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A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model

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EXPERT SYSTEMS WITH APPLICATIONS 2012年第3期39卷 3888-3895页

作者： Eduardo Cardenas-Barron, Leopoldo Trevino-Garza, Gerardo Wee, Hui Ming Inst Tecnol & Estudios Super Monterrey Dept Ind & Syst Engn Monterrey 64849 NL Mexico Inst Tecnol & Estudios Super Monterrey Dept Management Sch Business Monterrey 64849 NL Mexico Chung Yuan Christian Univ Dept Ind & Syst Engn Chungli 32023 Taiwan

This research presents an alternative heuristic algorithm to solve the vendor management inventory system with multi-product and multi-constraint based on EOQ with backorders considering two classical backorders costs: linear and fixed. For this type of inventory system, the optimization problem is a nonlinear integer programming (NLIP). Several numerical examples are given to demonstrate that the proposed heuristic algorithm is better than the previous genetic algorithm published based on three aspects: the total cost, the number of evaluations of the total cost function and computational time. Furthermore, the proposed algorithm is simpler and can be implemented by any people. (C)0 2011 Elsevier Ltd. All rights reserved.

关键词： Genetic algorithms Heuristic algorithms EOQ Vendor management inventory nonlinear integer programming

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On nonlinear multi-covering problems

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2017年第2期33卷 645-659页

作者： Cohen, Reuven Gonen, Mira Levin, Asaf Onn, Shmuel Bar Ilan Univ Dept Math IL-5290002 Ramat Gan Israel Ariel Univ Dept Comp Sci IL-40700 Ariel Israel Technion Israel Inst Technol Fac Ind Engn & Management IL-32000 Haifa Israel

In this paper we define the exact k-coverage problem, and study it for the special cases of intervals and circular-arcs. Given a set system consisting of a ground set of n points with integer demands and integer rewards, subsets of points, and an integer k, select up to k subsets such that the sum of rewards of the covered points is maximized, where point i is covered if exactly subsets containing it are selected. Here we study this problem and some related optimization problems. We prove that the exact k-coverage problem with unbounded demands is NP-hard even for intervals on the real line and unit rewards. Our NP-hardness proof uses instances where some of the natural parameters of the problem are unbounded (each of these parameters is linear in the number of points). We show that this property is essential, as if we restrict (at least) one of these parameters to be a constant, then the problem is polynomial time solvable. Our polynomial time algorithms are given for various generalizations of the problem (in the setting where one of the parameters is a constant).

关键词： Covering problems Circular-arcs Intervals nonlinear integer programming

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The Robust Deviation Redundancy Allocation Problem With Interval Component Reliabilities

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IEEE TRANSACTIONS ON RELIABILITY 2012年第4期61卷 957-965页

作者： Feizollahi, Mohammad Javad Modarres, Mohammad Sharif Univ Technol Dept Ind Engn Tehran Iran

We propose a robust deviation framework to deal with uncertain component reliabilities in the constrained redundancy optimization problem (CROP) in series-parallel reliability systems. The proposed model is based on a linearized binary version of standard nonlinear integer programming formulations of this problem. We extend the linearized model to address uncertainty by assuming that the component reliabilities belong to an interval uncertainty set, where only upper and lower bounds are known for each component reliability, and develop a Min-Max regret model to handle data uncertainty. A key challenge is that, because the deterministic model involves nonlinear functions of the uncertain data, classical robust deviation approaches cannot be applied directly to find robust solutions. We exploit problem structures to develop four exact solution methods, and present computational results demonstrating their performance.

关键词： Interval data nonlinear integer programming redundancy allocation robust deviation

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The split closure of a strictly convex body

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OPERATIONS RESEARCH LETTERS 2011年第2期39卷 121-126页

作者： Dadush, D. Dey, S. S. Vielma, J. P. IBM TJ Watson Res Ctr Business Analyt & Math Sci Dept Yorktown Hts NY 10598 USA Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15261 USA Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

The Chvatal-Gomory closure and the split closure of a rational polyhedron are rational polyhedra. It has been recently shown that the Chvatal-Gomory closure of a strictly convex body is also a rational polytope. In this note, we show that the split closure of a strictly convex body is defined by a finite number of split disjunctions, but is not necessarily polyhedral. We also give a closed form expression in the original variable space of a split cut for full-dimensional ellipsoids. (c) 2011 Elsevier B.V. All rights reserved.

关键词： Split cuts Split closure nonlinear integer programming

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SOLVING MIXED-integer nonlinear PROGRAMS BY OUTER APPROXIMATION

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MATHEMATICAL programming 1994年第3期66卷 327-349页

作者： FLETCHER, R LEYFFER, S UNIV DUNDEE DEPT MATH & COMP SCIDUNDEE DD1 4HNSCOTLAND

A wide range of optimization problems arising from engineering applications can be formulated as Mixed integer nonlinear programming problems (MINLPs). Duran and Grossmann (1986) suggest an outer approximation scheme for solving a class of MINLPs that are linear in the integer variables by a finite sequence of relaxed MILP master programs and NLP subproblems. Their idea is generalized by treating nonlinearities in the integer variables directly, which allows a much wider class of problem to be tackled, including the case of pure INLPs. A new and more simple proof of finite termination is given and a rigorous treatment of infeasible NLP subproblems is presented which includes all the common methods for resolving infeasibility in Phase I. The worst case performance of the outer approximation algorithm is investigated and an example is given for which it visits all integer assignments. This behaviour leads us to include curvature information into the relaxed MILP master problem, giving rise to a new quadratic outer approximation algorithm. An alternative approach is considered to the difficulties caused by infeasibility in outer approximation, in which exact penalty functions are used to solve the NLP subproblems. It is possible to develop the theory in an elegant way for a large class of nonsmooth MINLPs based on the use of convex composite functions and subdifferentials, although an interpretation for the l(1) norm is also given.

关键词： nonlinear integer programming MIXED integer nonlinear programming DECOMPOSITION OUTER APPROXIMATION

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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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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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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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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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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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