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

Abstract

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.

[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for supplemental resources containing details on some procedures and heuristics.]

Keywords:

• Job shops
• shop floor planning and control
• CONWIP
• closed queueing networks
• multiple chains
• non-linear integer program

Notes

¹For ease of exposition, we assume that N^j _HI and N^j _LO are integers. If they are not integers, the analysis can be suitably modified by fixing B_j to its binding value (i.e., B _LO or B _HI as the case may be) and solving for N_j .