• Journal of the Korean Operations Research and Management Science Society
• /
• v.23 no.2
• /
• pp.1-13
• /
• 1998

The purpose of this paper is to formulate the three-dimensional loading problem and to develop an exact algorithm. The three-dimensional loading problem is not only to load as many boxes as possible, but also to ensure load stability. In this Paper, we propose formulation by zero-one integer programming. Further we propose as an algorithm the branch-and-bound enforced by efficient bounding criteria. As an upper bound, we use the solution of the Lagrangean relaxation problem which relaxes constraints of zero-one IP, and as a lower bound, we use a heuristic solution induced by the solution of the Lagrangean relaxation problem. Last, we show computational experiments on convergency of upper and lower bounds.

• Industrial Engineering and Management Systems
• /
• v.3 no.2
• /
• pp.100-115
• /
• 2004

The network representation and branch and bound algorithm with efficient lower and upper bounding procedures are developed to determine a global optimal production schedule on a machine that minimizes sequence-dependent setup cost and earliness/tardiness penalties. Lower bounds are obtained based on heuristic and Lagrangian relaxation. Priority dispatching rule with local improvement procedure is used to derive an initial upper bound. Two dominance criteria are incorporated in a branch and bound procedure to reduce the search space and enhance computational efficiency. The computational results indicate that the proposed procedure could optimally solve the problem with up to 40 jobs in a reasonable time using a personal computer.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.33 no.1
• /
• pp.35-49
• /
• 2008

To load a container in a yard block onto a ship, a Transfer Crane (TC) moves to a target yard bay, then its hoist picks up a selected container and loads it onto a waiting Yard Truck (YT). An optimal routing problem of Transfer Crane is a decision problem which determines a given TC's the visiting sequence of yard-bays and the number of containers to transfer from each yard-bay. The objective is to minimize the travel time of the TC between yard-bays and setup time for the TC in a visiting yard. In this paper, we shows that the problem is NP-complete, and suggests a new formulation for it. Using the new formulation for the problem, we investigate some characteristics of solutions, a lower and upper bounds for it. Moreover, our lower and upper bound is very efficient to applying some instances suggested in a previous work.

• Journal of Communications and Networks
• /
• v.17 no.1
• /
• pp.21-26
• /
• 2015

The general wiretap channel with noiseless feedback is first investigated by Ahlswede and Cai, where lower and upper bounds on the secrecy capacity are provided in their work. The upper bound is met with equality only in some special cases. In this paper, we study a special case of the general wiretap channel with noiseless feedback (called non-degraded wiretap channel with noiseless feedback). Inner and outer bounds on the capacity-equivocation region of this special model are provided. The outer bound is achievable if the main channel is more capable than the wiretap channel. The inner bound is constructed especially for the case that the wiretap channel is more capable than the main channel. The results of this paper are further explained via binary and Gaussian examples. Compared with the capacity results for the non-degraded wiretap channel, we find that the security is enhanced by using the noiseless feedback.

• Journal of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.585-598
• /
• 2010

We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings of two-bridge knots and links, torus knots, some pretzel knots, and some theta-graphs. Using modified Heegaard complexity, we obtain upper bounds for their Matveev complexity, which linearly depend on the order of the covering. Moreover, using homology arguments due to Matveev and Pervova we obtain lower bounds.

• Journal of Korean Society for Quality Management
• /
• v.35 no.2
• /
• pp.99-105
• /
• 2007

Most of systems used in real fields are considered as multistate systems with multistate components. As one of methods for performance evaluation of the system, reliability analysis has been popularly used. In this paper, we propose an improved reliability analysis method which is based on state space decomposition method of Aven (1985). In deriving upper bounds, our method uses sets of unspecified states whereas Aven (1985) excludes sets of unacceptance states. Also, closer lower bounds to an exact reliability are obtained by considering of importance of min-path vectors.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.13 no.4
• /
• pp.267-280
• /
• 2009

In this paper we investigate a simple two-level additive Schwarz preconditioner for the P1 symmetric interior penalty Galerkin method of the Poisson equation on rectangular meshes. The construction is based on the decomposition of the global space of piecewise linear polynomials into the sum of local subspaces, each of which corresponds to an element of the underlying mesh, and the global coarse subspace consisting of piecewise constants. This preconditioner is a direct combination of the block Jacobi iteration and the cell-centered finite difference method, and thus very easy to implement. Explicit upper and lower bounds for the maximum and minimum eigenvalues of the preconditioned matrix system are derived and confirmed by some numerical experiments.

• Journal of Korean Institute of Industrial Engineers
• /
• v.34 no.2
• /
• pp.205-215
• /
• 2008

convergence networks (BcN). The problem seeks to minimize the total cost of switch and cable while satisfying the requirement of demand and quality of service (QoS). We develop mixed integer programming models to obtain the optimal switch location of the access network. We develop a Tabu Search (TS) heuristic algorithm for finding a good feasible solution within a reasonable time limit. We propose real networks with up to 25 nodes and 180 demands. In order to demonstrate the effectiveness of the proposed algorithm, we generate lower bounds from nonlinear QoS relaxation problem. Computational results show that the proposed heuristic algorithm provides upper bounds within 5% optimality gap in 10 seconds.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1845-1856
• /
• 2016

In this paper our aim is to study the classical Bessel-Struve kernel. Monotonicity and log-convexity properties for the Bessel-Struve kernel, and the ratio of the Bessel-Struve kernel and the Kummer confluent hypergeometric function are investigated. Moreover, lower and upper bounds are given for the Bessel-Struve kernel in terms of the exponential function and some $Tur{\acute{a}}n$ type inequalities are deduced.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.355-369
• /
• 2020

In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.