多周期混合整数规划购油模型及应用

采用PIMS软件中的多周期混合整数规划技术建立炼油企业购油计划模型,使优化结果与实际购油方式相吻合;采用虚拟周期方法解决原油期末库存质量控制问题;采用滚动处理方式解决炼厂月、季原油选购计划的衔接和全局优化问题。文中还给出了多周期MIP模型技术在某炼厂中的应用以及不同方案的效益对比。     

Improving the efficiency of a mixed integer linear programming based approach for multi-class classification problem

Data classification is one of the fundamental issues in data mining and machine learning. A great deal of effort has been done for reducing the time required to learn a classification model. In this research, a new model and algorithm is proposed to improve the work of Xu and Papageorgiou (2009). Computational comparisons on real and simulated patterns with different characteristics (including dimension, high overlap or heterogeneity in the attributes) confirm that, the improved method considerably reduces the training time in comparison to the primary model, whereas it generally maintains the accuracy. Particularly, this speed-increase is significant in the case of high overlap. In addition, the rate of increase in training time of the proposed model is much less than that of the primary model, as the set-size or the number of overlapping samples is increased.     

Regularization of a lexicographic vector problem of integer programming

A stability criterion for a vector integer linear problem of lexicographic optimization is obtained. A regularization method is proposed that allows us to reduce a possible unstable output problem to a sequence of perturbed stable equivalent problems. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 125–130, November–December, 1999.     

On reduction of the multistage problem of stochastic programming with quantile criterion to the problem of mixed integer linear programming

Consideration was given to the a priori formulation of the multistage problem of stochastic programming with a quantile criterion which is reducible to the two-stage problem. Equivalence of the two-stage problems with the quantile criterion in the a priori and a posteriori formulations was proved for the general case. The a posteriori formulation of the two-stage problem was in turn reduced to the equivalent problem of mixed integer linear programming. An example was considered.     

A novel 0-1 linear integer programming model for dynamic machine-tool selection and operation allocation in a flexible manufacturing system

This paper considers a problem of dynamic machine-tool selection and operation allocation with part and tool movement policies in a flexible manufacturing system (FMS) environment. For this purpose, a novel 0-1 linear integer programming model is presented in such a way that each part and each tool can move during the production phase. It is assumed that there are a given set of tools and machines that can produce different kinds of orders (or part types). The objective of this model is to determine a machine-tool combination for each operation of the part type by minimizing some production costs, such as machining costs, setup costs, material handling costs and tool movement costs. In addition, due to the NP-hard nature of the problem, a new heuristic method based on five simple procedures (FSP) is proposed for solving the given problem, whose performance is tested on a number of randomly generated problems. The related results are compared with results obtained by a branch-and-bound method. It has been found that the proposed heuristic method gives good results in terms of objective function values and CPU times.     

On a type of stability of a multicriteria integer linear programming problem in the case of a monotone norm

A multicriteria integer linear programming problem with a finite number of admissible solutions is considered. The problem consists in finding the Pareto set. Lower and upper attainable estimates of the radius of strong stability of the problem are obtained in the case when the norm in the space of solutions is arbitrary, and the norm in the criteria space is monotone. Using the Minkowski-Mahler inequality, a formula for calculating this radius is derived in the case when the Pareto set consists of a single solution. Estimates of the radius are also found in the case of the Hölder norm in the specified spaces. A class of problems is distinguished for which the radius of strong stability is infinite. As corollaries, certain results known earlier are derived. Illustrative numerical examples are also presented.     

Stand-alone renewable power system scheduling for a green data center using integer linear programming

Journal of Scheduling - In light of the rapid growth of data centers around the world and their huge energy consumption, several researchers have focused on the task scheduling and resource...     

Optimum integer number and position of several groups of prestressing tendons for given concrete dimensions

The following design problem is solved: Given are the concrete dimensions and the loadings (e.g. dead load plus traffic loading). The engineer can choose the number of groups of tendons he wishes to use. For each group the following data are given: the location of the cross-sections at which the tendons are anchored, the prestressing force of one tendon, which can also be variable along the length of the beam to take friction losses approximately into consideration, the maximum and minimum number of tendons, the lower and upper bounds of the zone permissible for guaranteeing sufficient concrete coverage (these bounds can also vary along the length of the beam), the smallest permissible radius of curvature, as well as a relative price. Several load combinations, under service conditions with specified allowable maximum and minimum concrete stresses are selected by the engineer. A reduction factor for creep and shrinkage is also included in the input.Determined are (a) the overall most favorable integer number of tendons in each group, and (b) the position along the length of the beams, such that the stress margin that results in every section and under the stress conditions formulated under the most unfavorable load positions shall be a maximum.The optimization algorithm employs in part a linear program. Methods to eliminate redundant constraints on the level of the cross-sections and the elements are discussed.The procedure is illustrated with a highway bridge (deck on raking legs), using three groups of tendons.     

Stability radius of a vector integer linear programming problem: case of a regular norm in the space of criteria

A multicriteria integer linear programming problem of finding a Pareto set is considered. The set of feasible solutions is supposed to be finite. The lower and upper achievable bounds for the radius of stability are obtained using a stability criterion and the Minkowski–Mahler inequality and assuming that the norm is arbitrary in the space of solutions and is monotone in the space of criteria. Bounds for the radius of stability in spaces with the Holder metric are given in corollaries.     

Stability radius of an efficient solution of a vector problem of integer linear programming in the Gölder metric

A vector (multicriterion) problem of integer linear programming is considered on a finite set of feasible solutions. A metric l_p, 1 ≤ p ≤ ∞, is defined on the parameter space of the problem. A formula of the maximum permissible level of perturbations is obtained for the parameters that preserve the efficiency (Pareto optimality) of a given solution. Necessary and sufficient conditions of two types of stability of the problem are obtained as corollaries. This work has been carried out with financial support from the Belgosuniversity within the framework of the Intercollegiate Program “Fundamental and Applied Investigations” (project No. 492/28). __________ Translated from Kibernetika I Sistemnyi Analiz, No. 4, pp. 175–181, July–August 2006.     

Enhanced mixed integer programming model for a transfer line design problem

Modular machining lines with multi-spindle workstations are considered. A multi-spindle head executes a set of operations. The problem of optimal design or reconfiguration of such lines is considered here. The set of all available spindle heads, operations executed by each spindle head, spindle head times and costs are assumed to be known. There are operations which can be executed by one of several candidate spindle heads, i.e., in different configuration with other operations. The problem consists in the choice of spindle heads from the given set and their assignment to workstations. The goal is to minimize the line cost while satisfying the precedence, inclusion and exclusion constraints. This problem is an extension of well known assembly line balancing and equipment selection problem. In our previous work, we proposed a MIP model which was significantly limited as to the size of the problems treated. In this paper, quite a few original approaches are suggested to improve the previous MIP model. The numerical tests reported show that the calculation time is drastically decreased, thereby expanding the model to larger and more realistic industrial problems.     

Fuzzy optimization of units products in mix-product selection problem using fuzzy linear programming approach

In this paper, the modified S-curve membership function methodology is used in a real life industrial problem of mix product selection. This problem occurs in the production planning management where by a decision maker plays important role in making decision in an uncertain environment. As analysts, we try to find a good enough solution for the decision maker to make a final decision. An industrial application of fuzzy linear programming (FLP) through the S-curve membership function has been investigated using a set of real life data collected from a Chocolate Manufacturing Company. The problem of fuzzy product mix selection has been defined. The objective of this paper is to find an optimal units of products with higher level of satisfaction with vagueness as a key factor. Since there are several decisions that were to be taken, a table for optimal units of products respect to vagueness and degree of satisfaction has been defined to identify the solution with higher level of units of products and with a higher degree of satisfaction. The fuzzy outcome shows that higher units of products need not lead to higher degree of satisfaction. The findings of this work indicates that the optimal decision is depend on vagueness factor in the fuzzy system of mix product selection problem. Further more the high level of units of products obtained when the vagueness is low.     

Reduction of the two-step problem of stochastic optimal control with bilinear model to the problem of mixed integer linear programming

Consideration was given to the two-step problem of stochastic optimization with a bilinear model which describes the problem of forming the securities portfolio consisting of some risk assets and one riskless asset. The probability of exceeding the given threshold of capital is used as the optimality criterion. At the second step, the piecewise constant control is used as the capital control. Determined were the upper and lower estimates of the probability functional. The problems of maximizing the upper and lower estimates of the probability functional were reduced to the problems of mixed integer linear programming by means of discretizing the probabilistic measure. An algorithm to seek an approximate solution to the original problem was proposed, and an example was considered.