Enhancing Make-to-Order Manufacturing Agility: When Flexible Capacity Meets Dynamic Pricing

The rise of online marketplaces has raised customer expectations regarding customization and lead time. It poses significant challenges to manufacturing firms and prompts a move from make-to-stock to a more flexible make-to-order system. Compared to make-to-stock settings, make-to-order systems cannot smooth fluctuations in demand using available stock. While viewing dynamic pricing as a useful strategy to balance supply with demand, many manufacturing firms can also create capacity flexibility. In that scenario, system costs could be cut by managing capacity and demand simultaneously. In this paper, we consider a make-to-order production environment with base and surge capacity as well as the ability to adjust product pricing. Our main focus is on operational decision-making, assuming that the base capacity and surge capacity are fixed, but activating the surge capacity incurs a setup cost. Initially, we propose a stochastic control model to reflect this complex decision problem. However, our initial model leads to an intractable dynamic programming problem. To overcome this, we convert the problem to a more tractable diffusion control problem. This approach helps to reveal the conditions under which utilizing flexible capacity is more advantageous than relying solely on fixed capacity. When flexible capacity is advantageous, we provide a solution to the diffusion control problem that can guide optimal capacity and price adjustments. We discover an interesting interplay between capacity adjustment and dynamic pricing. In particular, we find that the price, which aims at reducing congestion, may not monotonically increase with the congestion level when capacity adjustments incur a fixed cost.