Research Brief

Maximizing Capacity Utilization of Unique Equipment

An algorithm to reduce telescope repositioning time boosts productivity between 10% and 25%

Major industries have spent decades and lots of brain power figuring out how to wring the most from expensive capital equipment. And because many factories, warehouses, power plants and airliners are identical to each other, or nearly so, these continuing investments in efficiency can apply to hundreds or even thousands of separate major pieces of capital equipment, offering enormous payoff.

But what about unique, or nearly unique, capital equipment, where these economies of scale don’t apply? The two massive research telescopes at the Keck Observatory on Mauna Kea in Hawaii have operated since 1993 and 1996, respectively, and the laborious work of scheduling up to 100 nightly viewings — in an order that minimizes telescope repositioning time — is still done by staffers there.

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A paper, published in The Astronomical Journal, by Caltech’s Luke B. Handley, a Ph.D. student, UCLA’s Erik A. Petigura, and UCLA Anderson’s Velibor V. Mišić, offers an algorithm that does the job and reduces repositioning time dramatically. The algorithm could also be useful at some of the world’s other major research telescopes — there are only about a dozen.

Making the Most of the Night

Use of these telescopes is generally limited to night hours when objects in the sky are easier to view. The two Keck telescopes are considered the most productive by the number of papers published per telescope and the impact of those publications. Time on one of Keck’s telescopes is valued at about $100,000 per night. Researchers compete fiercely for slivers of this time through a proposal system.

Telescope operators seek to maximize the time that a telescope is available for the scientific community but they face challenges: A scientist’s targeted object may only be viewable for part of the night; repositioning from one area of the sky to the next scheduled viewing can be time-consuming; cables attached to a telescope can get tangled, limiting telescope movement; and weather can also cause delays and require recalculations of the schedule.

The authors call the problem the “traveling telescope problem,” in a nod to a well-known optimization problem, the “traveling salesman problem,” in which a salesperson needs to find the shortest route possible to visit a number of cities and return home without visiting a city more than once. The telescope problem, of course, is more complex because the objects to be viewed are moving across the sky and it takes time to reposition a telescope between viewings.

Telescope operators may need to schedule up to 100 viewings of stars in a 10-hour nighttime period. Most observatories still use manual scheduling. Some have moved to automated scheduling, but few have tackled the minimization of telescope repositioning time between viewings.

Trimming Time Between Viewings

Scheduling is done manually at Keck. An experienced scheduler with over 100 nights of scheduling experience can put together a full night’s schedule in about three hours. A novice scheduler typically spends about 10 hours.

The researchers’ algorithm reduces the time it takes to schedule a night to just 10 minutes. This also enables quick recalculation of a schedule when weather upsets the order.

Handley, Petigura and Mišić’s algorithm breaks scheduling into subproblems, reducing the complexity of the problem. 

To create a baseline for comparison, researchers determine that randomly scheduling 100 viewings results in three hours of repositioning time. Their algorithm cuts it to 30 minutes, they say.

The $100,000 per-night cost suggests a nightly savings of $25,000. Versus an experienced scheduler, cost savings could be around $10,000. More use of the telescopes, of course, opens up the possibility of further scientific breakthroughs.

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About the Research

Handley, L. B., Petigura, E. A., & Mišić, V. V. (2023). Solving the Traveling Telescope Problem with Mixed-integer Linear Programming. The Astronomical Journal, 167(1), 33.

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