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- W4247054776 abstract "Suppose you are a bicycle messenger in the busy business district of a large city. Here is what your day looks like: You are to deliver incoming mail to building i, and you are to pick up outgoing mail destined only for building i + 1. All in all you are responsible for m buildings. Your bike, however, is not of the highest quality: It can accommodate only mail for a single delivery. Riding from building i to building j requires tij minutes. Once you arrive at a building, you need d minutes to get off your bike, run into the building, and get onto your bike again. Moreover, once incoming mail has arrived at building i, it takes pi minutes for the outgoing mail to be ready (if this is too long, you may want to make another delivery and pickup in the meantime). You are to visit each building k times. Question: In which order should you visit the buildings so that you finish your work as fast as possible? The above description is a simplified version of the problem discussed in the paper by Milind W. Dawande, H. Neil Geismar, and Suresh P. Sethi. There the messenger is a robot, the buildings are machines, and the mail represents parts to be processed by the machines. The authors show that there exists a cyclic schedule that maximizes long-term throughput. Cyclic schedules are preferred in industrial environments, because they are easy to implement and control. Since the literature on robotic cell scheduling is full of different models for different kinds of industrial applications, it is important to know that all optimal schedules can be reduced to cyclic schedules. The authors end their paper by describing several challenging open problems. The paper by Miguel Torres-Torriti and Hannah Michalska describes a software package (LTP), implemented in Maple, for the symbolic manipulation of expressions that occur in the context of Lie algebra theory. This theory has found applications in classical and quantum mechanics, analysis of dynamical systems, construction of nonlinear filters, and the design of feedback control laws for nonlinear systems. Since the symbolic computations are often complex and tedious, the development of software for applications of Lie algebra theory is crucial. The LTP software package is targeted at applications such as solution of differential equations evolving on Lie groups, and structure analysis of general dynamical systems." @default.
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- W4247054776 date "2005-01-01" @default.
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- W4247054776 title "Problems and Techniques" @default.
- W4247054776 doi "https://doi.org/10.1137/siread000047000004000707000001" @default.
- W4247054776 hasPublicationYear "2005" @default.
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