Optimal work-in-process inventory levels for high-variety, low-volume manufacturing systems

This article considers a manufacturing system that operates in a high-variety, low-volume environment, with significant setup times. The goal is to determine the optimal Work-In-Process (WIP) inventory levels for operating the system to meet the required demand for each product. The decision variables are the number of pallets (containers) for each product and the number of units in each pallet (lot size). The objective is to minimize the total WIP inventory across all products. To capture congestion in the system, it is modeled as a closed queueing network with multiple product types. However, this leads to a complex non-linear integer program with a non-convex objective function. A lower bound on the objective function is developed that is used to develop upper and lower bounds on the number of pallets for each product. The bounds on the number of pallets allow the use of exhaustive enumeration within these bounds to obtain the optimal solution to this complex queueing network-based optimization problem. A simple heuristic is developed to further reduce the number of candidate configurations evaluated in the search for the optimal solution. A computational study reveals that the heuristic obtains the optimal solution in many of the test instances.