Optimal Batch Size and Process Setting in Light-Emitting Diode (LED) Coproduction Processes

This paper studies the challenges involved in production planning in coproduction systems, specifically the production of semiconductor chips for light-emitting diodes (LEDs). The production output in this industry is characterized by a stochastic distribution over the targeted production metric; thus the whole range of production is not suitable for a specific application. We formulate a novel stochastic profit optimization problem with random production output and random demand—based on information gleaned from interactions with a large integrated LED manufacturer—and determine the optimal production parameter setting and the batch size analytically; we solve the problem exactly in the special case of a single customer specification, and approximately in the case of an arbitrary number of customer specifications. We find that the optimal production setting depends on the sharpness of the density function governing the production output distribution and the range of parameter settings that are acceptable to customers. We show analytically that even under perfectly symmetric conditions, the optimal production setting is not necessarily symmetrically located with respect to the output range. We complement our analytical results with a Monte Carlo simulation of an augmented model with service level constraints. Our simulation results show that the approximate model that we develop serves as an excellent proxy for the intractable exact model, and illustrates the interplay between production output randomness, demand randomness, service levels, and production yield.