Demand-side management (DSM) has the potential to reduce electricity costs and the carbon emissions associated with electricity use for industrial consumers. It also has an important role to play in integrating variable forms of generation, such as wind and solar, into the grid. This will be a key part of any grid decarbonisation strategy. This paper describes a method that can be used to develop a new production schedule for a wide range of manufacturing facilities. The new schedule minimises either electricity costs or electricity-derived CO$2$ emissions. It does so by rescheduling production to low cost or low carbon periods, without loss of overall production, within the constraints of available inventory storage. A case study of a single cement plant in the UK was performed in order to determine the potential benefits of increased load-shifting DSM using this method. The alternative production scheduled showed the potential to decrease electricity costs by 4.2%. Scaled to values from a typical plant this would lead to a cost saving of £350,000, a substantial saving. A schedule optimised to minimise carbon emissions would save an estimated 2000 tonnes per year of CO$2$, a 4% decrease in electricity-derived emissions. It was also observed that the actual electricity consumption of the plant was considerably higher than the minimum consumption predicted by the model. This could indicate potential for significant savings in both cost and CO$2$ due to improvements in energy efficiency. The potential savings from DSM doubled when the prices passed to the plant were replaced with a price that varied in proportion to the wholesale cost of electricity. This indicates that a potential mutual benefit exists for both industrial consumers and electricity generators by passing on more of the variation in price. A larger share of generation from wind and solar will also lead to increased variation in prices and grid carbon intensity in future. The value of applying the method described in this paper is therefore likely to increase further in future.