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.     

Spinal metastasis of occult lung carcinoma causing cauda equina syndrome.

Cauda equina syndrome (CES) may be caused by tumor, herniated disc, trauma and spinal infections. However, CES due to occult lung cancer has not been reported in the literature. A 50-year-old man presented with a subacute CES caused by an intradural metastasis of an adenocarcinoma of the lung to the lumbosacral cauda fibers. His lumbosacral magnetic resonance imaging (MRI), showed a well-demarcated, intradural extramedullary mass lesion resembling a neurinoma at the L4/5 level. The patient underwent an L4-L5 laminectomy. The operative findings were also suggestive of neurinoma with involvement of three nerve roots, and a well-demarcated tumor without infiltration into the subarachnoid space. Although the findings of the operation were suggestive of neurinoma, final pathological diagnosis revealed metastatic carcinoma. Immunohistochemistry revealed clear cell adenocarcinoma metastasis. Chest X-ray and high resolution contrasted pulmonary computed tomography were normal. Positron emission tomography (PET) showed a lung mass, at the left apex. The patient was treated with chemotherapy and post-operative spinal radiotherapy was also performed. The CES resolved after the operation and the patient was followed up for 2 years with no recurrence. MRI of intradural cauda equina metastasis may be similar to that of intradural nerve sheath tumor. Surgery and postoperative radiotherapy may be effective for the treatment of CES due to lung carcinoma. Definitive diagnosis is by histopathological examination with immunohistochemistry. If the primary cancer cannot be detected by conventional radiological techniques, PET may be helpful.     

Clinical and epidemiologic evaluation of pressure ulcers in patients at a university hospital in Turkey.

OBJECTIVE: We sought to measure the incidence of pressure ulcer development at a university health center in Turkey, and to determine whether the Waterlow Pressure Sore Risk (PSR) Scale score predicted pressure ulcer development, stage, or number of ulcers. DESIGN: We prospectively evaluated patients who were hospitalized at our university-based medical center. SETTING AND SUBJECTS: We analyzed data from 22,834 patients hospitalized at the Baskent University Adana Teaching and Medical Research Center in Ankara, Turkey from January 1, 2004 to December 31, 2004, including 360 patients who developed pressure ulcers. INSTRUMENTS: The Waterlow PSR Scale was used to assess pressure ulcer risk. In addition, age, sex, the ward or unit in which the patient was hospitalized, reason for hospitalization, and location and stage of ulcers were collected on a data form designed specifically for this study. METHODS: A single nurse physiotherapist assessed all patients daily during their hospitalization. When a pressure ulcer was diagnosed by the nurse physiotherapist, a physician staged the pressure ulcers based on the US National Pressure Ulcer Advisory Panel (NPUAP) staging system. RESULTS: Three hundred sixty out of 22,834 patients developed 1 or more pressure ulcers, resulting in an incidence rate of 1.6%. Most ulcers (59.2%) occurred in patients hospitalized in the intensive care unit (n = 213). A positive correlation between the Waterlow PSR Scale score and number of ulcers per patient (r: 0.178, P < .01) was identified. No significant correlation was found linking Waterlow PSR Scale score and ulcer stage or the development of a single ulcer. CONCLUSION: We found significantly lower pressure ulcer incidence rates than those commonly reported in the literature, which we believe is principally attributable to short hospital stays and a strong emphasis on preventive nursing care. While high Waterlow PSR scale Scores correlated positively with development of multiple ulcers, this did not predict ulcer stage or the presence of a single pressure ulcer.     

Synovial chondromatosis of four compartments of the knee: medial and lateral tibiofemoral spaces,patellofemoral joint and proximal tibiofibular joint

A case of synovial chondromatosis of the proximal tibiofibular joint in addition to lateral and medial tibiofemoral spaces and patellofemoral joint has been presented.     

Comparison and validation of scoring systems in a cohort of patients treated for perforated peptic ulcer

Background and aims The aim of this study is to evaluate the predictive accuracy of different scoring systems on surgery for perforated peptic ulcer referred to an academic department of general surgery in a tertiary reference center. Patients and methods Seventy-five consecutive patients (Male/female ratio = 64:11; mean age, 44 years; range, 16–85) with perforated peptic ulcer disease were investigated. Disease severity scores and mortality predictions were calculated using the collected data during admission. Discrimination and calibration characteristics of each system, namely, the acute physiology and chronic health evaluation II and III, the simplified acute physiology score II, and the mortality probability models (MPM) II, were determined by using the area under receiver operating characteristics curve and the Hosmer–Lemeshow goodness-of-fit test, respectively. Results Among the 75 patients included, there were eight (10.6%) mortalities. All systems had a reliable power of discrimination and calibration. Among the systems tested, MPM II was the best performing as far as discrimination and calibration characteristics were considered. The parameters of MPM II system that were related to systemic perfusion of the patient were significantly positive in patients who died compared to those who survived. Conclusions MPM II that predicted mortality at admission is better than the other systems in predicting mortality. Results also indicate the importance of maintenance of systemic perfusion of the patient at the early phases of peptic ulcer perforation.     

Human lymphocyte antigens (HLA) and Graves' disease in Turkey

To evaluate the association of HLA types with Turkish patients with Graves' disease, HLA typing, clinical findings, and thyroid antibodies were correlated. The HLA types, clinical findings (ophthalmopathy and age at onset), and thyroid stimulating hormone (TSH) receptor (TRAb) and antithyroid microsomal antibodies (MAb) were analyzed. Seventy Turkish patients with Graves' disease and 306 control subjects were assessed. Serological HLA typing was performed in HLA A, B, C, DR, and DQ loci. There was a significantly increased prevalence of HLA B8, B49, DR3, DR4, and DR10 in Graves' disease. The association of Graves' disease with HLA DR3 was found to be less strong than previously described. The HLA DR4 antigen may contribute to the predisposition of Graves' disease in Turkey. The results suggest that HLA B7, B13, DR7, DQw2, and DQw3 may confer a protective effect for Graves' disease in Turkey. Patients carrying HLA B12, B18, and B44 haplotypes had a tendency to develop the disease at a later age. The difference from the other studies may be the result of the selection of the controls; in part, of the variability in serological typing reagents; and, also, of the rather weak HLA associations with the disease.This study was presented in part at the Annual Meeting of the National Endocrinology and Diabetes Association, Bursa, Turkey, May 25–28, 1992.     

Stature estimation based on hand length and foot length

This study was carried out to estimate the relationship between hand length, foot length and stature using multiple linear regression analyses based on a sample of male and female adult Turks residing in Adana. Measurements of hand length, foot length and stature were taken from 155 adult Turks (80 male, 75 female) aged 17-23 years. The participants were students of the Medical Faculty of Cukurova University. A multiple linear regression model was fitted to the observed data. Stature was taken as the response or dependent variable, hand length and foot length were taken as explanatory variables or regressors. All possible (simple and multiple) linear regression models for each of males, females and both genders together were tested for the best model. The multiple linear regression model for both genders together was found to be the best model with the highest values for the coefficients of determination R2 = 0.861 and R2adjusted = 0.859, and multiple correlation coefficient R = 0.928.