The effects of model parameter deviations on the variance of a linearly filtered time series

We consider a general linear filtering operation on an autoregressive moving average (ARMA) time series. The variance of the filter output, which is an important quantity in many applications, is not known with certainty because it depends on the true ARMA parameters. We derive an expression for the sensitivity (i.e., the partial derivative) of the output variance with respect to deviations in the model parameters. The results provide insight into the robustness of many common statistical methods that are based on linear filtering and also yield approximate confidence intervals for the output variance. We discuss applications to time series forecasting, statistical process control, and automatic feedback control of industrial processes. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Threshold incentives over multiple periods and the sales hockey stick phenomenon

In this article, we study threshold‐based sales‐force incentives and their impact on a dealer's optimal effort. A phenomenon, observed in practice, is that the dealer exerts a large effort toward the end of the incentive period to boost sales and reach the threshold to make additional profits. In the literature, the resulting last‐period sales spike is sometimes called the hockey stick phenomenon (HSP). In this article, we show that the manufacturer's choice of the incentive parameters and the underlying demand uncertainty affect the dealer's optimal effort choice. This results in the sales HSP over multiple time periods even when there is a cost associated with waiting. We then show that, by linking the threshold to a correlated market signal, the HSP can be regulated. We also characterize the variance of the total sales across all the periods and demonstrate conditions under the sales variance can be reduced. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Assessment of hazardous-inspection policies

Inspection procedures may at times pose a hazard to the system being monitored. In this article, a simple hazardous-inspection model is considered. The character of the optimal ongoing inspection policy (for inspections subsequent to the first) is reviewed, and the possible forms of the optimal initiation policy are established. Efficient computational procedures are developed for calculating optimal policies. Some discussion is included of the counterintuitive nature of some of the results.     

A simulation–optimization method: Its convergence and utility

An optimization method is given for solving problems where a portion of the explicit mathematical form is unknown but can be evaluated. The solution scheme is an iterative process utilizing optimization and subsystem evaluation (such as via simulation). Conditions for the convergence of the iterative process are given. Several published application articles are noted as using this basic methodology. The method is superior to most other numerical optimization procedures. However, the class of problems for which the method is applicable is restricted to problems with enough known structure to generate a convergent iterative procedure. Three numerical examples are given and comparisons made with several other methods of optimizing unknown systems.     

Optimal admission pricing and service rate control of an M[x]/M/s queue with reneging

In this article we consider the optimal control of an M^[X]/M/s queue, s ≧ 1. In addition to Poisson bulk arrivals we incorporate a reneging function. Subject to control are an admission price p and the service rate μ. Thus, through p, balking response is induced. When i customers are present a cost h(i,μ,p) per unit time is incurred, discounted continuously. Formulated as a continuous time Markov decision process, conditions are given under which the optimal admission price and optimal service rate are each nondecreasing functions of i. In Section 4 we indicate how the infinite state space may be truncated to a finite state space for computational purposes.     

Minimum-cost flows in convex-cost networks

An algorithm is given for solving minimum-cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max-Flow Min-Cut Theorem may all be formulated into minimum-cost flow problems in convex-cost networks.     

The formulation of some allocation and connection problems as integer programs

In this paper a component placement problem and a digital computer backboard wiring problem are formulated as integer linear programs. The component placement problem consists of making a unique assignment of components to column positions such that wireability is maximized. The backboard wiring problem consists of three interrelated subproblems, namely, the placement, the connection, and the routing problems. The placement and connection problems are combined and solved as one, thereby giving the optimal circuit connections as well as minimizing the total lead length. It is shown that under certain assumptions, the number of inequalities and variables in the problem can be greatly reduced. Further simplifying assumptions lead to a near optimal solution. Examples of other allocation problems to which the models presented here are applicable are given. The following concepts are formulated as linear inequalities: (1) the absolute magnitude of the difference between two variables; (2) minimize the minimum function of a set of functions; and (3) counting the number of (0, 1) adjacent component pairs in a vector.     

Values for optimum reject allowances

Industrial situations exist where it is necessary to estimate the optimum number of parts to start through a manufacturing process in order to obtain a given number of completed good items. The solution to this problem is not straightforward when the expected number of rejects from the process is a random variable and when there are alternative penalties associated with producing too many or too few items. This paper discusses various aspects of this problem as well as some of the proposed solutions to it. In addition, tables of optimum reject allowances based on a comprehensive model are presented.