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Optimal Price-Lead Time Menus for Queues with Customer Choice: Priorities, Pooling & Strategic Delay

How should a firm design a price-lead time menu and scheduling policy to maximize revenues from heterogeneous time-sensitive customers with private information about their preferences? We consider a queueing system with multiple customer types that differ in two dimensions, their valuations for instant delivery and their delay cost rates. The distinctive feature of our model is that the ranking of customer preferences depends on lead times: patient customers are willing to pay more for long lead times than impatient ones, and vice versa for speedier service. We provide necessary and sufficient conditions, in terms of the capacity, market size, and properties of the valuation-delay cost distribution, for three features of the optimal menu and segmentation: 1. Pooling types with different delay costs into a single class; 2. Pricing out the middle of the delay cost spectrum while serving both ends; and 3. Strategic delay to deliberately inflate lead times.