It is shown that modern Semi-infinite Optimization Methods provide a powerful method for determining the operating schedules of control set points for advanced turbofan engines. These methods give the engineer conside...
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It is shown that modern Semi-infinite Optimization Methods provide a powerful method for determining the operating schedules of control set points for advanced turbofan engines. These methods give the engineer considerable design freedom and they can be used to develop engine schedules which optimize complex performance objectives and explicitly satisfy performance requirements on engine variables . This approach is shown to provide insights as to the limits of engine performance and the control requirements of the engine as well as a framework in which to carry out engine performance trade-off studies. These methods are illustrated by determining portions of the steady-state and transient operating schedules of a state-of-the-art single bypass turbofan engine.
The computational utility of inductive linearizations for binary quadratic programs when combined with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established...
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The computational utility of inductive linearizations for binary quadratic programs when combined with a mixed-integer programming solver is investigated for several combinatorial optimization problems and established benchmark instances.
In this paper, a multi-period, multi-product, multi-site, multi-sles channel aggregate production planning problem including ordering preferences is presented in an integrated two-echelon supply chain to avoid the sub...
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In this paper, a multi-period, multi-product, multi-site, multi-sles channel aggregate production planning problem including ordering preferences is presented in an integrated two-echelon supply chain to avoid the suboptimality caused by separate, sequential decisions of production and the marketing/retailing chain. Each customer demand class is affected by price, marketing expenditures and product quality involving customer willingness-to-pay. In addition, the immigration of customers between submarkets (i.e. cannibalization) is considered in the market-segmented environment due to imperfect segmentation. This research develops a geometric programming model to formulate the issue of joint price differentiation and multi-site aggregate production planning decisions by maximizing the total profit of the supply chain. To tackle the model and obtain solutions, we tailor an efficient analytical solution procedure to convert the original highly non-linear programming model into a convex programming equivalent. Finally, a numerical study of garment supply chain is presented to demonstrate the performance of the model and solution approaches. The research findings indicate a positive relationship between the scaling constant of price-dependent demand and the total profit rate. Moreover, as price gaps grow, the utility of price differentiation is decreased.
A number of factors, including product proliferation and increased customer service-level requirements, have led many companies to consider adopting postponement as a supply chain strategy. Packaging postponement is t...
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A number of factors, including product proliferation and increased customer service-level requirements, have led many companies to consider adopting postponement as a supply chain strategy. Packaging postponement is the process of delaying packaging of a common item into a final product configuration until the customer order is received. For a given product, a portion of demand is known with a high level of certainty and would not benefit from postponement. The remaining portion of demand is known with little certainty and would benefit from delaying the differentiating stage of the operation until demand is known. We develop a single-period, two-product, order-up-to cost model to aid in setting the levels of finished-goods inventory and postponement capacity. Minimum-cost optimal solutions to inventory levels and capacity are obtained by solving the derived analytical expressions using a non-linear programming formulation. We examine the sensitivity of the model to different levels of the model parameters to generate managerial insights beyond those of previous work. We show that changing product value, packaging cost, cost of postponement, holding cost, fill rate, and demand correlation can decrease expected total cost and increase postponement capacity. (C) 2009 Elsevier B. V. All rights reserved.
The paper refers to previous works developed by the authors, dealing with the possibility of applying duality theorems to non-linear programs coming out from limit analysis (LA) of structures made by not resisting ten...
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The paper refers to previous works developed by the authors, dealing with the possibility of applying duality theorems to non-linear programs coming out from limit analysis (LA) of structures made by not resisting tension (NRT) or no-tension material. Under such perspective, after setting up the static or kinematic LA problem for NRT structures, the main task, for duality theorems to be applicable, is to demonstrate some convexity-related properties of the involved functions and domains. This feature, which is of basic importance for the whole procedure, is not trivial since all of the required conditions are to be accurately checked by analytical developments. Application of duality is finally demonstrated to give a complete and clear interpretation from a physical point of view about relationships relevant to LA approaches. (C) 2005 Elsevier Ltd. All rights reserved.
This paper addresses the NP hard optimization problem of packing identical spheres of unit radii into the smallest sphere (PSS). It models PSS as a non-linear program (NIP) and approximately solves it using a hybrid h...
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This paper addresses the NP hard optimization problem of packing identical spheres of unit radii into the smallest sphere (PSS). It models PSS as a non-linear program (NIP) and approximately solves it using a hybrid heuristic which couples a variable neighborhood search (VNS) with a local search (LS). VNS serves as the diversification mechanism whereas LS acts as the intensification one. VNS investigates the neighborhood of a feasible local minimum u in search for the global minimum, where neighboring solutions are obtained by shaking one or more spheres of u and the size of the neighborhood is varied by changing the number of shaken spheres, the distance and the direction each sphere is moved. LS intensifies the search around a solution u by subjecting its neighbors to a sequential quadratic algorithm with non-monotone line search (as the NIP solver). The computational investigation highlights the role of LS and VNS in identifying (near) global optima, studies their sensitivity to initial solutions, and shows that the proposed hybrid heuristic provides more precise results than existing approaches. Most importantly, it provides computational evidence that the multiple-start strategy of non-linear programming solvers is not sufficient to solve PSS. Finally, it gives new upper bounds for 29 out of 48 benchmark instances of PSS. (C) 2012 Elsevier Ltd. All rights reserved.
Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today's competitive business environment in which providers of goods and services are offering a broad ...
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Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today's competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs. We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer's surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment's surplus from this particular product to the segment's total surplus across all offered products with positive surplus for that segment. We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities. (C) 2002 Elsevier B.V. All rights reserved.
A computational methodology for optimizing the conceptual layout of unsteady flow problems at low Reynolds numbers is presented. The geometry of the design is described by the spatial distribution of a fictitious mate...
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A computational methodology for optimizing the conceptual layout of unsteady flow problems at low Reynolds numbers is presented. The geometry of the design is described by the spatial distribution of a fictitious material with continuously varying porosity. The flow is predicted by a stabilized finite element formulation of the incompressible Navier-Stokes equations. A Brinkman penalization is used to enforce zero-velocities in solid material. The resulting parameter optimization problem is solved by a non-linear programming method. The paper studies the feasibility of the material interpolation approach for optimizing the topology of unsteady flow problems. The derivation of the governing equations and the adjoint sensitivity analysis are presented. A design-dependent stabilization scheme is introduced to mitigate numerical instabilities in porous material. The emergence of non-physical artifacts in the optimized material distribution is observed and linked to an insufficient resolution of the flow field and an improper representation of the pressure field within solid material by the Brinkman penalization. Two numerical examples demonstrate that the designs optimized for unsteady flow differ significantly from their steady-state counterparts. Copyright (C) 2011 John Wiley & Sons, Ltd.
In this paper, a heuristic algorithm, different from the Frank-Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, ...
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In this paper, a heuristic algorithm, different from the Frank-Wolfe and its modified methods, is introduced for network equilibration. By using the column generation technique and the network equilibrium conditions, the new method need not enumerate initially all feasible paths for all origin/destination (O/D) pairs, but can give all paths used between each O/D pair and the path flows accordingly while the new algorithm obtains an optimal traffic assignment. Some convergence issues of the new method is discussed in this paper. Numerical experiments show that the new method is efficient and robust. (c) 2005 Elsevier Inc. All rights reserved.
An efficient algorithm is proposed for the buffer allocation in a continuous flow production line with unreliable machines. The problem is formulated as a non-linear programming with linear constraints, and the concep...
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An efficient algorithm is proposed for the buffer allocation in a continuous flow production line with unreliable machines. The problem is formulated as a non-linear programming with linear constraints, and the concept of pseudo gradient and gradient projection is employed in developing the algorithm. Numerical experiment shows that the algorithm yields quite good solutions to the large-sized problems with the generalized linear constraints. The robustness to the initial solution and the efficiency of the algorithm is also shown.
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