OPERATIONS RESEARCH SYMPOSIUM
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s a means of developing this subject, what I should A l i e to do is follow the kind of events that occur in the l i e cycle of a chemical project. I plan to review
some of the ways in which operations research can be applied, starting with exploratory research, and going through the development and commercialization stages. Since my own career has been spent entirely in the oil and chemical industries, I shall lean quite heavily on experiencei within thAe domains and I shall draw on them for illustrations as we proceed. The title of this article is couched in rather general terms and I think it is necessary to start hy defining how I shall construe operations research and contrast it with some more familiar ways of planning and decision making. First then, let me attempt to define operations research as I shall use the term. T o me, operations research is the rational application of quantitative methods to problems of planning and decision making. Now let me take several sentences to explain what I mean by this definition. We have used the adjective “rational” to indicate that the attempt to be quantitative will be reasonable relative to the accuracy ofthe numbers needed and to the difficulty in obtaining them. In specifying that the methods are quantitative, we do not mean to say that we are concerned only with numbers and equations. We are concerned with bettering the relationships between such things and the various factors that go into planning and decision making. Making these relationship explicit is included in our use of the word “quantitative.” It is a good approximation to say that operations research is an extension of the methods of engineering. It is pcrhap pertinent to a& at this point, what is there about today’s world that is different from the past and makes operations research of such importance. I think basically there are two things: One is our ability to generate vast quantities of data and information in a relatively short time and the other is the development of 14
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ot 0perations Research to Chemical Techno1ogy RICHARD C. McCURDY
The range of operations research and the power of its techniques cover all stages in the life of a chemical product, from initial research to marketing
techniques for handling and interpreting these materials. As an illustration we might consider a trader of the Middle Ages making his way generally down the river valleys from Switzerland to the sea. You will recall the vast number of principalities, both temporal and ecclesiastical through which he would have to pass. Each had its own markets, its tolls and tariffs, and various assorted charges. Undoubtedly the trader did his best to choose a route which would tend to minimize the dangers and cost and at the same time try to include the more profitable markets. We in today’s world, however, would consider him woefully lacking in information as to market prices, the exact tolls in force, the conditions of the roads and rivers, the extent of brigandage, and the like, so that his decision as to the route he chose was probably far from optimal. O n the other hand, when one again thinks of all the various possibilities open to him it seems fairly reasonable that even had he possessed all of this information, he still would have been hard put with the techniques then available to come out with an optimal solution. Techniques
You will note that in defining operations research I did not mention any specific techniques or tools. This was deliberate since I think of this as an open-ended field, with new techniques being developed and applied continuously. However, as currently practiced, operations research depends heavily on a few techniques. Since I will be referring to these later on, I will say a word about them now. Most of our problems in operations research have to do with finding the optimal setting of the controllable variables subject to the restrictions, requirements, and opportunities of the particular situation involved. The resources at our disposal over which we have a certain measure of control could be money, people, a raw material or intermediate product, capacity of a produc-
tion unit, or even time. We might be required to satisfy such needs as demands for products, using up all of a material, or quality specifications of products. Such a problem is called a mathematical programming problem. When the variables are related in a certain simple way, we have the. familiar linear programming problem. Certainly, real-life situations are seldom linear, but for small changes in the variables a linear program is a satisfactory approximation. Because linear programming is so well developed theoretically and is such a powerful computational tool, it is the most widely used mathematical technique of operations research. Great ingenuity has been applied in formulating problems so that the assumption of linearity is no handicap and the power of linear programming can be used. Since we are dealing with quantitative methods, we frequently develop mathematical representations of the systems we are studying. These highly simplified abstractions of the real world are usually called simulations. Sometimes we simulate events which occur sequentially in time, in which case we have a dynamic simulation. When the values of some factors or the outcomes of events are not certain, but are calculated from probability distributions, then we have a probabilistic or stochastic simulation. Such simulations are particularly useful in applications of decision theory. Decision theory is concerned with the means for making decisions in the face of uncertainty. I t considers techniques for structuring information for decision making, the information content of data, and the value of additional information. Its uses are growing rapidly. Finding these mathematical relationships leads us, of course, to the use of statistical methods for the correlation and interpretation of data. A wide variety of techniques are now available both for planning the taking of data and data treatment. To summarize, the mathematical tools we use in operations research include the classical ones of numerVOL. 6 0
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ical analysis and differential equations, the classical but only recently applied methods of probability theory and statistics, and the new fields of mathematical programming and decision theory. Operations Research Approach
Having attempted a definition of operations research and having mentioned a few of the current tools of the trade, I want to say a few words about how this approach differs from past ones. Most of the basic problems and the solutions, in principle, to some of them have been known by engineers for some time. However, it was clear that solution to them would require an impractical amount of data gathering and of computation. The stored-program digital computer has changed that situation. It is now practical to solve quantitatively problems for which we previously had to estimate, or even guess, answers. The availability of this computational power has, in turn, stimulated mathematical research which has led to even greater gains. There is a contest between the operational researcher formulating problems that strain the capacity of current computers and the computer manufacturers introducing yet more powerful and less expensive machines. The improvement in computer technology in the past two decades can only be described as dramatic. Since 1950, the number of computer operations we can buy for a dollar has increased at an average rate of about 80% a year. Expressed in another way, we now can get 20,000 times as much computation today for our dollar as we could in 1950. This rate of improvement has fallen off in recent years and predictions are for it to continue to decrease. However, computers are expected to continue their amazing increase in speed, with 1975 computing speeds 100 to 1000 times those of today. Does this mean that the mathematician and the computer will replace the intuition and judgment of the engineer and manager? Hardly. What it does mean is that the planners and decision makers will apply their intuition and judgment, and the tools of operations research can then be used to analyze the complex relationships between the variables. The analytical results show the possible consequences of the intuitive answers, and can be checked for reasonableness, thus helping guide intuition. Operations research can assist creativity, but it can never replace it. Let me give an example of what I mean. It is unreasonable to expect an individual to estimate singlehandedly the uncertainty in profitability of a complex venture involving several products. No one person can be aware of all the uncertainties in the estimates of capital and operating costs, of prices, and of sales volumes of the products. However, it is reasonable to ask someone to estimate the uncertainty in the price of a certain product in a certain year, and another person to estimate the uncertainty in yield of a certain reaction, and so forth. These estimates can then be combined in a mathematical model to produce estimates of the uncertainty in over-all profitability. Now, the price and volume estimates were based on the assumption of a particular marketing 16
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strategy. Another strategy would result in different estimates and in a different calculated profitability. The creation of these strategies depends on the intuition of the businessman-their consequences are estimated by the operations research study. Thus, a circular procedure of strategy proposal and testing by the model can be used to stimulate the imagination of marketing people. I hardly need to remind you that no amount of computational gymnastics will actually sell a product. The customer is still king and, as always, the best-laid plans can succeed or fail depending upon competition and the skill and energy of that all-important man, the salesman. Applications in Research and Development
Before describing the applications themselves, I should say a few words about their origin. Many of them represent work we have done in Shell and of course I will emphasize these. Applications have also been reported in the literature by others, either as real cases or as proposals illustrated with artificial examples. Our purpose is to show the very wide range of possible applications and to stimulate experiments in their use. Obviously, this does not represent a complete list by any means. Exploratory research. The life of a chemical project usually begins in exploratory research. The first problem faced here is what areas of chemistry should be explored and with what effort. This problem is among the most difficult for operations research to contribute guidance to intuition and judgment. All too often the benefit from an exploratory research project comes in an unexpected area. Thus, the possible economic value of an exploratory program is very hard to assess a priori. A few stumbling attempts have been made to develop ranking schemes for project selection, but no notable successes have been reported. One useful suggestion from these studies has been to include in the ranking criteria not only the possible economic value of the field to which the project is directed, but also the number of scientific fields to which the project might contribute. This latter factor is an attempt to account for the possible beneficial surprises. So I conclude, albeit reluctantly, that operations research has so far contributed little to this particular phase of a project. Research results. Operations research has more to contribute once exploration has begun and some results are in hand. Statistical methods can be used to explore efficiently the experimental region about a promising result. Thus, the effort can be reduced in getting the numbers needed for the first screening evaluation. Several models have been proposed for deciding on how much further effort should be expended on following up a lead. Imperial Chemical Industries has described a particularly interesting approach to decide how many screens should be applied to a new compound in determining if it has biological activity and is worthy of more extensive testing. The problem they consider is this: Testing is subject to error and this implies a risk that a compound of interest may be falsely classified. This
Construction of a mathematical model of the process can be valuable at an early stage of development
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risk is diminished by increasing the test effort per compound, but when this is done, fewer compounds can be tested, with the result that the chance of encountering an active compound is reduced. An optimum balance exists between these two opposing tendencies. The IC1 approach takes into account the quantities that are at stake-i. e., the value of a successful outcome, the probability of a successful outcome and the effect of thiis on competition in research by other companies, the resources available, and the costs of the compounds and tests. Development. Once a number of attractive leads have been found, we must choose which ones should enter the much more expensive process and product development stage, and here there are substantial opportunities for operations research to make a contribution. Du Pont has reported on the benefits of a probabilistic model at this stage for estimating the value of a project. Our limited experience at Shell confirms this. Quantities to be estimated include probabilities of degrees of technical success, of the length and expense of the development project, and of prices and sales volumes of the products. Du Pont has pointed out the usefulness of constructing the simulation for improving communication between the various parts of the company. Once our invention becomes a process and product development project, the operations research activity increases greatly. Dramatic successes have been claimed for new techniques of project management, such as critical path scheduling methods, in shortening develop ment time for military products. Chemical projects are usually less complex and so the expected benefits are smaller. Nevertheless, such management tools can be quite useful, particularly for coordinating the work in the various groups involved such as process development, product application, and market development. We have found great benefit early in development from constructing a mathematical model of the process. Of course, this will be a very crude one at first and perhaps be used only for automatic material balance calculations. As more information is gathered, equipment sizing and cost estimating routines can be added and preliminary optimization calculations made. The complex relationships between the process variables, typically 15 to 30 in number, and process economics challenge the intuition of even the best chemists and engineers. The model allows new ideas to be explored quickly and economically. Such calculations can be used to guide the development effort and greatly shorten development time. As new information is obtained, the model should be improved
and made more accurate. To make this practical, a flexible computing system is needed, such as our CHEOPS program described at the Fifth World Petroleum Congress held in 1963 in Frankfurt, Germany. Frequently, a crucial part ofdevelopment is the study of the effects of reactor variables on the yields of desirable and undesirable products. Such data are needed tor choosing reaction conditions and for designing the reactor. Mathematical models have proved very valuable here in reducing the number of experiments needed and in producing more accurate designs. Occasionally, it is impossible to model in a pilot plant the physical conditions of a commercial reactor. Then a mathematical model is the only way in which a reasonable design can be made. Currently we have just completed such a study which involves a terribly complicated situation, with high temperatures, critical contact times, extreme corrosion, expensive reagents, hitherto unknown reaction conditions-in fact, one of the most difficult projects we have ever undertaken. The fluid mechanical conditions expected in the commercial size reactor just cannot be matched in the pilot plant. The only practical or economic approach available was a series of studies on an ever-increasing scale using inert fluids. Takiig these results along with the results of separate kinetic studies which had elucidated the physical and chemical changes taking place within the reacting system, we were able to set up a very complex system of equations describing the over-all system. Our engineers have used the model not only to pick a beat design, but also to estimate the selectivity for the desired product at several confidence levels. The model doesn’t help to predict the confidence level of the company president (in this case myself) who is asked to risk millions OF dollars on the process, but it does help to raise it. During development, experiments are run to study process Variables, determine the reactor model, and study product applications. In each of these areas, statistically designed experiments can greatly reduce the number of experiments required. During the develop ment of one of Shell’s hydroformylation procmes for primary alcohols, we found ourselves in a most interesting situation. We had a system which contained a mcderately expensive catalyst which was pnsent in significant concentrations. Mild steel was slowly atracked by this catalyst with lo@ of the catalyst itself. On the other hand, stainless steel was immune but much more expensive. The reaction rate was of course dependent on the catalyst concentration. The question which faced us V O L 6 0 NO. 2 FEBRUARY 1 9 6 0
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then was which process is economically the better-one using low catalyst concentrations and long contact times in very large, mild steel vessels or one using high catalyst concentrations and short contact times in smaller stainless vessels. This was not an easy question to answer, and yet this area of the chemical industry is so competitive that it was imperative that we make the optimum choice. A statistically designed experiment was used to determine quickly the effect of catalyst concentration and its interaction with other variables such as temperature and pressure. The results were incorporated in a CHEOPS model of the process and the full economic effect of catalyst concentration was quickly found. I n this way we were able to provide guidance as to which way the development program should proceed, and all this in a very short period of time. If we had not had this sort of guidance we probably would have spent an additional six months of process development experimentation locating the optimum. I think it may also be of incidental interest to note that a single chemical engineer skilled in this kind of calculation was able on less than a full-time basis to provide this very valuable guidance to the development group during the whole course of the problem. Again, you may be interested in a few details of this guidance program. This program essentially took a number of independent variables and a number of parameters and brought them together to bring out evaluations of where we stood and where we might go. I n this particular case this program was handling some eight independent variables and over 200 parameters. The independent variables are such things as temperature, pressure, and catalyst concentration in the system. The parameters are certain numbers that you fix in advance in setting up your design-for example, what factor do you use in multiplying the cost of a bare piece of equipment to get its installed cost; what constants do you put in the rate equations that you are using to represent the process and that sort of thing. The parameters are thus invariant for each calculation but the calculations are easily repeated for other values of the parameters and in this way desirable directions for experimentation determined. We are quite satisfied that this approach did shorten the time required by a considerable amount, and it has in fact become standard practice with us. With the establishment of a satisfactory process model, optimization calculations then can be made to select conditions for extended pilot plant runs. These runs are made to demonstrate process feasibility and to study problems which cannot be investigated on a small laboratory scale. Typical problems which require large-scale tests are extended recycling of unconverted feed which can lead to a build-up of hitherto undetected by-products, corrosion, and selection of materials of construction. In some cases pilot plant runs are needed for the preparation of larger amounts of material for market development purposes. Before going on to the next stage in the life of our project, I would like to give one further illustration of the utility of the process model. After our polypropylene 18
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plant in Woodbury, N. J., was under construction, it appeared that it might be advantageous to change to a completely different feed purity than that for which the plant was designed, and some preliminary calculations indicated that even more far-reaching changes in reactor composition might be in order. Our process model using our CHEOPS program was quickly changed and the feasibility and desirability of these newly suggested process conditions were confirmed. Happily our commercial experience completely vindicated the calculated predictions. Perhaps the most dramatic example of the value of a process model is that of the Shell process for ethylene oxide by direct oxidation of ethylene. In the past nine years, 15 plants have been built and another four plants are in various stages of design or construction. These plants have a total capacity of 620,000 tons per year. Most of these plants were designed by Shell for other companies after they selected the Shell process over a competitive one. The model made it possible to produce optimal designs for each licensee’s peculiar combination of ethylene purity and availability, product purity and volume, and economic factors. This has helped in the competition for the most economical process. Of at least equal importance, Shell simply would not have had the necessary manpower to perform this volume of design calculations by hand. Applications in Planning
Returning again to our general subject, we have reached the stage in the life cycle where the process has been demonstrated, the product’s properties have been shown to be attractive, and the process economics are rather well known. Depending on the nature of the products, various product development and market testing activities have been carried out. Venture analysis. We are now ready for a final evaluation to assess the commercial venture and prepare the request for capital. Management requires answers to a number of questions, among which are: 0
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What is the expected profitability of the venture? What are the risks involved; that is, what are the uncertainties in profitability? What should be the capacity of the plant if it is built? What marketing strategy appears most attractive at this time? Where shall we locate the plant? Should we have one plant or several at different locations?
A method for improving our answers to such questions that we have found useful in Shell and reportedly is used by a number of companies is the probabilistic simulation. Such a model is similar to that which we described for estimating project value at the time of selecting development projects. Now, however, because of the increased gravity of the decision and the much greater knowledge
C. McCurdy is President of the Shell Oil co. with headquarters in h’ew York City.
AUTHOR Richard
available, a much more detailed model is justified. This model considers both the technical and the marketing sides and requires the skills of both these organizations for its formulation. Such a model considers all of the important factors which determine the operating and capital costs of the plant. For each of these factors for which there is significant uncertainty, a probability distribution is estimated for the level the factor might attain rather than a single “best” value. These distributions are estimated by the chemists and engineers who know the most about each of the factors. The most difficult, however, and usually the most critical, part of the model concerns the marketing sector. It must show the significant relationships between prices and sales volumes of the different products, all as functions of time, and the information here must be supplied by those most knowledgeable in markets. Frequently, it would be easy to visualize a model needing thousands of numbers to be estimated. For example, in a study for Shell’s entry into the detergent alcohol market, our market development people had no difficulty in suggesting so many interrelated factors for inclusion in a model that it would have required over 300,000 numbers to be estimated. The trick is to design the model so that it is a reasonable approximation of the market and still simple enough to be practical. Most of the uncertainty usually lies on the marketing side, so particular care is needed in getting probability estimates. The model is used in what is called a Monte Carlo calculation, a name meant to suggest the random way in which values are chosen for the uncertain factors, much like the numbers on a roulette wheel. As one who must act on proposals justified by such calculations, I would feel more confident with a name with less of an association with gambling. The calculation begins by choosing a value for each uncertain factor in accordance with its probability distribution. These values are then used for a normal economic evaluation of the project. We repeat this procedure many times, the resulting values forming a probability distribution for profitability. Returning to our analogy with a roulette wheel, we can find the probability of winning any particular bet on the wheel by observing many plays of the wheel. We do the same with the profitability of the venture. The probability distribution for profitability can then be used to calculate statistics such as the expected value of profitability and various measures of risk. There are several advantages to this approach. Primarily, we get a direct measure of venture worth and uncertainty based on well-defined quantities estimated by the people who know the most about them. We get away from the ambiguous single “best” estimate, which means different things to different people. Also, we are using most of the information our people have rather than only a small part of it. At least as important as any of the numbers produced by the analysis, is the improvement in communications between the different people working on the project. Many misconceptions about the venture are discovered and corrected during the course of formulating the
model. I n general, the exercise of formally writing down the relationships between the variables which go into the the success of a venture, and of estimating values and uncertainties for those variables, clarifies our thinking about the venture and helps to identify the most important ones. I n our own experience this has been very beneficial in assuring that the different parts of our organization do come together for a meeting of the minds. Plant location and product introduction. Another decision which needs to be made by now is where to locate the plant. We must balance raw material, manufacturing, and distribution costs to find the lowest-cost combination. For example, a relatively high-cost manufacturing operation can be justified in places like Alaska if supply and distribution savings result. Plant location models have been widely discussed in the literature and apparently are used frequently. Concurrent with process development and design and with the venture analysis, we have begun to consider in detail the problems of introducing our products in the market. Just how operations research can assist us here depends on the nature of the products. Suppose that we can make a number of grades, differing only slightly in cost, but differing enough in properties to allow them to penetrate different segments of the market, each having a different price-volume-time relationship. T o minimize risk, we may wish to start with a relatively small, but easily expanded plant and increase capacity as sales build. We can then simulate the market with a mathematical model and use it to estimate the optimal time to enter each of the markets. There are many variations of this problem depending on the nature of the products and of the market. I n any event, the selection of an initial price and a sequence of price changes as a new product is introduced is a common problem and one which usually can be studied with a mathematical simulation. By this time our model is ready to provide management with a pretty comprehensive picture of what probably will be returned from a given investment in the venture, and when. This can in turn be set against the background of the company’s aims and objectives, resources, commitments, responsibilities, and alternative opportunities, and can be studied to determine its fitness as a part of the organic whole which a good industrial enterprise should be. Sometimes the decision is easy, as when, for example, the venture appears attractive and fits nicely into a going segment of the business; but sometimes it can be quite difficult, as when important choices must be made. I n this area, models for finding optimum allocation of capital have been proposed, but I have not heard of any that appear to me to be able to assist an operating company’s top management much in this sort of knotty problem so peculiar to it. Financial planning. There is one area, however, in which probabilistic simulations of cash needs have proved useful to our top management in its over-all financial planning. With a flow of promising new processes or other projects coming along, the usual exVO1. 6 0
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Once the plant has been built, operating programs are needed to utilize it effectively
perience is that some, but not all of these wiU actually come to fruition. To provide for all of them in forward cash projections will probably overestimate capital needs. Shell Chemical has recently had considerable succew in estimating, for each new process under study, the probability that a plant using that p r m w wiU be built in a given period of time, and in using these data to arrive at their probable financing needs. Construction contracting. Once we have the capital, we must choose a contractor to construct the plant for us. Models of competitive bidding have been proposed for selecting how many and which contractors should be invited to bid. We would like to have as many bidders as possible so as to increase our chances of getting a very low bid. However, most capable contractors will not prepare a bid if too many competitors have been invited to bid. Afso, contractors would have to raise their bids in order to pay for the cost of preparing so many unsuccessful ones. These factors have to be balanced to choose the best number of bidders. I n another application, it is likely today that the contractor selected would use critical path or PERT techniques to manage the project. Knowledge of these techniques is spreading quickly because their use is required on important projects for the Department of Defense. Applications in Operations and Marketing
Now that we have our plant, we must develop a n operating program whick makes the best use of it. Mathematical models of manufacturing plants are very helpfd in developing minimum-cost running plans. For discussion purposes, I ahall divide these models into two main groups: planning models and control models. Planning models consider a relatively long-time scale, usually at least a month and possibly even years. Product demand and raw material availability are each aggregated to cover the planning period. A plan is prepared which represents an “average” operation for that period. The principal deficiency of this model is that it does not account for the day-to-day upsets which characterize actual operation. However, we may consider the plan as a strategic guideline for operations planning. Such questions ad the feasibility of making a particular product mix, determining plant capacity, and uncovering equipment bottlenecks can be studied in a gnm sense. When we have several plants making the same product and serving multiple markets, then we have a particularly challenging problem. Models of individual plants may, of course, be constructed and run separately. T o 20
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achieve a minimum-cost operation, some scheme must be developed to estimate the marginal cost of each plant-tomarket combination. When plants are able to exchange partially processed material, the figuring becomes even more complicated and we must construct multiplant models. A complete system description should also consider inventory costs and distribution costa. These models may be quite large. I n some c a w they can be formulated as linear programming models within the limitations for which solutions are practical; in other cases they have proved t w complicated to handle. Control models usually operate on a much shorter time scale. As an extreme, we may consider so-called plant computer control. I n thii case, a number of measurements are made very frequently, scanned, and converted into output signals which determine movements in key plant variables. This “conversion” is no trivial operation. I n fact, a mathematical model of the unit or plant is manipulated to seek improved operation -for example, greater yield or lower costs. Computer control has had a number of applications in the oil and chemical industries. In Shell, for example, we have applied it to a catalytic cracking unit and to our polypropylene plant. In the polypropylene plant, we are trying to control the molecular weight and molecular weight distribution of the polymer, characteristics which can only be measured in the laboratory, and with long time lags. This model in the computer predicts these p r o p erties dynamically and is used to control them. The data needed for the pddictions include some not usually measured, such as the air temperature and the wind direction and velocity. (These data are needed because of temperature effects.) The justification of control computers and models is tied closely to our justification of improved process instrumentation. Fortunately, lowcost, special-purpose computers are becoming available which have improved the over-all economics of computer control. Scheduling models. Intermediate in the hierarchy of operating models is the scheduling model. Here the time period might be a day, or possibly wen as little as several hours. Detailed information on equipment limitations is built into such models. By their nature they are expensive to develop and maintain. Furthermore, the mathematical structure of the problem usually defies simple solution. Linear programming cannot be used to find the optimal operating conditions as was p s i b l e with planning models. Sequencing of tasks is
particularly troublesome. So are start-up and shutdown decisions. A good deal of mathematical development work is under way to permit handling these short-term scheduling problems. Simulation offers a stopgap approach for studying certain scheduling problems. However, simulation per se is rather inefficient, particularly when one wishes to study a number of interacting decisions. Relatively little has been published on the application of short-term scheduling models and solution techniques. As I mentioned earlier, distribution questions impinge strongly on development of manufacturing plans, and vice versa. O n the other side, marketing decisions are affected by our ability to deliver product to the market place in a timely and economical manner. Thus, distribution models exist between two interfaces and can be considered independently only with difficulty and some danger. Inventory control is normally considered as part of distribution decision making. How much of each product should be carried in inventory? Where should it be held? What reorder policy should be followed? Pressures generally exist toward high inventories. Long manufacturing runs minimize setup costs and permit plant economies. Customer satisfaction is assured with higher inventories. These pressures must be balanced against the cost of carrying this inventory, including the capital costs for tankage, pressure spheres, and other equipment. A distribution system model can examine the effect of various inventory policies on over-all earnings. Few chemicals proceed directly from plant to customer. The location of intermediate storage, usually in the form of warehouses, can be formulated as a minimum-cost problem. The trade-off comes when we balance warehouse size against distance to ultimate customer. O n the one hand, we can have many small warehouses, with a large total cost, and relatively low transportation costs for delivery to customers. O n the other, a few large warehouses would reduce warehousing costs, but would increase transportation costs. The problem is to find the best balance of these alternatives. Distribution. Problems in distribution can often be described as networks. In a typical network, the sources represent plants and the sinks ultimate destinations. Intermediate points can represent warehouses or distributors. Such networks are often quite large. Fortunately very efficient methods have been developed to obtain minimum-cost flow patterns, while satisfying demands and availability requirements. Models with thousands of destinations and hundreds of sources are solved routinely. Mathematical complications are introduced when the means of transportation have limited capacities. For example, a pipeline has a finite capacity. This problem has also been solved efficiently. A more troublesome mathematical complication is posed by the sharing of facilities among several flows. This complication arises when the same pipeline, ships, barges, or trucks are used for a number of products. Methods are being tested for
solution of this problem. All the above comments assume that a fixed and uniform cost is established for shipment between points by a particular method (barge, tank car, or truck). When the unit cost depends on the amount shipped, present mathematical methods no longer work. Likewise, if we are required to use only integral units of transportation capacity (tank cars, ship cargoes, etc.), we do not have efficient means to solve the problems. The extension of network methods to cover these realistic problems is a very active area of research. The technology of chemical distribution is changing rapidly. Jumbo tank cars, three times the size of standard ones, containerization, pipelines-all are permitting unprecedented economies. Thus, choices now exist where none did before and operations research studies can be used to find the most economical ones. A final point may be made about distribution decisions, More than most operating decisions, they depend on uncertain and uncontrollable conditions. Weather changes can exert short-term effects. Gain or loss of a large account in one location can be significant. Thus, statistical forecasting methods can be fruitfully used, particularly in making investment decisions. Marketing. Since we are managing production and distribution so well, we must be selling a lot of product. What has operations research been doing to help our marketing effort? Traditionally, much of the analysis of the marketing function has been performed under the heading, “market research.” This discipline has attempted to apply statistical techniques to the problems of measuring performance in marketing and relating this performance to the contributing factors. Because of the uncertainties inherent in marketing, the mathematical techniques for handling problems involving stochastic processes have become popular in this field. Computer availability has given rise to studies in the simulation of consumer behavior. Statistical decision theory has been applied to problems of pricing. The competitive nature of marketing has been studied with game theory and competitive bidding models. Although there have been some successes in these efforts, the results have not been widely publicized. However, marketing and, more generally, mechanisms involving human behavior constitute a very difficult problem area in operations research because the current state of the art does not yet provide adequate techniques for analyzing comprehensively the highly complex mechanisms involved in human relations. Modeling these mechanisms presents a very great challenge. Models have been used, apparently with some success, in a few areas of marketing. Thus, the distribution of sales effort among different classes of customers has been studied. Advertising agencies say that they will find the optimal allocation of our advertising funds among the various media. Linear programming is used here. There is still a great deal of debate about how to measure the effectiveness of advertising. An impediment to the development of adequate marketing models has been the lack of reliable data for VOL. 6 0
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testing the proposed models. With the rapid advances in data processing techniques and equipment currently taking place, we can expect more rapid advancement in application of operations research to marketing problems. If we are really doing so well, there is a good chance that we should consider expanding our manufacturing facilities. Once again we have a venture to analyze and can use models to assist us. We can use a distribution model to help decide whether to expand our existing plant or whether to build a second one to serve a distant segment of the market. As with any investment, a venture simulation should be considered.
Finally, operations research has a quality that seems fundamental to all research, namely that it usually takes longer and costs more than we expected. Since we usually have more studies to make than we have people to make them anyway, we can choose those projects for which the anticipated benefits are much greater than the estimated costs. Then the higher costs will still be irritating, but at least the studies will be profitable. This technique seems to satisfy us with chemical research. However, again as with chemical research, the time factor may be all important. In some cases, the timeliness of the results may be crucial and late results may be useless.
Current limitations
Since I have described so many possible applications of operations research, you might think that it is easy to apply. Unfortunately, it isn’t. The problems seem to cluster about people, data, and money. Our first problem with people is to find really capable people to carry out the studies. Most operations research practitioners today are retreads-people trained to be mathematicians, or engineers, and who have taught themselves to use the tools of the trade. We are only now beginning to get graduates who are educated as operations research specialists. Even rarer are engineers who have received some training in operations research at the university. However, a knowledge of the techniques is not enough. We need people who can formulate the mathematical models, those approximations of the real situations, to which the quantitative tools are applied. Our second problem with people is to assist both our operations researchers and our managers to cross the communications barrier that sometimes exists between them. Those of you who were managers 20 years ago will probably agree with me that operations research then could to a considerable extent be described as sitting down yourself, or with a few of your people, and figuring out how to improve your operations, using methods that were really not at all difficult to understand; but now the large-scale employment of the computer has opened up new opportunities using procedures not so easy for the average manager to follow. The communications problem is not made any easier by, on the one hand, exaggerated claims about what the new methods can do, or on the other hand, by exaggerated opposition to giving the novel methods a trial. I am glad to gel1 you that in many cases where the communications barrier has been crossed, our experience has been that each side comes away with a considerably increased understanding and respect for the work of the other. Quantitative methods of planning and decision making usually require more data than qualitative ones. Much of the value of an operations research study is in finding which data would be most helpful. In many cases, the desired data are difficult and expensive to get, but are valuable and worth the effort. This problem of getting data is one of the principal reasons why many operations research projects fail. That is to say, often insufficient attention is given to how to implement, use, and update the results of the study. 22
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Future Prospects
What for the future? Predicting the future is always hazardous. However, since operations researchers are usually willing to give forecasts, properly qualified of course, so will I , properly qualified of course. The use of operations research is likely to continue to increase rapidly. Vigorous attempts are being made to overcome the problems I just discussed and to strengthen the techniques themselves. Most of the larger universities in the United States now have faculties in operations research and are training graduates and doing research to improve the methods. Some of the students have backgrounds in chemical engineering and so they should be particularly valuable. Also, many chemical engineering faculties now give their graduates some training in operations research, frequently taking advantage of courses offered by other faculties in the university. The solutions to the other problems of application will have to come from further research and from the computer manufacturers. Some on-line computers for data gathering and analysis have already been installed successfully. Much more powerful and more economical ones have been announced. Our data problems are not likely to be solved until almost all of our business and technical data are in computer-accessible form and easily retrieved and manipulated. That is a major research and development project in itself. Another new development that holds great promise is the time-sharing computer. This computer shares its attention among many users and can give each of them immediate access to large files of information, to mathematical techniques for manipulating the information, and to very flexible devices for displaying the results. My own feeling is that this type of computer is going to prove itself so useful and so accessible that our average scientist in the not too distant future will have to be as familiar with its use as he is today with his slide rule. These new systems will surely provide ease of usage and enhance the value of operations research. All-in-all, the operations researcher can look forward to the future with confidence. There is great competition for his services. Others are beginning to believe in and to use his results. He probably is young and time seems to be on his side. He has promised a great deal but, with hard work, good luck, and a great deal of our money, he just might redeem that promise.
