Optimal pricing and sequencing in a make-to-order system with batch demand

In this paper we consider the problem of jointly managing production sequencing and pricing in a two product manufacturing system where both products (type-1 and type-2) are made using the same resource. Type-1 product is made-to-order to fulfill contractual demand arriving according to a compound Poisson process. Type-2 product is also made-to-order but to fulfill demand arising in the open market where demand arrives according to a Poisson process that is a function of a price posted by the manufacturer. The objective of the manufacturer is to make production sequencing and pricing decisions that maximize the total expected discounted profit earned over an infinite time horizon. We characterize the optimal sequencing policy using a monotone threshold curve and the optimal pricing policy using monotone switching curves. We also conduct a sensitivity analysis to learn how the manufacturer's profitability and the optimal production sequencing and pricing policies are impacted by various problem parameters.