This paper studies alternative price-service mechanisms for a provider that serves customers whose delay cost depends on their service valuations. We propose a generalized delay cost structure that augments the standard additive model with a multiplicative component, capturing the interdependence between delay cost and values. We derive and compare the revenue-maximizing and socially optimal equilibria under uniform pricing, preemptive, and nonpreemptive priority auctions with an admission price. We find that the delay cost structure has a paramount effect on system behavior. The classical result that the revenue-maximizing admission price is higher and the utilization lower than is socially optimal can be reversed under our generalized structure, and we identify the conditions driving this reversal under each mechanism. We show that the conditional bid equilibria are unique and induce the socially optimal allocations. The auctions yield gains in system net value and provider profit over uniform pricing, which are dramatically larger for the preemptive mechanism. Both auctions perform better under multiplicative compared to additive delay costs. The highest-value customers always gain under the preemptive, but may lose under the nonpreemptive auction. The lowest-value customers always gain in either auction.auctions, congestion, delay cost, incentive compatibility, pricing, priority, queueing, quality of service, revenue management, scheduling, service differentiation
H ow 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 this question for a queueing system with two customer types and provide the following results. First, we develop a novel problem formulation and solution method that combines the achievable region approach with mechanism design. This approach extends to menu design problems for other systems. Second, the work conserving c priority rule, known to be delay cost minimizing, incentive-compatible, and socially optimal, need not be revenue maximizing. A strategic delay policy may be optimal: It prioritizes impatient customers, but artificially inflates the lead times of patient customers. This suggests a broader guideline: Revenue-maximizing firms that lack customer-level demand information should also consider customer incentives, not only operational constraints, in their scheduling policies. Third, we identify general necessary and sufficient conditions for optimal strategic delay: a price, a lead-time, and a segment-size condition. We translate these into demand and capacity parameter conditions for cases with homogeneous and heterogeneous valuations for each type. In some cases strategic delay is optimal if capacity is relatively abundant, in others if it is relatively scarce.
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 their valuations for instant delivery and their delay costs. The distinctive feature of our model is that the ranking of customer preferences depends on lead times: patient customers are willing to pay more than impatient customers for long lead times, and vice versa for speedier service. We provide necessary and sufficient conditions, in terms of the capacity, the market size, and the properties of the valuation-delay cost distribution, for three features of the optimal menu and segmentation: pricing out the middle of the delay cost spectrum while serving both ends, pooling types with different delay costs into a single class, and strategic delay to deliberately inflate lead times. This paper was accepted by Assaf Zeevi, stochastic models and simulation.
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