Robust simultaneous lot-sizing and scheduling with considering controllable processing time and fixed carbon emission in flow-shop environment

摘要

A new robust model is presented for simultaneous lot-sizing and scheduling problem in a flow-shop environment with controllable processing time in this study. In view of the importance of carbon emissions in green production, this model takes account of limitations in this respect. Different speeds of machines can also affect production, back order, inventory holding costs, scrap rates, as well as carbon emissions. In the present study, a new model is proposed under certainty and uncertainty. In order to deal with uncertainty, robust optimisation is employed. The robust model in this study is in non-deterministic polynomial-time (NP) hardness complexity class; therefore, a total of five heuristic algorithms are introduced based on fix-and-relax (F&R) and fix-and-optimise (F&O) approaches to solve larger instances. In conclusion, the results obtained from the algorithms based on F&O are given higher quality solutions compared with those based on F&R heuristic.