleet. The objective is to guarantee sufficient on-wing engines to reach service levels while effectively organizing shop visits for engines....
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We consider a long-term engine maintenance planning problem for an aircraft fleet. The objective is to guarantee sufficient on-wing engines to reach service levels while effectively organizing shop visits for engines. However, complexity arises from intricate maintenance policies and uncertainty in engine deterioration. To address this problem, we propose a graph-based approach representing high-dimensional engine statuses and transitions. We then formulate the problem as a multi-stagestochasticinteger program with endogenous uncertainty. We develop an approximate dynamic programming algorithm enhanced by dynamic graph generation and policy-sifting techniques so as to reduce the computational overhead in large problems. We demonstrate the efficacy of our method, compared with other popular methods, in terms of running time and solution quality. In the case study, we present an implementation in a real-world decision system in China Southern Airlines, in which the proposed method works seamlessly with other supporting modules and significantly improves the efficiency of engine maintenance management.
In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spo...
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In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi-stagestochasticinteger program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. (C) 2016 Wiley Periodicals, Inc.
Trends like globalization, shorter product life-cycles, and cost reduction strategies in the global business environment have exposed many supply chains to various risks. Disruptions are one of the supply chain risks ...
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Trends like globalization, shorter product life-cycles, and cost reduction strategies in the global business environment have exposed many supply chains to various risks. Disruptions are one of the supply chain risks that can interrupt product flow, delay customer deliveries, and reduce supply chain revenues considerably. Prior planning for disruptions could greatly alleviate these consequences. A method to cope with disruptions is to use product substitution in the case of a product shortage. In this research, the supply chain of a livestock-drug distribution company in Iran, facing demand disruptions, has been chosen as a case study. For this purpose, a multi-stage stochastic integer programming model is proposed and solved using a customized progressive hedging algorithm. Moreover, the effect of uncertainty on the supply chain performance is measured using the value of the stochastic solution (VSS) and the expected value of perfect information (EVPI) metrics. Based on the different instances of the problem solved, the VSS metric shows that modeling and solving the proposed stochastic model could enhance the company profit by about 3.27 percent on average. In addition, the EVPI metric demonstrates that planning and investing in proactive demand management could enhance the profit up to 9.42 percent. Finally, analyses indicate that when dealing with increased demand uncertainty levels, the importance of using the proposed method increases as the profitability of the company decreases.
We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent t...
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We seek to optimize the production planning of a three-echelon remanufacturing system under uncertain input data. We consider a multi-stage stochastic integer programming approach and use scenario trees to represent the uncertain information structure. We introduce a new dynamic programming formulation that relies on a partial nested decomposition of the scenario tree. We then propose a new approximate stochastic dual dynamic integerprogramming algorithm based on this partial decomposition. Our numerical results show that the proposed solution approach is able to provide near-optimal solutions for large-size instances with a reasonable computational effort.
This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (l, S) inequalities for the deterministic lot-sizing ...
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This paper addresses a multi-stage stochastic integer programming formulation of the uncapacitated lot-sizing problem under uncertainty. We show that the classical (l, S) inequalities for the deterministic lot-sizing polytope are also valid for the stochastic lot-sizing polytope. We then extend the (l, S) inequalities to a general class of valid inequalities, called the ( Q, S-Q) inequalities, and we establish necessary and sufficient conditions which guarantee that the ( Q, S-Q) inequalities are facet-defining. A separation heuristic for ( Q, S-Q) inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the ( Q, S-Q) inequalities as cuts.
Condition-Based Maintenance (CBM) is an effective maintenance strategy to improve system performance while lowering operating and maintenance costs. Real-world systems typically consist of a large number of components...
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Condition-Based Maintenance (CBM) is an effective maintenance strategy to improve system performance while lowering operating and maintenance costs. Real-world systems typically consist of a large number of components with various interactions among components. However, existing studies on CBM mainly focus on single-component systems. multi-component CBM, which joins the components' stochastic degradation processes and the combinatorial maintenance grouping problem, remains an open issue in the literature. In this article, we study the CBM optimization problem for multi-component systems. We first develop a multi-stagestochasticinteger model with the objective of minimizing the total maintenance cost over a finite planning horizon. We then investigate the structural properties of a two-stage model. Based on the structural properties, two efficient algorithms are designed to solve the two-stage model. Algorithm 1 solves the problem to its optimality and Algorithm 2 heuristically searches for high-quality solutions based on Algorithm 1. Our computational studies show that Algorithm 1 obtains optimal solutions in a reasonable amount of time and Algorithm 2 can find high-quality solutions quickly. The multi-stage problem is solved using a rolling horizon approach based on the algorithms for the two-stage problem. are available for this article. Go to the publisher's online edition of IISE Transaction, datasets, additional tables, detailed proofs, etc.
In this paper, we consider the multi-period single resource stochastic capacity expansion problem with three sources of capacity: permanent, contract, and spot market. The problem is modeled as a multi-stage stochasti...
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In this paper, we consider the multi-period single resource stochastic capacity expansion problem with three sources of capacity: permanent, contract, and spot market. The problem is modeled as a multi-stagestochasticinteger program. We show that the problem has the totally unimodular property and develop polynomial-time primal and dual algorithms to solve the problem. Crown Copyright (C) 2014 Published by Elsevier B.V.
In this paper, we consider capacity expansion for network models subject to uncertainty and budget constraints. We use a scenario tree approach to handle the uncertainty and construct a multi-stagestochastic mixed-in...
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In this paper, we consider capacity expansion for network models subject to uncertainty and budget constraints. We use a scenario tree approach to handle the uncertainty and construct a multi-stagestochastic mixed-integerprogramming model for the network capacity expansion problem. We assume that permanent capacity and spot market capacity are available, which can be used permanently or temporarily by the decision maker respectively. By relaxing the budget constraints, we propose a heuristic Lagrangian relaxation method to solve the problem. Two algorithms are developed to find tight upper bounds for the Lagrangian relaxation procedure. The experimental results show superior performance of the proposed Lagrangian relaxation method compared with CPLEX.
In this paper, we consider multi-period single resource stochastic capacity expansion problems with lost sales. We study two models. The first model does not consider fixed-charge for capacity purchases, while the sec...
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In this paper, we consider multi-period single resource stochastic capacity expansion problems with lost sales. We study two models. The first model does not consider fixed-charge for capacity purchases, while the second one incorporates fixed-charges. We use multi-stagestochasticinteger programs to present both models and show how adding the fixed-charge cost changes the structure of the mathematical models. For both models, we study their structures and design polynomial-time algorithms to solve them. We present computational results to show the performance of the designed algorithms.
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