Batching Problems with Constraints

There is an increasing demand for a phenomenon that can manifest benefits gained from grouping similar jobs together and then scheduling these groups efficiently. Batching is the decision of whether or not to put the jobs into same group based on certain criteria. Batching plays a major role in job scheduling in Information Technology, traffic controlling systems, and goods-flow management. A list batching problem refers to batching a list of jobs in the same order or priority as given in the problem. In this thesis we consider a one-machine list batching problem under weighted average completion. Given sequence of jobs are scheduled on single machine into distinct batches. Constraint is to batch these jobs into a fixed but arbitrary number ‘k’ of batches. Each batch can have any number of jobs (within the given list) grouped without changing the order of jobs. We call it a k-Batch problem. This is offline form of the batching problems, and is solved by reducing to a shortest path problem. We give an improved and faster version of the algorithm to solve k-Batch problem in O(n2) time

Mapping inequalities in exclusive breastfeeding in low- and middle-income countries, 2000–2018

Exclusive breastfeeding (EBF)—giving infants only breast-milk for the first 6 months of life—is a component of optimal breastfeeding practices effective in preventing child morbidity and mortality. EBF practices are known to vary by population and comparable subnational estimates of prevalence and progress across low- and middle-income countries (LMICs) are required for planning policy and interventions. Here we present a geospatial analysis of EBF prevalence estimates from 2000 to 2018 across 94 LMICs mapped to policy-relevant administrative units (for example, districts), quantify subnational inequalities and their changes over time, and estimate probabilities of meeting the World Health Organization’s Global Nutrition Target (WHO GNT) of ≥70% EBF prevalence by 2030. While six LMICs are projected to meet the WHO GNT of ≥70% EBF prevalence at a national scale, only three are predicted to meet the target in all their district-level units by 2030