The ELSP is a mathematical model that was developed to try to solve a common issue on almost any company or industry: planning what to manufacture, when to manufacture and how much to manufacture. The classic problem concerns with scheduling the production of several items on a single machine in order to minimize the total costs incurred (which include: setup costs, holding inventory costs and production costs). The problem is well known in the Operations Research community, and a large body of academic research work has created to improve the model and to create new variations that solve specific issues.
The model is known as a NP hard problem since it is not currently possible to find the optimal solution without checking nearly every possibility. What has been done are some different approaches to try to solve it, including heuristics, genetic algorithms and others.