Toshio Nishida

Stochastic spanning tree problem

Abstract The minimal spanning tree problem has been well studied and until now many efficient algorithms such as [5,6] have been proposed. This paper generalizes it toward a stochastic version, i.e., considers a stochastic spanning tree problem in which edge costs are not constant but random variables and its objective is to find an optimal spanning tree satisfying a certain chance constraint. This problem may be considered as a discrete version of P-model first introduced by Kataoka [4]. First it is transformed into its deterministic equivalent problem P. Then, an auxiliary problem P(R) with a positive parameter R is defined. After clarifying close relations between P and P(R), this paper proposes a polynomial order algorithm fully utilizing P(R). Finally, more improvement of the algorithm and applicability of this type algorithm to other discrete stochastic programming problems are discussed.

Multiple criteria decision problems with fuzzy domination structures

Abstract The concepts of domination structures and nondominated solutions in multiple criteria decision problems, which were introduced by Yu, enable us to tackle general situations in which there exists information concerning the decision makers preferences. In many of the multiple criteria decision problems the underlying domination structures are not known precisely but only fuzzily determined. Yu primarily works with the case where the domination structure at each point is a convex cone. As a result, there exists a sharp borderline dividing all solutions into nondominated solutions and the others. This paper fuzzifies the concepts of domination structures and nondominated solutions to allow them to be applied to a larger class of the multiple criteria decision problems mentioned above. Introducing the concepts of fuzzy convex cones and fuzzy polar cones, it is shown how some of the main results obtained by Yu are extended.

The mixed shop scheduling problem

In this paper, we consider a two-machine shop scheduling problem consisting of two disjoint job subsets F and O. F is a set of the flow shop type jobs, while O is a set of the open shop type jobs. Our objective is to find the schedule minimizing the maximum completion time. For the case that O is empty, this problem reduces to a two-machine flow shop scheduling problem for which Johnson developed an optimal algorithm. Also for the case that F is empty, the problem reduces to a two-machine open shop scheduling problem for which there is an optimal algorithm developed by Gonzalez and Sahni. While for the case that both F and O are not empty, the situation is complicated in the sense that the preceding two cases are not extensible to our case. We give the optimal algorithm for our nontrivial case.

Stochastic bottleneck spanning tree problem

This paper considers a stochastic version of bottleneck spanning tree problem in which edge costs are random variables. The problem is to find an optimal spanning tree under the chance constraint with respect to bottleneck (maximum cost) edge of spanning tree. The problem is first transformed into a deterministic equivalent problem. Then its subproblem is introduced and a close relation between these problems is clarified. Finally, based on the relation, an algorithm which finds an optimal spanning tree of the original problem in a polynomial order of its problem size is proposed.

On Multistate Coherent Systems

Recently, several authors have treated multistate systems and given some results. This paper summarizes the several concepts of s-coherency and shows the relationships between them. An interesting theorem for the existence of series and parallel coherent systems is presented. We have proved IFRA and NBU closure theorems under more general situation than has El-Neweihi, et alii and Ross. We discuss our IFR closure theorem.

N-unit parallel redundant system with correlated failure and single repair facility

Abstract The system treated in this paper is an N-unit parallel redundant system with correlated failure and single repair facility, where correlation means that any two units in the system or all the units are possible to fail at the same time. Two models, model 1 and model 2, are considered. And we obtain the following results; for both models Laplace transform (L-T) of the pointwise availability, stationary availability, L-T of the system reliability and, furthermore, for model 2, the distribution of the number of repairs completed in (0,t]. Finally stationary availability of model 1 is compared with that of model 2, and graphical results are presented.

Stochastic linear knapsack programming problem and its application to a portfolio selection problem

Abstract In this paper a probability maximization model of a stochastic linear knapsack problem is considered where the random variables consist of several groups with mutually correlated ones. We propose a solution algorithm to the equivalent nonlinear fractional programming problem with a simple ranking method. This approach will be effectively applied to one of the portfolio selection problems.

A Generalized Uniform Processor System

This paper considers a scheduling problem whose objective is to determine both the optimal speeds of processors and an optimal schedule in a preemptive multiprocessor environment. The jobs are independent and each processor can be assigned any speed; however, the cost associated with each processor is a function of the processors speed. Polynomial algorithms are presented to find optimal speed assignments for a variety of cost functions.

Perishable inventory management subject to stochastic leadtime

Abstract This paper discusses the model for a perishable product with the stochastic procurement leadtime. Zero or 1 unit leadtime is considered and its optimal ordering policy is derived. This is a generalization of the one period horizon model of Nahmias [4]. Further, the chance constraint as for shortage is added and under this additional constraint, again optimal ordering policy is obtained.

The branching nonhomogeneous Poisson process and its application to a replacement model

Abstract In studying and analysing the failure patterns of complex system, plausible stochastic models are needed to represent the sequence of events. A simple and frequently used model is derived by the assumption that the times-between-failures of a system are exponentially distributed and independent. Experience has shown, however, that successive times-between-failures are not exponentially distributed and not independent. These deviations are due to imperfect search of failed components. We constitute a plausible stochastic process which describes the sequence of events, and obtain the interval reliability and the expected number of failures. As an application of these results, we deal with the replacement model where a system undergoes minimal repair before time T and is replaced at time T. We discuss an optimum policy minimizing the total expected cost per unit time.