This special issue addresses the advances in stochastic programming and robust optimization for supply chain planning by examining novel methods, practices, and opportunities. The articles present and analyze opportun...
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This special issue addresses the advances in stochastic programming and robust optimization for supply chain planning by examining novel methods, practices, and opportunities. The articles present and analyze opportunities to improve supply chain planning through exploring various uncertainty situations and problems, sustainability assessment, vendor selection, risk mitigation, retail supply chain planning, and supply chain coordination. This editorial note summarizes the discussions on the stochastic models, algorithms, and methodologies developed for the evaluation and effective implementation of supply chain planning under various concerns. A dominant finding is that supply chain planning through the advancement of stochastic programming and robust optimization should be explored in a variety of ways and within different fields of applications. (C) 2018 Elsevier Ltd. All rights reserved.
The nonlinear stochastic programming problem involving CVaR in the objective and constraints is considered. Solving the latter problem in a framework of bi-level stochastic programming, the extended Lagrangian is intr...
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The nonlinear stochastic programming problem involving CVaR in the objective and constraints is considered. Solving the latter problem in a framework of bi-level stochastic programming, the extended Lagrangian is introduced and the related KKT conditions are derived. Next, the sequential simulation-based approach has been developed to solve stochastic problems with CVaR by finite sequences of Monte Carlo samples. The approach considered is grounded by the rule for iterative regulation of the Monte Carlo sample size and the stochastic termination procedure, taking into account the stochastic model risk. The rule is introduced to regulate the size of the Monte Carlo sample inversely proportionally to the square of the stochastic gradient norm allows us to solve stochastic nonlinear problems in a rational way and ensures the convergence. The proposed termination procedure enables us to test the KKT conditions in a statistical way and to evaluate the confidence intervals of the objective and constraint functions in a statistical way as well. The results of the Monte Carlo simulation with test functions and solution of the practice sample of trade-offs of gas purchases, storage and service reliability, illustrate the convergence of the approach considered as well as the ability to solve in a rational way the nonlinear stochastic programming problems handling CVaR in the objective and constraints, with an admissible accuracy, treated in a statistical manner.
This paper presents the evolution and design of the Swiss reserve market and describes its two-stage stochastic market-clearing model. In Switzerland, the reserve market comprises weekly and daily auctions. The decisi...
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This paper presents the evolution and design of the Swiss reserve market and describes its two-stage stochastic market-clearing model. In Switzerland, the reserve market comprises weekly and daily auctions. The decision-making problem is to determine the amount of reserves that should be procured in each market stage. The stochasticity stems from daily offers which are not available at the beginning of the week, when the first-stage decisions are made. The new market-clearing model minimizes expected procurement costs of reserves, while taking reserve dimensioning criteria and market properties into consideration. Since the last week of January 2014, this model has been clearing the reserve market in Switzerland. To our knowledge, this is the first real-world implementation of a stochastic market-clearing model in electricity markets.
One of the significant effects of the implementation of an open-door policy in China is that many Hong Kong-based manufacturers' production lines have been moved to China to take advantage of the lower production ...
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One of the significant effects of the implementation of an open-door policy in China is that many Hong Kong-based manufacturers' production lines have been moved to China to take advantage of the lower production costs, lower wages and lower rental costs, but as a consequence the finished products must be delivered from China to Hong Kong. It has been discovered that, given a noisy set of data, distribution management cannot determine an appropriate strategy, and hence unnecessarily high expenditure is being incurred. In this paper, a stochastic linear programming model is developed to solve cross-border distribution problems in an environment of uncertainty. Under different economic growth scenarios., decision-makers can determine a long-term distribution strategy, including the optimal delivery routes and the optimal vehicle fleet composition. A set of data from a Hong Kong-based manufacturing company is used to demonstrate the robustness and effectiveness of our model. The analysis of two possible changes in distribution strategies is also considered. The proposed model can provide appropriate distribution strategy with fleet management in an uncertain environment.
Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions,...
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Integrals of optimal values of random optimization problems depending on a finite dimensional parameter are approximated by using empirical distributions instead of the original measure. Under fairly broad conditions, it is proved that uniform convergence of empirical approximations of the right hand sides of the constraints implies uniform convergence of the optimal values in the linear and convex case.
Production planning problems play a vital role in the supply chain management area, by which decision makers can determine the production loading plan - consisting of the quantity of production and the workforce level...
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Production planning problems play a vital role in the supply chain management area, by which decision makers can determine the production loading plan - consisting of the quantity of production and the workforce level at each production plant - to fulfil market demand. This paper addresses the production planning problem with additional constraints, such as production plant preference selection. To deal with the uncertain demand data, a stochastic programming approach is proposed to determine optimal medium-term production loading plans under an uncertain environment. A set of data from a multinational lingerie company in Hong Kong is used to demonstrate the robustness and effectiveness of the proposed model. An analysis of the probability distribution of economic demand assumptions is performed. The impact of unit shortage costs on the total cost is also analysed.
In this work, we present methodologies for optimization of hydraulic fracturing design under uncertainty specifically with reference to the thick and anisotropic reservoirs in the Lower Tertiary Gulf of Mexico. In thi...
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In this work, we present methodologies for optimization of hydraulic fracturing design under uncertainty specifically with reference to the thick and anisotropic reservoirs in the Lower Tertiary Gulf of Mexico. In this analysis we apply a stochastic programming framework for optimization under uncertainty and apply a utility framework for risk analysis. For a vertical well, we developed a methodology for making the strategic decisions regarding number and dimensions of hydraulic fractures in a high-cost, high-risk offshore development. Uncertainty is associated with the characteristics of the reservoir, the economics of the fracturing cost, and the fracture height growth. The method developed is applicable to vertical wells with multiple, partially penetrating fractures in an anisotropic formation. The method applies the utility framework to account for financial risk. For a horizontal well, we developed a methodology for making the strategic decisions regarding lateral length, number and dimensions of transverse hydraulic fractures in a high-cost, high-risk offshore development, under uncertainty associated with the characteristics of the reservoir. The problem is formulated as a mixed-integer, nonlinear, stochastic program and solved by a tailored Branch and Bound algorithm. The method developed is applicable to partially penetrating horizontal wells with multiple, partially penetrating fractures in an anisotropic formation.
This research studies the impact of demand uncertainty to the supply chain design by using a stochastic programming approach. Each potential location has two modes of supply: long response time used before the demand ...
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This research studies the impact of demand uncertainty to the supply chain design by using a stochastic programming approach. Each potential location has two modes of supply: long response time used before the demand is realized and short response lead time mode (with higher cost) used after the demand is realized. The capacity of each model will be optimally determined from the model. This means that each location allow the manufacturer to install machines to produce in a large quantity at low cost (due to economy of scale) and keep in the internal warehouse or to install flexible rapid response machines to produce with short lead time at high cost after the demand shortage is expected. Moreover, the model allows different production cost functions which the unit cost could be different when production quantity is different using piecewise function. A stochastic programming model is developed to handle the situation explained. We have conducted 4 experiments to test the model in different perspective; (1) Sampling test – to test the effect of the sample size to the result, (2) Parameter variation – to test how each variable affect the results, (3) Cost function testing – to reveal the property of different cost function and (4) Pair-T test to prove how short LT response facility could improve certain situation and mitigate the effect of demand uncertainty. Furthermore, for heuristic part, we applied linear relaxation and decomposition method on two binary variables to separate the model into two phases; (1) Location decision and (2) Segmentation decision. For the result, heuristic model affords to contribute the optimal result for about 26 out of 32 instances or 81.25% of the total number of computable instances deriving from every cost function. The average overall total profit gap is 0.32%. The average computational time reduction is 71.65%. Moreover, our heuristics model is able to solve big size problems which the optimal model failed to do within acceptable ti
The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize prof...
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The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two-stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the departure of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivariate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated. Crown Copyright (C) 2011 Published by Elsevier B.V. All rights reserved.
Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable tec...
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Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies has motivated study of various classes of stochastic unit commitment models. In two-stage models, the generation schedule for the entire day is fixed while the dispatch is adapted to the uncertainty, whereas in multi-stage models the generation schedule is also allowed to dynamically adapt to the uncertainty realization. Multi-stage models provide more flexibility in the generation schedule;however, they require significantly higher computational effort than two-stage models. To justify this additional computational effort, we provide theoretical and empirical analyses of the value of multi-stage solution for risk-averse multi-stage stochastic unit commitment models. The value of multi-stage solution measures the relative advantage of multi-stage solutions over their two-stage counterparts. Our results indicate that, for unit commitment models, the value of multi-stage solution increases with the level of uncertainty and number of periods, and decreases with the degree of risk aversion of the decision maker.
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