Coordinating Batch Production and Pricing of a Make-to-Stock Product

Consider a make-to-stock product that is produced in batches and sold in individual units. The production process is stochastic with its mean time controllable in a fixed range; and the product is sold at either a high price with a low demand or a low price with a high demand. Coordinating the dynamic adjustment of the production rate and the sale price is crucial for maximizing the total discounted profit. We derive in this note that, the optimal control of the production rate follows a critical stock policy and the optimal pricing follows a price-switch threshold policy, with both associated with the finished goods inventory.