This paper treats an optimal inspection and maintenance policy of a continuous time Markovian deteriorating system, which minimizes the total discounted expected time in which the system is not operating. The problem is formulated by a semi-Markov decision process and some properties of an optimal policy are obtained, that is, a control limit rule holds and as the system degrades, an optimal inspection time interval becomes shorter. For a discrete time Markovian deterioration case, almost the same discussion is made.

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In this paper we consider two Palm measures P_a, P_d which are strictly stationary for the time sequences {a_n}^∞_n=-∞, {d_n}^∞_n=-∞ respectively, where {a_n} and {d_n} are the time sequences of arrival times and of departure times respectively at a certain station in the given network. And we give a sufficient condition for two events B'andB" to hold P_a(B') = P_d(B"). This result means that some statistics of a customer who arrives at the station in an equilibrium state can be evaluated by the measure P_d, and we apply this result to obtain a ramification of the theory of Burke[3] and Reich[11] about tandem queues, and new properties of residual sojourn times in Jackson type networks etc.

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A condition is given to decompose a large scheduling problem into two or more scheduling problems of smaller size. The applicability of the decomposition approach to scheduling problems is illustrated through the single machine scheduling problem n/1/F_w|T_<max> = 0, minimizing the weighted flow time with zero maximum tardiness, and a branch and bound algorithm incorporating the decomposition principle is presented to obtain the optimal schedule. This algorithm is then extended to obtain the optimal schedule to the single machine scheduling problem n/1/F_w|T_<max'> minimizing the weighted flow time with minimum/maximum tardiness, by reducing n/1/F_w|T_<max> = 0.

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Inventory level in production quantity model has been developed for items that deteriorate contin-uously in accordance with a general probability distribution under Last In First Out (LIFO) issuing policy. From the result developed, the earlier model by Misra for constant rate of deterioration can be obtained as a particular case. An approximate formula is derived using perturbation techniques. To illustrate the use of the formula an example problem is solved and an approximate optimum production quantity is found.

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We investigate the information exchange between duopolistic firms in a game theoretical framework. In a duopoly model where each of two firms knows his own cost function but not the rival's, we show that he has an incentive to inform the rival of his cost function, and that two firms agree to inform each other of their cost functions.

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