We consider the school bus scheduling problem (SBSP) which simultaneously determines school bell times and route schedules. Often, the goal of the SBSP is to minimize the number of buses required by a school district. We extend a time-indexed integer programming model to incorporate additional considerations related to equity and efficiency. We seek to equitably reduce the disutilities associated with changing school start times via a minimax model, then propose a lexicographic minimax approach to improve minimax solutions. We apply our models to randomized instances based on a moderately-sized public school district to show the impact of incorporating equity.

We study the linked tactical design problems of fleet sizing and partitioning a service region into vehicle routing zones for same-day delivery (SDD) systems. Existing SDD studies focus primarily on operational dispatch problems and do not consider system design questions. Prior work on SDD system design has not considered the fleet sizing decision when a service region may be partitioned into zones dedicated to individual vehicles; such designs have been shown to improve system efficiency in related vehicle routing settings. Using continuous approximations to capture average-case operational behavior, we consider first the problem of independently maximizing the area of a single-vehicle delivery zone. We characterize area-maximizing dispatching policies and leverage these results to develop a procedure for calculating optimal areas as a function of a zone’s distance from the depot, given a maximum number of daily dispatches per vehicle. We then demonstrate how to derive fleet sizes from optimal area functions and propose an associated Voronoi approach to partition the service region into single-vehicle zones. We test the fleet sizing and partitioning approach in a computational study that considers two different service regions and demonstrate its pragmatism and effectiveness via an operational simulation. Using minimal computation, the approach specifies fleet sizes and builds vehicle delivery zones that meet operational requirements, verified by simulation results.

No abstract

No abstract

Hypertension is one of the major non-communicable lifestyle disorders which has taken the form of modern-day epidemic affecting almost two times in 2019 than in 1990. Hypertension is also a major important risk factor for the occurrence of ischemic heart diseases and stroke in later life which stands to be the most important cause of morbidity and mortality according to the Global Burden of Disease studies. The incidence of hypertension in an individual depends on multiple inter related and unrelated factors which leads to the structural changes of the blood vessels and increases the turbulence of flow of blood and in the end leads to hypertension. Though there have been a number of studies done to find out the associations of different risk factors with the incidence of hypertension, they were focused upon the affect of those risk factors as a whole and not on specific adult age group. This study tried to shed some light on the different risk factors which specifically affect the men and women in reproductive age 30 years and more and give recommendations about factors on which special attention is needed to be given to prevent them. The National Family Health Survey 4 (NFHS-4) was conducted countrywide in 2015-16 among men and women of 15-54 years and 15-49 years respectively. The unit level data was used in this study to find prevalence of hypertension of men (30-54 age group) and women 30-49 age years for the four major states of Delhi (North), Odisha (East), Kerala (South), Maharashtra (West) and also analysed association with various socio demographic and others related variables using standard statistical tools of SPSS 23 and MS EXCEL.The most important factors leading to occurrence of hypertension in an individual of 30 years or more were found to be age, smoking and alcoholism, diabetes and unhealthy diet. But some socio and economic factors having an indirect association with prevention of hypertension were found to be female literacy and insurance coverage. The health seeking behaviour of hypertensives and the screening of people for hypertension were also not found up to the mark. Hypertension is preventable and treatable by proper lifestyle modification and medication. The screening of the adult population of 30 years and more needs to be strengthened, advocacy against smoking and alcoholism, stress management, and penetration of health insurance coverage needs to be increased.