Fluid Approximations for Revenue Management

When one encounters a stochastic optimization/control problem, one popular approach is to transform it into a deterministic problem by fluid approximation. The following highly-cited classic papers illustrate the applications of this approach:   

1. G. Gallego and G. van Ryzin. Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Science 40(8) 999–1020, 1994.
2. J.G. Dai, On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models, The Annals of Applied Probability, 5 (1), 49-77, 1995.

Motivated by a publicly available dataset from an online electronics retailer at Kaggle (*), the demand has high variance as shown in Figure 1 of the following paper. The traditional fluid approximation is not asymptotically tight as the resource capacities get large as demonstrated in Section 3. The authors introduce the universal fluid approximation in Section 4, prove its asymptotical tightness in Section 5, and show its performance improvement of an airline network over the traditional approach in Section 6.  

Y. Bai, O. El Housni, B. Jin, P. Rusmevichientong, H. Topaloglu, and D. P. Williamson, Fluid Approximations for Revenue Management under High-Variance Demand, Management Science, Vol. 69, No. 7, pp. 4016-4026, 2023.

(*) Kaggle. 2021. E-commerce purchase history from an electronics store. Last checked: May 30, 2022. URL https: //www.kaggle.com/datasets/mkechinov/ecommerce-purchase-history-from-electronics-store.