Dynamic lead time modeling for JIT production planning

We consider planning and control of production systems in a long supply chain just-in-time (JIT) manufacturing environment with stochastic disturbances. We propose an iterative algorithm where a master problem determines tentative production requirement targets for each cell/focused factory in a cellular manufacturing plant. Subproblems-one for each cell and for each period/time-bucket in the planning horizon-are solved after each iteration to determine part-type and period specific lead times needed to achieve the master problem's tentative production targets. In addition, lead time gradients with respect to production targets are estimated by subproblems and passed on to the master problem. This allows the master problem to learn about the behavior of cell and part type specific lead times as a function of capacity utilization and production mix. Under reasonable conditions, the proposed iterative algorithm can learn this behavior with arbitrary accuracy in the neighborhood of the optimal solution, and thus generate a production plan that minimizes inventory and backlog costs, and optimizes JIT objectives. Computational results are provided to illustrate possible efficiency gains.