The pure fixed charge transportation problem

The pure fixed charge transportation problem (PFCTP) is a variation of the fixed charge transportation problem (FCTP) in which there are only fixed costs to be incurred when a route is opened. We present in this paper a direct search procedure using the LIFO decision rule for branching. This procedure is enhanced by the use of 0–1 knapsack problems which determine bounds on partial solutions. Computational results are presented and discussed.     

Probabilistic formulations of the multifacility weber problem

The problem considered is to locate one or more new facilities relative to a number of existing facilities when both the locations of the existing facilities, the weights between new facilities, and the weights between new and existing facilities are random variables. The new facilities are to be located such that expected distance traveled is minimized. Euclidean distance measure is considered; both unconstrained and chance-constrained formulations are treated.     

A note on the stochastic shortest-route problem

This paper develops an algorithm for a “shortest route” network problem in which it is desired to find the path which yields the shortest expected distance through the network. It is assumed that if a particular arc is chosen, then there is a finite probability that an adjacent arc will be traversed instead. Backward induction is used and appropriate recursion formulae are developed. A numerical example is provided.     

One-person games of economic survival

This paper discusses the one-person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.     

The optimal burn-in testing of repairable equipment

The subject of this paper is the utilization of the “infant mortality” or decreasing failure rate effect to improve the reliability of repairable devices. Decreasing failure rate implies the possibility that devices which exhibit it can be improved by “burn-in testing” of each unit. Such a test serves to accumulate operating time while shielded from the full costs and consequences of failure. A general formulation of the burn-in test decision for repairable devices is presented and some special cases are solved. A class of models, indexed by the degree of partial replacement present in the repair process, is considered and numerical results for the optimal policy are given for several members of that class. A comparison of those results reveals the profitability of testing increases with the complexity of the repairable device.     

Probabilistic models of decreasing failure rate processes

The “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non-independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.     

‘Winston has gone mad’: Churchill,the British Admiralty,and the Rise of Japanese Naval Power

As Chancellor of the Exchequer during the late 1920s, Winston Churchill was at the center of British strategic decision making about how to respond to the naval challenge posed by Japan's rise as a rival sea power. Churchill downplayed the likelihood of war with Japan. The leadership of the Royal Navy disagreed: they saw Japan as a dangerous threat to the security of the British Empire. Examining this dispute between Churchill and the Admiralty highlights the awkward political, economic, and strategic tradeoffs confronting British leaders between the world wars.