An order batching and processing heuristic to address aisle congestion in a manual order picking warehouse with order due dates

A heuristic for batching orders in a manual order-picking warehouse has been developed. It prioritizes orders based on due time to prevent mixing of orders of different priority levels. The order density of aisles criterion is used to form batches. It also determines the number of pickers required and assigns batches to pickers such that there is a uniform workload per unit of time. The effectiveness of the heuristic was studied by observing computational time and aisle congestion for various numbers of total orders and number of orders that form a batch. An initial heuristic performed well for small number of orders, but for larger number of orders, a partitioning technique is computationally more efficient, needing only minutes to solve for thousands of orders, while preserving 90% of the batch quality obtained with the original heuristic. Comparative studies between the heuristic and other published heuristics are needed. ^

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.