A stochastic approach for the Lot Sizing problem

In this paper we extend the generalized surrogate optimization approaches and the stochastic comparison so as to tackle the lot-sizing problem in manufacturing system. In practice, with the surrogate methodology, the lot sizes are continuously adjusted on-line by the gradient-based approaches. The lot sizing determines the number of parts batched together for production. We utilize the queueing approach that evidences the existence of a convex relationship between batch size and waiting time (including processing). Large lot sizes will cause long lead times (the batching e®ect), as the lot size gets smaller the lead time will decrease but once a minimal lot size is reached a further reduction of the lot size will cause high tra±c intensities resulting in longer lead times (the saturation e®ect). The congestion phenomenon is due to the increased number of setups (and thus total setup time). We comparison two di®erent algorithms the "surrogate optimization" and the "stochastic comparison", and we show that the surrogate problem methodology recovers the optimal solution of the original discrete problem and exhibits very fast convergence compared to known discrete stochastic optimization methods. Some numerical results are reported.