Finite Markov chain models skip-free in one direction

Finite Markov processes are considered, with bidimensional state space, such that transitions from state (n, i) to state (m, j) are possible only if m ≤ n + 1. The analysis leads to efficient computational algorithms, to determine the stationary probability distribution, and moments of first passage times.     

Interactive solution of bi-criteria mathematical programs

In this paper, we develop efficient interactive methods for the solution of bicriteria nonlinear programming problems. The methods do not require trade-off information from the decision maker, pose less cognitive burden and converge to the “best compromise solution” fast. Two methods, called the paired comparison method and comparative trade-off method, are presented with examples. A real application of the interactive method to a bicriteria problem that arose in the planning of the cardiovascular disease control program in the U.S. Air Force is also presented.     

One- and two-stage scheduling of two products with distributed inserted idle time: The benefits of a controllable production rate

Consider the problem of scheduling two products on a single machine or through two machines in series when demand is constant and there is a changeover cost between runs of different products on the same machine. As well as setting batch sizes, it is assumed that the production scheduler can choose the production rate for each product, provided an upper bound is not exceeded. This is equivalent to permitting distributed inserted idle time over the production run. It is shown that characteristic of the optimum schedule is that there is no idle time concentrated between runs; it is all distributed over the run. If the inventory charge is based on average inventory then one product is always produced at maximum rate on the bottleneck stage; however, if there is an inventory constraint based on maximum inventory then in the single-stage case it can occur that neither product is produced at maximum rate.     

A two-state system with partial availability in the failed state

A generalization of the alternating renewal model of a repairable system to permit partial availability in the failed state is introduced. It is shown how, by making use of an embedded alternating renewal process, we can readily derive expressions for various measures of system availability. Expressions for the point availability of the generalized process are presented.     

Analytic approximations for (s,S) inventory policy operating characteristics

The operating characteristics of (s,S) inventory systems are often difficult to compute, making systems analysis a tedious and often expensive undertaking. Approximate expressions for operating characteristics are presented with a view towards simplified analysis of systems behavior. The operating characteristics under consideration are the expected values of: total cost per period, period-end inventory, period-end stockout quantity, replenishment cost per period, and backlog frequency. The approximations are obtained by a two step procedure. First, exact expressions for the operating characteristics are approximated by simplified functions. Then the approximations are used to design regression models which are fitted to the operating characteristics of a large number of inventory items with diverse parameter settings. Accuracy to within a few percent of actual values is typical for most of the approximations.     

Joint determination of optimum variable and attribute target means

This article considers the problem of joint control of attribute and variable quality characteristics of a given product. Items are acceptable if they meet the specifications for both types of quality characteristics at the same time. Otherwise, the items are sold as scrap at reduced prices. The objective is to determine simultaneously the target values for each characteristic so as to maximize the expected profit per item. Several item-by-item quality-inspection plans are formulated on the basis of various inspection strategies. These strategies are defined in terms of whether the inspection is to be carried out simultaneously for both characteristics, or sequentially, or whether inspection for one of the characteristics is to be ignored. All these plans are shown to differ in terms of their profitability. However, they all yield equivalent quality standards. A numerical example is provided to illustrate the application of these models.     

Maximization of long-run average rate-of-return by stochastic approximation

Suppose that an individual has a surplus stock of wealth and a fixed set of risky investment opportunities over a sequence of time periods. Assuming the criterion of maximal long-run average rate-of-return, the individual may select portfolios sequentially via a modified stochastic approximation procedure. This approach yields optimal asymptotic investment results under minimal assumptions.