Exploiting market size in service systems

W e study a profit-maximizing firm providing a service to price and delay sensitive customers. We are interested in analyzing the scale economies inherent in such a system. In particular, we study how the firm's pricing and capacity decisions change as the scale, measured by the potential market for the service, increases. These decisions turn out to depend intricately on the form of the delay costs seen by the customers; we characterize these decisions up to the dominant order in the scale for both convex and concave delay costs. We show that when serving customers on a first-come, first-served basis, if the customers' delay costs are strictly convex, the firm can increase its utilization and extract profits beyond what it can do when customers' delay costs are linear. However, with concave delay costs, the firm is forced to decrease its utilization and makes less profit than in the linear case. While studying concave delay costs, we demonstrate that these decisions depend on the scheduling policy employed as well. We show that employing the last-come, first-served rule in the concave case results in utilization and profit similar to the linear case, regardless of the actual form of the delay costs

Optimization of Inventory and Capacity in Large-Scale Assembly Systems Using Extreme-Value Theory

High-tech systems are typically produced in two stages: (1) production of components using specialized equipment and staff and (2) system assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which results in costly delays. Companies hedge this risk by strategic investments in excess production capacity and in buffer inventories of components. To optimize these, it is crucial to characterize the relation between component shortage risk and capacity and inventory investments. We suppose that component production capacity and produce demand are normally distributed over finite time intervals, and we accordingly model the production system as a symmetric fork-join queueing network with N statistically identical queues with a common arrival process and independent service processes. Assuming a symmetric cost structure, we subsequently apply extreme value theory to gain analytic insights into this optimization problem. We derive several new results for this queueing network, notably that the scaled maximum of N steady-state queue lengths converges in distribution to a Gaussian random variable. These results translate into asymptotically optimal methods to dimension the system. Tests on a range of problems reveal that these methods typically work well for systems of moderate size

Control Mechanisms in Queueing Systems with Nonlinear Waiting Costs

In many queueing systems, customers have been observed to exhibit strategic behavior. Each customer gains a value when receiving a product or getting served and suffers when incurring a delay. We consider a nonlinear waiting cost function to capture the sensitivity of customers toward delay. We investigate customers' behavior and system manager's strategy in two different settings: (1) customers are served in a service system, or (2) they receive a product in a supply chain. In the first model, we study an unobservable queueing system. We consider that customers are impatient, and are faced with decision problems whether to join a service system upon arrival, and whether to remain or renege at a later time. The goal is to address two important elements of queueing analysis and control: (1) customer characteristics and behavior, and (2) queueing control. The literature on customer strategic behavior in queues predominately focuses on the effects of waiting time and largely ignores the mixed risk attitude of customer behavior. Empirical studies have found that customers’ risk attitudes, their anticipated time, and their wait time affect their decision to join or abandon a queue. To explore this relationship, we analyze the mixed risk attitude together with a non-linear waiting cost function that includes the degree of risk aversion. Considering this behavior, we analyze individuals' joint balking and reneging strategy and characterize socially optimal strategy. To determine the optimal queue control policy from a revenue-maximizer perspective, which induces socially optimal behavior and eliminates customer externalities, we propose a joint entrance-fee/abandonment-threshold mechanism. We show that using a pricing policy without abandonment threshold is not sufficient to induce socially optimal behavior and in many cases results in a profit lower than the maximum social welfare the system can generate. Also, considering both customer characteristics and queue control policy, our findings suggest that customers with a moderate anticipation time provide higher expected revenue, acknowledging the importance of understanding customer behavior with respect to both wait time and risk attitude in the presence of anticipation time. In the second model, we consider a two-echelon production inventory system with a single manufacturer and a single distribution center (DC) where the manufacturer has a finite production capacity. There is a positive transportation time between the manufacturer and the DC. Each customer gains a value when receiving the product and suffers a waiting cost when incurring a delay. We assume that customers' waiting cost depends on their degree of impatience with respect to delay (delay sensitivity). We consider a nonlinear waiting cost function to show the degree of risk aversion (impatience intensity) of customers. We assume that customers follow the strategy p where they join the system and place an order with probability p. We analyze the inventory system with a base-stock policy in both the DC and the manufacturer. Since customers and supply chain holder are strategic, we study the Stackelberg equilibrium assuming that the DC acts as a Stackelberg leader and customers are the followers. We first obtain the total expected revenue and then derive the optimal base-stock level as well as the optimal price at the DC

Exploiting Market Size in Service Systems

We study a profit-maximizing firm providing a service to price and delay sensitive customers. We are interested in analyzing the scale economies inherent in such a system. In particular, we study how the firm's pricing and capacity decisions change as the scale, measured by the potential market for the service, increases. These decisions turn out to depend intricately on the form of the delay costs seen by the customers; we characterize these decisions up to the dominant order in the scale for both convex and concave delay costs. We show that when serving customers on a first-come, first-served basis, if the customers' delay costs are strictly convex, the firm can increase its utilization and extract profits beyond what it can do when customers' delay costs are linear. However, with concave delay costs, the firm is forced to decrease its utilization and makes less profit than in the linear case. While studying concave delay costs, we demonstrate that these decisions depend on the scheduling policy employed as well. We show that employing the last-come, first-served rule in the concave case results in utilization and profit similar to the linear case, regardless of the actual form of the delay costs.service systems, pricing, capacity planning, large market size, nonlinear delay costs, convex delay costs