Concave envelopes of monomial functions over rectangles

The construction of convex and concave envelopes of real‐valued functions has been of interest in mathematical programming for over 3 decades. Much of this interest stems from the fact that convex and concave envelopes can play important roles in algorithms for solving various discrete and continuous global optimization problems. In this article, we use a simplicial subdivision tool to present and validate the formula for the concave envelope of a monomial function over a rectangle. Potential algorithmic applications of this formula are briefly indicated. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A fluid queueing model for link travel time moments

We analyze the moments of the random time required for a vehicle to traverse a transportation network link of arbitrary length when its speed is governed by a random environment. The problem is motivated by stochastic transportation network applications in which the estimation of travel time moments is of great importance. We analyze this random time in a transient and asymptotic sense by employing results from the field of fluid queues. The results are demonstrated on two example problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Two‐dimensional failure modeling with minimal repair

In this paper, we discuss two‐dimensional failure modeling for a system where degradation is due to age and usage. We extend the concept of minimal repair for the one‐dimensional case to the two‐dimensional case and characterize the failures over a two‐dimensional region under minimal repair. An application of this important result to a manufacturer's servicing costs for a two‐dimensional warranty policy is given and we compare the minimal repair strategy with the strategy of replacement of failure. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Double Mover–Stayer model on customer switching in telecommunications industry

Customer acquisition and customer retention are the most important challenges in the increasingly competitive telecommunications industry. Traditional studies of customer switching always assume that customers are homogeneous, and thus that model customer switching behavior follows a Markov formulation. However, this postulation is obviously inappropriate in most instances. Blumen et al. (Cornell Studies of Industrial and Labor Relations, Cornell University Press, Ithaca, NY, 1955) developed the Mover–Stayer (MS) model, a generalization of the Markov chain model, to relax the requirement of homogeneity and allow the presence of heterogeneity with two different types of individuals—“stayers,” who purchase the same kinds of products or services throughout the entire observation period; and “movers,” who look for variety in products or services over time. There are two purpose of this article. First, we extend the MS model to a Double Mover‐Stayer (DMS) model by assuming the existence of three types of individuals in the market: (1) stable and loyal customers, who have stable usage within the same company; (2) instable but loyal customers, whose usage varies within the same company over time; and (3) disloyal customers, who switch from one company to another to seek for new experiences or/and benefits. We also propose an estimation method for the DMS model. Second, we apply the DMS model to telecommunications data and demonstrate how it can be used for pattern identification, hidden knowledge discovery, and decision making. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Aircraft routing under the risk of detection

The deterministic problem for finding an aircraft's optimal risk trajectory in a threat environment has been formulated. The threat is associated with the risk of aircraft detection by radars or similar sensors. The model considers an aircraft's trajectory in three‐dimensional (3‐D) space and represents the aircraft by a symmetrical ellipsoid with the axis of symmetry directing the trajectory. Analytical and discrete optimization approaches for routing an aircraft with variable radar cross‐section (RCS) subject to a constraint on the trajectory length have been developed. Through techniques of Calculus of Variations, the analytical approach reduces the original risk optimization problem to a vectorial nonlinear differential equation. In the case of a single detecting installation, a solution to this equation is expressed by a quadrature. A network optimization approach reduces the original problem to the Constrained Shortest Path Problem (CSPP) for a 3‐D network. The CSPP has been solved for various ellipsoid shapes and different length constraints in cases with several radars. The impact of ellipsoid shape on the geometry of an optimal trajectory as well as the impact of variable RCS on the performance of a network optimization algorithm have been analyzed and illustrated by several numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Vertically restrictive pricing in supply chains with price‐dependent demand

We examine the behavior of a manufacturer and a retailer in a decentralized supply chain under price‐dependent, stochastic demand. We model a retail fixed markup (RFM) policy, which can arise as a form of vertically restrictive pricing in a supply chain, and we examine its effect on supply chain performance. We prove the existence of the optimal pricing and replenishment policies when demand has a linear additive form and the distribution of the uncertainty component has a nondecreasing failure rate. We numerically compare the relative performance of RFM to a price‐only contract and we find that RFM results in greater profit for the supply chain than the price‐only contract in a variety of scenarios. We find that RFM can lead to Pareto‐improving solutions where both the supplier and the retailer earn more profit than under a price‐only contract. Finally, we compare RFM to a buyback contract and explore the implications of allowing the fixed markup parameter to be endogenous to the model. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.