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Kinds of Programming Problem Selected AbstractsAn Integer Linear Programming Problem with Multi-Criteria and Multi-Constraint Levels: a Branch-and-Partition AlgorithmINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2001Jun Li In this paper, we propose a branch-and-partition algorithm to solve the integer linear programming problem with multi-criteria and multi-constraint levels (MC-ILP). The procedure begins with the relaxation problem that is formed by ignoring the integer restrictions. In this branch-and-partition procedure, an MC linear programming problem is adopted by adding a restriction according to a basic decision variable that is not integer. Then the MC-simplex method is applied to locate the set of all potential solutions over possible changes of the objective coefficient parameter and the constraint parameter for a regular MC linear programming problem. We use parameter partition to divide the (,, ,) space for integer solutions of MC problem. The branch-and-partition procedure terminates when every potential basis for the relaxation problem is a potential basis for the MC-ILP problem. A numerical example is used to demonstrate the proposed algorithm in solving the MC-ILP problems. The comparison study and discussion on the applicability of the proposed method are also provided. [source] An Interactive Reference Direction Algorithm For Solving Multi-Objective Convex Nonlinear Integer Programming ProblemsINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 4 2001Vassil S. Vassilev We present a learning-oriented interactive reference direction algorithm for solving multi-objective convex nonlinear integer programming problems. At each iteration the decision-maker (DM) sets his/her preferences as aspiration levels of the objective functions. The modified aspiration point and the solution found at the previous iteration define the reference direction. Based on the reference direction, we formulate a mixed-integer scalarizing problem with specific properties. By solving this problem approximately, we find one or more integer solutions located close to the efficient surface. At some iteration (usually at the last iteration), the DM may want to solve the scalarizing problem to obtain an exact (weak) efficient solution. Based on the proposed algorithm, we have developed a research-decision support system that includes one exact and one heuristic algorithm. Using this system, we illustrate the proposed algorithm with an example, and report some computational results. [source] Multiobjective heuristic approaches to seismic design of steel frames with standard sectionsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 11 2007M. Ohsaki Abstract Seismic design problem of a steel moment-resisting frame is formulated as a multiobjective programming problem. The total structural (material) volume and the plastic dissipated energy at the collapse state against severe seismic motions are considered as performance measures. Geometrically nonlinear inelastic time-history analysis is carried out against recorded ground motions that are incrementally scaled to reach the predefined collapse state. The frame members are chosen from the lists of the available standard sections. Simulated annealing (SA) and tabu search (TS), which are categorized as single-point-search heuristics, are applied to the multiobjective optimization problem. It is shown in the numerical examples that the frames that collapse with uniform interstorey drift ratios against various levels of ground motions can be obtained as a set of Pareto optimal solutions. Copyright © 2007 John Wiley & Sons, Ltd. [source] On Optimal Rules of PersuasionECONOMETRICA, Issue 6 2004Jacob Glazer A speaker wishes to persuade a listener to accept a certain request. The conditions under which the request is justified, from the listener's point of view, depend on the values of two aspects. The values of the aspects are known only to the speaker and the listener can check the value of at most one. A mechanism specifies a set of messages that the speaker can send and a rule that determines the listener's response, namely, which aspect he checks and whether he accepts or rejects the speaker's request. We study mechanisms that maximize the probability that the listener accepts the request when it is justified and rejects the request when it is unjustified, given that the speaker maximizes the probability that his request is accepted. We show that a simple optimal mechanism exists and can be found by solving a linear programming problem in which the set of constraints is derived from what we call the L -principle. [source] Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee EarningsECONOMETRICA, Issue 1 2002Alberto Abadie This paper reports estimates of the effects of JTPA training programs on the distribution of earnings. The estimation uses a new instrumental variable (IV) method that measures program impacts on quantiles. The quantile treatment effects (QTE) estimator reduces to quantile regression when selection for treatment is exogenously determined. QTE can be computed as the solution to a convex linear programming problem, although this requires first-step estimation of a nuisance function. We develop distribution theory for the case where the first step is estimated nonparametrically. For women, the empirical results show that the JTPA program had the largest proportional impact at low quantiles. Perhaps surprisingly, however, JTPA training raised the quantiles of earnings for men only in the upper half of the trainee earnings distribution. [source] Optimal methodology for distribution systems reconfiguration based on OPF and solved by decomposition techniqueEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 6 2010H. M. Khodr Abstract This paper presents a new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach. The objective minimizes power losses, balancing load among feeders and subject to constraints: capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. The Generalized Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages; the first one is the Master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the Slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the Master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS. The effectiveness of the proposal is demonstrated through two examples extracted from the literature. Copyright © 2009 John Wiley & Sons, Ltd. [source] Optimal transformations of asymmetric elements in three-phase networksEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 2 2005Zdzislaw W. Trzaska Abstract This paper presents a procedure for optimal transformation of asymmetric three-phase elements. The proposed algorithm is based on the solution of the corresponding Steiner problem and improves the network voltage and current profiles. After identifying the phase quantities, the problem is formulated as a non-linear programming problem of the minimization of the sum of the r.m.s. values of the phase voltages and line currents under some constraint equations. A few test networks are used to verify the effectiveness and accuracy of the method. It is believed that practical applications of the proposed method will enhance the estimation of the phase asymmetry of the three-phase generator voltages and load currents. Copyright © 2005 John Wiley & Sons, Ltd. [source] Application and comparison of metaheuristic techniques to reactive power planning problemIEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, Issue 6 2008Mehdi Eghbal Non-Member Abstract This paper presents the application and comparison of metaheuristic techniques to reactive power planning (RPP) problem which involves optimal allocation and combination of to-be-installed VAr sources to satisfy voltage constraints during normal and contingency states for multiple load levels. The main objective of the proposed RPP problem is to minimize the investment cost through balanced installation of SCs and SVCs while keeping a specified security level and minimizing the amount of load shedding. The problem is formulated as a large scale mixed integer nonlinear programming problem, which is a nonsmooth and nondifferentiable optimization problem using conventional optimization techniques and induces lots of local minima. Among the metaheuristic techniques, genetic algorithm (GA), particle swarm optimization (PSO) and evolutionary particle swarm optimization (EPSO) are applied to solve the RPP problem. To investigate the effectiveness of the metaheuristic techniques, the proposed approaches have been successfully tested on IEEE-14 buses, as well as IEEE-57 buses test system. The results obtained are compared and the effectiveness of each technique has been illustrated. Copyright © 2008 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [source] The use of an SQP algorithm in slope stability analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2005Jian Chen Abstract In the upper bound approach to limit analysis of slope stability based on the rigid finite element method, the search for the minimum factor of safety can be formulated as a non-linear programming problem with equality constraints only based on a yield criterion, a flow rule, boundary conditions, and an energy-work balance equation. Because of the non-linear property of the resulting optimization problems, a non-linear mathematical programming algorithm has to be employed. In this paper, the relations between the numbers of nodes, elements, interfaces, and subsequent unknowns and constraints in the approach have been derived. It can be shown that in the large-scale problems, the unknowns are subject to a highly sparse set of equality constraints. Because of the existence of non-linear equalities in the approach, this paper applies first time a special sequential quadratic programming (SQP) algorithm, feasible SQP (FSQP), to obtain solutions for such non-linear optimization problems. In FSQP algorithm, the non-linear equality constraints are turned into inequality constraints and the objective function is replaced by an exact penalty function which penalizes non-linear equality constraint violations only. Three numerical examples are presented to illustrate the potentialities and efficiencies of the FSQP algorithm in the slope stability analysis. Copyright © 2004 John Wiley & Sons, Ltd. [source] Cost optimization of composite floors using neural dynamics modelINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2001Hojjat Adeli Abstract The design of composite beams is complicated and highly iterative. Depending on the design parameters a beam can be fully composite or partially composite. In the case of design on the basis of the American Institute of Steel Construction (AISC) Load and Resistance Factor Design (LRFD) one has to consider the plastic deformations. As pointed out by Lorenz, the real advantage of the LRFD code can be realized in the minimum cost design. In this article, we present a general formulation for the cost optimization of composite beams based on the AISC LRFD specifications by including the costs of (a) concrete, (b) steel beam, and (c) shear studs. The problem is formulated as a mixed integer-discrete non-linear programming problem and solved by the recently patented neural dynamics model of Adeli and Park (U.S. patent 5,815,394 issued on September 29, 1998). It is shown that use of the cost optimization algorithm presented in this article results in substantial cost savings. Copyright © 2001 John Wiley & Sons, Ltd. [source] Designing globally optimal delta,sigma modulator topologies via signomial programmingINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2009Yuen-Hong Alvin Ho Abstract We present a design methodology for globally optimizing the topologies of delta,sigma modulators (DSMs). Previous work cast the design task into a general non-convex, nonlinear programming problem, whereas we propose to recast it as a signomial programming problem. Convexification strategies are presented for transforming the signomial programming problem into its equivalent convex counterpart, thereby enabling the solution of globally optimal design parameters. It is also possible to include circuit non-ideal effects that affect the transfer function of the modulator into the formulation without affecting the computational efficiency. The proposed framework has been applied to topology synthesis problems of single-loop and multi-loop low-pass DSMs based on discrete-time circuitry. Numerical results confirm the effectiveness of the proposed approach over conventional nonlinear programming techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source] Heuristic and simulated annealing algorithms for solving extended cell assignment problem in wireless ATM networksINTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS, Issue 1 2002Der-Rong Din Abstract In this paper, we investigate the extended cell assignment problem which optimally assigns new adding and splitting cells in Personal Communication Service (PCS) to switches in a wireless Asynchronous Transfer Mode (ATM) network. Given cells in a PCS network and switches on an ATM network (whose locations are fixed and known), we would like to do the assignment in an attempt to minimize a cost criterion. The cost has two components: one is the cost of handoffs that involve two switches, and the other is the cost of cabling. This problem is modeled as a complex integer programming problem, and finding an optimal solution to this problem is NP-hard. A heuristic algorithm and a simulated annealing algorithm are proposed to solve this problem. The heuristic algorithm, Extended Assignment Algorithm (EEA), consists of two phases, initial assigning phase and cell exchanging phase. First, in the initial assigning phase, the initial assignments of cells to switches are found. Then, these assignments are improved by performing cell exchanging phase in which two cells are repeatedly exchanged in different switches with great reduction of the total cost. The simulated annealing algorithm, ESA (enhanced simulated annealing), generates constraint-satisfied configurations, and uses three configuration perturbation schemes to change current configuration to a new one. Experimental results indicate that EAA and ESA algorithms have good performances. Copyright © 2002 John Wiley & Sons, Ltd. [source] An Integer Linear Programming Problem with Multi-Criteria and Multi-Constraint Levels: a Branch-and-Partition AlgorithmINTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 5 2001Jun Li In this paper, we propose a branch-and-partition algorithm to solve the integer linear programming problem with multi-criteria and multi-constraint levels (MC-ILP). The procedure begins with the relaxation problem that is formed by ignoring the integer restrictions. In this branch-and-partition procedure, an MC linear programming problem is adopted by adding a restriction according to a basic decision variable that is not integer. Then the MC-simplex method is applied to locate the set of all potential solutions over possible changes of the objective coefficient parameter and the constraint parameter for a regular MC linear programming problem. We use parameter partition to divide the (,, ,) space for integer solutions of MC problem. The branch-and-partition procedure terminates when every potential basis for the relaxation problem is a potential basis for the MC-ILP problem. A numerical example is used to demonstrate the proposed algorithm in solving the MC-ILP problems. The comparison study and discussion on the applicability of the proposed method are also provided. [source] Scheduling Part-Families Under FMS: To Mix or Not to Mix?INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH, Issue 2 2001Henry C. Co This paper considers the issue of whether to mix part-types in one or several of the families to be produced in a flexible manufacturing system (FMS). For this input control problem in an FMS, we have derived conditions that support the mixing of a part-type, which can share the setup of other part-types, in deterministic environment. The problem is identified as a special economic lot scheduling problem (ELSP), and is formulated as a linear programming problem. Analytical insights are derived by considering the special case with three part-families. The results are illustrated with a numerical example. [source] An equity-based passenger flow control model with application to Hong Kong-Shenzhen border-crossingJOURNAL OF ADVANCED TRANSPORTATION, Issue 2 2002Hai Yang Cross-border passengers from Hong Kong to Shenzhen by the east Kowloon-Canton Railway (KCR) through the Lo Wu customs exceed nearly 200 thousand on a special day such as a day during the Chinese Spring Festival. Such heavy passenger demand often exceeds the processing and holding capacity of the Lo Wu customs for many hours a day. Thus, passengers must be metered off at all entrance stations along the KCR line through ticket rationing to restrain the number of passengers waiting at Lo Wu within its safe holding capacity. This paper proposes an optimal control strategy and model to deal with this passenger crowding and control problem. Because the maximum passenger checkout rate at Lo Wu is fixed, total passenger waiting time is not affected by the control strategy for given time-dependent arriving rates at each station. An equity-based control strategy is thus proposed to equalize the waiting times of passengers arriving at all stations at the same time. This equity is achieved through optimal allocation of the total quota of tickets to all entrance stations for each train service. The total ticket quota for each train service is determined such that the capacity constraint of the passenger queue at Lo Wu is satisfied. The control problem is formulated as a successive linear programming problem and demonstrated for the KCR system with partially simulated data. [source] A multi-objective optimization approach to polygeneration energy systems designAICHE JOURNAL, Issue 5 2010Pei Liu Abstract Polygeneration, typically involving co-production of methanol and electricity, is a promising energy conversion technology which provides opportunities for high energy utilization efficiency and low/zero emissions. The optimal design of such a complex, large-scale and highly nonlinear process system poses significant challenges. In this article, we present a multiobjective optimization model for the optimal design of a methanol/electricity polygeneration plant. Economic and environmental criteria are simultaneously optimized over a superstructure capturing a number of possible combinations of technologies and types of equipment. Aggregated models are considered, including a detailed methanol synthesis step with chemical kinetics and phase equilibrium considerations. The resulting model is formulated as a non-convex mixed-integer nonlinear programming problem. Global optimization and parallel computation techniques are employed to generate an optimal Pareto frontier. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] IS FISHING COMPATIBLE WITH ENVIRONMENTAL CONSERVATION: A STOCHASTIC MODEL WITH AN ELEMENT OF SELF-PROTECTIONNATURAL RESOURCE MODELING, Issue 3 2008D. AMI Abstract The purpose of this paper is to introduce the impact of fishing activity on a marine ecosystem. The fishing activity is considered not only through annual harvest but also through a second component, called the degree of protection of the fishery environment. This characterizes the environmental impact of fishing. A stochastic dynamic programming problem is presented in infinite horizon, where a sole owner seeks to maximize a discounted expected profit. The main hypothesis states that the stock,recruitment relationship is stochastic and that both components of the fishing activity have an impact on the probability law of the state of the fishery environment. The optimal fishing policy is obtained and compared with standard models. This optimal policy has the following properties: is not a constant escapement policy and indicates an element of self-protection by the fishery manager. The paper ends with a discussion on the existence of degrees of protection of the fishery environment that take into account the environmental conservation and preservation of economic activity. [source] A model to design recreational boat mooring fieldsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2009Ronald E. Giachetti Abstract This article develops a mathematical model and heuristic algorithm to design recreational boating mooring fields. The boating industry is important to the Florida economy, and boat storage is becoming a concern among those in the industry. The mooring field design problem is formulated to maximize the total number of boat feet moored in the mooring field. In the model, we allow two adjacent moorings to overlap, which introduces a risk that under certain conditions the boats on these moorings could contact each other. We identify the conditions when contact is possible and quantify the probability of contact. The mooring field design problem is formulated as a nonlinear mixed-integer programming problem. To solve the problem, we decompose it into two separate models, a mooring radii assignment model and a mooring layout model, which are solved sequentially. The first is solved via exhaustive enumeration and the second via a depth-first search algorithm. Two actual mooring fields are evaluated, and in both cases our model leads to better layouts than ones experts developed manually. The mooring field design model rationalizes the mooring field design and shows that in one case by increasing the risk from 0 to 1%, the mooring efficiency increases from 74.8% to 96.2%. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source] Optimal capacity in a coordinated supply chainNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2008Xiuli Chao Abstract We consider a supply chain in which a retailer faces a stochastic demand, incurs backorder and inventory holding costs and uses a periodic review system to place orders from a manufacturer. The manufacturer must fill the entire order. The manufacturer incurs costs of overtime and undertime if the order deviates from the planned production capacity. We determine the optimal capacity for the manufacturer in case there is no coordination with the retailer as well as in case there is full coordination with the retailer. When there is no coordination the optimal capacity for the manufacturer is found by solving a newsvendor problem. When there is coordination, we present a dynamic programming formulation and establish that the optimal ordering policy for the retailer is characterized by two parameters. The optimal coordinated capacity for the manufacturer can then be obtained by solving a nonlinear programming problem. We present an efficient exact algorithm and a heuristic algorithm for computing the manufacturer's capacity. We discuss the impact of coordination on the supply chain cost as well as on the manufacturer's capacity. We also identify the situations in which coordination is most beneficial. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008 [source] Robust tower location for code division multiple access networksNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2007Jay M. Rosenberger Abstract Designing Code Division Multiple Access networks includes determining optimal locations of radio towers and assigning customer markets to the towers. In this paper, we describe a deterministic model for tower location and a stochastic model to optimize revenue given a set of constructed towers. We integrate these models in a stochastic integer programming problem with simple recourse that optimizes the location of towers under demand uncertainty. We develop algorithms using Benders' reformulation, and we provide computational results. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [source] Discrete search allocation game with false contactsNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 1 2007Ryusuke Hohzaki Abstract This paper deals with a two-person zero-sum game called a search allocation game, where a searcher and a target participate, taking account of false contacts. The searcher distributes his search effort in a search space in order to detect the target. On the other hand, the target moves to avoid the searcher. As a payoff of the game, we take the cumulative amount of search effort weighted by the target distribution, which can be derived as an approximation of the detection probability of the target. The searcher's strategy is a plan of distributing search effort and the target's is a movement represented by a path or transition probability across the search space. In the search, there are false contacts caused by environmental noises, signal processing noises, or real objects resembling true targets. If they happen, the searcher must take some time for their investigation, which interrupts the search for a while. There have been few researches dealing with search games with false contacts. In this paper, we formulate the game into a mathematical programming problem to obtain its equilibrium point. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007 [source] A mathematical programming approach for improving the robustness of least sum of absolute deviations regressionNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2006Avi Giloni Abstract This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least-sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] Direct optimization of dynamic systems described by differential-algebraic equationsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2008Brian C. Fabien Abstract This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the DAE are approximated using a Rosenbrock,Wanner (ROW) method. In this way the infinite-dimensional optimal control problem is transformed into a finite-dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming (QP) technique that minimizes the L, exact penalty function, using only strictly convex QP subproblems. This paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem and (ii) an efficient technique for evaluating the function, constraints and gradients associated with the NLP problem. This paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Computational optimal control of the terminal bunt manoeuvre,Part 2: minimum-time caseOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 5 2007S. Subchan Abstract This is the second part of a paper studies trajectory shaping of a generic cruise missile attacking a fixed target from above. The problem is reinterpreted using optimal control theory resulting in a minimum flight time problem; in the first part the performance index was time-integrated altitude. The formulation entails non-linear, two-dimensional (vertical plane) missile flight dynamics, boundary conditions and path constraints, including pure state constraints. The focus here is on informed use of the tools of computational optimal control, rather than their development. The formulation is solved using a three-stage approach. In stage 1, the problem is discretized, effectively transforming it into a non-linear programming problem, and hence suitable for approximate solution with DIRCOL and NUDOCCCS. The results are used to discern the structure of the optimal solution, i.e. type of constraints active, time of their activation, switching and jump points. This qualitative analysis, employing the results of stage 1 and optimal control theory, constitutes stage 2. Finally, in stage 3, the insights of stage 2 are made precise by rigorous mathematical formulation of the relevant two-point boundary value problems (TPBVPs), using the appropriate theorems of optimal control theory. The TPBVPs obtained from this indirect approach are then solved using BNDSCO and the results compared with the appropriate solutions of stage 1. The influence of boundary conditions on the structure of the optimal solution and the performance index is investigated. The results are then interpreted from the operational and computational perspectives. Copyright © 2007 John Wiley & Sons, Ltd. [source] MILP modelling for the time optimal control problem in the case of multiple targetsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 2 2006H. H. Mehne Abstract Optimal guidance for a dynamical system from a given point to a set of targets is discussed. Detecting for the best target is done in such a way that the capture time is minimized and desirability of targets is maximized. By extending measure theoretical approach for the classical optimal control problem to this case, the nearly optimal control is constructed from the solution of a mixed integer linear programming problem. To find the lower bound of the optimal time a search algorithm is proposed. Numerical examples are also given. Copyright © 2005 John Wiley & Sons, Ltd. [source] PRODUCT OFFERING, PRICING, AND MAKE-TO-STOCK/MAKE-TO-ORDER DECISIONS WITH SHARED CAPACITYPRODUCTION AND OPERATIONS MANAGEMENT, Issue 3 2002GREGORY DOBSON In an era of mass customization, many firms continue to expand their product lines to remain competitive. These broader product lines may help to increase market share and may allow higher prices to be charged, but they also cause challenges associated with diseconomies of scope. To investigate this tradeoff, we considered a monopolist who faces demand curves, which for each of its potential products, decline with both price and response time (time to deliver the product). The firm must decide which products to offer, how to price them, whether each should be make-to-stock (mts) or make-to-order (mto), and how often to produce them. The offered products share a single manufacturing facility. Setup times introduce disceonomies of scope and setup costs introduce economies of scale. We provide motivating problem scenarios, model the monopolist's problem as a non-linear, integer programming problem, characterize of the optimal policy, develop near-optimal procedures, and discuss managerial insights. [source] Designing an accelerated degradation experiment by optimizing the estimation of the percentileQUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 3 2003Hong-Fwu Yu Abstract Degradation tests are widely used to assess the reliability of highly reliable products which are not likely to fail under traditional life tests or accelerated life tests. However, for some highly reliable products, the degradation may be very slow and hence it is impossible to have a precise assessment within a reasonable amount of testing time. In such cases, an alternative is to use higher stresses to extrapolate the product's reliability at the design stress. This is called an accelerated degradation test (ADT). In conducting an ADT, several decision variables, such s the inspection frequency, sample size and termination time, at each stress level are influential on the experimental efficiency. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of the estimation of the product's reliability at the use condition. The main purpose of this paper is to deal with the problem of designing an ADT. By using the criterion of minimizing the mean-squared error of the estimated 100th percentile of the product's lifetime distribution at the use condition subject to the constraint that the total experimental cost does not exceed a predetermined budget, a nonlinear integer programming problem is built to derive the optimal combination of the sample size, inspection frequency and the termination time at each stress level. A numerical example is provided to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd. [source] Reinsurance control in a model with liabilities of the fractional Brownian motion typeAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 5 2007N. E. Frangos Abstract We propose a model for reinsurance control for an insurance firm in the case where the liabilities are driven by fractional Brownian motion, a stochastic process exhibiting long-range dependence. The problem is transformed to a nonlinear programming problem, the solution of which provides the optimal reinsurance policy. The effect of various parameters of the model, such as the safety loading of the reinsurer and the insurer, the Hurst parameter, etc. on the optimal reinsurance program is studied in some detail. Copyright © 2007 John Wiley & Sons, Ltd. [source] Optimal model for warehouse location and retailer allocationAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2007Avninder Gill Abstract Warehouse location and retailer allocation is a high-level strategic decision problem that is commonly encountered by logisticians and supply chain managers, especially during the supply chain design phase. Considering the product distribution cost and warehouse capital cost trade-offs, this paper models the warehouse location and retailer allocation problem as a 0,1 integer programming problem and provides an efficient two-stage set covering heuristic algorithm to solve large-sized problems. Finally, concluding remarks and some recommendations for further research are also presented. Copyright © 2007 John Wiley & Sons, Ltd. [source] Best domain for an elliptic problem in cartesian coordinates by means of shape-measureASIAN JOURNAL OF CONTROL, Issue 5 2009Alireza Fakharzadeh Jahromi Abstract In (ZAA J. Anal. Appl., Vol. 16, No. 1, pp. 143,155) we introduced a method to determine the optimal domains for elliptic optimal-shape design problems in polar coordinates. However, the same problem in cartesian coordinates, which are more applicable, is found to be much harder, therefore we had to develop a new approach for these designs. Herein, the unknown domain is divided into a fixed and a variable part and the optimal pair of the domain and its optimal control, is characterized in two stages. Firstly, the optimal control for the each given domain is determined by changing the problem into a measure-theoretical one, replacing this with an infinite dimensional linear programming problem and approximating schemes; then the nearly optimal control function is characterized. Therefore a function that offers the optimal value of the objective function for a given domain, is defined. In the second stage, by applying a standard optimization method, the global minimizer pair will be obtained. Some numerical examples are also given. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] | |||||||||||||||||||||||||||||||||||||