Proportionate flow shop: New complexity results and models with due date assignment

It is known that the proportionate flow shop minimum makespan $Fm/prpt/C_{\max }$ problem is solved optimally by any permutation job sequence. We show that the $Fm/prpt/C_{\max }$ problem is at least ordinary NP‐hard when missing operations are allowed and present some solvable cases. We then consider the standard proportionate flow shop problem (with no missing operations) and show that the solution algorithms for a class of single‐machine due date assignment problems can be extended/generalized to the corresponding proportionate flow shop problems. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 98–106, 2015     

Defense spending and economic growth: Extended empirical analysis for the European Union

Previous empirical studies on the defense spending-economic growth nexus such as Kollias et al. (2007 Kollias, C., N. Mylonidis, and S. Paleologou. 2007. “A panel data analysis of the nexus between defense spending and growth in the European Union.” Defense and Peace Economics 18 (1): 75–85.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Mylonidis (2008 Mylonidis, N. 2008. “Revisiting the nexus between military spending and growth in the European Union.” Defense and Peace Economics 19 (4): 265–272.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Dunne and Nikolaidou (2012 Dunne, J. P., and E. Nikolaidou. 2012. “Defense spending and economic growth in the EU15.” Defense and Peace Economics 23 (6): 537–548.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) analyzed this relationship in the case of the EU15. This study extends the analysis with the inclusion of more EU members and investigates the long run causal ordering between the two variables. Findings reported herein are not uniformed across all EU members. It is also found that end of Cold War has significant negative impact on defense expenditures of former east-European countries.     

RAIN,GROWTH, AND CIVIL WAR: THE IMPORTANCE OF LOCATION

We re‐examine the Miguel et al. (2004 Miguel, E., Satyanath, S. and Sergenti, E. 2004. Economic shocks and civil conflict: an instrumental variables approach. Journal of Political Economy, 112(4): 725–753. [Crossref], [Web of Science ®] , [Google Scholar]) study of the impact of growth on civil war, using growth in rainfall as an instrument. Miguel et al. (2004 Miguel, E., Satyanath, S. and Sergenti, E. 2004. Economic shocks and civil conflict: an instrumental variables approach. Journal of Political Economy, 112(4): 725–753. [Crossref], [Web of Science ®] , [Google Scholar]) – in our view, erroneously – include countries participating in civil wars in other states. Restricting the conflict data to states with conflict on their own territory reduces the estimated impact of economic growth on civil war. We show how spatial correlations in rainfall growth and participation in civil conflicts induce a stronger apparent relationship in the mis‐classified data.     

THE FATE OF DISPUTED TERRITORIES: AN ECONOMIC ANALYSIS

This paper presents a simple model to characterize the outcome of a land dispute between two rival parties using a Stackelberg game. Unlike Gershenson and Grossman (2000 Gershenson, D. and Grossman, H.I. 2000. Civil conflict: ended or never ending?. Journal of Conflict Resolution, 44(6): 807–821.  [Google Scholar]), we assume that the opposing parties have access to different technologies for challenging and defending in conflict. We derive the conditions under which territorial conflict between the two parties is less likely to persist indefinitely. Allowing for an exogenous destruction term as in Garfinkel and Skaperdas (2000 Garfinkel, M. and Skaperdas, S. 2000. Conflict without misperceptions or incomplete information: how the future matters. Journal of Conflict Resolution, 44(6): 793–807. [Crossref], [Web of Science ®] , [Google Scholar]), we show that, when the nature of conflict becomes more destructive, the likelihood of a peaceful outcome, in which the territory’s initial possessor deters the challenging party, increases if the initial possessor holds more intrinsic value for the disputed land. Following Siqueira (2003 Siqueira, K. 2003. Conflict and third‐party intervention. Defence and Peace Economics, 14(6): 389–400. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), our model has policy implications for peace through third‐party intervention.     

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.     

RAISING THE COST OF REBELLION: THE ROLE OF THIRD‐PARTY INTERVENTION IN INTRASTATE CONFLICT

This paper presents a simple model to characterize explicitly the role that an intervening third party plays in raising the cost of rebellion in an intrastate conflict. Extending the Gershenson‐Grossman (2000 Gershenson, D. and Grossman, H.I. 2000. Civil conflict: ended or never ending?. Journal of Conflict Resolution, 44(6): 807–821.  [Google Scholar]) framework of conflict in a two‐stage game to the case involving outside intervention in a three‐stage game as in Chang et al. (2007b Chang, Y.‐M., Potter, J. and Sanders, S. 2007b. War and peace: third‐party intervention in conflict. European Journal of Political Economy, 23(4): 954–974.  [Google Scholar]), we examine the conditions under which an outside party optimally intervenes such that (i) the strength of the rebel group is diminished or (ii) the rebellion is deterred altogether. We also find conditions in which a third party optimally intervenes but at a level insufficient to deter rebellion. Such behavior, which improves the incumbent government’s potential to succeed in conflict, is overlooked in some conflict studies evaluating the effectiveness of intervention. One policy implication of the model is that an increase in the strength of inter‐governmental trade partnerships increases the likelihood that third‐party intervention deters rebellion.     

Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

Change as a cost driver in defence procurement

This paper discusses change transactions that occur in connection with the procurement of defence systems. The bases for the reasoning are the ideas of Miller and Vollman (1985 Miller JG Vollman TE (1985) The hidden factory – cutting the explosive growth of overhead costs requires mastery of more than just what happens on the shop floor Harvard Business Review Sept–Oct 142 150  [Google Scholar]) and Eppinger (2001 Eppinger DE (2001) Innovation at the speed of information Harvard Business Review January 149 158  [Google Scholar]). These researchers argue that unplanned flows of information lead to change transactions, causing significant overhead costs. According to this paper, change transactions in defence procurement could be caused by (a) the changes in technology taking place during the long lifetime of a defence system and (b) the structure and contents of the agreements between the defence agent (the procurer) and the defence industry (the supplier).     

Ho Chi Minh and the origins of the Vietnamese doctrine of guerrilla tactics

In a very important sense, the Vietnamese military history of the communist era began in 1941, when Ho Chi Minh prepared ‘Guerrilla Tactics’ (Cach Danh Du Kich).1 ?1. Ministry of Defense Center for the Military Encyclopedia Ministry of Defense Center for the Military Encyclopedia. 1996. Tu Dien Bach Hoa Quan Su Vietnam, Hanoi: People's Army Publishing Company.  [Google Scholar], Tu Dien Bach Hoa Quan Su Vietnam, 69. The publication of this essay, which was a manual on the tactics, techniques, and procedures of guerrilla warfare, preceded the founding of the first armed propaganda unit (Tuyen Truyen Doi Vo Trang) on 22 December 1944, which later became the People's Army of Vietnam (PAVN, Quan Doi Nhan Dan); as well as the revolutionary writings of Truong Chinh (1946–1947) and Vo Nguyen Giap (1959). The fact that ‘Tactics’ was published by the Viet Minh reinforces the claim made by the PAVN that it was the first authoritative Vietnamese writing on this important subject.     

Success and failures of the Gripen offsets in the Visegrad Group countries

The Soviet-led Council for Mutual Economic Assistance member, Central European countries found themselves in a difficult political and economic situation after the collapse of the Soviet Union. Three post-Eastern Bloc countries formed the Visegrad Group to strengthen their ties to the West, but the need for foreign investment, job creation and technology transfer was urgent.

This is when military modernisation also came into the picture and the counter-trade—as known as offset—as a tool to help these economies. A trade practice which was meant to energise these economies via defence acquisitions linked economic programmes.

Two Visegrad Group member countries, Hungary and the Czech Republic decided to sign offset agreement with the defence firm SAAB to license Gripen fighter aircrafts. This study intends to analyse if these deals were able to help governments to reach their objectives or the two countries were unable to take advantage of the offset programmes.     

The joint signature of coherent systems

We investigate the joint signature of $m$ coherent systems, under the assumption that the components have independent and identically distributed lifetimes. The joint signature, for a particular ordering of failure times, is an $m$‐dimensional matrix depending solely on the composition of the systems and independent of the underlying distribution function of the component lifetimes. The elements of the $m$‐dimensional matrix are formulated based on the joint signatures of numerous series of parallel systems. The number of the joint signatures involved is an exponential function of the number of the minimal cut sets of each original system and may, therefore, be significantly large. We prove that although this number is typically large, a great number of the joint signatures are repeated, or removed by negative signs. We determine the maximum number of different joint signatures based on the number of systems and components. It is independent of the number of the minimal cut sets of each system and is polynomial in the number of components. Moreover, we consider all permutations of failure times and demonstrate that the results for one permutation can be of use for the others. Our theorems are applied to various examples. The main conclusion is that the joint signature can be computed much faster than expected.     

Computing equilibria via nonconvex programming

The problem of determining a vector that places a system in a state of equilibrium is studied with the aid of mathematical programming. The approach derives from the logical equivalence between the general equilibrium problem and the complementarity problem, the latter being explicitly concerned with finding a point in the set S = {x: < x, g(x)> = 0, g(x) ≦ 0, x ≧ 0}. An associated nonconvex program, min{? < x, g(x) > : g(x) ≦ 0, x ≧ 0}, is proposed whose solution set coincides with S. When the excess demand function g(x) meets certain separability conditions, equilibrium solutions are obtained by using an established branch and bound algorithm. Because the best upper bound is known at the outset, an independent check for convergence can be made at each iteration of the algorithm, thereby greatly increasing its efficiency. A number of examples drawn from economic and network theory are presented in order to demonstrate the computational aspects of the approach. The results appear promising for a wide range of problem sizes and types, with solutions occurring in a relatively small number of iterations.     

Two-agent scheduling with linear resource-dependent processing times

This paper considers a two-agent scheduling problem with linear resource-dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is -hard in the ordinary sense, and there does not exist a polynomial-time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.     

The Battle of Mirbat: turning point in the Omani Dhofar rebellion

On 19 July 1972, the pivotal battle of the Dhofar rebellion occurred when over 250 communist guerillas, called adoos,1 ?1. ‘Enemy’ in Arabic. attacked the coastal garrison town of Mirbat2 ?2. Sometimes spelled Marbat. where nine men of the British 22nd Special Air Service Regiment were stationed. Their decisive defense of Mirbat led to decorations three years after the battle, the beginning of the end of the rebellion, and calls for the awarding of Britain's highest honor, the Victoria Cross. The Battle of Mirbat, let alone the Dhofar rebellion are little known outside the UK due3 ?3. Other than papers written for military staff colleges, there is no American written account of the battle. to the covert nature of the SAS deployment, the then Labour government's obsession with secrecy, and the remoteness of the area of operations. Nonetheless, of all the proxy wars of the Cold War this one had the most significance, because had the communist adoos won, Oman and its Musandam Peninsula, which sticks out like a dagger into the Straits of Hormuz and abuts the United Arab Emirates, would have fallen into the communist orbit; threatening the West's oil supply. This is the story of the pivotal battle that was won by Britain and Oman against a communist insurgency.     

Confidence intervals for ranked means

Suppose that observations from populations π₁, …, π_k (k ≥ 1) are normally distributed with unknown means μ₁., μ_k, respectively, and a common known variance σ². Let μ_[1] μ … ≤ μ_[k] denote the ranked means. We take n independent observations from each population, denote the sample mean of the n observation from π₁ by X _i (i = 1, …, k), and define the ranked sample means X _[1] ≤ … ≤ X _[k]. The problem of confidence interval estimation of μ₍₁₎, …,μ_[k] is stated and related to previous work (Section 1). The following results are obtained (Section 2). For i = 1, …, k and any γ(0 < γ < 1) an upper confidence interval for μ_[i] with minimal probability of coverage γ is (? ∞, X _[i]+ h) with h = (σ/n^1/2) Φ^?1(γ^1/k-i+1), where Φ(·) is the standard normal cdf. A lower confidence interval for μ_[i] with minimal probability of coverage γ is (X _i[i] – g, + ∞) with g = (σ/n^1/2) Φ^?1(γ^1/i). For the upper confidence interval on μ_[i] the maximal probability of coverage is 1– [1 – γ^1/k-i+1]ⁱ, while for the lower confidence interval on μ_[i] the maximal probability of coverage is 1–[1– γ^1/i] ^k-i+¹. Thus the maximal overprotection can always be calculated. The overprotection is tabled for k = 2, 3. These results extend to certain translation parameter families. It is proven that, under a bounded completeness condition, a monotone upper confidence interval h(X ₁, …, X _k) for μ_[i] with probability of coverage γ(0 < γ < 1) for all μ = (μ_[1], …,μ_[k]), does not exist.     

Antelope,Poseidon or a Hybrid: The Upgrading of the British Strategic Nuclear Deterrent, 1970–1974

It is the purpose of this article to illustrate how the British government reached its decision to upgrade the Polaris strategic nuclear deterrent in 1973. Using British and American documentation it is demonstrated that the strategic imperatives for upgrading Polaris were fundamental to the project. Existing accounts of the Polaris Improvement Project, however, have not given the appropriate attention to the wider US–UK political differences in this period. By doing so it is shown how in addition to the wider economic, strategic and political factors, this was of paramount significance in the Heath government opting for the ‘Super Antelope’ method in upgrading Polaris.1 ¹‘Super Antelope’ was the codename for the upgrade of Polaris. This was eventually changed to ‘Chevaline’. Peter Hennessy, Cabinets and the Bomb (Oxford: OUP 2007), 28–9. View all notes     

Westmoreland was right: learning the wrong lessons from the Vietnam War

Fourth Generation Warfare is a theory of contemporary warfare that posits a number of different ideas that are able to shed light on current conflicts. Whilst much of the debate has been concentrated on the linear development of warfare and also on analysis of the current situation of US forces in Iraq, it has resonance for a number of different conflicts taking place in Africa, if only because the US has become involved in contemporary conflicts in Somalia and the Mahgreb. There are clearly significant issues with the US-centric, flawed linear approach to history, but the actual analysis of modes of warfare has much to offer policymakers in a continent that is under-represented in the literature, and is also in danger of being forgotten in the shadow of analysis of Iraq. This paper moves on from criticising the stepped approach to history and looks at patterns of warfare in contemporary Africa, arguing that there is much in the theory that could be used to explain seemingly illogical tactics or patterns, and thus has much to tell policymakers engaged in conflict analysis.

Rebellions can be made 2 per cent active in a striking force, and 98 per cent passively sympathetic.1 ?1. T.E. Lawrence, ‘Science of Guerrilla Warfare’, 1929, published in Malcolm Brown (ed) T.E. Lawrence in War and Peace: An Anthology of the Military Writings of Lawrence of Arabia (London: Greenhill Books, 2005) p.284.