Rescheduling to minimize makespan on a changing number of identical processors

We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.     

Total optimality of incrementally optimal allocations

This paper considers the problem of finding optimal solutions to a class of separable constrained extremal problems involving nonlinear functionals. The results are proved for rather general situations, but they may be easily stated for the case of search for a stationary object whose a priori location distribution is given by a density function on R, a subset of Euclidean n-space. The functional to be optimized in this case is the probability of detection and the constraint is on the amount of effort to be used Suppose that a search of the above type is conducted in such a manner as to produce the maximum increase in probability of detection for each increment of effort added to the search. Then under very weak assumptions, it is proven that this search will produce an optimal allocation of the total effort involved. Under some additional assumptions, it is shown that any amount of search effort may be allocated in an optimal fashion.     

Operations analysis during the underwater search for Scorpions

This paper discusses the operations analysis in the underwater search for the remains of the submarine Scorpion The a priori target location probability distribution for the search was obtained by monte-carlo procedures based upon nine different scenarios concerning the Scorpion loss and associated credibility weights. These scenarios and weights were postulated by others. Scorpion was found within 260 yards of the search grid cell having the largest a priori probability Frequent computations of local effectiveness probabilities (LEPs) were carried out on scene during the search and were used to determine an updated (a posteriori) target location distribution. This distribution formed the basis for recommendation of the current high probability areas for search The sum of LEPs weighted by the a priori target location probabilities is called search effectiveness probability (SEP) and was used as the overall measure of effectiveness for the operation. SEP and LEPs were used previously in the Mediterranean H-bomb search On-scene and stateside operations analysis are discussed and the progress of the search is indicated by values of SEP for various periods during the operation.     

MAD,not Marx: Khrushchev and the nuclear revolution

The revival of nuclear strategy in US policy and scholarship has been strengthened by arguments that the ‘nuclear revolution’ – the assumption that thermonuclear bombs and missiles had made major war too dangerous to wage – does not affect international behaviour as much as nuclear revolution advocates claim. This article shows that the Soviet leader Nikita Khrushchev indeed regarded nuclear war as too dangerous to wage, a decision which manifested itself not so much in foreign policy or military doctrine but in his determination to avoid war when the possibility arose. We argue that Khrushchev’s experience provides us with a more useful way to characterise the nuclear revolution and suggest some implications of this argument for contemporary debates about nuclear weaponry.     

Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

A Proxemic Account of Bayonet Fighting

The bayonet has long been regarded as an obsolete piece of military technology. This article advances a proxemic account of close combat, which points to its continuing utility under modern battlefield conditions. It is argued that bayonet training remains an effective way of preparing soldiers to psychologically dominate contested spaces on the battlefield. Thus, although other weapons and techniques can fulfil the same role, it can nevertheless be argued that the bayonet’s enduring presence is not simply the result of some atavistic military mind-set.     

Incremental approximation of optimal allocations

This paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.     

Book reviews

John Horsfield, The Art of Leadership in War. The Royal Navy From the Age of Nelson to the End of World War II. Westport, Conn. and London: Greenwood Press, 1980. Pp. 240; £14.75.

John Joseph Timothy Sweet, Iron Arm: The Mechanization of Mussolini's Army, 1920–1940. Westport, Connecticut &; London: Greenwood Press. 1980. Pp. 207; £15.50.

Peter H. Merkl, The Making of a Stormtrooper. Princeton, N.J: Princeton U.P., 1980. Pp. 328; £8.60.

Greg Herken, The Winning Weapon: The Atomic Bomb in the Cold War 1945–1950. New York: Alfred A. Knopf, 1980. Pp. 425; $15.00.

Geoffrey Smith and Nelson W. Polsby, British Government and its Discontents. New York: Basic Books, and London: Harper and Row, 1981. Pp. 202; £7.95.

Seweryn Bialer (ed.), The Domestic Context of Soviet Foreign Policy. Boulder, Colorado: Westview Press and London: Croom Helm, 1981. Pp. 441; £14.95.

Jerry F. Hough, Soviet Leadership in Transition. Washington, D.C.: Brookings Institution and Oxford, Basil Blackwell, 1981. Pp. 175; £12.00 (hb.) and £3.95 (pb.)

Edward F. Mickolus, Transnational Terrorism: A Chronology of Events 1968–1979. London: Aldwych Press, 1980. Pp. 967; £39.95.

Barry Rubin, The Great Powers in the Middle East, 1941–47; The Road to the Cold War, London: Frank Cass, 1980. Pp. 254; £14.50;

Daniel Heradstveit, The Arab‐Israeli Conflict; Psychological Obstacles to Peace. Oslo: Universittsforlaget, 1979. Pp. 234; £11.60;

Janice Gross Stein, and Raymond Tanter, Rational Decision‐making; Israel's Security Choices 1967. Columbus. Ohio; Ohio State University Press, 1980. Pp. 399; $35.     

ACCRUAL BUDGETING AND DEFENCE FUNDING: THEORY AND SIMULATIONS

This paper explores the impact of moving to accrual budgeting on resources allocation in defence. Standard defence budgeting and investment models are used to assess the theoretical implications of accrual budgeting. In addition, a number of simulations are conducted to assess the long-term implications of moving to accrual accounting and budgeting. The result of the simulations shows that changes to deployed operations and other operational shocks will have manageable impacts on readiness but systematic shocks associated with defence unit prices, procurement policies and defence specific inflation will put considerable strain on the defence department's flexibility.