Determination of optimal lot size and production rate for multi-production channels with limited capacity

Due to the constantly changing business environment, producers often have to deal with customers by adopting different procurement policies. That is, manufacturers confront not only predictable and regular orders, but also unpredictable and irregular orders. In this study, from the perspective of upstream manufacturers, both regular and irregular orders are considered in coping with the situation in which an uncertain demand is faced by the manufacturer, and a capacity confirming mechanism is used to examine such demand. If the demand is less than or equal to the capacity of the ordinary production channel, the general supply channel is utilised to fully account for the manufacturing process, but if the demand is greater than the capacity of the ordinary production channel, the contingency production channel would be activated along with the ordinary channel to satisfy the upcoming high demand. Besides, the reproductive property of the probability distribution is employed to represent the order quantity of the two types of demand. Accordingly, the optimal production rates and lot sizes for both channels are derived to provide managers with insights for further production planning.