Timothy I. Matis

Optimal price and pro rata decisions for combined warranty policies with different repair options

A repairable product under a non-renewing combined warranty policy that is subject to a displaced log-linear demand function of the products price and pro rata period length is considered. Expressions for the manufacturers long-run average profit per unit time under replacement, minimal and general repair options are obtained. In addition, expressions for the stationary points and second-order conditions of the profit function are presented. Numerical illustrations that demonstrate optimal product pricing, pro rata length determination, and repair option selection to maximize the manufacturers, profit are given.

A mechanistic model based analysis of cotton aphid population dynamics data

1 A 2‐year field study was conducted to generate data on seasonal abundance patterns of cotton aphids Aphis gossypii Glover and to develop a mechanistic model based on cumulative population size. The treatments consisted of three irrigation levels (Low, Medium and High) with 65%, 75% and 85% evapotranspiration replacement and three nitrogen fertility treatments (blanket‐rate‐N, variable‐rate‐N and no nitrogen).

Application of population growth models based on cumulative size to pecan aphids

Models for aphid population growth based on cumulative (past) population size have been developed with both a deterministic formulation and a stochastic formulation. This article applies these mechanistic models to analyze a large dataset on pecan aphid. The models yield symmetric and right-skewed curves, which differ qualitatively from the observed data which tend to be left-skewed. Nevertheless this model-based analysis of data shows that the models are (1) useful representations of the data, (2) biologically reasonable descriptions of aphid population dynamics, and (3) a statistically powerful basis for the analysis of experimental data. The models also provide user-friendly predictive equations for aphid abundance. The deterministic model gives accurate point predictions of the peak and final cumulative population sizes, and the stochastic model gives, in addition, an accurate interval estimate of cumulative size. The models should be applicable to numerous other aphid abundance curves, as all aphid species have a similar reproductive mechanism.

Two-terminal reliability of a mobile ad hoc network under the asymptotic spatial distribution of the random waypoint model

The random waypoint (RWP) mobility model is frequently used in describing the movement pattern of mobile users in a mobile ad hoc network (MANET). As the asymptotic spatial distribution of nodes under a RWP model exhibits central tendency, the two-terminal reliability of the MANET is investigated as a function of the source node location. In particular, analytical expressions for one and two hop connectivities are developed as well as an efficient simulation methodology for two-terminal reliability. A study is then performed to assess the effect of nodal density and network topology on network reliability.

Applying healthcare systems engineering methods to the patient discharge process

The patient discharge process has been a perennial problem for hospitals of all sizes. Four decades worth of research have resulted in many insights for improving the quality of the process, but fewer breakthroughs regarding improving the speed of the process. Meanwhile, the timing of patient discharges is a key constraint on hospital capacity. Specifically, achieving better control over the discharge process may help hospitals alleviate one of their most severe capacity issues: gridlock in the emergency room. This paper presents results from a case study in a 362-bed regional teaching hospital in Texas, USA, where healthcare systems engineering methods were applied to document the current state of the discharge process and identify the most significant root causes of delays. Directions for future research on the design and management of the patient discharge process are identified and discussed, based on the case study findings and the literature review of previous work on patient discharge planning.

Fast-fading, an additional mistaken axiom of wireless-network research

The perplexity of designing an effective underlying communication protocol for Mobile Wireless Ad Hoc Networks (MANETs) is quite prevalent. In recent years, many protocols have been designed and evaluated through discrete event simulators. The lack of fidelity in these simulations, however, often yields results that support the incremental addition of control overhead to increase end-to-end performance measures of the protocol. It is argued herein that this additional overhead is largely ineffective when a fast-fading model is incorporated into the simulation. In particular, a comparison of the well established Ad Hoc On-Demand Distance Vector (AODV) protocol and its simplified version, known as the (AODVjr) protocol, under Ricean and Rayleigh fading models is presented. It is shown that the end-to-end performance of AODV is negligible in comparison to the AODVjr protocol, which possess minimal control overhead, when fast-fading models are incorporated into the simulation environment.

Optimal replacement policies of repairable systems subject to shocks

We consider a repairable system subject to a sequence of randomly occurring shocks, each of which results in a random amount of damage to the system. There are k general repair actions available, out of which one is chosen at each instant of shock arrival. The distributions of successive operating times between shocks and successive repair times are degenerative and dependent on the repair actions chosen earlier. System failure takes place when the accumulated damage crosses a fixed threshold level. We discuss optimal replacement strategies under an N-policy and a T-policy.

Using Cumulant Functions in Queueing Theory

A new approach for obtaining the transient solution for the first and second moments of the system size in a finite capacity M/M/1 queueing systems is developed. The approach uses the cumulant generating function which has previously been used in the analysis of compartmental models but has not been used to analyze queueing systems.

Bilevel Programming, Equilibrium, and Combinatorial Problems with Applications to Engineering

1Department of Systems & Industrial Engineering, Tecnologico de Monterrey (ITESM), Campus Monterrey, Avenida Eugenio Garza Sada 2501 Sur, 64849 Monterrey, NL, Mexico 2Department of Social Modeling, Central Economics & Mathematics Institute (CEMI), Russian Academy of Sciences, Nakhimovsky pr. 47, Moscow 117418, Russia 3Department of Computing, Sumy State University, Rimsky-Korsakov St. 2, Sumy 40007, Ukraine 4Department of Industrial Engineering, Texas Tech University, P.O. Box 43061, Lubbock, TX 79409, USA 5Facultad de Ciencias Fisico-Matematicas, Universidad Autonoma de Nuevo Leon, Avenida Universidad S/N, 66450 San Nicolas de los Garza, NL, Mexico 6Kharkiv Institute of Banking of the University of Banking of the National Bank of Ukraine, Peremogy Avenue 55, Kharkiv 61174, Ukraine

Generalized aphid population growth models with immigration and cumulative-size dependent dynamics.

Mechanistic models in which the per-capita death rate of a population is proportional to cumulative past size have been shown to describe adequately the population size curves for a number of aphid species. Such previous cumulative-sized based models have not included immigration. The inclusion of immigration is suggested biologically as local aphid populations are initiated by migration of winged aphids and as reproduction is temperature-dependent. This paper investigates two models with constant immigration, one with continuous immigration and the other with restricted immigration. Cases of the latter are relatively simple to fit to data. The results from these two immigration models are compared for data sets on the mustard aphid in India.