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A new discrete filled function algorithm for discrete-global optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2007年第2期202卷 280-291页

作者： Yang Yongjian Liang Yumei Shanghai Univ Dept Math Shanghai 200444 Peoples R China

A definition of the discrete filled function is given in this paper. Based on the definition, a discrete filled function is proposed. Theoretical properties of the proposed discrete filled function are investigated, and an algorithm for discrete global optimization is developed from the new discrete filled function. The implementation of the algorithms on several test problems is reported with satisfactory numerical results. (c) 2006 Elsevier B.V. All rights reserved.

关键词： filled function method discrete global optimization nonlinear integer programming

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A heuristic for the label printing problem

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COMPUTERS & OPERATIONS RESEARCH 2007年第9期34卷 2576-2588页

作者： Yiu, K. F. C. Mak, K. L. Lau, H. Y. K. Univ Hong Kong Dept Ind & Management Syst Engn Hong Kong Hong Kong Peoples R China

Label printing finds many applications in industry. However, this task is still labor intensive in many printing factories. Since each template can only accommodate a fixed number of labels, an important task is to work out the compositions of templates by allocating suitable labels to each template in order to fulfill the order requirements effectively. The template design could be rather arbitrary, which usually ends up with a lot of excessive printed labels. Enhancing the template design will significantly improve the efficiency of the printing process, and, at the same time, reduce the waste of resources. This motivates the study of more automatic design methods. In this paper, the problem is first formulated as a nonlinear integer programming problem. The main variables in the formulation are the compositions and the printing frequencies of templates. For practical purpose, each type of label is confined to one template only which allows automated packing and handling. The structure of the problems is carefully analyzed and a new algorithm is proposed. Numerical results show that the proposed method is a simple but effective way of generating good template designs. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： label printing nonlinear integer programming heuristic simulating annealing

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Supply chain models for an assembly system with preprocessing of raw materials

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第2期181卷 733-752页

作者： Rahman, Mohammad Anwar Ashek Sarker, Bhaba R. Louisiana State Univ Dept Ind Engn Baton Rouge LA 70803 USA

In this paper.. we investigate the material procurement and delivery policy in a production system where raw materials enter into the assembly line from two different flow channels. The system encompasses batch production process in which the finished product demand is approximately constant for an infinite planning horizon. Two distinct types of raw materials are passed through the assembly line before to convert them into the finished product. Of the two types of raw materials, one type requires preprocessing inside the facility before the assembly operation and other group is fed straightway in the assembly line. The conversion factors are assigned to raw materials to quantify the raw material batch size required. To analyze such a system, we formulate a nonlinear cost function to aggregate all the costs of the inventories, ordering, shipping and deliveries. An algorithm using the branch and bound concept is provided to find the best integer values of the optimal solutions. The result shows that the optimal procurement and delivery policy minimizes the expected total cost of the model. Using a test problem, the inventory requirements at each stage of production and their corresponding costs are calculated. From the analysis, it is shown that the rate and direction change of total cost is turned to positive when delivery rates per batch reaches close to the optimal value and the minimum cost is achieved at the optimal delivery rate. Also. it is shown that total incremental cost is monotonically increasing, if the finished product batch size is increased, and if, inventory cost rates are increased. We examine a set of numerical examples that reveal the insights into the procurement-delivery policy and the performance of such an assembly type inventory model. (c) 2006 Elsevier B.V. All rights reserved.

关键词： inventory model raw materials nonlinear integer programming

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Knowledge management system for operating parameters in two-echelon VMI supply chains

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2007年第11期45卷 2479-2505页

作者： Nachiappan, S. P. Gunasekaran, A. Jawahar, N. Univ Massachusetts Dartmouth Dept Management N Dartmouth MA 02747 USA Thiagarajar Coll Engn Dept Mech Engn Madurai 625015 Tamil Nadu India

This paper presents an information technology (IT)-driven normative model of vendor-managed inventory system in a two-echelon supply chain comprising of m vendors and n buyers, referred as Two-echelon Multiple Vendor Multiple Buyers Supply Chain (TMVMBSC). The operational parameters to the above model are: sales quantities and their corresponding sales price of the buyers and transaction quantities that determine channel profit of supply chain and their respective contract prices between vendors and buyers. In order to find out the optimal transaction quantities for each buyer in TMVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal transaction quantity. A knowledge management system (KMS) using genetic algorithm is proposed to solve this TMVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed KMS is evaluated for its solution quality and computational time. Besides, the robustness of model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed.

关键词： operational parameters nonlinear integer programming knowledge management system vendor-managed inventory supply chain IT-driven normative models

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A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期182卷 1433-1452页

作者： Nachiappan, S. P. Jawahar, N. Thiagarajar Coll Engn Dept Mech Engn Madurai 625015 Tamil Nadu India

This paper deals with the operational issues of a two-echelon single vendor multiple buyers supply chain (TSVMBSC) model under vendor managed inventory (VMI) mode of operation. The operational parameters to the above model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. In order to find out the optimal sales quantity for each buyer in TSVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal sales quantity. A genetic algorithm (GA) based heuristic is proposed to solve this TSVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed methodology is evaluated for its solution quality. Furthermore, the robustness of the model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed. (c) 2006 Elsevier B.V. All rights reserved.

关键词： operational parameters nonlinear integer programming genetic algorithm vendor managed inventory supply chain

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New Implicit Enumeration Method for Polynomial 0-1 programming

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Systems Engineering - Theory & Practice 2007年第3期27卷 21-27页

作者： Jun WANG Duan LI Department of Management Science and Engineering Qingdao University Qingdao 266071 China Department of Systems Engineering and Engineering Management Chinese University of Hong Kong Hong Kong China

A new implicit enumeration method for polynomial zero-one programming is proposed in this article. By adopting the p-norm surrogate constraint method, a polynomial zero-one programming problem with multiple constraints can be converted into an equivalent polynomial zero-one programming problem with a single surrogate constraint. A new solution scheme is then devised to take the advantage of this prominent feature in carrying out the “fathoming” procedure and the “backtrack” procedure in a searching process of an implicit enumeration. We demonstrate the efficiency of this new algorithm by some promising computational results. Finally, we conclude by proposing certain topics for future research.

关键词： nonlinear integer programming zero-one programming implicit enumeration combinatorial optimization

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A gradually descent method for discrete global optimization

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Journal of Shanghai University(English Edition) 2007年第1期11卷 39-44页

作者：杨永建张连生 Department of Mathematics College of Sciences Shanghai University

In this paper, a new method named as the gradually descent method was proposed to solve the discrete global optimization problem. With the aid of an auxiliary function, this method enables to convert the problem of finding one discrete minimizer of the objective function f to that of finding another at each cycle. The auxiliary function can ensure that a point, except a prescribed point, is not its integer stationary point if the value of objective function at the point is greater than the scalar which is chosen properly. This property leads to a better minimizer of f found more easily by some classical local search methods. The computational results show that this algorithm is quite efficient and reliable for solving nonlinear integer programming problems.

关键词： gradually descent method nonlinear integer programming integer programming algorithm

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Generalized nonlinear Lagrangian formulation for bounded integer programming

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JOURNAL OF GLOBAL OPTIMIZATION 2005年第2期33卷 257-272页

作者： Xu, YF Liu, CL Li, D Fudan Univ Sch Management Shanghai 200433 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China

Several nonlinear Lagrangian formulations have been recently proposed for bounded integer programming problems. While possessing an asymptotic strong duality property, these formulations offer a success guarantee for the identification of an optimal primal solution via a dual search. Investigating common features of nonlinear Lagrangian formulations in constructing a nonlinear support for nonconvex piecewise constant perturbation function, this paper proposes a generalized nonlinear Lagrangian formulation of which many existing nonlinear Lagrangian formulations become special cases.

关键词： duality gap integer programming Lagrangian relaxation nonlinear integer programming nonlinear Lagrangian formulation

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Partner selection with a due date constraint in virtual enterprises

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APPLIED MATHEMATICS AND COMPUTATION 2006年第2期175卷 1353-1365页

作者： Zeng, Zhi-Bin Li, Yan Zhu, Wenxing Xian Univ Technol Sch Machinery & Precis Instrument Engn Xian 710048 Peoples R China Fuzhou Univ Dept Comp Sci & Technol Fuzhou 350002 Peoples R China

In this paper, the partner selection problem with a due date constraint in virtual enterprises is proved to be an NP-complete problem. So it cannot have any polynomial time solution algorithm at present. A nonlinear integer programming model for this problem is established. The objective function and a constraint function of the model have monotone properties. Based on the above observations, a Branch & Bound algorithm is constructed to solve the problem. Numerical experiments show that the algorithm is efficient. (c) 2005 Elsevier Inc. All rights reserved.

关键词： virtual enterprise partner selection nonlinear integer programming Branch & Bound

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Optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection

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MATHEMATICAL FINANCE 2006年第1期16卷 83-101页

作者： Li, D Sun, XL Wang, J Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Shanghai Univ Shanghai 200444 Peoples R China

The pioneering work of the mean-variance formulation proposed by Markowitz in the 1950s has provided a scientific foundation for modern portfolio selection. Although the trade practice often confines portfolio selection with certain discrete features, the existing theory and solution methodologies of portfolio selection have been primarily developed for the continuous solution of the portfolio policy that could be far away from the real integer optimum. We consider in this paper an exact solution algorithm in obtaining an optimal lot solution to cardinality constrained mean-variance formulation for portfolio selection under concave transaction costs. Specifically, a convergent Lagrangian and contour-domain cut method is proposed for solving this class of discrete-feature constrained portfolio selection problems by exploiting some prominent features of the mean-variance formulation and the portfolio model under consideration. Computational results are reported using data from the Hong Kong stock market.

关键词： portfolio selection mean-variance formulation concave transaction costs cardinality constraint nonlinear integer programming

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