Military spending and growth: a small open economy stochastic growth model

The paper analyzes the effects of military spending on economic growth in a small open stochastic endogenous growth model involving the supply-side and demand-side effects produced by military spending. We show that a rise in the military spending affects economic growth through four channels, including the crowding-out effect, the spin-off effect, the resource mobilization effect, and the portfolio effect. The net effect which depends on these four channels is ambiguous. Hence, we demonstrate that there exists an optimal defense burden that maximizes the economic growth rate.     

Note on “An Optimal Recursive Method for Various Inventory Replenishment Models with Increasing Demand and Shortages” by Teng et al.

In a recent paper, Teng, Chern, and Yang consider four possible inventory replenishment models and determine the optimal replenishment policies for them. They compare these models to identify the best alternative on the basis of minimum total relevant inventory costs. The total cost functions for Model 1 and Model 4 as derived by them are not exact for the comparison. As a result, their conclusion on the least expensive replenishment policy is incorrect. The present article provides the actual total costs for Model 1 and Model 4 to make a correct comparison of the four models. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 602–606, 2000     

Bayesian inference for a Lanchester type combat model

We undertake inference for a stochastic form of the Lanchester combat model. In particular, given battle data, we assess the type of battle that occurred and whether or not it makes any difference to the number of casualties if an army is attacking or defending. Our approach is Bayesian and we use modern computational techniques to fit the model. We illustrate our method using data from the Ardennes campaign. We compare our results with previous analyses of these data by Bracken and Fricker. Our conclusions are somewhat different to those of Bracken. Where he suggests that a linear law is appropriate, we show that the logarithmic or linear‐logarithmic laws fit better. We note however that the basic Lanchester modeling assumptions do not hold for the Ardennes data. Using Fricker's modified data, we show that although his “super‐logarithmic” law fits best, the linear, linear‐logarithmic, and logarithmic laws cannot be ruled out. We suggest that Bayesian methods can be used to make inference for battles in progress. We point out a number of advantages: Prior information from experts or previous battles can be incorporated; predictions of future casualties are easily made; more complex models can be analysed using stochastic simulation techniques. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 541–558, 2000     

An application of yield management for Internet Service Providers

In this paper we study strategies for better utilizing the network capacity of Internet Service Providers (ISPs) when they are faced with stochastic and dynamic arrivals and departures of customers attempting to log‐on or log‐off, respectively. We propose a method in which, depending on the number of modems available, and the arrival and departure rates of different classes of customers, a decision is made whether to accept or reject a log‐on request. The problem is formulated as a continuous time Markov Decision Process for which optimal policies can be readily derived using techniques such as value iteration. This decision maximizes the discounted value to ISPs while improving service levels for higher class customers. The methodology is similar to yield management techniques successfully used in airlines, hotels, etc. However, there are sufficient differences, such as no predefined time horizon or reservations, that make this model interesting to pursue and challenging. This work was completed in collaboration with one of the largest ISPs in Connecticut. The problem is topical, and approaches such as those proposed here are sought by users. © 2001 John Wiley & Sons, Inc., Naval Research Logistics 48:348–362, 2001     

The dynamic transshipment problem

We investigate the strategy of transshipments in a dynamic deterministic demand environment over a finite planning horizon. This is the first time that transshipments are examined in a dynamic or deterministic setting. We consider a system of two locations which replenish their stock from a single supplier, and where transshipments between the locations are possible. Our model includes fixed (possibly joint) and variable replenishment costs, fixed and variable transshipment costs, as well as holding costs for each location and transshipment costs between locations. The problem is to determine how much to replenish and how much to transship each period; thus this work can be viewed as a synthesis of transshipment problems in a static stochastic setting and multilocation dynamic deterministic lot sizing problems. We provide interesting structural properties of optimal policies which enhance our understanding of the important issues which motivate transshipments and allow us to develop an efficient polynomial time algorithm for obtaining the optimal strategy. By exploring the reasons for using transshipments, we enable practitioners to envision the sources of savings from using this strategy and therefore motivate them to incorporate it into their replenishment strategies. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:386–408, 2001     

Lateral stock transshipments in a two‐location inventory system with fixed and joint replenishment costs

We address the problem of inventory management in a two‐location inventory system, in which the transshipments are carried out as means of emergency or alternative supply after demand has been realized. This model differs from previous ones as regards its replenishment costs structure, in which nonnegligible fixed replenishment costs and a joint replenishment cost are considered. The single period planning horizon is analyzed, with the form and several properties of the optimal replenishment and transshipment policies developed, discussed and illustrated. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 525–547, 1999     

Economic design of a two-stage control chart based on both performance and surrogate variables

The traditional approach to economic design of control charts is based on the assumption that a process is monitored using only a performance variable. If, however, the performance variable is costly to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled by using both performance and surrogate variables. In this article we propose a model for economic design of a two-stage control chart which uses a highly correlated surrogate variable together with a performance variable. The process is assumed to be monitored by the surrogate variable until it signals out-of-control behavior, then by the performance variable until it signals out-of-control behavior or maintains in-control signals for a prespecified amount of time, and the two variables are used in alternating fashion. An algorithm based on the direct search method of Hooke and Jeeves [6] is used to find the optimum values of design parameters. The proposed model is applied to the end-closure welding process for nuclear fuel to compute the amount of reduction in cost compared with the current control procedure. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 958–977, 1999     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

Decomposition algorithms for the maximum-weight connected graph problem

Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph problem (MCG) is to find a connected subgraph with R vertices that maximizes the sum of their weights. MCG has applications to communication network design and facility expansion. The constrained MCG (CMCG) is MCG with a constraint that one predetermined vertex must be included in the solution. In this paper, we introduce a class of decomposition algorithms for MCG. These algorithms decompose MCG into a number of small CMCGs by adding vertices one at a time and building a partial graph. They differ in the ordering of adding vertices. Proving that finding an ordering that gives the minimum number of CMCGs is NP-complete, we present three heuristic algorithms. Experimental results show that these heuristics are very effective in reducing computation and that different orderings can significantly affect the number of CMCGs to be solved. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 817–837, 1998     

Iterative methods for dynamic stochastic shortest path problems

We consider a routing policy that forms a dynamic shortest path in a network with independent, positive and discrete random arc costs. When visiting a node in the network, the costs for the arcs going out of this node are realized, and then the policy will determine which node to visit next with the objective of minimizing the expected cost from the current node to the destination node. This paper proposes an approach, which mimics the classical label-correcting approach, to compute the expected path cost. First, we develop a sequential implementation of this approach and establish some properties about the implementation. Next, we develop stochastic versions of some well-known label-correcting methods, including the first-in-first-out method, the two-queue method, the threshold algorithms, and the small-label-first principle. We perform numerical experiments to evaluate these methods and observe that fast methods for deterministic networks can become very slow for stochastic networks. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 769–789, 1998