Chemical and Petroleum

Operations Research (OR) has a rich history in the chemical and petroleum industry. This industry was an early adopter of OR, especially of mathematical programming, and in turn motivated and contributed to the development of OR.  

Although Standard Oil of California Vice President G. L. Parkhurst told the 1956 annual meeting of Operations Research Society of America (ORSA) (Parkhurst 1955) that “the broad principals of operations research had been applied to industrial problems many years before the name given to your field was invented,” perhaps the earliest formally recognized OR problem in this industry is the classical blending problem. Mathematically it involves maximizing a linear profit with linear constraints on availability, capacity, and quality; see, e.g., (Symonds 1956). In a petroleum blending problem, the aim is to find the composition of a mixture which meets certain quality specifications.  

W.W.Cooper recalls (Cooper 2002) a chance luncheon encounter with A. Charnes that resulted in introducing Charnes to the problem of ameliorating the “octane giveaway” that he, R. Mellon at Gulf, and D. Rosenblatt at Carnegie were working on for Gulf; and providing Charnes with unpublished papers intended for presentation at the upcoming landmark Cowles Commission Conference in June, 1949.  These included the seminal paper by G. B. Dantzig called “Maximization of a Linear Function of Variables Subject to Linear Inequalities,” later published in a conference volume (Dantzig 1951).  As a consequence, Charnes, Cooper and Mellon (1952) presented a LP formulation that meets requirements for a mixture's ignition and volatility.

In 1953, G. H. Symonds, then at Esso Standard Oil Co., presented another blending formulation for gasoline refining in a book published by Esso (Symonds 1955). In 1957, Lee and Aronofsky (1958), then at the Magnolia Petroleum Co., provided a LP formulation for scheduling crude oil production from different sources to maximize profit. (This is a non-linear problem, but the authors formulate it as a LP under certain restrictions).

Linear programming and other OR methods also saw early use for several other problems in the industry.  Some were described at a symposium organized at the 1955 ORSA meeting at the behest of Dantzig-including optimizing the schedule by which each oil should be produced over time from a set of reservoirs, product distribution in an expanding market, and routing of gasoline deliveries to service stations (Garvin, et al. 1957).  In 1968, with specific reference to the chemical industry, Shell Oil President R. C. McCurdy (1968) outlined a broad array of applications in research and development, planning, plant location, product introduction, operations and marketing. Bodington and Baker (1990) provide a historical account of the development of mathematical programming in the petroleum industry.

In the chemical and petroleum industry, a process typically involves several integrated unit-processes, such as heat exchangers, reactors, and distillation columns, with an aim of economic feasibility. Like the blending problem, a significant number of chemical engineering problems arise with respect to systems involving these processes which are non-linear and may also require global optimization solvers. For example, a chemical process could consist of several steps that are related non-linearly, and we may seek to determine its optimum operating conditions. Dantzig et al. (White, Johnson and Dantzig 1958) provide two examples of non-linear models for such problems: (i) an alkylation process, with interdependent decision variables, in a petroleum refinery that maximizes a quadratic revenue, and (ii) a chemical equilibrium problem, to minimize a gaseous mixture's free energy governed by a non-linear convex function subject to linear mass-balance constraints.

Moreover, there are often uncertainties in the demand and availability of materials in the chemical and petroleum industries. One such early problem considers the uncertainty in weather-related demand for a grade of heating oil whose production schedule we seek to determine. This application motivated the development of chance-constrained programming (CCP), which is a subset of stochastic programming. CCP is attributed to Charnes and Cooper’s work (1959) from the 1950s, and involves satisfying a probabilistic constraint with some degree of confidence.  Significant research effort has been invested in CCP and other methods to deal with uncertainty in optimization since then.

As has been the case in many industries, petroleum and chemical companies set up internal OR groups in the US and elsewhere. The work of some of these groups is described here.

  • In 1951, an internal OR group was set up by Britain's largest producer of viscose yarns, Courtaulds (Kirby 2003). This group studied various applications to the sewing industry, central to Courtaulds’ work, such as the optimal usage of bobbins and length of spinning runs, and used standard statistical methods.
  • In 1959, C.W.Carroll presented his doctoral thesis on a kraft paper pulping process (Carroll 1959) to the Institute of Paper Chemistry in Wisconsin (now Renewable Bioproducts Institute in Atlanta).  Fiacco and McCormick’s Sequential Unconstrained Minimization Technique, subject of a book (Fiacco and McCormick 1968) that won the 1968 Frederick W. Lanchester prize for the best publication in OR, was at least partially motivated by Carroll’s approach, which is described in (Carroll 1959) for which Fiacco was an acknowledged referee.
  •  In 1965, an OR group was set up at the oil company Petrobras, now the largest business corporation in Brazil. The group developed their first LP model in 1967; see (Iachan 2009) for a history of its developments.
  • Esso Mathematics and Systems, a unit of what eventually became ExxonMobil, was established in 1967. The unit was largely devoted to applications of OR, as well as information technology.  For example, T. E. Baker (Baker 1981) of this unit developed a branch and bound algorithm for multi-product multi-facility process scheduling for unit operations in a refinery, and also embedded the algorithm in an interface for users with no knowledge of mathematical programming.
  • Shell's OR activities in the 1960's and 1970's were conducted at Shell Development Company in Emeryville, California. M.H.Rothkopf provides a personal view of his research there (Rothkopf 2001). He describes optimization problems at Shell dealing with scheduling oil tankers, deciding when to accept a construction bid and bidding for offshore oil leases, and determining the projected demand of future energy.  He also describes analytical solutions for these optimization problems.
  • Like Esso/Exxon and Magnolia (and formerly, Standard Oil Company), the Chevron Corporation solved refinery problems. In 1991, Chevron also started employing decision analysis in its operations, and in 2014 won the Raiffa-Howard Award for Organizational Decision Quality. Chevron won the INFORMS prize for the Best Analytics & O.R. Company of the Year for 2015. 

Carnegie Mellon University (CMU) has been an important center of academic work on OR applicable to the petroleum and chemical industries.  For example, the research of CMU professor I. Grossmann and his late student C. A. Floudas (Floudas 1995), and CMU professor L. Beigler (Biegler 2010) is motivated by process systems.  They have made several contributions in mixed-integer programming and global optimization methods.  

-Bismark Singh

Links and References

Baker, Thomas E. "A Branch and Bound Network Algorithm for Interactive Process Scheduling." In Network Models and Associated Applications, 43-57. Springer, 1981.

Biegler, Lorenz T. Nonlinear Programming: Concepts, Algorithms, and Applications to Chemical Processes. Vol. 10. SIAM, 2010.

Bodington, Charles E., and Thomas E. Baker. "A History of Mathematical Programming in the Petroleum Industry." Interfaces (INFORMS) 20, no. 4 (1990): 117-127.

Carroll, Charles W. An Operations Research Approach to the Economic Optimization of a Kraft Pulping Process. Georgia Institute of Technology, 1959.

Charnes, Abraham, and William W. Cooper. "Chance-Constrained Programming." Management Science (INFORMS) 6, no. 1 (1959): 73-79.

Charnes, Abraham, William W. Cooper, and Bob Mellon. "Blending Aviation Gasolines---A Study in Programming Interdependent Activities in an Integrated Oil Company." Econometrica: Journal of the Econometric Society (JSTOR), 1952: 135-159.

Cooper, William W. "Abraham Charnes and WW Cooper (et al.): A Brief History of a Long Collaboration in Developing Industrial Uses of Linear Programming." Operations Research (INFORMS) 50, no. 1 (2002): 35-41.

Dantzig, G. B. "Maximization of a Linear Function of Variables Subject to linear Inequalities." In Activity Analysis of Production and Allocation, by T. C. (ed.) Koopmans, 359-373. New York: John Wiley & Sons, 1951.

Fiacco, Anthony V., and Garth P. McCormick. Nonlinear Programming: Sequential Unconstrained Minimization Techniques. New York: John Wiley and Sons, 1968.

Floudas, Christodoulos A. Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. Oxford University Press on Demand, 1995.

Garvin, W. W., H. W. Crandall, J. B. John, and R. A. Spellman. "Applications of Linear Programming in the Oil Industry." Management Science (INFORMS) 3, no. 4 (1957): 407-430.

Iachan, Roberto. "A Brazilian Experience: 40 Years Using Operations Research at Petrobras." International Transactions in Operational Research (Wiley Online Library) 16, no. 5 (2009): 585-593.

Kirby, Maurice W. Operational Research in War and Peace: The British Experience from the 1930s to 1970. Imperial College Press, 2003.

Lee, A. S., and J. S. Aronofsky. "A Linear Programming Model for Scheduling Crude Oil Production." Journal of Petroleum Technology (Society of Petroleum Engineers) 10, no. 07 (1958): 51-54.

McCurdy. "Application of Operations Research to Chemical Technology." Industrial and Engineering Chemistry 40, no. 2 (February 1968).

Parkhurst, George L. "A Challenge to Operations Research." Journal of the Operations Reearch Society of America 3, no. 4 (November 1955): 376-382.

Rothkopf, Michael H. "Tales from a Nonstandard Career in Operations Research." INFOR: Information Systems and Operational Research (Taylor \& Francis) 39, no. 4 (2001): 367-393.

Symonds, Gifford H. "Linear Programming Solves Gasoline Refining and Blending Problems." Industrial \& Engineering Chemistry (ACS Publications) 48, no. 3 (1956): 394-401.

—. Linear Programming: The Solution of Refinery Problems. Esso Standard Oil Company, 1955.

White, William B., Selmer Martin Johnson, and George Bernard Dantzig. "Chemical Equilibrium in Complex Mixtures." The Journal of Chemical Physics (AIP Publishing) 28, no. 5 (1958): 751-755.

Associated Historic Individuals

Frey, Donald N.
Green, Paul E.
Hess, Sidney W.
Hirshfeld, David S.
Jaikumar, Ramchandran
Klingman, Darwin D.
Lasdon, Leon S.
Manne, Alan S.
Muckstadt, John A.
Pollock, Stephen M.
Rothkopf, Michael H.
Silver, Edward A.
White, Jr., John A.