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JORSJ Vol. 50 No. 1 Abstract & Keywords

1. An EOQ Model with Noninstantaneous Receipt under Supplier Credits

Yung-Fu Huang and Kuang-Hua Hsu

abstract  This paper tries to incorporate all Huang and Chung [4], Chung and Huang [2] and Teng [7] to develop the retailer's inventory model. That is, we want to investigate the retailer's optimal replenishment policy with noninstantaneous receipt under trade credit, cash discount and the retailer's unit selling price is not lower than the unit purchasing price. Mathematical models have been derived for obtaining the optimal cycle time for item so that the annual total relevant cost is minimized. One easy-to-use theorem is developed to efficiently determine the optimal cycle time for the retailer. Some previously published results of other researchers are deduced as special cases. Furthermore, numerical examples are given to illustrate the results and managerial insights are drawn.
keywords Inventory, EOQ, trade credit, permissible delay in payments, cash discount

2. Outer Approximation Method for the Minimum Maximal Flow Problem

Yoshitsugu Yamamoto and Daisuke Zenke

abstract
The minimum maximal flow problem is the problem of minimizing the flow value on the set of maximal flows of a given network. The optimal value indicates how inefficiently the network can be utilized in the presence of some uncontrollability. After extending the gap function characterizing the set of maximal flows, we reformulate the problem as a D.C.\ optimization problem, and then propose an outer approximation algorithm. The algorithm, based on the idea of $\varepsilon$-optimal solution and local search technique, terminates after finitely many iterations with the optimal value of the problem.
keywords Network flow, minimum maximal flow, optimization over the efficient set, D.C. optimization, outer approximation, global optimization

3. A Nonmonotone Memory Gradient Method for Unconstrained Optimization

Yasushi Narushima

abstract

Memory gradient methods are used for unconstrained optimization, especially large scale problems. They were first proposed by Miele and Cantrell~(1969) and Cragg and Levy~(1969).
Recently Narushima and Yabe~(2006) proposed a new memory gradient method which generates a descent search direction for the objective function at every iteration and converges globally to the solution if the Wolfe conditions are satisfied within the line search strategy. In this paper, we propose a nonmonotone memory gradient method based on this work. We show that our method converges globally to the solution. Our numerical results show that the proposed method is efficient for some standard test problems if we choose a parameter included in the method suitably.

keywords Nonlinear programming, optimization, memory gradient method, nonmonotone line search, global convergence, large scale problems

4. Optimal Timing for Investment Decisions

Yasunori Katsurayama

abstract

The net present value (NVP) is an important concept in investment decisions. As Ingersoll and Ross \cite{ingersoll} have pointed out, the future fluctuation of interest rates is expected to have significant effects on the present value (PV) of the project concerned. If interest rates are expected to fall off in the next year, deferring an investment for yet another year is likely to be more gainful even if its current NPV is positive. The effects of deferment can be valued from its corresponding American option value. Berk \cite{berk} proposed a simple criterion for investment decisions which incorporate this American option value of investment. The simplicity of this model is obtained from the appropriate usage of a callable bond. It is admirable that this model does not postulate any assumptions on the behavior of interest rates. But this construction of the model has the pros and cons. It is easy to implement this model in business because the only adjustment required in this model is to replace the interest rate in NPV with the callable rate.
On the other hand, the properties of this criterion have not been clarified.
  In this paper we analyze Berk's model under the assumption that interest rates follow the geometric Brownian motion (GBM). By assuming the movement of interest rates, we can derive an analytical solution for the optimal timing for the investments in terms of the parameters of the GBM. This enables us to perform comparative statics and simulation. These results extract some properties of Berk's model and help the decision makers in implementing Berk's model.

keywords Finance, decision making, NPV, geometric Brownian motion, American option, real option

5. Algorithmic Computation of the Transient Queue Length Distribution in the BMAP/D/$c$ Queue

Kentaro Daikoku, Hiroyuki Masuyama, Tetsuya Takine, and Yutaka Takahashi

abstract 

This paper proposes a numerically feasible algorithm for the transient queue length distribution in the BMAP/D/$c$ queue. The proposed algorithm ensures the accuracy of the computational result and it is applicable not only to the stable case but also to the unstable case. This paper also discusses a numerical procedure to compute moments of the transient queue length distribution. Finally, some numerical examples are presented to demonstrate the applicability of the proposed algorithm.

keywords Queue, transient queue length distribution, batch Markovian arrival process (BMAP), MAP/D/$c$ queue, deterministic service, multi-server

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