Optimal leadtimes planning in serial production systems with earliness andtardiness costs

We consider a production system consisting of N processing stages. The actu al leadtimes at the stages are stochastic. The objective is to determine th e planned leadtimes at each stage so as to minimize the expected total inve ntory costs, tardiness penalties, and a backlog penalty for not meeting dem and due date at the last stage. Recursive relationships are used for automa tic generation and efficient computation of the objective function. The eff iciency of the proposed algorithms allows us to obtain new insights regardi ng operating policies, leadtime delivery reliability, and production line d esign. The problem is formulated as a convex non-linear programming problem . The latter is then solved using classical convex optimization algorithms. For the special case of exponentially distributed leadtimes, the objective function is derived in a closed form.