Analysis of supply contracts with commitments and flexibility

In this article we address an important class of supply contracts called the Rolling Horizon Flexibility (RHF) contracts. Under such a contract, at the beginning of the horizon a buyer has to commit requirements for components for each period into the future. Usually, a supplier provides limited flexibility to the buyer to adjust the current order and future commitments in a rolling horizon manner. We present a general model for a buyer's procurement decision under RHF contracts. We propose two heuristics and derive a lower bound. Numerically, we demonstrate the effectiveness of the heuristics for both stationary and non‐stationary demands. We show that the heuristics are easy to compute, and hence, amenable to practical implementation. We also propose two measures for the order process that allow us to (a) evaluate the effectiveness of RHF contracts in restricting the variability in the orders, and (b) measure the accuracy of advance information vis‐a‐vis the actual orders. Numerically we demonstrate that the order process variability decreases significantly as flexibility decreases without a dramatic increase in expected costs. Our numerical studies provide several other managerial insights for the buyer; for example, we provide insights into how much flexibility is sufficient, the value of additional flexibility, the effect of flexibility on customer satisfaction (as measured by fill rate), etc. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Dynamic service rate control for a single‐server queue with Markov‐modulated arrivals

We consider the problem of service rate control of a single‐server queueing system with a finite‐state Markov‐modulated Poisson arrival process. We show that the optimal service rate is nondecreasing in the number of customers in the system; higher congestion levels warrant higher service rates. On the contrary, however, we show that the optimal service rate is not necessarily monotone in the current arrival rate. If the modulating process satisfies a stochastic monotonicity property, the monotonicity is recovered. We examine several heuristics and show where heuristics are reasonable substitutes for the optimal control. None of the heuristics perform well in all the regimes and the fluctuation rate of the modulating process plays an important role in deciding the right heuristic. Second, we discuss when the Markov‐modulated Poisson process with service rate control can act as a heuristic itself to approximate the control of a system with a periodic nonhomogeneous Poisson arrival process. Not only is the current model of interest in the control of Internet or mobile networks with bursty traffic, but it is also useful in providing a tractable alternative for the control of service centers with nonstationary arrival rates. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 661–677, 2013     

An application of yield management for Internet Service Providers

In this paper we study strategies for better utilizing the network capacity of Internet Service Providers (ISPs) when they are faced with stochastic and dynamic arrivals and departures of customers attempting to log‐on or log‐off, respectively. We propose a method in which, depending on the number of modems available, and the arrival and departure rates of different classes of customers, a decision is made whether to accept or reject a log‐on request. The problem is formulated as a continuous time Markov Decision Process for which optimal policies can be readily derived using techniques such as value iteration. This decision maximizes the discounted value to ISPs while improving service levels for higher class customers. The methodology is similar to yield management techniques successfully used in airlines, hotels, etc. However, there are sufficient differences, such as no predefined time horizon or reservations, that make this model interesting to pursue and challenging. This work was completed in collaboration with one of the largest ISPs in Connecticut. The problem is topical, and approaches such as those proposed here are sought by users. © 2001 John Wiley & Sons, Inc., Naval Research Logistics 48:348–362, 2001