An integrated optimization model for procurement and production lot sizing and scheduling problems

Lot sizing is a prevalent issue within manufacturing companies, where determining the optimal procurement and production lot sizes is crucial for maximizing profits. This problem has become more complex, given that numerous suppliers can provide the same raw materials with different prices and quantity discount schemes. A company should also determine optimal carriers to deliver materials to the company’s warehouse. In a manufacturing process, the company should determine the optimal production lot size and its schedules. In this paper, a model was developed to solve simultaneously procurement and production lot sizing, as well as production scheduling problems. The model encompasses multiple suppliers offering quantity discounts, aiming to maximize company profit by accounting for various costs, including procurement, production, inventory, and quality costs. A case study is taken from a company producing noodles and its related derivative products to illustrate the application of the model. Based on the optimization results, the company obtained a total profit of IDR. 14,656,550,000 or $950,921.30 (the exchange rate of $1 at IDR. 15,413). The sensitivity analysis results show that the objective function is sensitive to changes in the purchase cost, sale revenue, and discount rate parameters. The decision variables for accepted product demand, product quantity, and the starting and completion time of product family are only sensitive to changes in certain parameters. Meanwhile, the decision variables for product inventory, product backlog, raw material inventory, and purchased raw material quantity are sensitive to the changes in all the analyzed parameters.