Synchronizing production planning and job scheduling: MILP models and exact algorithms

We address the synchronization of a resource production process with the consumption of related resources by jobs. Both processes interact through transfer transactions, which become the key components of the resulting scheduling problem. This Synchronized Resource Production/Job Processing problem (SRPJP) problem typically arises when the resource is a form of renewable energy (e.g., hydrogen, photovoltaic) stored in tanks or batteries. We first cast SRPJP into the Mixed-Integer Linear Programming (MILP) format and handle it through a branch-and-cut process involving specific No_Antichain constraints derived from the structure of the feasible transfer transactions. Subsequently, we explore another approach, which involves eliminating non-binary decision variables and applying a Benders decomposition scheme. Finally, we reformulate the SRPJP problem as a path search problem, which we efficiently handle by designing a tailored adaptation of the A* algorithm.