On a variant of the change-making problem

Letchford, Adam and Cheng, Licong (2024) On a variant of the change-making problem. Operations Research Letters, 57: 107165. ISSN 0167-6377

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Abstract

The change-making problem (CMP), introduced in 1970, is a classic problem in combinatorial optimisation. It was proven to be NP-hard in 1975, but it can be solved in pseudo-polynomial time by dynamic programming. In 1999, Heipcke presented a variant of the CMP which, at first glance, looks harder than the standard version. We show that, in fact, her variant can be solved in polynomial time.