Classical models of service systems with rational and strategic customers assume queues to be either fully visible or invisible. In practice, however, most queues are only “partially visible” or “opaque”, in the sense that customers are not able to discern precise queue length upon arrival. This is because assessing queue length and associated delays require time, attention, and cognitive capacity which are all limited. Service firms may influence this information acquisition process through their choices of physical infrastructure and technology.
In this paper, we study rational queueing behavior when customers have limited time and attention. Following the theory of rational inattention, customers optimally select the type and amount of information to acquire and ignore any information that is not worth obtaining, trading off the benefits of information against its costs before deciding to join. We establish the existence and uniqueness of a customer equilibrium and delineate the impact of information costs. We show that although limited attention is advantageous for a firm in a congested system that customers value highly, it can be detrimental for less popular services that customers deem unrewarding. These insights remain valid when the firm optimally selects the price. We also discuss social welfare implications and provide prescriptive insights regarding information provision. Our framework naturally bridges visible and invisible queues, and can be extended to analyze richer customer behavior and complex queue structures, rendering it a valuable tool for service design.
We consider the financial hedging problem of a risk-sensitive firm whose operational cash flow is affected by both price and demand uncertainties. We assume that selling prices and demand arrival process are governed by an exogenous continuous stochastic price process which is assumed to be correlated with prices of
various products in financial markets. During the selling horizon, the firm dynamically invests in a financial
portfolio of these products to manage its exposure to price and demand risks by observing the current inventory, wealth and price levels. We explore the problem in a minimum-variance framework where we look for the variance minimizing financial hedge for a given operational inventory policy. The framework leads to explicit results for the optimal static and dynamic financial hedges in single period problems with complicated within-period dynamics. We also obtain characterizations of optimal dynamic hedges for multi-period problems using dynamic programming. We explore the risk reduction effects of minimum-variance financial hedges through numerical examples and show that significant risk reductions may be possible by using the right hedge.
We study the optimal inventory policy of a firm selling an item whose price is affected by an exogenous stochastic price process which consequently affects customer arrivals. This case is typical for retailers that operate in different currencies, or trade products consisting of commodities or components whose prices are subject to market fluctuations. We assume that there is a stochastic input price process for the inventory item which determines purchase and selling prices according to a general selling price function. We also assume that unit demands arrive according to a doubly-stochastic Poisson process which is modulated by the stochastic input price process. We analyze optimal ordering decisions for both backorder and lost-sale cases. We show that under certain conditions a price-dependent base stock policy is optimal. The models are then extended to a price-modulated compound Poisson demand case. We present a numerical study on the sensitivity of the optimal profits to various parameters of the operational setting and stochastic price process such as price volatility, customer sensitivity to price changes etc. In another numerical setup, we compare the model with a corresponding discrete-time benchmark model that ignores within period price fluctuations and present the optimality gap when using the benchmark model as an approximation.