The production planning and scheduling include all the kinds of administrative processes necessary for manufacturing systems to have sufficient and raw material, human resource, etc. so that the supply chain will not be disturbed. This significantly helps in efficient planning of the operations at the shop floor as well as every segment of the supply chain. The processes are associated with estimation of the product demand, alternatives of the resources, continuous monitoring and adjustments and revisions in the production schedule. Optimization methods and tools play a significant part in this process which is very much required for the small and medium enterprises. This chapter discusses optimization methodologies solving the associated single and multi-objective problems. The methods such as Krill Heard based algorithm solving the scheduling problem, multi-level capacitated lot-sizing and scheduling problem using particle swarm optimization, Petri nets for the production floor processes problems, stochastic mixed-integer program, CPLEX, Jaya algorithm and simulated annealing algorithms, reinforcement learning, for maintenance scheduling and programming have been discussed. In addition, mixed-integer linear programming model for addressing disassembly scheduling model, ML Methods for transportation scheduling, reverse logistics network for product recovery using best worst method, contemporary MCDM techniques, NSGA for job-shop scheduling, etc. have also been discussed in very details with several test and real-world cases.