Statistical Control Applications in Linear Programming

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Abstract
Solution of the product mix problem of Linear Programming leads to recommended quantities of various product styles that must be sold if the firm's ideal profit potential, based on productive capacity and market requirements, is to be realized. In practice, management has the task of making day-to-day and hour-to-hour decisions, designed to lead towards the attainable maximum profit. Sometimes, sudden opportunities arise for management to contract for the production of one product style for one customer, with quantities far in excess of those recommended in the L. P. solution. An on-the-spot decision to accept or reject the customer's bid must be made. Indeed, he may still be on the long-distance wire, expecting a response. Statistical control limits will help management in such situations, by showing the extent to which a recommended quantity on any product style may be violated, while still remaining within a predetermined percentage of the plant's ideal profit potential. Without such statistical control limits, management would have to await the outcome of a new L. P. analysis before knowing the effect of accepting or rejecting special bids, such as just described.

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