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An optimization problem to obtain the optimal replacement interval is studied. The system is minimally repaired at failure and is replaced by a new one at age T. The model assumes that the time horizon associated with the number of replacements is random. The total expected cost is calculated, and the optimal replacement interval minimizing the cost is found. A numerical example is used to compare the costs associated with an infinite time line and a random time line, which this model used.

This paper aims to investigate the optimization of the replacement with minimal repair policy for a system which experiences a time horizon of random length. Under such policy system replacement occurs at multiples of some period while minimal repair is performed at system failure between two successive replacements.

The objective function is the expected total cost composed of minimal repairs and replacements costs. A simple and compact expression is derived for the expected total costs and conditions under which an optimal replacement period exits are given. For sake of illustration, a numerical example is provided.

The paper finds that by the recent great technological development, the life cycle of present products is seen to be reduced more and more. This has motivated the development of maintenance optimization models for systems which experience an exact finite time horizon.

To ensure the benefits from the improved technologies, the information concerning the technological change must be taken into account. Such information is based on technological forecasting and difficult to obtain and merely rely on uncertainties.

Based on a continuous version of the Lanchester advertising model for a duopoly, a mathematical model is developed to determine the optimal advertising policy of a firm responding to the advertising pulsation policy of its competitor. A Dynamic Programming (DP) approach has been employed to arrive at the optimal solution.

It has been mainly demonstrated that under a concave or linear advertising response function, the focal firm's DP policy is superior to its Uniform Advertising Policy (UAP) counterpart (constant advertising spending over time), irrespective of the advertising pulsation policy employed by its rival. Under a convex advertising response function, on the other hand, the focal firm's DP policy is superior to its Advertising/Maintenance Pulsing Policy (APMP) and Advertising Pulsing Policy (APP) counterparts (alternating advertising spending at two levels), irrespective of the advertising pulsation policy used by the competitor.

Beginning with the assumption that antidumping laws are used to address adverse shocks in import-competing industries, this chapter provides an explanation for the infrequent utilization of the Dispute Settlement Understanding under the Antidumping Agreement. It does so with a very simple model that represents the shock by a one-dimensional random variable. This is found on an interpretation of the ADA as a de facto escape clause. ADA signatories are homogeneous, which enables the representation of the expected frequency of shocks over each member's import-competing sectors by the binomial distribution with identical parameters. The explanation for the infrequency of utilization of the DSU invokes a repeated Prisoners’ Dilemma with two levels of cooperation in an infinite horizon game. The high level is free trade in all sectors. The low level is the application of ADA duties in sectors incurring the shock in a manner that is consistent with the ADA. The high level of cooperation in all sectors in every period is not sustainable for any degree of patience. A convex combination of the high and low levels of cooperation is sustainable for some degrees of patience under the folk theorem. However, this combination of cooperation is attainable only with the support of the DSU. The extent of importance of the DSU depends on the completeness of information with which signatories are endowed. With complete information, dispute resolution does not occur in equilibrium. However, its presence supports cooperation through its mandate to sanction retaliation. If filing were prohibitively costly, disputes would never arise, and cooperation would be expected to evaporate. In the instance of incomplete information with costless filing, disputes would occur in equilibrium whenever an AD action was taken. In the most realistic circumstance, that of incomplete information and nonprohibitive filing costs, disputes would arise only when the number of AD actions exceeded their (common) expectation. This provides a conceptual explanation for the observations of Tarullo (2002) and Bown (2005) that ADA disputes are infrequent.

To determine the optimal spare part order‐replacement policy for any high cost single unit complex system in a discrete‐time circumstance.

The expected total discounted cost over an infinite planning horizon is taken as a criterion of optimality as it allows us to put emphasis on the present behavior of the system.

The problem under consideration is a two‐dimensional discrete optimization problem (regular ordering time and inventory time limit for the spare are decision variables) which is difficult to handle, in general. However, it is explored that the problem can be reduced to a simple one‐dimensional one and the optimal ordering time is to be determined under the two extreme situations: no replacement of the spare until the original unit fails and replacement of the spare as soon as it is delivered.

For modeling simplicity, deterministic lead time is considered for both regular and expedited orders. A more appropriate assumption would be to consider randomized lead time for both the orders.

The research provides a useful order‐replacement strategy for a single‐unit system where the failure of the unit is better measured by the number of cycles completed before failure rather than the instant of failure.

The work done in this paper carries certain values as any continuous time model for the problem under consideration can be regarded as only an approximate model.

We suggest the method of evaluation of illiquid assets on the market in the presence of proportional transaction costs by using two consumption/investment models. We study an investor's implicit evaluation of an illiquid asset whose trading incurs a proportional transaction cost. We show that the investor assigns an implicit value between the bid and ask price and uses it for his investment and/or consumption decisions. We also show that the implicit value is an increasing function of the investor's liquidity ratio, which is a measure of liquidity of the investor's asset holdings.

Wind energy plays a very important role in the future electrical power supply. With growing shares, the focus of the plant control will have to shift from maximum power yield to grid friendly aspects, like stable power output despite fluctuating wind power. The purpose of this paper is to design a new operation management for wind energy converters that combines high‐energy yield, grid friendly power output characteristics and the ability to adapt to changing wind conditions.

An operation control based on stochastic dynamic optimization was developed for the special demands of variable speed wind energy converters. The task of the operation control is to set the appliance to the optimal operation point, following the above‐mentioned goals by adapting the control pattern to changing wind conditions.

It is shown that the novel control concept, the iterative self‐adapting system management with stochastic dynamic optimization, is able to control wind energy converters in such a way that the effect of the stochastic fluctuating wind energy supply on the output power fluctuation is smoothed while maintaining a high‐energy yield.

This non‐linear stochastic dynamic optimization structure has two special characteristics, first is the iterative self‐adaptation, and second is the optimization for an infinite process, while the optimization criteria are high‐power yield and low‐power output fluctuations. This will be of great value for further increase of wind energy converters in the electrical power supply.