We consider a monotone optimal policy for a discrete, time problem of controlling the arriving customers. At each period one customer arrives at a manufacturing factory to order a job distinguished by the reward and the service time with a constant delivery interval. The basic properties of optimal policies are obtained. It is shown that, contrary to intuition, from counterexamples an optimal policy cannot generally be monotone in such cases as finite-horizon problems with and without discounting and an infinite-horizon problem with discounting, while there exists a monotone optimal policy for infinite-horizon problems without discounting.

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This short paper gives solution algorithm of obtaining an optimal sequence to give minimum total elapsed time in a 'n-job, 2-machine' flow-shop scheduling problem in which jobs involve Arbitrary Time Lags (i.e. Start Lags and Stop Lags) and Transportation Times. All the times (Processing Times, Arbitrary Lags, and Transportation times) are given prior and are of deterministic nature.

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In this paper we consider a coherent system consisting of n components. Each component is repaired upon failure. This maintained coherent system is monitored continuously, and based upon the results of monitoring a decision must be made as to whether or not to replace the system. We show that the optimal group replacement policy has a monotone property without regard to the values of failure and repair rates. Further we discuss sufficient conditions for the replacement of the maintained coherent system.

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We consider a Markovian deteriorating complex system which fails with state- dependent probability. The following two features on cost associated with maintaining such a complex system seem to be reasonable: Replacing a whole system at any failure ocassion is more expensive than minimally repairing and using it again. And a replacement at a failure is more costly than a planned replacement of an unfailed system. This paper develops both countable infinite- and finite-state minimal repair models taking into account the above two features, and discusses a maintenance policy which minimizes the expected total discounted cost. It is shown that the optimal policy is of (i, I) type under some conditions on the transition probabilities and the cost structure.

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In the medical insurance system in Japan, the drug price standards are determined by the Ministry of Welfare, according to which medical institutions are paied for the drugs used in their activities. These drug price standards are revised periodically by so called 90%-bulk-line method in, which the new standards correspond to 90% points of the cummulative distributions of the market prices. On the other hand, the drug dealers usually offer their goods to medical institutions at prices lower than the standards. The differences are counted as the incomes of the medical institutions. This paper presents a mathematical model to describe how these real prices, are determined in competition between two drug dealers, assuming that the medical institutions would select the drugs yielding the largest incomes. More precisely, we assume that the bidding prices are distributed on intervals whose upper bounds are the price standards and the lower bounds are strategically set by the dealers. Assuming also the shapes of the distributions of the bidding prices, the distributions of the market prices of the both competitors are determined mathematically. Other factors, such as the incomes of the dealers, market shares, revised price standards etc., are determined also mathematically from the market price distributions thus obtained. As mentioned above, the dealers can set the lowest prices strategically so far as they are not less than the costs. 180 simulations are worked out on this model for different conditions. They showed, first of all, the overwhelming effects of the difference between the price standard and the cost on the incomes of the competing dealers. Effects of the discount policies are also discussed in game-theoretical sense.

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In this paper we discuss the stochastic facility location model in which the distances between the facility and demand points are rectangular and each weight is normally distributed independent random variable with unknown mean and known variance. We are interested in finding the value. of information. In general, perfect information is not attainable, but sample information may be obtained. Thus in this paper we find the expected value of sample information. In addition, the expected net gain of sampling and the optimal sample size are found.

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In a branch-and-bound algorithm, a partial problem P_i is terminated if the lower bound of the optimal value of Pi is greater (in case all optimal solutions are sought) or not smaller (in case a single optimal solution is sought) than the least upper bound on the optimal value of the original minimization problem P_0 currently available. Although it seems obvious that tighter lower bounding function and upper bounding function always improve the efficiency of a branch-and-bound algorithm, counterexamples can be easily constructed. In this paper, therefore, it is extensively studied when such improvement is guaranteed, for typical search strategies such as heuristic search, best-bound search and depth-first search. The model of branch-and-bound algorithms used for investigation is quite general in the sense that it allows the dominance test as well as the lower bound test mentioned above. The efficiency is measured by the number of partial problems decomposed in the execution of the algorithm.

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