A two product dynamic economic lot size production model with either-or production constraints

This paper considers the production of two products with known demands over a finite set of periods. The production and inventory carrying costs for each product are assumed to be concave. We seek the minimum cost production schedule meeting all demands, without backlogging, assuming that at most one of the two products can be produced in any period. The optimization problem is first stated as a nonlinear programming problem, which allows the proof of a result permitting the search for the optimal policy to be restricted to those which produce a product only when its inventory level is zero. A dynamic programming formulation is given and the model is then formulated as a shortest route problem in a specially constructed network.     

Stochastic duels involving reliability

The reliability of weapons in combat has been treated by Bhashyam in the context of a stochastic duel characterized by fixed ammunition supplies. negative exponentially distributed firing times and weapon lifetimes, and a fixed number of spare weapons for each duelist. The present paper takes a different approach by starting with the fundamental duel of Ancker and Williams, characterized by unlimited ammunition and by ordinary renewal firing times, and adding to it weapon lifetimes which can be functions of time or of round position in the firing sequence. Probabilities of winning and tieing are derived and it is shown that under certain conditions the weapon lifetimes are equivalent to random time and ammunition limits.     

Cyclical schedules for the joint replenishment problem with dynamic demands

The Joint Replenishment Problem (JRP) involves production planning for a family of items. The items have a coordinated cost structure whereby a major setup cost is incurred whenever any item in the family is produced, and an item-specific minor setup cost is incurred whenever that item is produced. This paper investigates the performance of two types of cyclical production schedules for the JRP with dynamic demands over a finite planning horizon. The cyclical schedules considered are: (1) general cyclical schedules—schedules where the number of periods between successive production runs for any item is constant over the planning horizon—and (2) power-of-two schedules—a subset of cyclical schedules for which the number of periods between successive setups must be a power of 2. The paper evaluates the additional cost incurred by requiring schedules to be cyclical, and identifies problem characteristics that have a significant effect on this additional cost. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 577–589, 1997.     

The residual life of the renewal process: A simple algorithm

We develop a simple algorithm, which does not require convolutions, for computing the distribution of the residual life when the renewal process is discrete. We also analyze the algorithm for the particular case of lattice distributions, and we show how it can apply to an inventory problem. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 435–443, 1999     

How old is too old? An economic approach to replacing military aircraft

The US Air Force is asking when to replace its aging aircraft. We develop a framework to identify economically optimal replacement strategies that recognizes cost trade-offs and incorporates age effects. We also preview a stochastic methodology. We use the framework to identify an optimal strategy, defined by the replacement age, for a generic fleet and conduct a sensitivity analysis. Quantitative illustrations show that the range of strategies that provides close-to-optimal outcomes widens as the operating and support (O&S) cost growth rate decreases and the ratio of the acquisition price to the initial O&S cost increases. A wider range implies more decision-making leeway.     

Book Reviews

Patrick Finney (ed.), The Origins of the Second World War. London: Arnold, 1997. Pp.xvi + 461, index. £15.99. ISBN 0–340–67640‐X.

Maria Emilia Paz, Strategy, Security, and Spies: Mexico and the US as Allies in World War II. University Park, PA: The Pennsylvania State University Press, 1997. Pp.xii + 264, 10 illus., biblio., index. $55 (cloth); $19.95 (paper). ISBN 0–271–01665–5 and 01666–3.

Norman J.W. Goda, Tomorrow the World: Hitler, Northwest Africa and the Path toward America. College Station, Texas A&;M University Press, 1998. Pp.xxvi + 307, 2 maps, biblio., index. $39.95. ISBN 0–89096–807–1.

Michael J. Hogan, A Cross of Iron: Harry S. Truman and the Origins of the National Security State, 1945–1954. Cambridge; New York: Cambridge University Press, 1998. Pp.xii + 525, biblio., index. £25; $34.95. ISBN 0–521–64044‐X.

Stephen Van Evera, Causes of War: Power and the Roots of Conflict. Ithaca, NY: Cornell University Press, 1999. Pp.viii + 270, index. $35. ISBN 0–801403201–4.

Eric Arnett (ed.), Nuclear Weapons and Arms Control in South Asia after the Test Ban, SIPRI Research Report No.14. Oxford: Oxford University Press/Stockholm Int Peace Research Institute, 1998. Pp.viii + 98, index. £12.99. ISBN 0–19–8294115.

T.V. Paul, Richard J. Harknett and James J. Wirtz (eds.), The Absolute Weapon Revisited: Nuclear Arms and Emerging International Order. Ann Arbor, Michigan: The University of Michigan Press, 1998. Pp.vi + 312, index. $47.50/£36. ISBN 0–472–10863–8.