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Precise scheduling is an effective way to improve energy efficiency, since it typically requires little capital investment and has a short payback period. However, making optimal scheduling decisions can be complicated by frequent price changes in the marketplace. This creates a large-scale energy cost minimization problem, which can be difficult to solve. We study this problem for a manufacturing or computer resource with discretely variable speeds, where energy usage increases with speed. We provide a scalable optimal algorithm for minimizing energy cost with discrete speeds under frequently changing energy prices. The result is a more precise, faster and more scalable planning tool for scheduling to control energy costs than is currently available.<\/jats:p>","DOI":"10.1007\/s10951-026-00872-5","type":"journal-article","created":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T14:27:25Z","timestamp":1771424845000},"page":"157-171","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimal energy scheduling under time-of-use tariffs"],"prefix":"10.1007","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4484-9252","authenticated-orcid":false,"given":"Nicholas G.","family":"Hall","sequence":"first","affiliation":[]},{"given":"Marc E.","family":"Posner","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,2,18]]},"reference":[{"key":"872_CR1","volume-title":"Network flows: Theory, algorithms, and applications","author":"RK Ahuja","year":"1993","unstructured":"Ahuja, R. 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