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Journal of Industrial & Management Optimization

2007 , Volume 3 , Issue 3

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Conjugate duality for generalized convex optimization problems
Anulekha Dhara and Aparna Mehra
2007, 3(3): 415-427 doi: 10.3934/jimo.2007.3.415 +[Abstract](479) +[PDF](178.1KB)
Abstract:
Equivalence between a constrained scalar optimization problem and its three conjugate dual models is established for the class of generalized C-subconvex functions. Applying these equivalent relations, optimality conditions in terms of conjugate functions are obtained for the constrained multiobjective optimization problem.
Learning algorithms for finite horizon constrained Markov decision processes
A. Mittal and N. Hemachandra
2007, 3(3): 429-444 doi: 10.3934/jimo.2007.3.429 +[Abstract](547) +[PDF](204.8KB)
Abstract:
We propose a heuristic and two stochastic approximation based learning algorithms for finite horizon, finite state-action constrained Markov decision models. We include models and numerical examples arising from risk management in fund allocation, retailer-depot product availability in a supply chain and admission control in a simple queue, that have to satisfy performance based constraints.
A solution framework for scheduling a BPM with non-identical job dimensions
M. Ramasubramaniam and M. Mathirajan
2007, 3(3): 445-456 doi: 10.3934/jimo.2007.3.445 +[Abstract](454) +[PDF](148.0KB)
Abstract:
This paper considers the problem of scheduling a single job family, where each job has non-identical job-sizes, non-identical job-dimensions and a furnace (a batch processing machine) that can process up to $B (B < n)$ jobs as a batch simultaneously. The motivation for this problem is the heat-treatment operation in the post casting stage of steel casting manufacturing. We propose (0-1) integer non-linear programming for minimizing the completion time of the last job, makespan. We also propose heuristic and a simple computational analysis which indicates heuristic algorithm has very good solution quality.
Revenue management via multi-product available to promise
Sandeep Dulluri and N. R. Srinivasa Raghavan
2007, 3(3): 457-479 doi: 10.3934/jimo.2007.3.457 +[Abstract](515) +[PDF](305.6KB)
Abstract:
Today's industries are highly complex in nature offering multiple customized quality products with shorter product life-cycles, volatile demand and tighter due-dates etc. to the customers. Manufacturers are focussing on Available-To-Promise (ATP) to their customers as a retention strategy. In other words manufacturers are forced to commit in advance to the customers the amount they can deliver by the specified due-date. In the current work we address a single manufacturer and multi-customer supply chain setting wherein there are multiple products, stochastic demands, varying profit rates, different learning rates etc. We restrict our focus to the multi-product ATP (MATP) strategies that maximize net profit of the manufacturer. We present optimization models in which there is a possibility of cancelling prior committed orders. We also model the dynamic pricing decision integrated with revenue management in MATP setting. We present the results of weak concavity of the MATP models and related structural insights. We support our thesis with rigorous numerical experimental results.
Finite algorithm for minimizing the product of two linear functions over a polyhedron
Nguyen Thi Bach Kim
2007, 3(3): 481-487 doi: 10.3934/jimo.2007.3.481 +[Abstract](500) +[PDF](112.5KB)
Abstract:
In this article we propose a finite algorithm for minimizing the product of two linear functions over a polyhedron. Preliminary computational results are reported.
Optimization of composition and processing parameters for alloy development: a statistical model-based approach
Alexandr Golodnikov, Stan Uryasev, Grigoriy Zrazhevsky, Yevgeny Macheret and A. Alexandre Trindade
2007, 3(3): 489-501 doi: 10.3934/jimo.2007.3.489 +[Abstract](423) +[PDF](176.2KB)
Abstract:
We describe the second step in a two-step approach for the development of new and improved alloys. The first step, proposed by Golodnikov et al [3], entails using experimental data to statistically model tensile yield strength and the 20th percentile of the impact toughness, as a function of alloy composition and processing variables. We demonstrate how the models can be used in the second step to search for combinations of the variables in small neighborhoods of the data space, that result in alloys having optimal levels of the properties modeled. The optimization is performed via the efficient frontier methodology. Such an approach, based on validated statistical models, can lead to a substantial reduction in the experimental effort and cost associated with alloy development. The procedure can also be used at various stages of the experimental program, to indicate what changes should be made in the composition and processing variables in order to shift the alloy development process toward the efficient frontier. Data from these more refined experiments can then be used to adjust the model and improve the second step, in an iterative search for superior alloys.
Semilocally prequasi-invex functions and characterizations
Jin-bao Jian, Hua-qin Pan and Han-jun Zeng
2007, 3(3): 503-517 doi: 10.3934/jimo.2007.3.503 +[Abstract](431) +[PDF](197.8KB)
Abstract:
In this paper, based on semilocal convexity, invexity and prequasi-invexity, a new kind of generalized convexity called (strictly/ semistrictly) semilocally prequasi-invex functions is presented, and some of their basic characterizations are discussed. Then, several necessary and sufficient conditions for the proposed generalized convexity are established. Finally, some important properties of the optimal solutions to the associated generalized convex optimization problems are discussed.
Semicontinuity of the solution set map to a set-valued weak vector variational inequality
C. R. Chen and S. J. Li
2007, 3(3): 519-528 doi: 10.3934/jimo.2007.3.519 +[Abstract](681) +[PDF](152.8KB)
Abstract:
This paper investigates the semicontinuity of the solution set map for a parametric set-valued weak vector variational inequality in Banach spaces. The upper semicontinuity and closedness of the solution set map are obtained. A parametric gap function is proposed by using a nonlinear scalarization function. By virtue of the parametric gap function and a key assumption, the lower semicontinuity of the solution set map is established.
Spline function smooth support vector machine for classification
Yubo Yuan, Weiguo Fan and Dongmei Pu
2007, 3(3): 529-542 doi: 10.3934/jimo.2007.3.529 +[Abstract](687) +[PDF](180.8KB)
Abstract:
Support vector machine (SVM) is a very popular method for binary data classification in data mining (machine learning). Since the objective function of the unconstrained SVM model is a non-smooth function, a lot of good optimal algorithms can't be used to find the solution. In order to overcome this model's non-smooth property, Lee and Mangasarian proposed smooth support vector machine (SSVM) in 2001. Later, Yuan et al. proposed the polynomial smooth support vector machine (PSSVM) in 2005. In this paper, a three-order spline function is used to smooth the objective function and a three-order spline smooth support vector machine model (TSSVM) is obtained. By analyzing the performance of the smooth function, the smooth precision has been improved obviously. Moreover, BFGS and Newton-Armijo algorithms are used to solve the TSSVM model. Our experimental results prove that the TSSVM model has better classification performance than other competitive baselines.
A two-step algorithm for layout optimization of structures with discrete variables
Lianshuan Shi, Enmin Feng, Huanchun Sun and Zhaosheng Feng
2007, 3(3): 543-552 doi: 10.3934/jimo.2007.3.543 +[Abstract](418) +[PDF](136.3KB)
Abstract:
This paper presents a mathematical model for Layout optimization of structure with discrete variables. The optimization procedure is composed of two kinds of sub-procedures of optimization: the topological optimization and the shape optimization. In each one, a comprehensive algorithm is used to treat the problem. The two kinds of optimization procedures are used in turn until convergence appears. After the dimension of the structure is reduced, the delimiting combinatorial algorithm is used to search for the better objective value. A couple of classical examples are presented to show the efficiency of the method. Numerical results indicate that the method is efficient and the optimal results are satisfactory.
A semismooth Newton method for solving optimal power flow
Xiaojiao Tong, Felix F. Wu, Yongping Zhang, Zheng Yan and Yixin Ni
2007, 3(3): 553-567 doi: 10.3934/jimo.2007.3.553 +[Abstract](579) +[PDF](317.3KB)
Abstract:
In this paper, we present some new optimization approaches to solve optimal power flow (OPF) problems. By using a so-called Nonlinear Complementarity Problem (NCP) function, the optimality condition (KKT system) of the original optimization problem is reformulated into a set of nonsmooth equations. The advantage of the new reformulation lies in that the inequality constraints are transformed into equations. The semismooth Newton-type method is applied to solve the reformulated equations. Moreover, we present a decoupled semismooth Newton method according to the inherent weak-coupling characteristics of power systems. The convergence of the new methods, especially for the decoupled method, are established. Numerical examples of both OPF and available transfer capability (ATC) problems demonstrate that the new algorithms are effective.
Convergence properties of a non-interior-point smoothing algorithm for the P*NCP
Zheng-Hai Huang and Shang-Wen Xu
2007, 3(3): 569-584 doi: 10.3934/jimo.2007.3.569 +[Abstract](463) +[PDF](203.3KB)
Abstract:
In this paper, a non-interior-point smoothing algorithm is applied to solve the $P_*$ nonlinear complementarity problem (NCP). The algorithm is proved to be globally convergent under an assumption that the $P_*$ NCP has a nonempty solution set. In particular, the solution obtained by the algorithm is shown to be a maximally complementary solution of the $P_*$ NCP. The results we obtained strictly generalize the relative results appeared in the literature.
Optimal control of a batch crystallization process
Volker Rehbock and Iztok Livk
2007, 3(3): 585-596 doi: 10.3934/jimo.2007.3.585 +[Abstract](513) +[PDF](356.7KB)
Abstract:
A dynamic model of an aluminium trihydroxide batch crystallization is considered in this work. The process model, which takes into account kinetics of nucleation, growth and agglomeration, is based on the mass balance of the process and the population balance of the dispersed crystals. Assuming that the temperature of the solution and the seeding policy are variable, optimal control techniques are applied to the model to optimize various performance criteria. Some interesting numerical results for the behaviour of the model are presented.
Evolution of operating parameters for multiple vendors multiple buyers vendor managed inventory system with outsourcing
SP. Nachiappan, N. Jawahar and A. C. Arunkumar
2007, 3(3): 597-618 doi: 10.3934/jimo.2007.3.597 +[Abstract](701) +[PDF](442.0KB)
Abstract:
This paper discusses the operating parameters of a two-echelon 'm' Vendors - 'n' Buyers Vendor Managed Inventory (VMI) System with outsourcing (MVMBO). The operational parameters to the above model are the selling prices at the buyer's market and the contract prices between the vendors and the buyers. Selling prices depend on sales quantities and determines the channel profit of the supply chain (SC). Contract prices depend on the understanding between partners on their revenue sharing agreement. A mathematical model of the MV MBO model is formulated to find optimal sales quantities (summation of optimal transaction quantities) for maximum channel profit. Optimal outsourcing quantities, selling prices and acceptable contract prices are derived from the obtained optimal transaction quantities. The mathematical model formulation of MV MBO involves mixed integer variable, a non-linear objective function and linear constraints which fall under the category of Mixed Integer Non-linear Programming (MINP) optimization problem. Simulated Annealing Algorithm (SAA) based heuristic is proposed to find the optimal operational parameters of the MVMBO problem. The proposed methodology is evaluated for its solution quality.

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