A joint internal production and external supplier order lot size optimization under defective manufacturing and rework

The traditional production-inventory problems do not consider joint production and order lot sizes in manufacturing systems. This paper considers a defective system to jointly decide on order and production lot sizes in a manufacturing company. The manufacturer produces items with finite processing rate where a percentage of these items are of imperfect quality. At the end of production process, the rework of imperfect items is carried out. The demand rate and the number of defective items are considered to be uncertain parameters. The aim is to determine optimal number of sub-production cycles, as well as optimal order quantity. To address this problem, we first define the problem and describe its characteristics, build the model via deriving total cost function, design an appropriate solution algorithm, and then illustrate and evaluate the results. The solution algorithm is based on an ant colony optimization (ACO) which is enhanced by an adaptive learning strategy. A numerical example is presented and discussed, and the results are compared with basic ACO and genetic algorithm (GA). Finally, sensitivity analysis and robustness analysis are performed and discussed. The observed results reveal the robust performance of proposed approach against basic ACO and GA. Moreover, we observed that the performance of basic ACO and GA is approximately the same, and the basic ACO is more robust than GA in our experiments.