Edge scheduling optimization (ESO) is concerned with finding short-term supply and demand opportunities that would otherwise not be captured given the current schedule-by-simulation (SBS) approaches ubiquitous in industry today. ESO automates the scheduling decision-making specifically between the "edges" or boundaries of the supply, production and demand-chains to exploit occasions when profit and/or performance can be improved. In this presentation, we highlight several industrial case studies where significant benefits can be achieved through better optimization techniques at both the front- and back-ends of the production-chain as well as discussing the current technological and mathematical challenges.