Dynamic pricing and production control in a two-item make-to-stock system with flexible dual sourcing and lost sales

We consider a joint control of pricing and production in a two-item inventory system, where each item can be produced by its dedicated source or a shared flexible source, under the lost-sales setting. The demands of the two items are correlated. Due to the complexity caused by the lost-sales assumption and the interplay between pricing and production decisions, we show the optimal value function satisfies five structural properties under certain conditions. The optimal ordering and pricing policies are then fully characterized by five production curves and two pricing functions. Different from existing literature, we show that the optimal price path may not be monotone in the inventory level of either item. Next, we estimate the value of flexibility by comparing two systems, one with the flexible source only and the other with the dedicated source only, and show that the value of flexibility is positive (or negative) if the flexible source has a faster (or slower) production rate and a lower (or higher) production cost. Through numerical experiments, we find that in most cases flexibility and dynamic pricing are substitutes except for a few exceptions; and product substitution can either increase or decrease the value of flexibility.