Newsvendor Model for Multi-Inputs and -Outputs with Random Yield: Applications to Agricultural Processing Industries

Consider a newsvendor model, which we extend to include both multiple inputs and outputs. Different input types possess different levels of quality, and are purchased at different prices by a processing firm. Each type of input is processed into multiple outputs, which are sold at different prices. The yield for each output type is random and depends on the input type. We need to determine the purchase quantities of different types of input, before demands of different types of output are known. In our analytical results, we show that the expected total profit is jointly concave in the purchasing quantities and derive the optimality condition. Our multi-input and -output newsvendor model is suitable for processing industries in agriculture supply chain. In our numerical example, we apply our model to the rice milling industry, whose primary output is head rice and byproducts are broken rice, bran and husk. Our model can help the rice mill to decide which paddy types to procure and how much, in order to maximize the total expected profit from all outputs. We also show that the expected profit can be significantly better than using the standard newsvendor model.