Economic lot-sizing problem with remanufacturing option: complexity and algorithms

Ashwin Arulselvan, Kerem Akartunali, Wilco van den Heuvel

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In a single item dynamic lot-sizing problem, we are given a time horizon and demand for a single item in every time period. The problem seeks a solution that determines how much to produce and carry at each time period, so that we will incur the least amount of production and inventory cost. When the remanufacturing option is included, the input comprises of number of returned products at each time period that can be potentially remanufactured to satisfy the demands, where remanufacturing and inventory costs are applicable. For this problem, we first show that it cannot have a fully polynomial time approximation scheme (FPTAS). We then provide a polynomial time algorithm, when we make certain realistic assumptions on the cost structure.
Original languageEnglish
Pages (from-to)421–432
Number of pages12
JournalOptimization Letters
Issue number2
Early online date29 Jun 2021
Publication statusPublished - Mar 2022


  • lot-sizing
  • remanufacturing
  • complexity
  • polynomial algorithms


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