The conditional p-center problem in the plane

An algorithm is given for the conditional p-center problem, namely, the optimal location of one or more additional facilities in a region with given demand points and one or more preexisting facilities. The solution dealt with here involves the minimax criterion and Euclidean distances in two-dimensional space. The method used is a generalization to the present conditional case of a relaxation method previously developed for the unconditional p-center problems. Interestingly, its worst-case complexity is identical to that of the unconditional version, and in practice, the conditional algorithm is more efficient. Some test problems with up to 200 demand points have been solved. © 1993 John Wiley & Sons, Inc.     

A network reformulation of an electric utility expansion planning model

We reformulate a multiperiod capacity expansion model of electric utilities as a network model. We show how to reconstruct the dual solution of the original mathematical program from the network model solution. To formulate the network model, we use information about the properties of the optimal solution of the mathematical program to reduce the number of constraints. The remaining constraints are then readily converted into network constraints. © 1993 John Wiley & Sons. Inc.     

General models for the supplier's all-unit quantity discount policy

The purpose of this article is to investigate some managerial insights related to using the all-unit quantity discount policies under various conditions. The models developed here are general treatments that deal with four major issues: (a) one buyer or multiple buyers, (b) constant or price-elastic demand, (c) the relationship between the supplier's production schedule or ordering policy and the buyers' ordering sizes, and (d) the supplier either purchasing or manufacturing the item. The models are developed with two objectives: the supplier's profit improvement or the supplier's increased profit share analysis. Algorithms are developed to find optimal decision policies. Our analysis provides the supplier with both the optimal all-unit quantity discount policy and the optimal production (or ordering) strategy. Numerical examples are provided. © 1993 John Wiley & Sons. Inc.     

Decomposition-based approximation algorithms for the one-warehouse multi-retailer problem with concave batch order costs

We study the one-warehouse multi-retailer problem under deterministic dynamic demand and concave batch order costs, where order batches have an identical capacity and the order cost function for each facility is concave within the batch. Under appropriate assumptions on holding cost structure, we obtain lower bounds via a decomposition that splits the two-echelon problem into single-facility subproblems, then propose approximation algorithms by judiciously recombining the subproblem solutions. For piecewise linear concave batch order costs with a constant number of slopes we obtain a constant-factor approximation, while for general concave batch costs we propose an approximation within a logarithmic factor of optimality. We also extend some results to subadditive order and/or holding costs.     

Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems

We consider the classical problem of whether certain classes of lifetime distributions are preserved under the formation of coherent systems. Under the assumption of independent and identically distributed (i.i.d.) component lifetimes, we consider the NBUE (new better than used in expectation) and NWUE (new worse than used in expectation) classes. First, a necessary condition for a coherent system to preserve the NBUE class is given. Sufficient conditions are then obtained for systems satisfying this necessary condition. The sufficient conditions are satisfied for a collection of systems which includes all parallel systems, but the collection is shown to be strictly larger. We also prove that no coherent system preserves the NWUE class. As byproducts of our study, we obtain the following results for the case of i.i.d. component lifetimes: (a) the DFR (decreasing failure rate) class is preserved by no coherent systems other than series systems, and (b) the IMRL (increasing mean residual life) class is not preserved by any coherent systems. Generalizations to the case of dependent component lifetimes are briefly discussed.     

On gamma estimation via matrix kriging

In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.     

Path optimization for the resource‐constrained searcher

We formulate and solve a discrete‐time path‐optimization problem where a single searcher, operating in a discretized three‐dimensional airspace, looks for a moving target in a finite set of cells. The searcher is constrained by maximum limits on the consumption of one or more resources such as time, fuel, and risk along any path. We develop a specialized branch‐and‐bound algorithm for this problem that uses several network reduction procedures as well as a new bounding technique based on Lagrangian relaxation and network expansion. The resulting algorithm outperforms a state‐of‐the‐art algorithm for solving time‐constrained problems and also is the first algorithm to solve multi‐constrained problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal service rates of a service facility with perishable inventory items

In this paper we optimally control service rates for an inventory system of service facilities with perishable products. We consider a finite capacity system where arrivals are Poisson‐distributed, lifetime of items have exponential distribution, and replenishment is instantaneous. We determine the service rates to be employed at each instant of time so that the long‐run expected cost rate is minimized for fixed maximum inventory level and capacity. The problem is modelled as a semi‐Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several numerical examples which provide insight to the behavior of the system are presented. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 464–482, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10021     

Two‐stage component test plans for testing the reliability of a series system

A system reliability is often evaluated by individual tests of components that constitute the system. These component test plans have advantages over complete system based tests in terms of time and cost. In this paper, we consider the series system with n components, where the lifetime of the i‐th component follows exponential distribution with parameter λ_i. Assuming test costs for the components are different, we develop an efficient algorithm to design a two‐stage component test plan that satisfies the usual probability requirements on the system reliability and in addition minimizes the maximum expected cost. For the case of prior information in the form of upper bounds on λ_i's, we use the genetic algorithm to solve the associated optimization problems which are otherwise difficult to solve using mathematical programming techniques. The two‐stage component test plans are cost effective compared to single‐stage plans developed by Rajgopal and Mazumdar. We demonstrate through several numerical examples that our approach has the potential to reduce the overall testing costs significantly. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 95–116, 2002; DOI 10.1002/nav.1051     

Threshold optimization for weighted voting classifiers

Weighted voting classifiers considered in this paper consist of N units each providing individual classification decisions. The entire system output is based on tallying the weighted votes for each decision and choosing the one which has total support weight exceeding a certain threshold. Each individual unit may abstain from voting. The entire system may also abstain from voting if no decision support weight exceeds the threshold. Existing methods of evaluating the reliability of weighted voting systems can be applied to limited special cases of these systems and impose some restrictions on their parameters. In this paper a universal generating function method is suggested which allows the reliability of weighted voting classifiers to be exactly evaluated without imposing constraints on unit weights. Based on this method, the classifier reliability is determined as a function of a threshold factor, and a procedure is suggested for finding the threshold which minimizes the cost of damage caused by classifier failures (misclassification and abstention may have different price.) Dynamic and static threshold voting rules are considered and compared. A method of analyzing the influence of units' availability on the entire classifier reliability is suggested, and illustrative examples are presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 322–344, 2003.