We demonstrate that Karmarkar's projective algorithm is fundamentally an algorithm for fractional linear programming on the simplex. Convergence for the latter problem is established assuming only an initial lower...
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We demonstrate that Karmarkar's projective algorithm is fundamentally an algorithm for fractional linear programming on the simplex. Convergence for the latter problem is established assuming only an initial lower bound on the optimal objective value. We also show that the algorithm can be easily modified so as to assure monotonicity of the true objective values, while retaining all global convergence properties. Finally, we show how the monotonic algorithm can be used to obtain an initial lower bound when none is otherwise available.
Despite many advances in biotechnology being futuristic, in some industries such technological improvements are:now becoming generally available for absorption into commercial practice. The new reproductive technologi...
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Despite many advances in biotechnology being futuristic, in some industries such technological improvements are:now becoming generally available for absorption into commercial practice. The new reproductive technologies for bovine animals are such an example. For a regulated industry like agriculture, an ex ante evaluation of the impact of their adoption is the concern of policy makers. This paper describes a modelling strategy devised to assess these impacts, using a sequence of stochastic, financial and linear programming models. A set of individual farm type models were developed and later extended to a national model to simulate the interactions that occur between dairy and beef enterprises and the competition between them for resources on individual farms. Restraints reflecting national policies such as quotas on milk production and industry support through subsidies are built into the model to explore several scenarios. These models are used to assess the impact of new technologies on dairy and beef production nationally and for regions which have been identified by the Ministry of Agriculture, Fisheries and Food.
The sintering characteristics of powder blends are greatly influenced by the characteristics of the particle size distribution, typically well-modeled as lognormal. Some sintering processes combine individual powder b...
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The sintering characteristics of powder blends are greatly influenced by the characteristics of the particle size distribution, typically well-modeled as lognormal. Some sintering processes combine individual powder batches of different sizes to produce a mixture with a specific mean, standard deviation and distribution. This work demonstrates how the technique of linear programming can be employed to produce accurate estimates of the proportions of the original manufactured powders that should be mixed in order to produce a final particle size distribution that closely matches a lognormal shape with a specific mean diameter and a specific diameter standard deviation. This approach is carried out using data describing the particle diameter distributions for eleven basic grades of alumina powder, and a linear programming formulation which uses the universally available Excel Solver spreadsheet software. (c) 2007 Elsevier B.V. All rights reserved.
This paper proposes the event-triggered control of positive systems with state saturation both in discrete-time and continuous-time cases. A 1-norm based event-triggered mechanism is established for positive systems. ...
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This paper proposes the event-triggered control of positive systems with state saturation both in discrete-time and continuous-time cases. A 1-norm based event-triggered mechanism is established for positive systems. Under the event-triggered mechanism, the error term between actual and sample states is transformed into interval uncertain form. Together with the properties of saturation, the systems with state saturation are transformed into interval uncertain systems and the corresponding lower and upper bounds of the system matrices are obtained, respectively. Using a linear co-positive Lyapunov function, the event-triggered controller and the auxiliary gain matrix of the domain of attraction are designed in terms of linear programming, respectively. Then, the systems with state and input saturation are also described via interval uncertain systems. An event-triggered controller is designed and thus the closed-loop systems are positive and stable under the designed controller. Furthermore, the presented event-triggered control approach is extended to the continuous-time case. Compared to existing control approaches, the event-triggered control can reduce energy consumption and increase the practicability. Finally, several numerical examples are given to illustrate the effectiveness of the proposed design.
Distribution system reconfiguration (DSR) is a critical process that improves the power transfer efficiency and reduces the over-all operational cost. There have been various methods for addressing the DSR problems. R...
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Distribution system reconfiguration (DSR) is a critical process that improves the power transfer efficiency and reduces the over-all operational cost. There have been various methods for addressing the DSR problems. Recently, DSR problems formulated in mixed-integer linear programming (MILP) has gained popularity as they generally can be solved by the state-of-the-art commercially accessible linear programming solvers, and is able to solve the system with thousands of unknown variables within a reasonable time. However, in some MILP formulations, the distribution line losses are omitted in the nodal power injections for the sake of simplicity. This compromises the accuracy of the linearised model and contributes to the disparity between the MILP and the true non-linear model. Hence, in this study, new formulations are introduced for embedding the expressions of line losses inside load flow equations so that the deviations between the modelled and exact losses notably reduce. Moreover, other novel formulations have also been presented for simultaneously optimising distributed generation (DG) locations and sizes, while at the same time considering various DG's modes of connection to the distribution grid. The validity and effectiveness of the proposed MILP model is tested on standard IEEE systems and actual distribution network.
This paper offers a general approach to valuating investments in end-of-pipe-technologies (EOP-technologies) with special regard to an emissions trading scheme. Since investments of this kind affect production, it is ...
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This paper offers a general approach to valuating investments in end-of-pipe-technologies (EOP-technologies) with special regard to an emissions trading scheme. Since investments of this kind affect production, it is necessary to derive the required payments for a financial valuation and the constraints from production theory and production planning. On this basis, it is possible to develop a valuation model. This model considers joint production, activity-level-dependent and -independent payments and specifically includes the indivisibility of the investment. Applying duality theory enables us to examine the determinants of the price ceiling for such an investment. Sensitivity analysis shows that tradable permits have several effects on an investment and do not always encourage environmentally beneficial investments - in particular cases they may even be counterproductive. (C) 2008 Elsevier B.V. All rights reserved.
The class of multiset combinatorial batch codes (MCBCs) was introduced by Zhang et al. (2018) as a generalization of combinatorial batch codes (CBCs), which are replication-based batch codes. The MCBCs allow multiple ...
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The class of multiset combinatorial batch codes (MCBCs) was introduced by Zhang et al. (2018) as a generalization of combinatorial batch codes (CBCs), which are replication-based batch codes. The MCBCs allow multiple users to retrieve items in parallel in a distributed storage and a fundamental objective in this study is to determine the minimum total storage given certain requirements. We formulate linear programs so that the optimal solutions provide lower bounds on the total storage of MCBCs. Borrowing techniques from linear programming, we improve known lower bounds in some cases. Furthermore, for some parameters, we showed that these lower bounds are either tight or asymptotically tight by constructing the corresponding codes.
The short-term hydrothermal scheduling (SHS), typically a complicated nonlinear, nonconvex and non-smooth optimization problem, is very important for the economic operation of power systems. Instead of heuristic algor...
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The short-term hydrothermal scheduling (SHS), typically a complicated nonlinear, nonconvex and non-smooth optimization problem, is very important for the economic operation of power systems. Instead of heuristic algorithms popularly used in previous studies, this paper employs a mathematical approach, where a two-stage linear programming with special ordered sets (TLPSOS) is proposed to solve the SHS problem. The nonlinear thermal cost functions and hydropower output functions are approximated by using the special ordered sets. The TLPSOS involves two stages: solve the linearized model in the first stage, and eliminate the linearization errors in the second. Superior to heuristic algorithms, the TLPSOS does not rely on parameters, and can always give stable results. Applied to a widely used hydrothermal system which consists of four hydroplants and three thermal plants, the present method shows its efficiency and strength in obtaining results better than those of previous studies.
The metabolic pathway and the properties of many of the enzymes involved in the citric acid biosynthesis in the mold Aspergillus niger are well known. This fact, together with the availability of new theoretical frame...
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The metabolic pathway and the properties of many of the enzymes involved in the citric acid biosynthesis in the mold Aspergillus niger are well known. This fact, together with the availability of new theoretical frameworks aimed at quantitative analyses of control and dynamics in metabolic systems, has allowed us to construct a mathematical model of the carbohydrate metabolism in Aspergillus niger under conditions of citric acid accumulation. The model makes use of the S-system representation of biochemical systems, which renders it possible to use linear programming to optimize the process. It was found that maintaining the metabolite pools within narrow physiological limits (20% around the basal steady-state level) and allowing the enzyme concentrations to vary within a range of 0.1 to 50 times their basal values it is possible to triple the glycolytic flux while maintaining 100% yield of substrate transformation. To achieve these improvements it is necessary to modulate seven or more enzymes simultaneously. Although this seems difficult to implement at present, the results are useful because they indicate what the theoretical limits are and because they suggest several alternative strategies. (C) 1996 John Wiley & Sons, Inc.
In this paper, we propose three decomposition techniques for linear programming (LP) problems: (1) Method 1, in which we decompose the variables into the working set and the fixed set, but we do not decompose the cons...
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In this paper, we propose three decomposition techniques for linear programming (LP) problems: (1) Method 1, in which we decompose the variables into the working set and the fixed set, but we do not decompose the constraints, (2) Method 2, in which we decompose only the constraints and (3) Method 3, in which we decompose both the variables and the constraints into two. By Method 1 the value of the, objective function is proved to be non-decreasing (non-increasing) for the maximization (minimization) problem and by Method 2, the value is non-increasing (non-decreasing) for the maximization (minimization) problem. Thus, by Method 3, which is a combination of Methods I and 2, the value of the objective function is not guaranteed to be monotonic and there is a possibility of infinite loops. We prove that infinite loops are resolved if the variables in an infinite loop are not released from the working set and Method 3 converges in finite steps. We apply Methods I and 3 to LP support vector machines (SVMs) and discuss a more efficient method of accelerating training by detecting the increase in the number of violations and restoring variables in the working set that are released at the previous iteration step. By computer experiments for microarray data with huge input variables and a small number of constraints, we demonstrate the effectiveness of Method 1 for training the primal LP SVM with linear kernels. We also demonstrate the effectiveness of Method 3 over Method I for the nonlinear LP SVMs. (C) 2008 Elsevier B.V. All rights reserved.
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