Use of Mathematical Programming Techniques in Production Planning
Authors: Kahle R.V. 
Published: December 2007

Introduction
This paper will address itself to the management question "How can advanced mathematical tools aid in the broad scope planning of the producing activity?". This general topic of the application of math techniques to business planning is becoming a familiar one in that numerous articles have been published in Harvard Business Review, Fortune, and in the Operations Research/Management Sciences journals. Perhaps the new element in this paper is the discussion of the application of these concepts and quantitative tools to the over-all operations and investment planning of a producing operation. Other authors have noted that little work on the application of operations research techniques to broad scope production planning has been reported in the literature. (This is not to say that there have not been numerous articles describing profitable applications of math and computer techniques to technical problems such as reservoir engineering and well logging.) One notices a striking contrast between the work published concerning the development of comprehensive mathematical planning models in manufacturing and supply with that reported in the producing function. a paper presented at the American Petroleum Institute Meeting in May 1962, it was reported that 55 per cent of the refineries using computers for any calculations had developed over-all refinery planning models using linear programming techniques.* No such statement appears justified in the producing area. These applications in manufacturing and supply are; paying off. During discussions at the Sixth World Petroleum Congress on a paper entitled "Corporate Planning Using Mathematical Techniques", British Petroleum Co. reported that the measured benefits from their first year's use of an integrated manufacturing supply linear programming model was just under two million pounds or 5.6 million dollars. The costs were reported to be less than 5 per cent of savings, or put another way, the payout was more than 20:1. Informal discussions with others have led this author to believe that, while this payout ratio is high, others have been obtaining similar results. In the face of such success in the application of mathematical tools to other functions in the petroleum industry, why so apparently little use of these tools in producing? It has been said that lack of evidence of activity in a technical field can be attributed to one of three factors. They are:1. No one, in fact, is engaged in the work.2. Attempts have been made but have failed completely.3. The very few people who are obtaining successful results do not publish because they wish to maintain a competitive advantage. This author suspects that all of these factors may be playing a part. In any case, today it is technically feasible to formulate and solve broad scope production planning models. These models can be a significant aid in the development and analysis of operations and investment plans. If this is the case, why have not more applications actually been made? While this field of advanced mathematical methods and so-called "scientific management" has had its glamorous aspects, it has, nevertheless, been a subject of considerable controversy-particularly when applied to general over-all planning problems. Some proponents have stated that "computers will soon be running the business" or that "soon it will be possible to develop computer tools to replace middle management." It is felt that not only are such claims wrong, but they also are dangerous. But what of the critics?
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