Loren K. Platzman

Decentralized Control of Automated Guided Vehicles on a Simple Loop

Abstract A highly decentralized greedy heuristic will enable a fleet of automated guided vehicles to deliver unit loads quickly on a simple loop track.

Spacefilling curves and the planar travelling salesman problem

To construct a short tour through points in the plane, the points are sequenced as they appear along a spacefilling curve. This heuristic consists essentially of sorting, so it is easily coded and requires only <italic>O</italic>(<italic>N</italic>) memory and <italic>O</italic>(<italic>N</italic> log <italic>N</italic>) operations. Its performance is competitive with that of other fast methods.

Retrieval Strategies for a Carousel Conveyor

Abstract We analyze algorithms that sequence the retrieval of items from a carousel conveyor, and show how the appropriate algorithm depends on the load to which the carousel is subjected. In general, as the load increases, so does the quality of solutions produced by simple heuristics. We conclude by recommending certain greedy heuristics for the problems of sequencing the retrieval of orders and for sequencing the retrieval of the items within each order.

A simple and efficient algorithm to compute tail probabilities from transforms

We present an algorithm to approximately compute the “tail” probability that a random variable exceeds a specified number, given only an expression for its transform. We also show that the problem is #P-hard (more difficult than NP-hard), suggesting that no efficient procedure can solve it exactly. Our method consists essentially of summing a power series, and thus is easy to perform and requires little memory. Furthermore, its computational effort is nearly linear in the reciprocal of a prespecified worst-case error bound.

A fast heuristic based on spacefilling curves for minimum-weight matching in the plane

Abstract We present a heuristic to find a good matching on n points in the plane. It is essentially sorting and so runs in O(n log n) worst-case time and linear expected time. Its performance is competitive with that of previously suggested methods. However, it has the advantages of being trivial to code and of being indifferent to the choice of metric or the probability distribution from which the points are drawn.

Explicit Representation of the Two-Dimensional Section of a Production Possibility Set

Technical and scale efficiencies of Data Envelope Analysis are associated with a two dimensionalsection (a convex set) representing the amounts by which the input and output vectors of a reference decision making unit, may be scaled and still lie in the production possibility set. We describe a simple algorithm, closely resembling the simplex algorithm of linear programming, to traverse the boundary of this set. Given the output of our algorithm, the scalar efficiency measures and return-to-scale characterization are trivially determined. Moreover, the set may be graphically displayed for any problem in any number of dimensions with only a minimum of additional computing effort.

Technical Note—Improved Conditions for Convergence in Undiscounted Markov Renewal Programming

In a simply connected Markov renewal problem, each state is either transient under all policies or an element of a single chain under some policy. This property is easily verified; it implies invariance of the maximal long-term average return (gain) with respect to the initial state, which in turn assures convergence of Odonis bounds in the damped value-iteration algorithm due to Schweitzer, even when the maximal-gain process is multiple-chained and/or periodic.

Building a Self-Organizing Urban Bus Route

We built a control system to realize the idea of self-coordinating buses recently proposed by Bartholdi and Eisenstein. It has been extensively tested and by the end of 2012 will manage the most heavily-traveled bus route through the campus of the Georgia Institute of Technology in Atlanta, GA, USA. Here we review the idea, describe the architecture of a control system that implements it, and provide a snapshot of progress towards full implementation.

An assignment principle for urban networks based on travel budgets

A new assignment principle for traveler behavior in an urban network is described which is based on empirical findings in the theory of travel budgets. It characterizes the distribution of travelers, demand, and modal split. It treats all travel decisions (whether to travel, where to go, how to get there) and the important costs (time and money) in a single, unified way. A numerical technique is proposed and it is applied to several examples to illustrate qualitative features.

A real-time AGV-scheduling system that combines human decision-making with integer-programming algorithms

A description is given of the interaction of a human operator and an automated transportation system within a cell of an FMS. The interaction of a human operator with operations-research-based scheduling algorithms is the research focus. The human role in management of the cell transportation system consists of monitoring the status of parts requiring transportation and, when necessary, interacting with the automated scheduling system to affect the produced schedules in such a way that compensation is made for late parts. Specific operator interaction methods are proposed. Experiments to test the detailed supervisory control philosophy are then discussed.<<ETX>>