We consider the planning and scheduling of production in a multitask/multistage batch manufacturing process typical of industries such as chemical manufacturing, food processing, and oil refining. We allow instances in which multiple sequences of tasks may be used to produce end products. We formulate the problem as a mixed-integer linear program and show that the linear programming relaxation has a large integrality gap and requires significant computational effort to solve to optimality for large instances. Using echelon inventory, we construct a new family of valid inequalities for this problem. The formulation with the additional constraints leads to a significantly tighter linear programming relaxation and to greatly reduced solution times for the mixed-integer linear program.