Explicit steady state solutions for a particular M(x)/M/1 queueing system

An explicit steady state solution is determined for the distribution of the number of customers for a queueing system in which Poisson arrivals are bulks of random size. The number of customers per bulk varies randomly between 1 and m, m arbitrary, according to a point multinomial, and customer service is exponential. Queue characteristics are given.     

ON THE RELATIONSHIP BETWEEN MILITARY EXPENDITURE,THREAT, AND ECONOMIC GROWTH: A NONLINEAR APPROACH

The main objective of the paper is to decipher the military expenditure–economic growth relationship, taking the level of economic development (income) into consideration. Our findings suggest the following: (i) military expenditure has a significantly negative relationship to economic growth for the 23 countries with initial incomes (threshold variable) less than or equal to $475.93; (ii) when the threat level is heightened, economic growth (23 countries) is expected to decrease. However, military expenditure in the presence of sufficiently large threats increases growth; (iii) for the remaining 69 countries whose initial incomes (real GDP per capita in 1992 price) exceed $475.93, no significant relationship exists whether the threat variable is taken into consideration or not.     

Using the Feder-Ram and Military Keynesian Models to Examine the Link Between Defence Spending and Economic Growth in Sri Lanka

This study uses the Feder-Ram model in conjunction with the military Keynesian model to examine the nexus between defence spending and economic growth in Sri Lanka. We find that the Keynesian aggregate demand model is better suited to analyse the link than the Feder-Ram model for the case of Sri Lanka. Based upon our results we expect a higher economic growth rate in Sri Lanka if more public resources are diverted from the defence to civilian sectors of the economy, now that the war between the government and separatist guerrillas has come to an end. However, recent post war events cast doubt upon whether a diversion of sources from military to non-military spending will actually occur. We conclude that the sanguine predictions of our economic analysis are entirely dependent upon the political decisions of the Sri Lankan government for their realization.     

Military Spending and Economic Growth in South Asia: A Panel Data Analysis

Despite the large number and variety of studies addressing the relationship between military spending and economic growth, a consensus regarding the exact nature of any relationship between the two has proven elusive. This study uses a panel co-integration approach to examine the relationship between military spending and economic growth in the five South Asian countries of India, Pakistan, Nepal, Sri Lanka and Bangladesh over the period of 1988–2007. It finds that a 1% increase in military spending increases real GDP by only 0.04%, suggesting that the substantial amount of public expenditure that is currently directed towards military purposes in these countries has a negligible impact upon economic growth.     

Revenue sharing contracts in a supply chain with uncontractible actions

We consider a supplier–customer relationship where the customer faces a typical Newsvendor problem of determining perishable capacity to meet uncertain demand. The customer outsources a critical, demand‐enhancing service to an outside supplier, who receives a fixed share of the revenue from the customer. Given such a linear sharing contract, the customer chooses capacity and the service supplier chooses service effort level before demand is realized. We consider the two cases when these decisions are made simultaneously (simultaneous game) or sequentially (sequential game). For each game, we analyze how the equilibrium solutions vary with the parameters of the problem. We show that in the equilibrium, it is possible that either the customer's capacity increases or the service supplier's effort level decreases when the supplier receives a larger share of the revenue. We also show that given the same sharing contract, the sequential game always induces a higher capacity and more effort. For the case of additive effort effect and uniform demand distribution, we consider the customer's problem of designing the optimal contract with or without a fixed payment in the contract, and obtain sensitivity results on how the optimal contract depends on the problem parameters. For the case of fixed payment, it is optimal to allocate more revenue to the supplier to induce more service effort when the profit margin is higher, the cost of effort is lower, effort is more effective in stimulating demand, the variability of demand is smaller or the supplier makes the first move in the sequential game. For the case of no fixed payment, however, it is optimal to allocate more revenue to the supplier when the variability of demand is larger or its mean is smaller. Numerical examples are analyzed to validate the sensitivity results for the case of normal demand distribution and to provide more managerial insights. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

MILITARY SPENDING AND ECONOMIC GROWTH IN SOUTH ASIA: A REPLY

We review some critical comments upon our earlier paper in this journal and respond to these. We also critically evaluate a proposed alternative methodology giving reasons why our own provides a more robust approach for examining the nexus between military spending and economic growth in South Asia.     

Supplier‐buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation

We consider the problem of designing a contract to maximize the supplier's profit in a one‐supplier–one‐buyer relationship for a short‐life‐cycle product. Demand for the finished product is stochastic and price‐sensitive, and only its probability distribution is known when the supply contract is written. When the supplier has complete information on the marginal cost of the buyer, we show that several simple contracts can induce the buyer to choose order quantity that attains the single firm profit maximizing solution, resulting in the maximum possible profit for the supplier. When the marginal cost of the buyer is private information, we show that it is no longer possible to achieve the single firm solution. In this case, the optimal order quantity is always smaller while the optimal sale price of the finished product is higher than the single firm solution. The supplier's profit is lowered while that of the buyer is improved. Moreover, a buyer who has a lower marginal cost will extract more profit from the supplier. Under the optimal contract, the supplier employs a cutoff level policy on the buyer's marginal cost to determine whether the buyer should be induced to sign the contract. We characterize the optimal cutoff level and show how it depends on the parameters of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 41–64, 2001     

Stock-rationing policy for a make-to-stock production system with two priority classes and backordering

This article considers the problem of production control and stock rationing in a make-to-stock production system with two priority customer classes and backordering. The problem is formulated as a queueing control model. With Poisson arrivals and exponential production times, we show that the optimal production control and stock-rationing policies can be characterized by a single, monotone switching curve. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44 : 457–472, 1997     

Interdiction models for delaying adversarial attacks against critical information technology infrastructure

Information technology (IT) infrastructure relies on a globalized supply chain that is vulnerable to numerous risks from adversarial attacks. It is important to protect IT infrastructure from these dynamic, persistent risks by delaying adversarial exploits. In this paper, we propose max‐min interdiction models for critical infrastructure protection that prioritizes cost‐effective security mitigations to maximally delay adversarial attacks. We consider attacks originating from multiple adversaries, each of which aims to find a “critical path” through the attack surface to complete the corresponding attack as soon as possible. Decision‐makers can deploy mitigations to delay attack exploits, however, mitigation effectiveness is sometimes uncertain. We propose a stochastic model variant to address this uncertainty by incorporating random delay times. The proposed models can be reformulated as a nested max‐max problem using dualization. We propose a Lagrangian heuristic approach that decomposes the max‐max problem into a number of smaller subproblems, and updates upper and lower bounds to the original problem via subgradient optimization. We evaluate the perfect information solution value as an alternative method for updating the upper bound. Computational results demonstrate that the Lagrangian heuristic identifies near‐optimal solutions efficiently, which outperforms a general purpose mixed‐integer programming solver on medium and large instances.     

The rise and fall of counterproliferation policy

The US government initiated a Defense Counterproliferation Initiative to address the concern that, in the post-Cold War years, the proliferation of nuclear, biological, and chemical weapons would be widespread and create a significant challenge to the US military’s combat operations. In particular, non-nuclear states might use chemical or biological warfare agents against US forces with the belief that nuclear weapons would not be used against them in retaliation. Following the events of September 11, 2001, defense strategy and policy shifted to a wider view of the threat of adversarial use of “weapons of mass destruction” (WMD) and the term “counterproliferation” was replaced by “combating” or “countering WMD.” Over time, the Defense Department increasingly moved away from counterproliferation principles with the detrimental effect of losing capabilities that US forces still need for contemporary adversaries. This shift has been aggravated by other US government agencies’ use of “counterproliferation” in lieu of what would have been termed “nonproliferation” activities in the 1990s. The loss of clarity within the US government on these terms has led to the inability to focus the “whole of government” on this significant national security challenge. To alleviate this challenge, the US government needs a top-down initiative to refocus policy on the distinctly different aspects of WMD with respect to military combat operations, combating terrorism, and homeland security.