Dynamic pricing, scheduling, and order rejection of a multiclass omnichannel hybrid production system
Amir Alwan and Nasser Barjesteh
Abstract
Many production systems now fulfill demand through both walk-in and online channels, producing some goods to order and others to stock on shared capacity. Coordinating production, pricing, and admission across these channels and fulfillment modes is a central operational challenge in these systems. Motivated by such settings, we study joint dynamic pricing, scheduling, and order rejection in a multiclass omnichannel hybrid production system in which the firm offers make-to-order and make-to-stock goods through walk-in and online channels, with online customers selecting from multiple quote times for future pickup. Make-to-order goods incur earliness and tardiness costs, while make-to-stock goods incur holding and tardiness costs. Walk-in customers may abandon if their waiting time is excessive. We model this problem as a stochastic processing network and analyze it in the heavy-traffic regime, approximating the original control problem by a Brownian control problem. We then reduce it to an equivalent workload formulation and solve it in closed form. The optimal policy depends on the aggregate congestion in the system, with the workload space partitioned into three regions across which the structure of the policy changes. At moderate congestion, the firm exploits a scheduling buffer created by the quote times of the online classes, incurring no congestion cost. At low congestion, this scheduling buffer cannot be fully utilized, so earliness or holding costs are unavoidable, and the firm idles deliberately when these costs become excessive. At high congestion, the scheduling buffer is insufficient, so tardiness or abandonment costs are unavoidable, and the firm rejects orders when these costs become excessive. Pricing regulates congestion by adjusting demand in response to the system workload. Building on this structure, we propose three variants of a dynamic control policy that differ in their degree of pricing flexibility: fully dynamic, online-only dynamic, and static pricing. In a numerical study, we demonstrate that the proposed policy is effective and that both dynamic pricing and congestion-aware static pricing deliver significant gains. Moreover, dynamic pricing delivers the largest gains when demand is concentrated online or in make-to-stock goods. Notably, online-only dynamic pricing captures most of these gains, providing a practical entry point for firms seeking to implement dynamic pricing.