Coordination of pricing and inventory control across products

We consider the joint pricing and inventory‐control problem for a retailer who orders, stocks, and sells two products. Cross‐price effects exist between the two products, which means that the demand of each product depends on the prices of both products. We derive the optimal pricing and inventory‐control policy and show that this policy differs from the base‐stock list‐price policy, which is optimal for the one‐product problem. We find that the retailer can significantly improve profits by managing the two products jointly as opposed to independently, especially when the cross‐price demand elasticity is high. We also find that the retailer can considerably improve profits by using dynamic pricing as opposed to static pricing, especially when the demand is nonstationary. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Optimizing fishbone aisles for dual‐command operations in a warehouse

Unit‐load warehouses store and retrieve unit‐loads, typically pallets. When storage and retrieval operations are not coordinated, travel is from a pickup and deposit (P&D) point to a pallet location and back again. In some facilities, workers interleave storage and retrieval operations to form a dual‐command cycle. Two new aisle designs proposed by Gue and Meller (“Improving the unit‐load warehouse.” In Progress in Material Handling Research: 2006. Material Handling Industry of America, Charlotte, NC, 2006) use diagonal aisles to reduce the travel distance to a single pallet location by approximately 10 and 20[percnt] for the two designs, respectively. We develop analytical expressions for travel between pallet locations for one of these—the fishbone design. We then compare fishbone warehouses that have been optimized for dual‐command to traditional warehouses that have been optimized in the same manner, and show that an optimal fishbone design reduces dual‐command travel by 10–15%. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 54: 389–403, 2009     

Consecutive k‐within‐m‐out‐of‐n:F system with exchangeable components

As a generalization of k‐out‐of‐n:F and consecutive k‐out‐of‐n:F systems, the consecutive k‐within‐m‐out‐of‐n:F system consists of n linearly ordered components such that the system fails iff there are m consecutive components which include among them at least k failed components. In this article, the reliability properties of consecutive k‐within‐m‐out‐of‐n:F systems with exchangeable components are studied. The bounds and approximations for the survival function are provided. A Monte Carlo estimator of system signature is obtained and used to approximate survival function. The results are illustrated and numerics are provided for an exchangeable multivariate Pareto distribution. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Dynamic signatures and their use in comparing the reliability of new and used systems

The signature of a system with independent and identically distributed (i.i.d.) component lifetimes is a vector whose ith element is the probability that the ith component failure is fatal to the system. System signatures have been found to be quite useful tools in the study and comparison of engineered systems. In this article, the theory of system signatures is extended to versions of signatures applicable in dynamic reliability settings. It is shown that, when a working used system is inspected at time t and it is noted that precisely k failures have occurred, the vector s [0,1]^n‐k whose jth element is the probability that the (k + j)th component failure is fatal to the system, for j = 1,2,2026;,n ‐ k, is a distribution‐free measure of the design of the residual system. Next, known representation and preservation theorems for system signatures are generalized to dynamic versions. Two additional applications of dynamic signatures are studied in detail. The well‐known “new better than used” (NBU) property of aging systems is extended to a uniform (UNBU) version, which compares systems when new and when used, conditional on the known number of failures. Sufficient conditions are given for a system to have the UNBU property. The application of dynamic signatures to the engineering practice of “burn‐in” is also treated. Specifically, we consider the comparison of new systems with working used systems burned‐in to a given ordered component failure time. In a reliability economics framework, we illustrate how one might compare a new system to one successfully burned‐in to the kth component failure, and we identify circumstances in which burn‐in is inferior (or is superior) to the fielding of a new system. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

In urban rail transit systems of large cities, the headway and following distance of successive trains have been compressed as much as possible to enhance the corridor capacity to satisfy extremely high passenger demand during peak hours. To prevent train collisions and ensure the safety of trains, a safe following distance of trains must be maintained. However, this requirement is subject to a series of complex factors, such as the uncertain train braking performance, train communication delay, and driver reaction time. In this paper, we propose a unified mathematical framework to analyze the safety‐oriented reliability of metro train timetables with different corridor capacities, that is, the train traffic density, and determine the most reliable train timetable for metro lines in an uncertain environment. By employing a space‐time network representation in the formulations, the reliability‐based train timetabling problem is formulated as a nonlinear stochastic programming model, in which we use 0‐1 variables to denote the time‐dependent velocity and position of all involved trains. Several reformulation techniques are developed to obtain an equivalent mixed integer programming model with quadratic constraints (MIQCP) that can be solved to optimality by some commercial solvers. To improve the computational efficiency of the MIQCP model, we develop a dual decomposition solution framework that decomposes the primal problem into several sets of subproblems by dualizing the coupling constraints across different samples. An exact dynamic programming combined with search space reduction strategies is also developed to solve the exact optimal solutions of these subproblems. Two sets of numerical experiments, which involve a relatively small‐scale case and a real‐world instance based on the operation data of the Beijing subway Changping Line are implemented to verify the effectiveness of the proposed approaches.     

Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work

We consider the problem of scheduling n independent and simultaneously available jobs without preemption on a single machine, where the machine has a fixed maintenance activity. The objective is to find the optimal job sequence to minimize the total amount of late work, where the late work of a job is the amount of processing of the job that is performed after its due date. We first discuss the approximability of the problem. We then develop two pseudo‐polynomial dynamic programming algorithms and a fully polynomial‐time approximation scheme for the problem. Finally, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 172–183, 2016     

Validation of a strategy for harbor defense based on the use of a min‐max algorithm receding horizon control law

We present a validation of a centralized feedback control law for robotic or partially robotic water craft whose task is to defend a harbor from an intruding fleet of water craft. Our work was motivated by the need to provide harbor defenses against hostile, possibly suicidal intruders, preferably using unmanned craft to limit potential casualties. Our feedback control law is a sample‐data receding horizon control law, which requires the solution of a complex max‐min problem at the start of each sample time. In developing this control law, we had to deal with three challenges. The first was to develop a max‐min problem that captures realistically the nature of the defense‐intrusion game. The second was to ensure the solution of this max‐min problem can be accomplished in a small fraction of the sample time that would be needed to control a possibly fast moving craft. The third, to which this article is dedicated, was to validate the effectiveness of our control law first through computer simulations pitting a computer against a computer or a computer against a human, then through the use of model hovercraft in a laboratory, and finally on the Chesapeake Bay, using Yard Patrol boats. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 247–259, 2016     

Approximations for heavily loaded G/GI/n + GI queues

Motivated by applications to service systems, we develop simple engineering approximation formulas for the steady‐state performance of heavily loaded G/GI/n+GI multiserver queues, which can have non‐Poisson and nonrenewal arrivals and non‐exponential service‐time and patience‐time distributions. The formulas are based on recently established Gaussian many‐server heavy‐traffic limits in the efficiency‐driven (ED) regime, where the traffic intensity is fixed at ρ > 1, but the approximations also apply to systems in the quality‐and‐ED regime, where ρ > 1 but ρ is close to 1. Good performance across a wide range of parameters is obtained by making heuristic refinements, the main one being truncation of the queue length and waiting time approximations to nonnegative values. Simulation experiments show that the proposed approximations are effective for large‐scale queuing systems for a significant range of the traffic intensity ρ and the abandonment rate θ, roughly for ρ > 1.02 and θ > 2.0. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 187–217, 2016     

On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes

This article studies coherent systems of heterogenous and statistically dependent components' lifetimes. We present a sufficient and necessary condition for a stochastically longer system lifetime resulted by allocating a single active redundancy. For exchangeable components' lifetimes, allocating the redundancy to the component with more minimal path sets is proved to produce a more reliable system, and for systems with stochastic arrangement increasing components' lifetimes and symmetric structure with respect to two components, allocating the redundancy to the weaker one brings forth a larger reliability. Several numerical examples are presented to illustrate the theoretical results as well. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 335–345, 2016     

Approximation algorithms for sequential batch‐testing of series systems

We introduce and study a generalization of the classic sequential testing problem, asking to identify the correct state of a given series system that consists of independent stochastic components. In this setting, costly tests are required to examine the state of individual components, which are sequentially tested until the correct system state can be uniquely identified. The goal is to propose a policy that minimizes the expected testing cost, given a‐priori probabilistic information on the stochastic nature of each individual component. Unlike the classic setting, where variables are tested one after the other, we allow multiple tests to be conducted simultaneously, at the expense of incurring an additional set‐up cost. The main contribution of this article consists in showing that the batch testing problem can be approximated in polynomial time within factor , for any fixed . In addition, we explain how, in spite of its highly nonlinear objective function, the batch testing problem can be formulated as an approximate integer program of polynomial size, while blowing up its expected cost by a factor of at most . Finally, we conduct extensive computational experiments, to demonstrate the practical effectiveness of these algorithms as well as to evaluate their limitations. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 275–286, 2016