Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

Influence of pain and urinary symptoms on quality of life in young men with chronic prostatitis-like symptoms

BACKGROUND: Our aims in the present study were to estimate the influences of pain and urinary symptoms on quality of life, and to determine which of these two variables has the most predictive power with respect to quality of life in young men with chronic prostatitis-like symptoms. METHODS: Chronic prostatitis-like symptoms were measured by the National Institutes of Health-Chronic Prostatitis Symptom Index. Of the 28,841 men aged 20 years who lived in the study community, 18,495 men (a response rate 64.1%) agreed to participate in the study. A total of 1057 men who complained of symptoms indicative of chronic prostatitis were included in the study. The influences of pain and urinary symptoms on quality of life were determined using logistic regression analysis. The receiver operating characteristic (ROC) curve was used to estimate the predictive ability of each of these variables with respect to quality of life. RESULTS: Results from multivariate analysis showed that both pain and urinary symptoms were associated with an increased likelihood of impaired quality of life, although pain contributed more to a reduced quality of life than urinary symptoms. Relative to men who experienced mild pain, men who experienced moderate pain had a 3.9-fold risk of poor quality of life (odds ratio [OR], 3.87; 95% confidence interval [CI], 2.86-5.23; P < 0.001) and those who experienced severe pain had a 15.7-fold risk of reduced quality of life (OR, 15.68; 95% CI, 6.59-37.35; P < 0.001). Moderate urinary symptoms were associated with a 1.4-fold risk of bother (OR, 1.41; 95% CI, 1.01-1.99; P < 0.001) and severe urinary symptoms were associated with 2.4-fold risk (OR, 2.39; 95% CI, 1.37-4.12; P < 0.001), relative to mild urinary symptoms. Comparison of the effects of pain and urinary symptoms showed that pain severity had the most predictive power for bother, quality of life, and quality-of-life impact. The areas under the ROC curves for bother, quality of life, and quality-of-life impact were 71.3%, 69.3% and 72.5%, respectively. CONCLUSION: Urinary symptoms and pain might be associated with an increased likelihood of impaired quality of life in young men with chronic prostatitis-like symptoms. In addition, our findings suggest that pain severity is the most influential variable for determining quality of life in this population.     

Short-Ti inversion-recovery pulse sequence: analysis and initial experience in cancer imaging

Inversion recovery (IR), commonly considered a pulse sequence capable of producing T1-weighted images with excellent display of normal anatomy, is versatile: The null point and peak time provide a useful, succinct summary of the properties of IR and its capacity for producing both T1- and T2-weighted images. Shortening of the inversion time (TI) and creation of a short-TI inversion-recovery (STIR) pulse sequence increases sensitivity to malignancy and other abnormalities by making the effects of prolonged T1 and T2 on signal intensity additive and by nulling the signal from fat. The authors examined over 300 patients with various malignancies and compared STIR images with T1- and T2-weighted images obtained at 0.5 T. In 43 cases, signal-difference-to-noise ratios (SD/Ns) were calculated between tumor, fat, and muscle. In general, STIR images demonstrated tumor as a conspicuously high-intensity area in a background of muted, discernible anatomic detail. The good contrast achieved with STIR sequences between tumor and fat (SD/N = 18.1) and tumor and muscle (SD/N = 12.9) consolidated into a single image the information contained separately on T1- and T2-weighted images, which facilitates efficient detection and localization of malignancy.