Ramandeep S. Randhawa

Optimal Flexibility Configurations in Newsvendor Networks: Going Beyond Chaining and Pairing

We study the classical problem of capacity and flexible technology selection with a newsvendor network model of resource portfolio investment. The resources differ by their level of flexibility, where “level-k flexibility” refers to the ability to process k different product types. We present an exact set-theoretic methodology to analyze newsvendor networks with multiple products and parallel resources. This simple approach is sufficiently powerful to prove that (i) flexibility exhibits decreasing returns and (ii) the optimal portfolio will invest in at most two, adjacent levels of flexibility in symmetric systems, and to characterize (iii) the optimal flexibility configuration for asymmetric systems as well. The optimal flexibility configuration can serve as a theoretical performance benchmark for other configurations suggested in the literature. For example, although chaining is not optimal in our setting, the gap is small and the inclusion of scale economies quickly favors chaining over pairing. We also demonstrate how this methodology can be applied to other settings such as product substitution and queuing systems with parameter uncertainty.

Capacity Sizing Under Parameter Uncertainty: Safety Staffing Principles Revisited

We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the model is that the mean arrival rate of work is random (in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity prescriptions, and relates these to well established rules-of-thumb such as the square-root safety staffing principle. We establish a simple and intuitive relationship between the incoming load (measured in Erlangs) and the extent of uncertainty in arrival rates (measured via the coefficient of variation) that characterizes the extent to which uncertainty dominates stochastic variability or vice versa. In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.

A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

We analytically study optimal capacity and flexible technology selection in parallel queuing systems. We consider N stochastic arrival streams that may wait in N queues before being processed by one of many resources technologies that differ in their flexibility. A resources ability to process k different arrival types or classes is referred to as level-k flexibility. We determine the capacity portfolio consisting of all resources at all levels of flexibility that minimizes linear capacity and linear holding costs in high-volume systems where the arrival rate λ → ∞. We prove that “a little flexibility is all you need”: the optimal portfolio invests Oλ in specialized resources and only O√λ in flexible resources and these optimal capacity choices bring the system into heavy traffic. Further, considering symmetric systems with type-independent parameters, a novel “folding” methodology allows the specification of the asymptotic queue count process for any capacity portfolio under longest-queue scheduling in closed form that is amenable to optimization. This allows us to sharpen “a little flexibility is all you need”: the asymptotically optimal flexibility configuration for symmetric systems with mild economies of scope invests a lot in specialized resources but only a little in flexible resources and only in level-2 flexibility, but effectively nothing o√λ in level-k > 2 flexibility. We characterize “tailored pairing” as the theoretical benchmark configuration that maximizes the value of flexibility when demand and service uncertainty are the main concerns.

Dynamics of New Product Introduction in Closed Rental Systems

We study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of reusable products. The online DVD rental firm Netflix provides the motivation. We assume that rental durations of each user are independent and identically distributed with finite mean. We study transient behavior in this system following the introduction of a new product that is desired by all the users. We represent the usage process for this new product in terms of an empirical distribution. This allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound, via appropriate versions of Glivenko-Cantelli and Donskers theorems. Analyzing the usage process, we demonstrate that an increase in the variability of the rental duration distribution can actually help the firm by allowing it to set lower capacity levels to provide a desired quality of service. Further, we show that the firm is better off not imposing any deadlines for the return of the product.

Pricing in Queues Without Demand Information

We consider revenue and social optimization in an M/M/1 queue with price and delay sensitive customers, and study the performance of uninformed pricing that does not require any arrival rate information. We formally characterize the optimal uninformed price and its performance relative to pricing with precise arrival rate knowledge. For uniformly distributed customer valuations, under a large set of parameters, we find that uninformed prices can capture more than 99% of the optimal revenue and more than 85% of the optimal social welfare. We further prove that the performance of uninformed prices improves as the customers become more delay sensitive and is always better under revenue optimization compared with social optimization.

Accuracy of fluid approximations for queueing systems with congestion-sensitive demand and implications for capacity sizing

We study the accuracy of fluid approximations in single- and many-server queueing systems in which the arrival rate depends on the congestion in the system. If the potential demand rate exceeds the systems capacity, the fluid approximations are found to exhibit O(1)-accuracy --- their error does not increase with system size. These fluid approximations are used to solve two capacity sizing problems: minimizing total system cost and maximizing social welfare. We find that the solutions to both these problems exhibit interesting differences, and further that under some conditions, the fluid prescriptions exhibit o(1)-optimality, that is, their optimality gap is asymptotically zero.

Near-Optimality of Coarse Service Grades for Customer Differentiation in Queueing Systems

We analyze a service firm that caters to price and delay sensitive customers who are differentiated on both their value for the service and the cost of waiting. There is a continuum of customer types in our setting and we model each customers cost of waiting to be linear in the delay incurred with a multiplier that is an increasing linear or sub-linear function of the customers value for the service. Using a large system approach, we characterize the firms revenue maximizing menu of price and delay quotations and the value of customer differentiation. We further characterize the value of offering coarse or few service grades and find that offering two service grades is asymptotically optimal on the typical square-root scale, relative to the optimal policy.

Designing flexible systems using a new notion of submodularity

Abstract We study the problem of optimal flexibility capacity portfolio selection by introducing a new notion of submodularity for correspondences, which extends the classical notion of submodular functions. In particular, we prove that the correspondence that maps flexible resources to the set of demands that they can process is submodular, and use the properties of submodular correspondences to compare different flexibility configurations and derive insights into the optimal capacity portfolio.

Dynamic Pricing for Heterogeneous Time-Sensitive Customers

A core problem in the area of revenue management is pricing goods in the presence of strategic customers. We study this problem when customers are heterogeneous with respect to their initial valuations for the item and their time sensitivities, i.e., the customers differ in both their initial valuations and the rates at which their initial valuation decreases with delay in purchase. We characterize the optimal mechanism for selling durable goods in such environments and show that delayed allocation and dynamic pricing can be effective screening tools for maximizing firm profit. We also investigate the impact of production and holding costs on the optimal mechanism.

Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems

Problem definition: We study optimal scheduling of customers in service systems, such as call centers. In such systems, customers typically hang up and abandon the system if their wait for service is too long. Such abandonments are detrimental for the system, and so managers typically use scheduling as a tool to mitigate it. In this paper, we study the interplay between customer impatience and scheduling decisions when managing heterogeneous customer classes. Academic/practical relevance: Call centers constitute a large industry that has a global spending of around