Higher‐order Markov chain models for categorical data sequences*

In this paper we study higher‐order Markov chain models for analyzing categorical data sequences. We propose an efficient estimation method for the model parameters. Data sequences such as DNA and sales demand are used to illustrate the predicting power of our proposed models. In particular, we apply the developed higher‐order Markov chain model to the server logs data. The objective here is to model the users' behavior in accessing information and to predict their behavior in the future. Our tests are based on a realistic web log and our model shows an improvement in prediction. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

AN ENDOGENOUS GROWTH MODEL OF CAPITAL AND ARMS ACCUMULATION

This paper attempts to examine the effect of an anticipated foreign military threat on the steady‐state growth rate and the transitional behavior of the economy. The modeling strategy follows the Sandler and Hartley (1995 Sandler, T. and Hartley, K. 1995. The Economics of Defense, Cambridge: Cambridge University Press.  [Google Scholar]) and Dunne et al. (2005 Dunne, J.P., Smith, R.P. and Willenbockel, D. 2005. Models of military expenditure and growth: a critical review. Defence and Peace Economics, 16: 449–461. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) viewpoints to emphasize the role of national defense in affecting growth from the perspective of both the demand and the supply sides. We thus combine the public capital version of endogenous growth with a framework of competitive arms accumulation. It is found that the key factor determining the steady state and the transitional effects of a rise in the foreign military threat on the home weapon–capital ratio, the consumption–capital ratio, and the rate of economic growth, is the degree of relative risk aversion.     

TERRORIST THREATS AND TRANSITIONAL DYNAMICS IN AN OVERLAPPING GENERATIONS MODEL

Previous research has shown that the duration of a civil war is in part a function of how it ends: in government victory, rebel victory, or negotiated settlement. We present a model of how protagonists in a civil war choose to stop fighting. Hypotheses derived from this theory relate the duration of a civil war to its outcome as well as characteristics of the civil war and the civil war nation. Findings from a competing risk model reveal that the effects of predictors on duration vary according to whether the conflict ended in government victory, rebel victory, or negotiated settlement.     

Determining a threshold control policy for an imperfect production system with rework jobs

Consider a threshold control policy for an imperfect production system with only a work center handling both regular and rework jobs. An imperfect production system studied here, generates defect jobs by factors other than machine failures. A threshold control or (ω, s) policy sets the guideline for a work center to switch between regular and rework jobs. A production cycle begins with loading and processing of several batches of regular jobs with a lot size equal to s. The outcome of each completed regular job is an independent Bernoulli trial with three possibilities: good, rework, or scrap. Once the work center accumulates more than a threshold ω of rework jobs, it finishes the last batch of regular jobs and switches to rework jobs. The objective of this research is to find a threshold ω and a lot size s that maximize the average long‐term profit. The ultimate goal is to construct a simple algorithm to search for ω and s that can be implemented directly in production management systems, as a result of this work. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 273–301, 1999     

A branch‐and‐price approach for the stochastic generalized assignment problem

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014     

The impact of inventory information distortion due to customer order cancellations

In this paper we study the impact of cancellations of customer orders on an inventory system. We develop a periodic review (s, S) inventory model with Poisson demands, deterministic demand leadtimes and supply leadtimes. When no set up cost is present for replenishment, the behavior of the system cost can be studied analytically. For the case with a fixed set up cost, we derive the operating characteristics of the model via an embedded Markov chain analysis. Based on this, we formulate the total cost function and suggest a two‐phase approach to optimization. Our model can be used to compute cancellation fees and to evaluate the impacts of various conditions of cancellation. We find that cancellations, as major sources of inventory information distortion, increase total system costs, and the magnitude of the cost impact depends on the probability of cancellation and the expected cancellation time. Other relevant lessons and insights are also discussed. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 213–231, 1999     

Combined variance reduction techniques in fully sequential selection procedures

In the past several decades, many ranking‐and‐selection (R&S) procedures have been developed to select the best simulated system with the largest (or smallest) mean performance measure from a finite number of alternatives. A major issue to address in these R&S problems is to balance the trade‐off between the effectiveness (ie, making a correct selection with a high probability) and the efficiency (ie, using a small total number of observations). In this paper, we take a frequentist's point of view by setting a predetermined probability of correct selection while trying to reduce the total sample size, that is, to improve the efficiency but also maintain the effectiveness. In particular, in order to achieve this goal, we investigate combining various variance reduction techniques into the fully sequential framework, resulting in different R&S procedures with either finite‐time or asymptotic statistical validity. Extensive numerical experiments show great improvement in the efficiency of our proposed procedures as compared with several existing procedures.     

Markovian approximation for manufacturing systems of unreliable machines in tandem

This paper studies production planning of manufacturing systems of unreliable machines in tandem. The manufacturing system considered here produces one type of product. The demand is assumed to be a Poisson process and the processing time for one unit of product in each machine is exponentially distributed. A broken machine is subject to a sequence of repairing processes. The up time and the repairing time in each phase are assumed to be exponentially distributed. We study the manufacturing system by considering each machine as an individual system with stochastic supply and demand. The Markov Modulated Poisson Process (MMPP) is applied to model the process of supply. Numerical examples are given to demonstrate the accuracy of the proposed method. We employ (s, S) policy as production control. Fast algorithms are presented to solve the average running costs of the machine system for a given (s, S) policy and hence the approximated optimal (s, S) policy. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 65–78, 2001     

Heuristic algorithms for routing yard‐side equipment for minimizing loading times in container terminals

This paper discusses a method of routing yard‐side equipment during loading operations in container terminals. Both the route of yard‐side equipment (such as transfer cranes or straddle carriers) and the number of containers picked up at each yard‐bay is determined simultaneously. The objective of the problem in this paper is to minimize the total container‐handling time in a yard. The size of the search space can be greatly reduced by utilizing inherent properties of the optimal solution. An encoding method is introduced to represent solutions in the search space. A genetic algorithm and a beam search algorithm are suggested to solve the above problem. Numerical experiments have been conducted to compare the performances of the proposed heuristic algorithms against each other and against that of the optimal solution. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 498–514, 2003