A game theoretic approach is used to analyze an inventory problem with two products, random demand, and random supply. The supply chain analyzed includes two retailers that sell two substitutable products and two suppliers. Each retailer faces a stochastic demand for the product she sells and replenishes her inventory from her supplier. The supplier provides a random fraction of the quantity requested. A given percentage of customers with unmet demand will substitute the product sold by the other retailer. We assume that the two retailers who make ordering decisions are rational players. Since each retailer's decision affects the single period expected profit of the other retailer, game theory is used to find the order quantities when the retailers use a Nash strategy.

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In a packet radio network, multiple terminals broadcast information over a shared communications medium. Messages are transmitted from a source terminal to a destination terminal over multiple relays or hops. The actions of one terminal in the network directly affect the actions of other terminals within its range. The analysis of packet radio networks is complex because system performance depends on the topology of the terminals in the network along with the random access protocol used. Researchers have been unable to model a packet radio network in its most general form. In this project, a model is developed for specific topologies of a packet radio network with a given random access protocol. The sponsor of this project has developed a packet radio network for an indoor wireless alarm system. At the start of the project, the effect of message collisions on system performance was unknown. As a result of this research, a collision model for the network has been developed for topologies of four, five, and six alarm units. The model has been validated with actual system testing. Furthermore, the effects of indoor propagation on system performance have been studied. The results of this work have led to the development of an installation plan for the indoor wireless alarm system. / Master of Science

<p> This thesis deals with linear combinations of a set of random variables uniformly distributed on a simplex. The exact joint distribution of two general linear combinations with real constant coefficients is considered and the results found in the form of the joint probability density function. Application of the result is also illustrated. </p> / Thesis / Master of Science (MSc)

Thesis / Doctor of Philosophy (PhD)

<p> This thesis is concerned with control procedures employed in Pavlovian conditioning, in particular, the "truly random" control. Pilot work indicated that this procedure employed in a CER paradigm resulted in response suppression. Our first objective then was to examine this finding in a more formal experiment, as well as attempting to determine the cause of the observed suppression. In a second experiment, a variable predicted to affect the amount of conditioning within traditional conditioning theory was employed to determine the possible role of this variable in suppression produced by the random control procedure.</p> <p> It was found, in the first experiment, that two variations of the random procedure resulted in suppression in testing. The results of a third group indicated that the suppression was not due to a between-session discriminative function of the CS. A fourth group demonstrated, within contingency logic, inhibitory control, but this group, like the others, showed suppression.</p> <p> In the second experiment, variations of stimulus conditions, none of which made the US contingent on the CS, resulted in marked differences in suppression in testing. Further, significantly different recovery rates of the operant baseline were noted both as a function of the recovery condition and of the CS employed in training.</p> / Thesis / Master of Arts (MA)

Although sampling techniques have been used effectively in education research and practice it is not clear how stratified random sampling techniques apply to high-stakes testing in the current educational environment. The present study focused on representative sampling as a possible means for reducing the quantity of state-administered tests in Texas public education. The purpose of this study was two-fold: (1) to determine if stratified random sampling is a viable option for reducing the number of students participating in Texas state assessments, and (2) to determine which sampling rate provides consistent estimates of the actual test results among the population of students. The study examined students’ scaled scores, percent of students passing, and student growth over a three-year period on state-mandated assessments in reading, mathematics, science, and social studies. Four sampling rates were considered (10%, 15%, 20%, & 25%) when analyzing student performance across demographic variables, including population estimates by socioeconomic status, limited English proficiency, and placement in special education classes. The data set for this study included five school districts and 68,641 students. Factorial ANOVAs were used initially to examine the effects of sampling rate on bias in reading and mathematics scores and bias in percentage of students passing these tests. Also 95% confidence intervals (CIs) and effect sizes for each model were examined to aid in the interpretation of the results. The results showed main effects for sampling rate and campus as well as a two-way interaction between these variables. The results indicated that a 20% sampling rate would closely approximate the parameter values regarding the mean TAKS reading and mathematics scale scores and the percentage of students passing these assessments. However, as population size decreases, sampling rate may have to be increased. For example, in populations with 30 or fewer students in a subgroup it is recommended that all students be included in the testing program. This study situated in one state contributes to the growing body of research being conducted on an international basis in sample-based educational assessments.

A Linear Program is a problem where the goal is to maximize a linear function subject to a set of linear inequalities. Geometrically, this can be rephrased as finding the highest point on a polyhedron. The Simplex method is a commonly used algorithm to solve Linear Programs. It traverses the vertices of the polyhedron, and in each step, it selects one adjacent better vertex and moves there. There can be multiple vertices to choose from, and therefore the Simplex method has different variants deciding how the next vertex is selected. One of the most natural variants is Random Edge, which in each step of the Simplex method uniformly at random selects one of the better adjacent vertices. It is interesting and non-trivial to study the complexity of variants of the Simplex method in the number of variables, d, and inequalities, N. In 2011, Friedmann, Hansen, and Zwick found a class of Linear Programs for which the Random Edge algorithm is subexponential with complexity 2^Ω(N^(1/4)), where d=Θ(N). Previously all known lower bounds were polynomial. We give an improved lower bound of 2^Ω(N^(1/2)), for Random Edge on Linear Programs where d=Θ(N). Another well studied variant of the Simplex method is Random Facet. It is upper bounded by 2^O(N^(1/2)) when d=Θ(N). Thus we prove that Random Edge is not faster than Random Facet on Linear Programs where d=Θ(N). Our construction is very similar to the previous construction of Friedmann, Hansen and Zwick. We construct a Markov Decision Process which behaves like a binary counter with linearly many levels and linearly many nodes on each level. The new idea is a new type of delay gadget which can switch quickly from 0 to 1 in some circumstances, leading to fewer nodes needed on each level of the construction. The key idea is that it is worth taking a large risk of getting a small negative reward if the potential positive reward is large enough in comparison. / Ett linjärt program är ett problem där målet är att maximiera en linjär funktion givet en mängd linjära olikheter. Geometriskt kan detta omformuleras som att hitta den högsta punkten på en polyeder. Simplexmetoden är en algoritm som ofta används för att lösa linjära program. Den besöker hörnen i polyedern, och i varje steg väljer den ett närliggande bättre hörn och flyttar dit. Det kan finnas flera hörn att välja mellan, och därför finns det olika varianter av simplexmetoden som bestämmer hur nästa hörn ska väljas. En av de mest naturliga varianterna är Random Edge, som i varje steg av simplexmetoden, uniformt slumpmässigt väljer ett av de närliggande bättre hörnen. Det är intressant och icke-trivialt att studera komplexiteten av olika varianter av simplexmetoden i antalet variabler, d, och olikheter N. År 2011 hittade Friedmann, Hansen och Zwick en familj av linjära program där Random Edge är subexponentiell med komplexitet 2^Ω(N^(1/4)), där d=Θ(N). Innan dess var alla kända undre gränser polynomiska. Vi ger en förbättrad undre gräns på 2^Ω(N^(1/2)), för Random Edge på linjära program där d=Θ(N). En annan välstuderad variant av simplexmetoden är Random Facet. Dess komplexitet har en övre gräns på 2^O(N^(1/2)) när d=Θ(N). Alltså bevisar vi att Random Edge inte är snabbare än Random Facet på linjära program där d=Θ(N). Vår konstruktion är väldigt lik den tidigare konstruktionen av Friedmann, Hansen och Zwick. Vi konstruerar en Markov-beslutsprocess som beter sig som en binär räknare med linjärt många nivåer och linjärt många noder på varje nivå. Den nya idén är en ny typ av försenings-multinod som kan byta snabbt från 0 till 1 i vissa fall, vilket leder till att det behövs färre noder på varje nivå av konstruktionen. Nyckelidén är att det är värt att ta en stor risk att få en liten negativ poäng om den potentiella positiva poängen är stor nog i jämförelse.