A 'surrogate problem' approach for lot size optimization in manufacturing systems

We extend a 'surrogate problem' approach developed for a class of stochastic discrete optimization problems so as to tackle the lot sizing problem in manufacturing systems. The lot size determines the number of parts batched together for processing with setup costs involved with every new lot. In a multi-product manufacturing environment it is a control parameter that drastically affects the mean system time of parts. With the surrogate problem methodology, the discrete lot sizing optimization problem is transformed into a "surrogate" continuous optimization problem where gradient-based approaches are used and lot sizes are continuously adjusted online. The approach recovers the optimal solution of the original discrete problem and exhibits very fast convergence compared to known discrete stochastic optimization methods.