A decomposable transshipment algorithm for a multiperiod transportation problem

A dynamic version of the transportation (Hitchcock) problem occurs when there are demands at each of n sinks for T periods which can be fulfilled by shipments from m sources. A requirement in period t₂ can be satisfied by a shipment in the same period (a linear shipping cost is incurred) or by a shipment in period t₁ < t₂ (in addition to the linear shipping cost a linear inventory cost is incurred for every period in which the commodity is stored). A well known method for solving this problem is to transform it into an equivalent single period transportation problem with mT sources and nT sinks. Our approach treats the model as a transshipment problem consisting of T, m source — n sink transportation problems linked together by inventory variables. Storage requirements are proportional to T² for the single period equivalent transportation algorithm, proportional to T, for our algorithm without decomposition, and independent of T for our algorithm with decomposition. This storage saving feature enables much larger problems to be solved than were previously possible. Futhermore, we can easily incorporate upper bounds on inventories. This is not possible in the single period transportation equivalent.     

A simulated port facility in a theatre of operations

A hypothetical port facility in a theatre of operations is modeled and coded in a special purpose simulation language, for the purpose of conducting simulation experiments on a digital computer. The experiments are conducted to investigate the resource requirements necessary for the reception, discharge, and clearance of supplies at the port. Queue lengths, waiting times, facility utilizations, temporary storage levels, and ship turn-around times are analyzed as functions of transportation and cargo handling resources, using response surface methodology. The resulting response surfaces are revealing in regard to the sensitivity of port operations to transportation resource levels and the characteristics of the port facility's load factor. Two specific conclusions of significant value are derived. First, the simulation experiments clearly show that the standard procedures for determining discharge and clearance capacities take insufficient account of the effects of variability. Second, the response surfaces for ship turn-around times and temporary storage levels indicate that an extremely steep gradient exists as a function of troop levels.     

Minimizing reductions in readiness caused by time-phased decreases in aircraft overhaul and repair activities

The Navy is often required to conduct personnel planning studies, A recent study on the assessment of effects of personnel reductions at the various aircraft Overhaul and Repair Activities (O & Rs) of the Bureau of Naval Weapons was carried out by one of the writers of the present paper. The methodology was systematic but relied on informal, judgmental decision procedures rather than on formal models incorporating optimization. Later study of the problem resulted in the approach described herein. The paper addresses this question: How can a personnel reduction in the Navy's aircraft O & Rs be distributed among activities with minimum reduction in readiness? A two-stage procedure involving linear programming models is developed. Solutions involve either extensions of aircraft overhaul cycles or a combination of such extensions with reductions in aircraft inventories.     

Book reviews

The Balkanization of the West: The Confluence of Postmodernism and Postcommunism By Stjepan G. Mestrovic, Routledge, London (1994). ISBN: 0-414-08755-4, Price £40.00 hardback, £13.99 paperback.

A Naval History of World War I By Professor Paul G. Halpern, UCL Press, 1994. pp. 624 ISBN 1-85728-295-7. Price £25.00

Arms Watch - SIPRI Report on the First Year of the UN Register of Conventional Arms By Edward J. Laurance, Siemon T. Wezeman and Herbert Wulf, Oxford University Press for SIPRI (1993) ISBN 019-829-1795, Price £25.00 hardback, £16.50 paperback.

A League of Airmen By J. A. Winnefeld, (Ed.), RAND, Santa Monica, ISBN 08330-1503-6, Price $30.00 (Hardcover) $15.00 (Softcover)     

A stochastic constrained optimal replacement model

In this paper a stochastically constrained replacement model is formulated. This model determines a sequence of replacement dates such that the total “current account” cost of all future costs and capital expenditures over an infinite time horizon for the n initial incumbent machines is minimized subject to the constraints that an expected number of machines are in a chosen utility class at any point in time. We then indicate one possible solution method for the model.     

Adaptive competitive decision in repeated play of a matrix game with uncertain entries

This study is concerned with a game model involving repeated play of a matrix game with unknown entries; it is a two-person, zero-sum, infinite game of perfect recall. The entries of the matrix ((pij)) are selected according to a joint probability distribution known by both players and this unknown matrix is played repeatedly. If the pure strategy pair (i, j) is employed on day k, k = 1, 2, …, the maximizing player receives a discounted income of β^{k - 1} X_ij, where β is a constant, 0 ≤ β ? 1, and X_ij assumes the value one with probability p_ij or the value zero with probability 1 - p_ij. After each trial, the players are informed of the triple (i, j, X_ij) and retain this knowledge. The payoff to the maximizing player is the expected total discounted income. It is shown that a solution exists, the value being characterized as the unique solution of a functional equation and optimal strategies consisting of locally optimal play in an auxiliary matrix determined by the past history. A definition of an ?-learning strategy pair is formulated and a theorem obtained exhibiting ?-optimal strategies which are ?-learning. The asymptotic behavior of the value is obtained as the discount tends to one.     

On the minimization of a certain convex function arising in applied decision theory

The author, in an expository paper [4], has presented an algorithm for choosing a non-negative vector

     

Biomedical applications of simulated environments

Environmental physiology assumes great significance in our national context in view of the diverse climatic conditions prevailing in different regions. Troops have to operate in diverse environmental conditions guarding the frontiers. Hence, the research in this area has been focused on the usage of field studies in the natural environments or simulated environments in the laboratory. Besides, the application of the simulation chambers in the research on the physiological effects of diverse environments, these studies may have applications in the control and management of certain clinical disorders. Some simulation chambers and specialised set-ups have been designed and developed at the Defence Institute of Physiology and Allied Sciences to carry out simulation studies. This paper describes these developments and the potentials of these biomedical applications of simulated environments.