The present paper considers a system in which components stochastically deteriorate with age. When the component fails, it is repaired with a specified repair time distribution or left as it is until the next planned replacement opportunity. As a result of this action, an idle time occurs and the cost is incurred during the idle time. The optimal policy which minimizes the total expected cost is derived and the critical point in time to distinguish the above two actions is found by the method of dynamic programming. Some simple examples are discussed to illustrate our model.
The problem in which a firm has to meet the demand for the services of several distinct but related equipment over a planning horizon is considered. An equipment of one type can be converted into an equipment of the other type at some costs. Hence demands may be met by direct capacity installation (expansion) or by conversion from another type of equipment. Capacity installation and conversion costs are assumed to be concave reflecting possible economies of scale in these activities. The objective is to find a policy of capacity installations and conversions between the types of equipment such that the present value of the total installation and conversion costs is minimized. The problem is formulated and given a network representation. A dynamic programming algorithm, an extension and refinement to that developed in [2] , is then developed which can be used to solve the problem efficiently when the number of distinct equipment is not too large.
Six approximation algorithms for the one-machine scheduling problem with ready and due times to minimize the maximum lateness are analyzed. The performance is measured by the relative deviation of approximate values to optimal ones. Best possible upper bounds on the worst case performance of all six algorithms are derived. The average performance is also examined by solving randomly generated problems; one of the six algorithms outperforms others and keeps the average relative deviation within 2%.
Nakamura establishes a theorem which gives necessary conditions for a simple game with ordinal preferences to have a nonempty core. The conditions are also sufficient, if the set of alternative outcomes is finite. In the present paper, we will show that Nakamura's method of the proof of this theorem makes it possible to generalize the theorem to an arbitrary characteristic function game with ordinal preferences.
This paper considers an E-model having a random linear inequality constraint and provides an algorithm for solving it. An original problem P is first transformed into deterministric equivalent problem P'. For solving P', a subsidiary problem P (μ) with a parameter p is defined. The dual-like relation between P and P (μ) is clarified. Then an algorithm for solving P (μ) is proposed. This algorithm is based on the parametric quadratic programming technique. Next fully utilizing this algorithm for P (μ), main algorithm is constructed. Finally, applicability of the above dual-like relation to other nonlinear problems is suggested.