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12
Facility Location under Uncertainty: A Review
 IIE Transactions
, 2004
"... Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made th ..."
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Cited by 77 (7 self)
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Plants, distribution centers, and other facilities generally function for years or decades, during which time the environment in which they operate may change substantially. Costs, demands, travel times, and other inputs to classical facility location models may be highly uncertain. This has made the development of models for facility location under uncertainty a high priority for researchers in both the logistics and stochastic/robust optimization communities. Indeed, a large number of the approaches that have been proposed for optimization under uncertainty have been applied to facility location problems. This paper reviews the literature...
Minmax and minmax regret versions of combinatorial optimization problems: A survey
 European Journal of Operational Research
"... Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spannin ..."
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Cited by 21 (1 self)
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Minmax and minmax regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the minmax and minmax regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min st cut, knapsack. Since most of these problems are NPhard, we also investigate the approximability of these problems. Furthermore, we present algorithms to solve these problems to optimality.
A MinMax Regret Robust Optimization Approach for Interval Data Uncertainty
 Journal of Optimization Theory and Applications
"... This paper presents a threestage optimization algorithm for solving twostage robust decision making problems under uncertainty with minmax regret objective. The structure of the first stage problem is a general mixed integer (binary) linear programming model with a specific model of uncertainty t ..."
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Cited by 7 (0 self)
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This paper presents a threestage optimization algorithm for solving twostage robust decision making problems under uncertainty with minmax regret objective. The structure of the first stage problem is a general mixed integer (binary) linear programming model with a specific model of uncertainty that can occur in any of the parameters, and the second stage problem is a linear programming model. Each uncertain parameter can take its value from a finite set of real numbers with unknown probability distribution independently of other parameters ’ settings. This structure of parametric uncertainty is referred to in this paper as the fullfactorial scenario design of data uncertainty. The proposed algorithm is shown to be efficient for solving largescale minmax regret robust optimization problems with this structure. The algorithm coordinates three mathematical programming formulations to solve the overall optimization problem. The main contributions of this paper are the theoretical development of the threestage optimization algorithm, and improving its computational performance through model transformation, decomposition, and preprocessing techniques based on analysis of the problem structure. The proposed algorithm is applied to solve a number of robust facility location problems under this structure of parametric uncertainty. All results illustrate significant improvement in computation time of the proposed algorithm over existing approaches.
A Robust Approach to LocationAllocation Problem under Uncertainty
, 2008
"... This paper presents a new mathematical model for locationallocation problem considering uncertain parameter. In realworld cases, demand, distance, traveling time or any parameters in classical models may change over the period of time. So, considering uncertainty yields more flexibility for the re ..."
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This paper presents a new mathematical model for locationallocation problem considering uncertain parameter. In realworld cases, demand, distance, traveling time or any parameters in classical models may change over the period of time. So, considering uncertainty yields more flexibility for the results and its applications. In our study, environmental uncertainty is described by discrete scenarios where probability of occurrence each of them is not known. So, we use robust optimization technique to analyze the model. Therefore, we introduce a formulation of the robust locationallocation problem in which we have budget constraint. Also, we present mean value model where each uncertain parameter is replaced by its mean to compare with robust model. Finally, some numerical examples are illustrated to show effectiveness of the robust solutions.
Theory and Methodology A heuristic to minimax absolute regret for linear programs with interval objective function coecients
"... Abstract Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex p ..."
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Abstract Decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected. Models that minimize the maximum regret can be useful in such situations, especially when decisions are subject to ex post review. Of particular interest are those decision problems that can be modeled as linear programs with interval objective function coecients. The minimax regret solution for these formulations can be found using an algorithm that, at each iteration, solves ®rst a linear program to obtain a candidate solution and then a mixed integer program (MIP) to maximize the corresponding regret. The exact solution of the MIP is computationally expensive and becomes impractical as the problem size increases. In this paper, we develop a heuristic for the MIP and investigate its performance both alone and in combination with exact procedures. The heuristic is shown to be eective for problems that are signi®cantly larger than those previously reported in the literature. Ó
Service System Design Under Uncertainty
"... Abstract We consider designing a service system in which the service provider performs an operation on incoming transactions from a client. In the design process it is critical to balance the cost invested in provisioning the system capacity against the benefit of satisfying the system performance ..."
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Abstract We consider designing a service system in which the service provider performs an operation on incoming transactions from a client. In the design process it is critical to balance the cost invested in provisioning the system capacity against the benefit of satisfying the system performance requirements specified in service level agreements with clients. The service capacity decision is based on information on parameters such as transaction arrival rate, service level required by the client, and fixed/variable cost rates. In most cases, some input parameters such as demand/transaction arrival rate are uncertain at design time and values used are estimates. Nonetheless, violating the service level requirement during actual operation may result in a penalty cost. We identify alternative approaches suitable for analyzing this design problem by surveying the literature on service system design and related areas. To compare several selected approaches, we develop a model using each approach to determine the optimal system capacity of a singleserver service system. We conclude by presenting our thoughts on when to use what approach. Keywords Service system design, uncertain demand/customer arrival rate, optimal system capacity, service level agreement
Biofuel multistage . . .
"... Biofuel multistage activity modelling to determine efficient public policy in uncertain agricultural markets ♣ ..."
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Biofuel multistage activity modelling to determine efficient public policy in uncertain agricultural markets ♣
Robustesse et dualité en programmation linéaire
, 2008
"... Dans cet article, nous étudions un programme linéaire dans lequel les valeurs des second membres des contraintes sont entachées d’incertitude et d’indétermination. Cette incertitude est modélisée par un intervalle, c’estàdire que le second membre de chaque contrainte peut prendre une valeur quelcon ..."
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Dans cet article, nous étudions un programme linéaire dans lequel les valeurs des second membres des contraintes sont entachées d’incertitude et d’indétermination. Cette incertitude est modélisée par un intervalle, c’estàdire que le second membre de chaque contrainte peut prendre une valeur quelconque dans un intervalle indépendamment des autres contraintes. Dans la littérature, les programmes linéaires, dont les coefficients des variables dans la fonction objectif sont incertains et approchés par un intervalle, ont été largement étudiés. Il s’agit alors de déterminer une solution qui résiste au mieux aux incertitudes, une telle solution étant qualifiée de robuste. Pour cela, les critères classiques du pire cas et du regret maximum sont appliqués pour définir différentes versions robustes du programme linéaire de départ. Des modèles de robustesse plus récents, généralisant le critère du pire cas (dû à Bertsimas et Sim), ont également été proposés. Le sujet de ce papier est d’établir des correspondances entre programmes linéaires avec second