Optimal timing of switches between product sales for sports and entertainment tickets

Like airlines and hotels, sports teams and entertainment venues can benefit from revenue management efforts for their ticket sales. Teams and entertainment venues usually offer bundles of tickets early in their selling horizon and put single‐event tickets on sale at a later date; these organizations must determine the best time to offer individual tickets because both types of ticket sales consume the same fixed inventory. We model the optimal a priori timing decision for a seller with a fixed number of identical tickets to switch from selling the tickets as fixed bundles to individual tickets to maximize the revenue realized before the start of the performance season. We assume that bundle and single‐ticket customers each arrive according to independent, nonhomogeneous Markovian death processes with a linear death rate that can vary over time and that the benefit from selling a ticket in a package is higher than from selling the ticket individually. We characterize the circumstances in which it is optimal for the seller to practice mixed bundling and when the seller should only sell bundles or individual tickets, and we establish comparative statics for the optimal timing decision for the special case of constant customer arrival rates. We extend our analytical results to find the optimal time for offering two groups of tickets with high and low demand. Finally, we apply the timing model to a data set obtained from the sports industry. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Scheduling with earliest start and due date constraints on multiple machines

We consider the scheduling of n jobs on m identical machines when the jobs become available for processing at ready times a_i, a_i, ? 0, require d_i time units for processing and must be completed by times b_i for i = 1, 2, … n. The objective chosen is that of minimizing the total elapsed time to complete all jobs subject to the ready time and due date constraints, preemption is not allowed. We present a multi-stage solution algorithm for this problem that is based on an implicit enumeration procedure and also uses the labelling type algorithm which solves the problem when preemption is allowed.     

Air Power in the Six-Day War

In the aftermath of Israel's stunning victory over Egyptian, Jordanian and Syrian forces during the 1967 Six-Day War, accolades for the victory were often showered upon the Israeli Air Force (IAF). Indeed, many believed that it had been Israeli air power that had been the decisive element in the war by first eliminating the Arab air forces and then obliterating the Arab armies in turn. While the IAF did play an extremely important role in the fighting, it was not the decisive element of Israeli victory, and its impact was felt in very different ways from the common perception. Indeed, an appreciation of the true role of Israeli air power in the war reinforces both the importance of psychological factors in combat, and the ability of air forces to have a psychological impact disproportionate to their physical impact.     

The use of phase-type distributions in inventory-control models

This article investigates the use of phase-type distributions to model the demand process and the replenishment leadtimes in the standard reorder-point/order-quantity model of inventory control. Our main result is that the marginal distribution of leadtime demand has a discrete phase-type distribution with the same number of phases as the leadtime distribution, regardless of the complexity of the inter-demand times. This result leads to relatively tractable formulas for several standard performance criteria.     

Performance and properties of Q‐Statistic monitoring schemes

In this article, we study the Shewhart chart of Q statistics proposed for the detection of process mean shifts in start‐up processes and short runs. Exact expressions for the run‐length distribution of this chart are derived and evaluated using an efficient computational procedure. The procedure can be considerably faster than using direct simulation. We extend our work to analyze the practice of requiring multiple signals from the chart before responding, a practice sometimes followed with Shewhart charts. The results show that waiting to receive multiple signals severely reduces the probability of quickly detecting shifts in certain cases, and therefore may be considered a risky practice. Operational guidelines for practitioners implementing the chart are discussed. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Prices and quantities in the arms trade*

There are two main sources of information about the Arms Trade, SIPRI and ACDA. These two sources give very different pictures of the evolution of the market, primarily because their measures are designed to capture conceptually different features. Although they are both expressed in constant dollars, the SIPRI series is designed to be a volume index of physical transfers, the ACDA series a constant price value index. Thus in principle, the ratio of the ACDA to SIPRI series should provide an implicit price index of arms; though in practice there are many measurement problems. In this paper, we discuss the basis of these indices and show that the ratio, the implicit price, not only looks plausible in the light of the evolution of the market, but has a significant negative effect on the demand for arms imports in an econometric equation.