Computing the discounted return in markov and semi-markov chains

This paper addresses the problem of computing the expected discounted return in finite Markov and semi-Markov chains. The objective is to reveal insights into two questions. First, which iterative methods hold the most promise? Second, when are interative methods preferred to Gaussian elimination? A set of twenty-seven randomly generated problems is used to compare the performance of the methods considered. The observations that apply to the problems generated here are as follows: Gauss-Seidel is not preferred to Pre-Jacobi in general. However, if the matrix is reordered in a certain way and the author's row sum extrapolation is used, then Gauss-Seidel is preferred. Transforming a semi-Markov problem into a Markov one using a transformation that comes from Schweitzer does not yield improved performance. A method analogous to symmetric successive overrelaxation (SSOR) in numerical analysis yields improved performance, especially when the row-sum extrapolation is used only sparingly. This method is then compared to Gaussian elimination and is found to be superior for most of the problems generated.     

Preventive maintenance and replacement under additive damage

A system deteriorates due to shocks received at random times, each shock causing a random amount of damage which accumulates over time and may result in a system failure. Replacement of a failed system is mandatory, while an operable one may also be replaced. In addition, the shock process causing system deterioration may be controlled by continuous preventive maintenance expenditures. The joint problem of optimal maintenance and replacement is analyzed and it is shown that, under reasonable conditions, optimal maintenance rate is decreasing in the cumulative damage level and that beyond a certain critical level the system should be replaced. Meaningful bounds are established on the optimal policies and an illustrative example is provided.     

A note on integer solutions to linear fractional interval programming problems by a branch & bound technique

This paper provides a method for solving linear fractional interval programming problems in integers with the help of a branch and bound technique.     

The M/G/1 queue with instantaneous bernoulli feedback

In this paper we are concerned with several random processes that occur in M/G/1 queues with instantaneous feedback in which the feedback decision process is a Bernoulli process. Queue length processes embedded at various times are studied. It is shown that these do not all have the same asymptotic distribution, and that in general none of the output, input, or feedback processes is renewal. These results have implications in the application of certain decomposition results to queueing networks.     

An algorithm for 0-1 multiple-knapsack problems

The 0-1 multiple-knapsack problem is an extension of the well-known 0-1 knapsack problem. It is a problem of assigning m objects, each having a value and a weight, to n knapsacks in such a way that the total weight in each knapsack is less than its capacity limit and the total value in the knapsacks is maximized. A branch-and-bound algorithm for solving the problem is developed and tested. Branching rules that avoid the search of redundant partial solutions are used in the algorithm. Various bounding techniques, including Lagrangean and surrogate relaxations, are investigated and compared.     

Markov chain with taboo states and reliability

A computationally feasible matrix method is presented to find the first-passage probabilities in a Markov chain where a set of states is taboo during transit. This concept has been used to evaluate the reliability of a system whose changes in strength can be thought of as a Markov chain, while the environment in which it is functioning generates stresses which can also be envisaged as another Markov chain.     

An algorithm for a class of loading problems

The loading problem we consinder is to assign a set of discrete objects, each having a weight, to a set of boxes, each of which has a capacity limit, in such a way that every object is assigned to a box and the number of boxes used is minimized. A characterization of the assignments is offered and used to develop a set of rules for generating nonredundant assignments. The rules are incorporated into an implicit enumeration algorithm. The algorithm is tested against a very good heuristic. Computational experience shows that the algorithm is highly efficient, solving problems of up to 3600 0-1 variables in a CPU second.     

Some comparative & design aspects of fixed cycle production systems

A serial production line is defined wherein a unit is produced if, and only if, all machines are functioning. A single buffer stock with finite capacity is to be placed immediately after one of the first N-1 machines in the N machine line. When all machines have equal probability of failure it is shown that the optimal buffer position is exactly in the middle of the line. This result is synthesized with the earlier work of Koenigsberg and Buzacott including an analysis of the covariance between transition states. An alternative model formulation is presented and integrated with previous results. Finally, a sufficient condition and solution procedure is derived for the installation of a buffer where there is a possible trade-off between increasing the reliability of the line versus adding a buffer stock.     

Application of the fundamental theorem of games to an example concerning antiballistic missile defense

This paper considers a two sided resource allocation game in which both players initially have fixed resources which may be distributed over various targets. Their effectiveness depends on the manner of distribution and also on the strategy of the opponent, a natural payoff function for such a situation being used. The complete solution to the game is derived and a numerical example given.     

An improved branch and bound procedure for n × m flow shop problems

This paper considers the classical nXm flow shop sequencing problem. An improved branch and bound procedure is proposed. Computational experience shows that the proposed procedure is more efficient compared to the existing optimizing procedures.