A simple linear heuristic for the service constrained random yield problem

We consider the problem of setting order quantities for purchased components subject to uncertainty in the delivery amounts. Assuming the periodic production volumes (demands)to be known and constant, we model this as a random yield problem with the objective of minimizing average inventory cost subject to a service level constraint over the infinite horizon. We first demonstrate that under conditions of random yield, conventional definitions of service can be inappropriate. Then we refine the definition of service for random yield cases and use this to formulate an optimization model. Exact solution of this model proves to be computationally impractical and, as we show, the common heuristic of inflating demands by a constant proportion is not robustly accurate. Therefore, we develop a new heuristic, which we term the linear inflation policy, that specifies a linear function for the inflation factors. Numerical tests indicate that this heuristic can substantially outperform the traditional constant inflation policy and works well relative to a lower bound on the optimal solution on a range of examples.