TOM Solves Transport
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Distribution Problems
Computing Machine Provides Quick Answers to Questions on Transport Organization and Costs that Would Require Abstruse Mathematical Calculations By a Special Correspondent
IN a few minutes TOM can solve many transport problems that might occupy a mathematician several hours, or a whole day, using normal arithmetical methods. The name is an abbreviation of Transport Optimising Machine, which was developed by Dr. E. R. F. W. Crossrnan, formerly a Research Fellow of the Production Department of Birmingham University, and Mr. K. B. Haley, a research student of the department, who is preparing a thesis on the applications of linear programming to transport organization.
In its present form Tom comprises a number of pulleys, weights and strings based on a Meccano structure, and the influence of friction may reduce the accuracy of the readings. No doubt a production model will be evolved which will enable all errors to be eliminated.
Goods From Several Factories
In the syllabus for the senior executive residential courses on " Linear Programming, Theory and Practice," run by the Institute for Engineering Production at the University, the problem is cited of reducing costs to a minimum in the case of products being supplied from a number of factories to several customers or depots.
This is a linear problem in that transportcosts are directly proportional to the quantities sent, and the variables are interdependent, so that, if goods are sent from factory A to warehouse X, fewer goods may be sent from factory B to warehouse X.
• Consequently, the surplus goods must be sent elsewhere, which will affect all the other factories and warehouses. Simple examples of such a problem may be solved by trial-and-error methods, hut when the number of possibilities is large, linear programming offers a solution that may be impossible to achieve by other means.
During a visit to the production department I had the opportunity of studying the operation of TOM. Although the machine had been set up to solve a set of fairly simple transport
D I 0 problems which could be determined arithmetically in a comparatively short time, a description of the principle should serve to illustrate both the scope of the machine and of linear programming.
The production outputs of four factories (per day or week) are represented by the position of pins located in members projecting from the lower side of the machine and attached to a series of strings on one of the pulley systems; the proportions in which the goods are required at depots (or by individual customers) are shown by pins in members projecting at right angles from the side of the machine at a higher level.
These are attached to another series of strings of a second pulley system, the units of which are incorporated in the same assemblies above the first series. The number of pulley units is a product of the number of factories and the number of depots, and in this case the total is 12.
Calculating Cost
Attached to every pulley unit is a weight, the value of which is equivalent to the cost of sending goods from factory to depot, represented by the two strings. The cost would be determined in the normal way, being based on the length of route, type of vehicle employed and so on.
When one of the lower pins is moved inwards a certain distance to represent the factory output, the three pulley units through which the string passes move vertically downwardS. This can be compensated by moving the three depot pins outwards in any proportion, with a total movement equivalent to the total production output from the one factory.
Vertical displacements of the pulley units indicate in every case the proportions in which the goods Should be diktributed to the depots or centres from
the factory, if transport costs are to be reduced to a minimum.
The operation is repeated by moving the remaining_ three factory pins an appropriate amount and restoring the equilibrium of the system by moving the depot pins distances equivalent to the intake of goods. Twelve readings can then be made of the vertical displacements of the pulley units to discover the most economical method of distribution. This assumes that the same type of produce is manufactured at every factory, but it is generally possible to make allowance for a certain percentage of specialized traffic.
Another interesting example of a machine being employed to solve a transport problem and evolved in the department (this time a non-linear problem) relates to the choice of the most suitable site for a depot to which goods will be sent from a factory for re-distribution to three centres.
What It Is
The apparatus consists simply of four pulleys, representing the position of the factory and the centres, which are arranged on a wall at distances apart equivalent to the map readings. A weight proportionate to the output of the factory is attached to the string passing over the factory pulley, and the end of this string is tied to the ends of the other three, to which weights are attached equivalent to the respective input of goods.
When the system is released, the point at which the strings arc joined will settle down at a position on the board representing the best site for the depot. Mathematically, this could only be determined by calculating to the 16th order.
Liriear programming has been applied by the Operations Headquarters of the Central Electricity Authority on a divisional basis, involving up to 100 pits and 30 power stations. It has been shown that the routeing of coal transport within a division is very nearly at an optimum, but that some changes could be made which would reduce transport costs by amounts up to one per cent.
Confirmation, by the application of linear programming, of the efficiency of the existing transport organization was of particular value to the Authority, and they point out that the estimated improvement is probably Much smaller than the potential gain in many other applications.
The study of linear programming is -being extended to include analysis of transport problems on a national scale% but no results are yet available. The
method of computation employed has been developed from published techniques and has facilitated the clarification of problems that were thought impracticable 12 months ago.
A spokesman of the Authority states that if he "might hazard a guess into the future" he would envisage a national allocation pattern, to be worked out. Say, twice a year, after which dayto-day changes in circumstance could be dealt with divisionally, using linear programming.
The system is applicable also to many manufacturing problems, and it can be used to assess the optimum proportions of various derivatives in the fuel-crack • ing process.
• It is confirmed by the C.E.A. that the linear programming technique does not require great mathematical skill. It is recommended that those who consider the system applicable to their transport organization should read "An Introduction to Linear Programming," by Charnes, Cooper and Henderson, published by ,Chapman and Hall, or "The Theory of Games and Linear Programming," by S. Vajda, published by Methuen.