This paper considers a special class of dynamic programs which satisfies the monotone and contraction assumptions. This class of dynamic programs is characterized by the piecewise linearity that the cost function is piecewise linear whenever the terminal cost function is piecewise linear. Partially observable Markov decision processes have this property. An algorithm based on policy improvement is developed to construct e-optimal policies and e-optimal cost functions. This algorithm has the advantage of involving only linear functions. A numerical example is also presented.

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This paper considers a new variant of maximum network flow problem, which has a constraint that each unit of network flow has to visit a specified node called a check node on the way from source to sink. For this problem an efficient algorithm is given which is an improved version of Hu's two-commodity flow algorithm. Moreover this paper discusses the applicability of this type of algorithm to the problem where the check node only has a positive gain.

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This paper deals with the problem of minimizing the weighted mean flow-time in n/m flow-shop scheduling where no passing is allowed. Analysis, through the adjacent pairwise interchange method, leads to a condition for determining the precedence relation between adjacent jobs. The condition consists of inequalities, the number of which equals the square of the number of machines. An algorithm based on these inequalities is proposed to obtain the optimal or near optimal solution. The numerical examples show that the algorighm can produce a solution which has an average approximation ratio of 91.4 percent over 160 problems. The three factors: the number of jobs, the number of machines and the range of weights do not affect the approximation ratio of the tested problems. The computational time required to obtain a solution through the proposed algorithm is proportional to (the number of jobs) x (the number of machines)^2 . As a result, the CPU time needed to solve a seven job and six machine problem through TOSBAC 5600/120 is 0.25sec.

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This paper deals with a maintainability analysis of a system which consists of three subsystems. Two subsystems in the system are the same and constitute a warm standby redundant system. This warm standby redundant system and the residual subsystem are connected in series. In this paper, two repair disciplines are considered. One is a priority repair discipline and the other is a non priority repair discipline. The Laplace transform of the point-wise availability and the steady state availability for the system are derived under each repair discipline, and comparisions of the two results are made. Then the effect of the priority repair discipline on an increment of the system availability is discussed.

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We present a procedure for constructing a group theoretic dual problem with no duality gap to a given bounded integer programming problem. An optimal solution of this dual problem is easily determined and an optimal solution of the integer programming problem can be obtained by solving only one group optimization problem.

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Suppose there are two persons each with limited resources to gain the value of n targets. The targets appear one by one in sequential order, and the value of each target is a random variable X. One of the players has two kinds of resources (high and low) and the other has only one type (middle). Whenever the target arrives with the realized value x, both player either choose one of their cards or pass. If both player choose the card, the one who discards the high wins an amount equal to x. The card chosen in this stage is never used again. This case is a variant of the game Goofspiel discussed by Ross [2] . We formulate the problem as a two-person zero-sum sequential game and derive a system of recursive equations with some boundary conditions which is solvable in sequence and determines the optimal strategy. A deterministic case is solved completely.

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This paper deals with a new algorithm for obtaining a global maximum of a convex quadratic function over a unit hypercube, which is a classical and tough combinatorial problem. The basic idea of our algorithm is to reformulate this problem as an equivalent bilinear programming problem and to apply cutting plane approach developed by the author for solving bilinear knapsack problem. It will be shown that a deep cut can be generated with a nominal amount of computation. Some of the potential advantages of this algorithm over total enumeration are that it can generate a good local maximum at the earlier stage and that it has a good chance of obtaining a global maximum by searching only a minor portion of all solutions so that it can handle larger problems.

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