• Journal of the Korea Society of Computer and Information
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• v.16 no.4
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• pp.127-135
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• 2011

Efficient ordering of decision variables is one of the methods that find solutions quickly in the depth first search using backtracking. At this time, development of variables ordering algorithms considering dynamic and static properties of the problems is very important. However, to exploit optimal variable ordering algorithms appropriate to the problems. In this paper, we propose a problem classifying rule which provides problem type based on variables' properties, and use this rule to predict optimal type of variable ordering algorithms. We choose frequency allocation problem as a DS-type whose decision variables have dynamic and static properties, and estimate optimal variable ordering algorithm. We also show the usefulness of problem classifying rule by applying base station problem as a special case whose problem type is not generated from the presented rule.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.6
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• pp.868-875
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• 1995

This paper presents a method of constructing the multiple-valued combinational logic systems(MVCLS) by decision diagram. The switching function truth table of MVCLS is transformed into canonical normal form of sum-of-products(SOP) with literals at first. Next, the canonical normal form of SOP is transfered into multiple-valued logic decision diagram(MVLDD). The selecting of variable ordering is very important in this stage. The MVLDDs are quite different from each other according to the variable ordering. Sometimes the inadequate variable ordering produces a very large size of MVLDD means the large size of circuit implementation. An algorithm for generating the proper variable ordering produce minimal MVLDD and an example shows the verity of the algorithm. The circuits are realized with T-gate acceording to the minimal MVLDD.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.39 no.2
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• pp.82-90
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• 2002

BDD have become widely used for various CAD applications because Boolean functions can be represented uniquely and compactly by using BDD. The size of the BDD representation for a function is very sensitive to the choice of orderings on the input variable. Therefore, it is very important to find a good variable ordering which minimize the size of the BDD. Since finding an optimal ordering is NP-complete, several heuristic algorithms have been proposed to find good variable orderings. In this paper, we propose a variable ordering algorithm, Faster-${\mu}$0, based on the ${\mu}$0(microcanonical optimization). In the Faster-${\mu}$0 algorithm, the initialization phase is replaced with a shifting phase to produce better solutions in a fast local search. We find values for algorithm parameters experimentally and the proposed algorithm has been experimented on well known benchmark circuits and shows superior performance compared to various existing algorithms.

• The KIPS Transactions:PartA
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• v.8A no.1
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• pp.48-55
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• 2001

Using BDD, we can represent Boolean functions uniquely and compactly, Hence, BDD have become widely used for CAD applications, such as logic synthesis, formal verification, and etc. The size of the BDD representation for a function is very sensitive to the choice of orderings on the input variables. Therefore, it is very important to find a good variable ordering which minimize the size of the BDD. Since finding an optimal ordering is NP-complete, several heuristic algorithms have been proposed to find good variable orderings. In this paper, we propose a variable ordering algorithm based on the $\mu$O(microcanonical optimization). $\mu$O consists of two distinct procedures that are alternately applied : Initialization and Sampling. The initialization phase is to executes a fast local search, the sampling phase leaves the local optimum obtained in the previous initialization while remaining close to that area of search space. The proposed algorithm has been experimented on well known benchmark circuits and shows superior performance compared to a algorithm based on simulated annealing.

• International Journal of Advanced Culture Technology
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• v.9 no.3
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• pp.271-276
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• 2021

In this paper we analyze the effect of the credit period on inventory policy under trade credit with ordering cost including a fixed cost and freight cost, where the freight cost has a quantity discount. For marketing purposes, some supplier offers credit period to his buyer to stimulate the demand for the product he produces. The delay in payments during the credit period has the effect of reducing the buyer's capital opportunity cost. It is also assumed that the buyer pays the freight cost for the order and hence, the ordering cost consists of a fixed ordering cost and a variable freight cost which depends on the order quantity. As a result, the possibilities of trade credit and discounts on freight costs are expected to play an important role in the buyer's inventory policy. Based on the economic order quantity inventory model, we analyze how the buyer can determine the optimal inventory policy and we examine the effect of the length of credit period on the buyer's inventory policy.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.8
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• pp.2113-2119
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• 1998

The optimization problem of BDDs plays an improtant role in the area of logic synthesis and formal verification. Since the variable ordering has great impacts on the size and form of BDD, finding a good variable order is very important problem. In this paper, a new variable ordering scheme called incremental optimization algorithm is presented. The proposed algorithm reduces search space more than a half of that of the conventional sifting algorithm, and computing time has been greatly reduced withoug depreciating the performance. Moreover, the incremental optimization algorithm is very simple than other variable reordering algorithms including the sifting algorithm. The proposed algorithm has been implemented and the efficiency has been show using may benchmark circuits.

• International Journal of Advanced Culture Technology
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• v.8 no.1
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• pp.62-70
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• 2020

As an effective means of price discrimination, some suppliers offer trade credit to the distributors in order to stimulate the demand for the product they produce. The availability of the delay in payments from the supplier enables discount of the distributor's selling price from a wider range of the price option in anticipation of increased customer's demand. Since the distributor's lot-size is affected by the demand for the customer, the distributor's lot-size and the selling price determination problem is interdependent and must be solved at the same time. Also, in many common business transactions, the distributor pays the shipping cost for the order and hence, the distributor's ordering cost consists of a fixed ordering cost and the shipping cost that depend on the order quantity. In this regard, we deal with the joint lot-size and price determination problem when the supplier allows delay in payments for an order of a product. The positive effects of credit transactions can be integrated into the EOQ (economic order quantity) model through the consideration of retailing situations, where the customer's demand is a function of the distributor's selling price. It is also assumed that the distributor's order cost consists of a fixed ordering cost and the variable shipping cost. We formulate the distributor's mathematical model from which the solution algorithm is derived based on properties of an optimal solution. A numerical example is presented to illustrate the algorithm developed.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.875-888
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• 2008

Mosaic plots, proposed by Hartigan and Kleiner (1981, 1984), are very useful in visualizing categorical data. In mosaic plot, multi-way classified cell frequencies are represented by rectangles with proportional area. The plot is easy to understand while preserving the information contained in the data. Plot's appearance, however, does change substantially depending on the order of variables and the orders of categories with variable put into the plot. In this study, we propose the algorithms for ordering variables and categories of the categorical data to be explored via mosaic plots. We demonstrate our methods to three well-known datasets: Titanic, Housing and PreSex.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.87-96
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• 1989

We develop an algorithm to determine the optimal loading policy, which minimizes the congestion in general queueing networks with variable stations. Under more specified condition, majorization and arrangement ordering are established to compare, respectivity, various loading and assignment policies. Implications of results are also discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.11
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• pp.1581-1593
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• 2001

An efficient variable-reordering method for finite element meshes is used and the effect of variable-reordering is investigated. For the element renumbering of unstructured meshes, Cuthill-McKee ordering is adopted. The newsy reordered global matrix has a much narrower bandwidth than the original one, making the ILU preconditioner perform bolter. The effect of variable reordering on the convergence behaviour of saddle point type matrix it studied, which results from P2/P1 element discretization of the Navier-Stokes equations. We also propose and test 'level(0) preconditioner'and 'level(2) ILU preconditioner', which are another versions of the existing 'level(1) ILU preconditioner', for the global matrix generated by P2/P1 finite element method of incompressible Navier-Stokes equations. We show that 'level(2) ILU preconditioner'performs much better than the others only with a little extra computations.