The green capacitated lot sizing for industrial symbiosis

Given the detrimental effects that climate change is having on the ecosystems and general health of our world, we must all work to mitigate or prevent it. Cutting back on carbon emissions is one method we can use to mitigate the effects of climate change. At levels that nature is unable to balance on its own, manufacturing has been a major contributor to the dramatic rise in carbon emissions. In this context, a green capacitated lot-sizing problem in the structure of an industrial symbiosis (GCLS-IS), where two production units (PU1 and PU2) must plan their production over a planning horizon of T periods was considered. PU1 must limit its emissions to a certain government approved CO2 quota in a production period t to satisfy a deterministic time-dependent demand. In this paper, carbon emission is assumed to be proportional to the number of units produced per period and can be expressed as a unitary environmental impact. Two types of carbon emission constraints were studied: periodic carbon emission constraints and cumulative carbon emission constraints. Valuable insights derived from this analysis are subsequently used to discuss the managerial implications of setting up the considered industrial symbiosis in terms of model complexity. The periodic and cumulative cases are proven to be NP-hard. Three models were developed; (i) without carbon emissions (ii) periodic carbon emissions (iii) cumulative carbon emission. Upon solving the models with pyomo, model 3 was found to be better than model 2 since it had a lower cost, lower inventory, lower disposal quantity, and did not exceed the approved carbon emissions. Additionally, perspectives to extend this work are discussed.