The single-item lot-sizing problem with two production modes, inventory bounds, and periodic carbon emissions capacity

Abstract

We consider the single-item lot-sizing problem with inventory bounds under a carbon emissions constraint with two options for producing items: regular or green. We wish to find the optimal production plan so that the total carbon emissions from production cannot exceed the carbon emissions capacity in each period. Extending a problem without fixed carbon emissions and inventory bounds, we show that the extended problem is polynomially solvable by a dynamic programming algorithm.