Optimizing Multi-stage Production for an Assembly-Type Supply Chain with Unequal Sized Batch Shipments

This paper studies the multi-stage logistics and inventory problem in an assembly-type supply chain where a uniform lot size is produced uninterruptedly with a single setup at each stage. Partial lots, or sub-batches, can be transported to next stage upon completion. Unequal sub-batch sizes at each stage follow geometric series and the numbers of sub-batches across stages are allowed to be different. Since the mainline and each branch line of an assembly-type supply chain are series-type supply chains, a model of the series-type supply chain is first established and a model of the assembly-type supply chain is subsequently developed. Optimization algorithms that determine the economic lot sizes, the optimal sub-batch sizes and the number of sub-batches for each stage are developed. The polynomial-time algorithms incorporate the optimality properties derived in the paper to find the lower and upper bounds of the solutions by constructing the solution ranges and then the optimal solutions accordingly.