# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

All Issues

## Journal of Industrial & Management Optimization

October 2007 , Volume 3 , Issue 4

A special issue dedicated to Professor Changyu Wang in recognition of his contributions

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2007, 3(4): i-iv doi: 10.3934/jimo.2007.3.4i +[Abstract](1467) +[PDF](32.6KB)
Abstract:
This special issue is dedicated to Professor Changyu Wang on the occasion of his 70th birthday in recognition of his contributions to Operations Research and its applications and his lasting impact as an educator.
2007, 3(4): 619-624 doi: 10.3934/jimo.2007.3.619 +[Abstract](1962) +[PDF](124.9KB)
Abstract:
Clustering method is one of the most important tools in statistics. In a graph theory model, clustering is the process of finding all dense subgraphs. In this paper, a new clustering method is introduced. One of the most significant differences between the new method and other existing methods is that this new method constructs a much smaller hierarchical tree, which clearly highlights meaningful clusters. Another important feature of the new method is the feature of overlapping clustering or multi-membership. The property of multi-membership is a concept that has recently received increased attention in the literature (Palla, Derényi, Farkas and Vicsek, (Nature 2005); Pereira-Leal, Enright and Ouzounis, (Bioinformatics, 2004); Futschik and Carlisle, (J. Bioinformatics and Computational Biology 2005))
2007, 3(4): 625-643 doi: 10.3934/jimo.2007.3.625 +[Abstract](1625) +[PDF](241.2KB)
Abstract:
As a generalization of the traditional path protection (PP) scheme in WDM networks where a backup path is needed for each active path, the partial path protection (PPP) scheme uses a collection of backup paths to protect an active path, where each backup path in the collection protects one or more links on the active path such that every link on the active path is protected by one of the backup paths. While there is no known polynomial time algorithm for computing an active path and a corresponding backup path using the PP scheme for a given source destination node pair, we show that an active path and a corresponding collection of backup paths using the PPP scheme can be computed in polynomial time, whenever they exist, under each of the following four network models: (a) dedicated protection in WDM networks without wavelength converters; (b) shared protection in WDM networks without wavelength converters; (c) dedicated protection in WDM networks with wavelength converters; and (d) shared protection in WDM networks with wavelength converters. This is achieved by proving that that for any given source $s$ and destination $d$ in the network, if one candidate active path connecting $s$ and $d$ is protectable using PPP, then any candidate active path connecting $s$ and $d$ is also protectable using PPP. It is known that the existence of PP implies the existence of PPP while the reverse is not true. We demonstrate a similar result in the case of segmented path protection. This fundamental property of the PPP scheme is of great importance in the context of achieving further research advances in the area of protection and restoration of WDM networks.
2007, 3(4): 645-654 doi: 10.3934/jimo.2007.3.645 +[Abstract](1511) +[PDF](137.9KB)
Abstract:
This paper presents a relaxed extragradient-like method for solving the convexly constrained minimization with optimal value zero. The method is a combination of the extragradient-like algorithm and a halfspace-relaxation technique to the constrained set of the problem. Each iteration of the proposed method consists of the projection onto a halfspace containing the given closed convex set. The method is implemented very easily and is proven to be fully convergent to the solution. Preliminary computational experience is also reported.
2007, 3(4): 655-670 doi: 10.3934/jimo.2007.3.655 +[Abstract](1416) +[PDF](228.1KB)
Abstract:
In this paper we present a globally and quadratically convergent method for the problem of minimizing a sum of Euclidean norms with linear constraints. The quadratic convergence result of this method is obtained without requiring strict complementarity.
2007, 3(4): 671-684 doi: 10.3934/jimo.2007.3.671 +[Abstract](1849) +[PDF](191.8KB)
Abstract:
In this paper, we study Levitin-Polyak type well-posedness for generalized variational inequality problems with functional constraints, as well as an abstract set constraint. We will introduce several types of generalized Levitin-Polyak well-posednesses, and give various criteria and characterizations for these types of well-posednesses.
2007, 3(4): 685-692 doi: 10.3934/jimo.2007.3.685 +[Abstract](1623) +[PDF](125.8KB)
Abstract:
In this paper, we firstly propose a technique named Duplicating , which duplicates machines in batch scheduling environment. Then we discuss several applications of Duplicating in solving batch scheduling problems. For the batch scheduling problem on unrelated parallel machines to minimize makespan, we give a $(4 - \frac{2}{B})$- approximation algorithm and a $(2 - \frac{1}{B} + \epsilon)$ algorithm when $m$ is fixed. We also present a $4(2 - \frac{1}{B} + \epsilon)$-competitive algorithm for the on-line scheduling problem on identical machines to minimize total weighted completion time by another technique-$\rho-dual$, which is proposed originally by Hall et al.(1997).
2007, 3(4): 693-700 doi: 10.3934/jimo.2007.3.693 +[Abstract](1701) +[PDF](133.9KB)
Abstract:
For constrained nonconvex optimization, we first show that under second-order sufficient conditions, a class of augmented Lagrangian functions possess local saddle points, and then prove that global saddle points of these augmented Lagrangian functions exist under certain mild additional conditions.
2007, 3(4): 701-713 doi: 10.3934/jimo.2007.3.701 +[Abstract](1434) +[PDF](122.2KB)
Abstract:
The Web document is organized by a set of textual data according to a predefined logical structure. It has been shown that collecting Web documents with similar structures can improve query efficiency. The XML document has no vectorial representation, which is required in most existing classification algorithms. The kernel method has been applied to represent structural data with pairwise similarity. In this case, a set of Web data can be fed into classification algorithms in the format of a kernel matrix. However, since the distance between a pair of Web documents is usually obtained approximately, the derived distance matrix is not a kernel matrix. In this paper, we propose to use the nearest correlation matrix (of the estimated distance matrix) as the kernel matrix, which can be fast computed by a Newton-type method. Experimental studies show that the classification accuracy can be significantly improved.
2007, 3(4): 715-726 doi: 10.3934/jimo.2007.3.715 +[Abstract](1993) +[PDF](156.0KB)
Abstract:
In this paper, we develop a model to analyze the coordination of a supply chain with the demand influenced by the buyer's promotion. The supply chain consists of a supplier and a group of homogeneous buyers. The buyers choose inventories ex ante and promotional levels ex post. The annual demand rate depends on the promotional level and the operating cost---including the ordering and inventory holding cost---depends on the promotional level and the order quantity. It is shown that quantity discount alone is not sufficient to guarantee joint profit maximization. Then we propose a contract, discount quantity with transfer profit contract, and show that this contract can coordinate the supply chain. Moreover, it is shown that this policy is robust because it can allocate the supply chain profit arbitrarily between the supplier and the buyer and lead the buyer to choose the joint optimal promotional level and the supplier need not to observe and verify the buyer's promotional level. For the special case that the operating cost is a fixed constant, we show that there is no contract which can coordinate the supply chain if the promotion is unobservable and unverifiable and the discount policy can guarantee the coordination of the supply chain if the promotion is observable and verifiable.
2007, 3(4): 727-737 doi: 10.3934/jimo.2007.3.727 +[Abstract](1971) +[PDF](165.2KB)
Abstract:
We study a nonlinear complementarity formulation of the supply chain network equilibrium problem, which is parallel to the variational inequality model established by Dong et al. (2004). In this setting, we obtain weaker conditions to guarantee the existence and uniqueness of the equilibrium pattern for a supply chain. A smoothing Newton method that exploits the network structure is proposed and convergence results are presented. Numerical examples show that the algorithm is more applicable than the modified projection method presented by Dong et al. (2004).
2007, 3(4): 739-748 doi: 10.3934/jimo.2007.3.739 +[Abstract](1570) +[PDF](137.0KB)
Abstract:
Tumor classification is one of the important applications of microarray technology. In gene expression-based tumor classification systems, gene selection is a main and very important component. In this paper, we propose a new approach for gene selection. With the genes selected in colon cancer data, acute lymphoblastic leukemia (ALL) and acute myeloid leukemia (AML) data using our approach, we apply support vector machines to classify tissues in these two data sets, respectively. The results of classification show that our method is very useful and promising.
2007, 3(4): 749-761 doi: 10.3934/jimo.2007.3.749 +[Abstract](1676) +[PDF](139.2KB)
Abstract:
In this paper, we treat the split feasibility problem with uncertain linear operator (USFP). For this problem, we first reformulate it as an uncertain optimization problem (UOP) with zero optimal value, and then we introduce robust counterparts of the UOP and reformulate them as the tractable convex optimization problems. These convex optimization problems have close connection with the robust counterparts of USFP and the minimum SFPs under the appropriate conditions. In the end of this paper, we give some numerical results to illustrate the effectiveness of the robust solutions of the concerned problem.
2007, 3(4): 763-774 doi: 10.3934/jimo.2007.3.763 +[Abstract](1753) +[PDF](154.0KB)
Abstract:
Based on the conclusion that have been put forward by Sougata Poddar and Uday Bhanu Sinha (2002), in "The Role of Fixed Fee and Royalty in Patent Licensing", we construct a model to analyze the behavior of the patentee when the licensee have private information about its marginal product costs before licensing. In the paper, the patentee is not considered as an independent R&D institute anymore but an insider. Moreover, we extend the model to Homogeneous Stackelberg and present the patentee's optimal linear licensing schemes in the sense of maximizing its profits under the licensing contract. It is found that the expected profit of the patentee under the separating contract is higher than any pooling contract in this model.
2007, 3(4): 775-781 doi: 10.3934/jimo.2007.3.775 +[Abstract](1774) +[PDF](110.4KB)
Abstract:
For the constrained optimization problem, under the condition that the objective function is strongly convex, we obtain a global error bound for the distance between any feasible solution and the optimal solution by using the merit function in the sequential quadratic programming (SQP) method.

2018  Impact Factor: 1.025

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