In this paper we study the infinite planning horizon, countable state, semi-Markov decision processes (SMDP's) with the incomplete state observation under the average cost criterion. We show that this model can be transformed to ordinary SMDP's, i.e., SMDP's with the complete state observation. Furthermore, when the action space is assumed to be finite, we present some sufficient conditions under which there exists an optimal stationary I-policy, and the method of successive approximations is applicable for obtaining a solution of the optimality equation.

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This paper discusses the problem of determining the optimal ordering policies and their properties with respect to a fixed-life perishable commodity subject to stochastic procurement leadtime. In addition, set-up cost for placing an order is introduced. Again, several properties of optimal ordering policies are derived. Finally, some further research problems are discussed.

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This paper has the objective to obtain optimal schedule principle for 2 × n sequencing problem wherein transportation times of jobs and equivalent-jobs for job-blocks are assumed to occur. The optimal schedule rule is based upon a theorem as established in the paper.

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We consider a stochastic version of minimal spanning tree problem in which edge costs are random variables. The problem is to find an optimal spanning tree and optimal probability level of a certain chance constraint. The problem is first transformed into a deterministic equivalent problem. Then its subproblem with positive parameter and further an auxiliary problem of subproblem are introduced. Finally, fully utilizing relations among these problems, we propose an algorithm which finds an optimal solution of the original problem in a polynomial order of its problem size.

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Consider the problem of sequencing n jobs with general precedence constraints on a single machine to minimize total weighted completion time, which is NP-complete. However some class of problems can be solved in polynomial time, i.e., the problems whose precedence constraints are trees or series parallel. This paper proposes an 0(n^4) algorithm for implementing a decomposition procedure due to Sidney. It also shows that if each decomposed subgraph is series parallel, then the problem is solved in 0(n^5 ) running time, even if the whole graph is not series parallel.

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In this paper we give an algorithm for the Hitchcock transportation problems (HTPQ). The algorithm de-scribed below has been studied in connection with "Network transportation problems with quadratic costs functions (NTQ)" by l. Takahashi and "Algorithms for optimal allocation problems having quadratic objective function (APQ)" by authors. Takahashi proposed a procedure which involves successively minimizing the Lagrangian with respect to each of its dual coordinates. We investigated the fact that the algorithms for APQ can be used for maximizing procedure in NTQ and studied APQ in detail. We consider the application of algorithms proposed by authors to solving HTPQ. In particular we give several examples of relatively large-scale (3000-20000 variables) problems with computational times (1 -10 sec. on a HITAC M-180 computer for these large-scale problems).

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Many practical engineering design problems are the free boundary-value type problem. In this work, free boundary-value problem is solved by combining method of characteristics and invariant imbedding approach. To show the effectiveness of this approach, the length of a chemical reactor with axial mixing process is estimated by the pro-posed approach. It is shown that with reasonable step size, we can get very accurate length of a chemical reactor process.

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