The inventory control of repair parts has recently become an important subject in rationalizing logistics department. Information network systems for repair parts are being constructed. The purpose of this study is to propose a fixed interval ordering policy for repair parts of single item and clarify its effects. The proposed policy specifically takes into account the characteristic of repair part demands ocurring for corrective and preventive maintenance (CM and PM) and the predictability of PM demand. A new fixed interval ordering policy is discussed for negligible lead time in case where PM demands are predictable and thus their distributions are known from the first to the n-th period. In the analysis, it is theoretically clarified that the optimal expected inventory control cost decreases monotonously with respect to an increase in the predictable periods n for PM demand. It is shown that this policy can also be applied to a fixed interval ordering system considering lead time. Finally, some quantitative effects are examined by numerical examples. The proposed policy, based on the stratification of CM and PM demands and the wide-range prediction of PM demand, is considered to be effective in repair parts inventory control under information network.

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In the field of system engineering, numerous attempts have been made by scholars to propose for structural modeling. In the many structural modeling methods, the first process of structural modeling is to make binary relation matrix by a modeler. This process is difficult for modeler because the number of questions to extract binary relation is n(n- 1); where n is the number of elements. Structural modeling can be divided into two types. One has 1-0 type of binary relation. Another has quantifiable, more general, binary relation. In the former, this process is doing the procedure that, to suppose the relation has transitive property, it infers the unknown binary relation using transitive property. But, the latter has never such procedure in this process. So we propose the procedure in this paper. The proposed procedure based on the same idea as the former. To suppose the binary relation has transitive property in quantification, it infers the unknown binary relation using this property In this paper, the quantifiable binary relation is represented by rank scale. The set of system elements is S = {s_i | 1 &le; i &le; n} (n is the number of system elements). 'S_i has R relation to s_j ' shows s_iRs_j . Finite ordinal set I = {0, 1,…, w}, r : R → I, r(s_i, s_j) means quantifiable binary relation for all (s_i, s_j) ∈ S. The binary relation must have 'reflexive property' and 'transitive property' like reflexiveness and transitiveness. The reflexive property is r(s_i, s_j) = w. The transitive property is r(s_i, s_j) &ge; max_1&le;k&le;n min{r(s_i, s_k), r(s_i, s_j)}. The procedure is based on 1-1 implication, 1-0 implication, 0-0 implication in 1-0 type. Let us denoted M = [m_<ij> = r(s_i, s_j)] by quantifiable binary relation matrix. m_<ij> divided into m_<lij> (1 &le; 1 &le; w) by defining m_<lij> as 1 if m_<ij> &le; l, 0 if m_<ij> &ge; l, and x others. M divided M_l as same. If m_<ij> is extract, m_<ij> divided m_<lij>, and do 3 implication on each M_l. If 0 occur on m_<kij> , do m_<lij> = 0(1 &ge; k). This algorithm requires O(wn^2) time. In this algorithm, if w = 1 we can apply 1-0 type binary relation. We can make quantifiable structural model easily using this algorithm, so it is easy to apply structural modeling.

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Apportionment problem has a very long history of more than 200 years and has been challenged actively by many applied mathematicians and operations researchers. In the last 200 years many apportionment methods have been proposed and various types of properties, which they should desirably satisfy, have been proposed and investigated although the apportionment problem itself has not been completely solved yet. Unbiasedness is an important property for the apportionment method, and has been studied intensively by Balinski and Young and others. In this paper we investigate the unbiasedness of parametric divisor method, comparing with that of most traditional apportionment methods. First we characterize parametric divisor method by explicitly showing the corresponding local measure of bias and deriving several useful facts concerning the unbiasedness of apportionment methods. Then we show the numerical results using Japan's House of Representatives data and exhibit parametric divisor method is preferable to other apportionment methods from the viewpoint of the unbiasedness by adjusting the parameter value appropriately in the certain range. Finally we discuss the possibility for the parametric divisor method to be accepted by our society in the future.

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In this paper, we study a local property of the zero set of a differentiable map F : R^<n+d> → R^n. We prove that, under a regular value condition, for each x∈ F^<-1>(o), there exist a neighborhood U of x and a sign c ∈ {-1, 1} such that sign det[x(p)^T_<σ_d> = c ・ sgnσ・ sign det D_xF(x(p))_<σ^n> for all permutation σ of degree (n + d), where p is a d-dimensional parametrization parameter vector of the zero set F^<-1>(o) in an open subset V of R^d and [x(p) ^T__<σ_d>] := (∂x_j/∂p_l)T(j ∈ σ^<-1>(n + 1,…, n+ d), l ∈ {1,…, d}), D_xF(x(p))_<σ^n> = [∂F_i(x(p))/∂x_k](i ∈ {1,…,n},k ∈ σ^<-1>(1,…,n)). This results naturally leads to an index theory. We show a local property of the change of the Morse index and the orientation of critical point set w.r.t. the multiparametric function f :R^<n+d> → R. Finally, we discuss the change of the stationary index of the equality constrained multiparametric nonlinear programs.

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Let G be an undirected graph with V vertices and E edges. We consider the problem of enumerating all spanning trees of G. In order to explicitly output all spanning trees, the output size is of Θ(NV), where N is the number of spanning trees. This, however, can be compressed into Θ(N) size. In this paper, we propose a new algorithm for enumerating all spanning trees of G in such compact form. The time and space complexities of our algorithm are O(N + V + E) and O(VE), respectively. The algorithm is optimal in the sense of time complexity.

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Many solution methods have been presented for solving a linear two-level decentralized planning problem. Unfortunately, existing methods require too much computation time to apply and some methods can not always provide the global optimum. This paper proposed a new method, called a "two-level simplex algorithm," for solving a linear two-level decentralized problem. This method is one of the vertex enumeration approach which exploits the properties that an optimal solution to the linear two-level decentralized problem is an extreme point of a feasible solution set in the upper-level problem and that the feasible solution set is non-convex, closed and connected. In order to enumerate an adjacent vertex satisfying optimality conditions of the lower-level problem with a resource allocation given by the upper-level, the proposed method newly employs dual simplex pivot iterations in the lower-level problem, which successfully provides the adjacent vertices according to a parametric linear programming method. Computation time of the proposed method tends to decrease as the conflict of the objective functions between the upper and lower problems increases, especially when the lower-level problem is decomposable to be solved more efficiently.

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This study proposes a curtailment strategy for catalog delivery to direct mail for customers, where catalog delivery to a customer is curtailed when he/she shows no response for the last K issues of catalogs successively delivered to the customer. For the purpose of determining the value of K, the expected catalog profit per customer is defined which is to be maximized. Two types of models for the expected catalog profit are formulated; (i) a model for a customer who has responded to catalogs only a few times up to this point, and (ii) a model for a customer who has responded many times. The conditions under which an optimal curtailment time exists are then clarified for both models. The optimal curtailment strategy for catalog delivery is also discussed based on the above two models, Numerical illustrations are presented to illustrate the proposed optimal curtailment strategy.

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We present a greedy algorithm for minimizing a separable convex function over a finite jump system (E,f), where E is a nonempty finite set and f is a nonempty finite set of integral points in Z^E satisfying a certain exchange axiom. The concept of jump system was introduced by A. Bouchet and W. H. Cunningham. A jump system is a generalization of an integral bisubmodular polyhedron, an integral polymatroid, a (poly-)pseudomatroid and a delta-matroid, and has combinatorially nice properties. The algorithm starts with an arbitrary feasible solution and a current feasible solution incrementally moves toward an optimal one in a greedy way. We also show that the greedy algorithm terminates after changing an initial feasible solution at most[numerical formula] times, where for each e ∈ E [numerical formula].

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