Lot size optimization in manufacturing systems: The surrogate method

Abstract

In this paper we extend a stochastic discrete optimization approach so as to tackle the lot-sizing problem in manufacturing systems. In practice, with the surrogate methodology, the lot sizes are continuously adjusted on-line by the gradient-based approach. 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 effect), 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 traffic intensities resulting in longer lead times (the saturation effect). The congestion phenomenon is due to the increased number of setups (and thus total setup time). In this paper, we consider the Surrogate method and the Stochastic comparison algorithm. According to our findings, the Surrogate method finds the optimal solution of the original discrete problem and exhibits a very fast convergence. Some numerical results are reported.