This bibliography consists of the early papers on linear programming model ...
includes some papers that are not about linear programming models but are ...
ANNOTATED BIBLIOGRAPHY ON LINEAR PROGRAMMING MODELS Originally Published in ITORMS ,volume 1, No.4 Frederic H. Murphy, Temple University, Philadelphia, PA 19122
To be cited as: Frederic H. Murphy , ANNOTATED BIBLIOGRAPHY ON LINEAR PROGRAMMING MODELS @ http://www.informs.org/Pubs/ITORMS/Archive/Volume-1/No.-4-Murphy
ANNOTATED BIBLIOGRAPHY ON LINEAR PROGRAMMING MODELS Frederic H. Murphy Temple University Philadelphia PA 19122
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OVERVIEW This bibliography consists of the early papers on linear programming model formulations. It includes some papers that are not about linear programming models but are relevant to understanding the early literature. Examples of these non-LP papers are the Markowitz portfolio model, some integer programming models and papers on input-output analysis. The summaries of the paper are mine and not abstracts, since many of the papers from this era did not have abstracts. I have not read the papers that do not have summaries because I was not able to get copies of them. The value of this bibliography resides in bringing together a literature that is still relevant for understanding LP modeling issues and modeling in general. By scanning the papers, one can see the evolution of issues and trends in the thinking of those involved in developing the field. Personal creativity in model formulation often follows the same pattern as historical creativity, that is, the first formulation of a new model, and this bibliography allows one to trace the historical roots of model formulation. See Murphy and Panchanadam (1995) for an example of how this bibliography can be used for current research. There has been little systematic examination of how one formulates models. We too often dismiss the subject by calling it an art. However, there are basic principles. H.P Williams (1975) articulates some of these principles. One can see in these papers the evolution in the understanding of the natural structures one uses in models to represent certain situations that cut across industries. To make model formulation more of a science, we need to understand the thought processes that lead to successful modeling. One can see how ideas on a model evolve. For example, the LP model for media planning has been the source of many articles and the model is not applied now. Yet, it still appears as a homework problem in all of the textbooks. The literature shows the attempts to fix the model to be sufficiently realistic and the ultimate failure to develop an adequate model. See Bass and Lonsdale (1966) and Engel and Warshaw. With models of production processes, the successes were immediate and the models grew in size and scope in subsequent papers.
One can see how one gets economic insights from models and why certain formulations are inappropriate and others are. Charnes and Cooper were especially concerned about articulating these insights into their articles. Another use is to see who contributed to the development of the field. Charnes and Cooper and Dantzig stand out in the development of new models. However, the number of people involved is large and goes well beyond those we commonly recognize in the field. Interestingly, there are few non-U.S. modeling papers. This can reflect several of possibilities: I could have missed the non-U.S. papers, Europe was recovering from the war and European companies did not have the resources to experiment with new technologies, U.S. companies may have been quicker to adopt ideas from universities in the 50's, the basic technology was developed in the U.S. and national boundaries were more meaningful then. I would welcome more non-US examples. This bibliography also illustrates the kinds of overlaps that existed and, to some extent, still exists with other fields. It contains a remarkable number of papers in economics, agricultural economics, and agriculture. The connection with economics in the early years was quite strong. The fields have far less in common now. Operations research/management science suffers from the reduced interactions. LP models become much more useful in a corporate and governmental policy context when combined with economic concepts. Another area that appears early on is engineering design in the form of models on the plastic limits of structures. Optimization continues to play an important role in engineering design. However, this literature does not make it into our journals. Many of the models in common use now were new inventions at one time. The authors describe these models and, to some extent, what they were thinking about when they developed them. Many of the issues raised in these papers continue, just on a different scale. For example, Swanson and Woodruff (1964) describe how to use advanced bases and a sequencing of models to make it economic to solve the feedmix model. There are many clever reformulations. For example, Bowman (1956) reformulated the production planning problem as a transportation problem. Then S. Johnson (1957) showed that this problem could be solved directly, without resort to an iterative algorithm. The main period covered in this bibliography is the 1940's and 1950's, essentially the first decade of the field. I have included some particularly interesting later articles. As time permits, I will be extending this bibliography through the 1960's. Online databases contain the more recent years, typically starting with material from the 1970's. If readers note that I am missing an article on model formulation from the period through 1970, please contact me with the reference. If it is in an obscure journal, please send me a copy. My intention is also to create a physical archive of these papers.
Bibliography
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REFERENCES NOT IN THE BIBLIOGRAPHY Boden, M.A. (1990), The Creative Mind, Myths and Mechanisms, Basic Books, NY, NY. Murphy, F.H., and V. Panchanadam (1995), "Understanding the Relationships among Linear Programming Problems and Models through an Examination of the Early Papers on Model Formulation," working paper, Temple University.
BIBLIOGRAPHY
Antosiewicz, H. and A.J. Hoffman, "A remark on the smoothing problem," Management Science, vol. 1, October, 1954, pp. 92-95. Characterizes the solution to an intertemporal LP of production smoothing with increasing demand. Uses sums of demands in constraints, rather than inventory variables.
Aronofsky, J.S., "Linear programming--a problem-solving tool for petroleum industry management," Journal of Petroleum Technology, July, 1962. Aronofsky, J.S., "Growing applications of linear programming," Communications of the ACM, vol 7., no. 6, June, 1964, pp. 325- 332. Illustrates the change in the definition of expertise. Pointed out the rapid increase in the size of problems that could be solved. Describes the alternatives for solving larger problems, brute force and taking advantage of special structures. Explains problems of solution stop codes, matrix generation. Flow sheets as visualization, a kind of block-link view.
Aronofsky, J. S., and A. S. Lee, "LP model for scheduling crude oil production," Journal of Petroleum Technology, July 1957. Aronofsky, J. S., and A.C. Williams, "The use of linear programming and mathematical models in underground oil production," Management Science, vol. 8, no. 4, 1962. Models cash flow from production focus.
Babbar, M.M., "A note on aspects of linear programming technique," Journal of Farm Economics, May 1956, vol.38, no.2, pp. 607-612. General LP issues building on a survey by E.O Heady.
Babbar, M. M., Gerhard Tintner, E.O. Heady, "Programming with consideration of variations in input coefficients," Journal of Farm Economics, May 1955, vol. 37, no.2, p 333-341. Estimates of statistical parameters for LP outputs, looks at data uncertainty.
Bailey, M.J., "Generalized comparative statics in linear programming," Review of Economic Studies, vol. 21, pp. 236-240, 1955-1956. Uses linear programming to understand the comparative statics of the Giffen paradox, where when something costs more it is consumed more.
Balderston, J., and T. Whitin, "Aggregation in the input-output model," in Morgenstern, O., ed. Economic Activity Analysis, Wiley, NY, 1954. An I/O focus. However, the same problem arises in policy models that use linear programming.
Bartlett, T.E., F.R. Cassilly, and H.W. Jones, "A mathematical model of job evaluation," The Journal of Industrial Engineering, vol. 8, pp. 283-287, Sept-Oct., 1957. Bass, F.M. and R.T. Lonsdale, "An exploration of linear programming in media selection," Journal of Marketing Research, vol. 3, May 1966, pp. 179-188. Shows negative consequences of the linearity assumption. Since this is a model that failed, it is an example of a model that could not be repaired and made useful.
Batchelor, J.H., "A Commercial use of linear programming," in H.A. Antosiewicz (ed), Proceedings of the Second Symposium in Linear Programming, vol. 2., NBS and USAF Washington D.C., 1955. Describes a situation in the abstract for a production/distribution problem that looks like a transportation problem. The implementation issues are still current and a good discussion.
Baumol, W.J., "The transactions demand for cash: An inventory theoretic approach," Quarterly Journal of Economics, 66, 1952, 545-556. A misapplication of the EOQ model where a network model is the appropriate formulation. Not LP but a good example of a mistake in modeling. This is a situation where LP is the appropriate representation. See Orgler or Srinivasin.
Baumol, W.J., "Activity analysis in one easy lesson," The American Economic Review, vol. 48, December, 1958. An excellent overview of the role of linear programming in economic theory, ties in to I/O and, economic equilibrium theory, and welfare economics. Makes an important distinction between understanding an economy and mathematics.
Beale, E.M.L., " On minimizing a convex function subject to linear inequalities," Journal of the Royal Statistical Society, Series B, vol. 17, 1955, pp. 173-184. Introduces the concept of stochastic programming with recourse independently from Dantzig.
Beckmann, M.J., "A continuous model of transportation," Econometrica, vol. 20, 1952, pp. 643-660. Not an LP paper, but a continuous space model with integrals over regions. Knows of Enke and Samuelson papers on spatial equilibria.
Beckman, M.J., "Comparative statics in linear programming and the Giffen paradox," Review of Economic Studies, vol. 23, p. 62, 1956. Uses linear programming to understand the comparative statics of the Giffen paradox, a situation where a good is consumed more as it costs more.
Beckman, M., and T. Marschak, "An activity analysis approach to location theory," Kyklos, vol. 8, 1955. Relates activity analysis to von Thunen's 1826 model of location. Examines how much to produce at each location for a multi-regional firm, relates to efficiency conditions of a market.
Beckwith, R.E. and R. Vaswani, "The assignment problem--a special case of linear programming," Industrial Engineering, vol. 8, no. 3, pp. 167-172, May-june, 1957. Tutorial on the assignment model, its uses, and solution procedure.
Bellman, R., "Dynamic programming and multi-stage decision processes of stochastic type," in H.A. Antosiewicz (ed), Proceedings of the second symposium in linear programming, vol. 2., NBS and USAF Washington D.C., 1955, pp. 229-250. Notes the connection between mathematical programming and DP in the deterministic case.
Bellman, R., "Dynamic programming and the smoothing problem," Management Science, vol. 2, October, 1956, pp. 111-113. Reformulates Antosiewicz and Hoffman smoothing model as a DP.
Bellman, R., "On the dynamic programming approach to the caterer problem," Management Science, vol. 3, April 1957, pp. 271-278. Reformulates Prager's LP formulation of the caterer problem as a DP.
Bellman, R., "Notes on the theory of dynamic programming-- transportation models," Management Science, vol. 4, April1957. Shows how to solve the transportation model using DP. An inefficient algorithm.
Berman, E.B., "A model for maximizing a vector of final demand deliveries under regional production and transportation network constraints," Papers and Proceedings of the Regional Science Association, vol. 5, 1959. Presents a multi-period, spatial model. It can be considered a corporate model for planning or an economic growth model. The author does a good job of describing the different kinds of approximations one uses depending on the planning horizon and period length. An interesting schematic for presenting models.
Berman, Edward B., "A regional production and transportation model," Management Science, Vol. 5, no. 10, pp. 319-326, 1959. A large LP. He uses an early block-schematic to represent the model. He connects with the I/O literature through the work of Isard.
Bishop, C.E., "Programming farm-nonfarm allocation of farm family resources," Journal of Farm Economics, May 1956, vol.38, no.2, pp. 396-407. Uses LP to evaluate effectiveness of part-time farming. An early data envelopment analysis, before the approach was defined.
Bishop, G.T. "On a problem of production scheduling," Operations Research, vol. 5, no. 1, 1957, pp. 97-103. A better algorithm than the stepping stone algorithm, given the special cost structure of the Bowman transportation model. The author was a high school teacher.
Boles, J. N., "Linear programming and farm management analysis," Journal of Farm Economics, Feb 1955, vol. 37, no. 1, pp. 1-24. Illustration of crop mix using LP. Includes irrigation constraint & cotton acreage restrictions.
Bowman, E.H., "Production scheduling by the transportation method of linear programming," Operations Research, vol. 4, no. 1, 1956. Reformulated the production scheduling problem as a transportation problem. Uses fixed labor, regular time, overtime and inventory. Now the model is well recognized as a netform. S.E. Johnson shows how to solve the problem directly, without any iterations.
Bowman, E.H., "The schedule-sequencing problem," Operations Research, vol. 7, 1959, pp. 621-624. Formulates as an LP and recognizes that it is an IP.
Bowman, E.H., "Assembly line balancing by linear programming," Operations Research, vol. 8, 1960, pp. 385-389. Integer programming formulation.
Brewer, M.A., "The formulation of some allocation and connection problems as integer programs," Naval Research Logistics Quarterly,vol. 13, pp. 83-95, 1966. Laying out components on a board for wiring.
Brigham, G., "A classroom example of linear programming," Operations Research, vol. 7, no. 4, 1959. Formulates the feedmix model and preprocesses to solve more easily. Good example of current concerns with preprocessing for simplex solvers.
Cahn, A. S., "The warehouse problem," Bulletin of the American Mathematical Society, Vol. 54, 1948, pp. 1073. An abstract. The model represents an inventory arbitrage situation.
Catchpole, A.R., "The Application of linear programming to integrated supply problems in the oil industry," Operational Research Quarterly, vol 13, no. 2, pp.161-169, 1962. Applications at Shell Oil. Decomposition and production/distribution. Uses blockschematic representation.
Chambers, D. and A. Charnes (1961), "Inter-temporal analysis and optimization of bank portfolios," Management Science, vol. 7, pp. 393-410. No measure of risk or reference to Markowitz. Meets regulatory constraints for a bank with objective of maximizing profits. Works on yield curve.
Charnes, A., "Constrained games and linear programming," Proceedings of the National Academy of Sciences, July 1953. Mixed strategy games with extra constraints.
Charnes, A., "Future of mathematics in management science," Management Science, vol. 1, no. 2, pp. 180-182, 1955.
Address that relates mathematical developments to different needs. Notes that the importance of calculus was not in numerical solution but in the qualitative formulations.
Charnes, A. and W.W. Cooper, "The stepping stone method of explaining linear programming calculations in Transportation Problems," Management Science, vol. 1, pp. 49-69, 1954. Charnes, A., and W.W. Cooper, "Generalizations of the warehousing model," Operational Research Quarterly, vol. 6, no. 4, 1955. Emphasizes the importance of model analysis. Examines uncertain prices, heavy focus on duals. Uses triangular structures for inventory rather than inventory variables.
Charnes, A., and W.W. Cooper, "Management models and industrial applications of linear programming," Management Science, vol. 4, no. 1, 1957. Explication of LP. Addresses many managerial issues. Extensive bibliography.
Charnes, A. and W.W. Cooper, "Chance constrained programming," Management Science, vol. 6, no. 1, Oct 1959. Model of terminal tankage. Uses block-diagonal structure instead of the now standard inventory constraint. A theoretical statement of the technique with problem as an example.
Charnes, A. and W.W. Cooper, "Some uses of model prototypes in an operations research study," California Management Review, vol. 1 no. 3 pp. 79-96, Spring 1959. Summarizes three models: Lee and Aronofsky on optimizing the cash flow from oil wells, a warehousing model and Charnes, Cooper and Miller on optimizing the flow of funds. Interesting network models.
Charnes, A., W.W. Cooper and D. Farr, "Linear programming and profit preference scheduling for a manufacturing firm," Operations Research, vol. 1, no. 3, 1953. Product mix with minimum demands. Initially presents a static model then adds a dynamic structure. Uses production schedules rather than accounting balances as they always did in this period.
Charnes, A., W.W. Cooper, and R.O. Ferguson, "Optimal estimation of executive compensation by linear programming," Management Science, vol.1, no.2, 1955. Uses absolute value rather than min square deviation in regression. Precursor to DEA.
Charnes, A., W.W. Cooper, and B. Mellon, "Blending aviation gasolines - A study in programming interdependent activities in an integrated oil company," Econometrica, vol.20, 1952.
Use totals rather than ratios for blending. Then subtract to get ratio form. Solution focussed on the blending aspect of refining. Goal was to find business applications of LP. Govt. Funded to do so.
Charnes, A., W.W. Cooper, and B. Mellon, "A model for programming and sensitivity analysis in an integrated oil company," Econometrica, vol. 24, no. 2, April, 1954, pp. 193-217. Uses a refinery model to do sensitivity analysis. They solve the dual because it is smaller. Dealt with some nonlinearities by taking a point and adding some deviations.
Charnes, A., W.W. Cooper, and B. Mellon, "A model for optimizing production by reference to cost surrogates," Econometrica, vol. 23, no. 3, 1955. Presents a convex approximation and separable programming.
Charnes, A., W.W. Cooper, and M.H. Miller, "Application if linear programming to financial budgeting and the costing of funds," Journal of Business of the University of Chicago, vol. 32, no. 1, pp. 20-46, Jan. 1959. Much of the paper devoted to the role of duality in valuing assets. They use Cahn's warehouse model as the example. This model is an arbitrage model. Did extensions to taxes, etc. Still using triangular structure rather than inventory variables.
Charnes, A., W.W. Cooper, and M.H. Miller, "Dyadic models and sub-dual methods," Naval Research Logistics Quarterly, March 1961. Charnes, A., W.W. Cooper, and G.H. Symonds, "Cost horizons and certainty equivalents: An approach to stochastic programming of heating oil," Management Science, vol.4, 1958, pp. 235-263. Chance constrained programming implementation. Good discussion of effects of planning horizon. Sophisticated analytic treatment.
Charnes, A., W.W. Cooper, and G.L. Thompson, "Critical path analysis via chance constrained programming,"Operations Research, vol. 12, no. 3, May 1964. Applies chance-constrained programming to network flow formulation of PERT.
Charnes, A. and H.J. Greenberg, "Plastic collapse and linear programming," (abstract) Bulletin of the American Mathematics Society, vol. 57, p. 480, Oct. 1951. The abstract states that the plastic collapse problem in structural engineering can be formulated as a linear program.
Charnes, A., M.J.L. Kirby, and A.S. Walters, " Horizon models for social development," Management Science, vol. 17, no. 4, December, 1970.
An inappropriate model, should be an equilibrium model. The model views government as profit making enterprize and takes wages as costs, not noting that wages allow purchases. Misses economic equilibrium literature.
Charnes, A., and C.E. Lemke, "The minimization of non-linear separable convex functionals," Naval Research Logistics Quarterly, vol. 1, pp. 301-312, 1954. Introduces concept of separable programming for approximating nonlinear separable functions in an LP. The example used is constrained least squares. The approximation is not the standard convex combinations formulation.
Charnes, A., C.E. Lemke, and O.C. Zienkiewicz, "Virtual Work, Linear programming and plastic limit analysis, Proceedings of the Royal Society (Series A),vol. 251, No. 1264, pp. 110-116, 1959. Charnes, A., J. Logan, and W. Pipes, "A model for the planning and evaluation of sewage treatment systems, ONR Research Memorandum, 1959. Charnes, A., and M.H. Miller, "Part 2: Analysis," Naval Research Logistics Quarterly, vol. 1, pp. 243-252, 1954. Describes the model formulation and solution to the situation at the Union Railroad described by Soyster (1954). A clear exposition of why the assignment model does not work. They formulated a set covering model.
Charnes, A., and M.H. Miller, "A model for optimal programming of railway freight train movements," Management Science, vol. 3, no. 1, 1956, pp. 74-93. Applies the set covering model. Predecessor to airline work in crew pairing, etc.
Chipman, J., "Linear programming," Review of Economics and Statistics, vol. 35, no. 2, pp. 101-117, May 1953. An explanatory paper, taking the requirements view. Examines issues of technology change and other nonlinearities. Shows how to approximate to get closer to economic theory.
Cohen, K.J., and F. S. Hammer, "Optimal coupon schedules for municipal bonds," Management Science, vol. 12, no. 1, 1965. Reformulates Percus and Quinto to simpler model. Uses LP to price coupons to minimize simple interest to municipalities.
Cooper, W.W., "Operations research and economics," (symposium with C. Hitch, W.J. Baumol, M. Shubik, T.C. Schelling, S. Valavanis, and D. Ellsberg), The Review of Economics and Statistics, vol. 40, no. 3, pp. 195-199, August, 1958.
Overview of a symposium, not really LP but a good discussion of what skills are necessary to be an OR practitioner. Subsequent paper by Hitch gives excellent examples of suboptimization and choosing the wrong objective.
Cooper, W.W. and A. Charnes, "Linear programming," Scientific American, pp. 21-23, August, 1954. Early popular article.
Corner, L.J., "Linear programming: Some useful applications," Omega, vol. 7, no. 3, 1979. Good examples where linear programming is used first but other cognitive representations do better. OR people place cognitive bounds by taking constraints as given. Used both a max and min objective on the same problem to see if LP makes any difference.
D'Esopo, D.A. and B. Lefkowitz, "Note on an integer linear programming model for determining a minimum embarkation fleet," Naval Research Logistics Quarterly, vol. 11, pp. 74-82, 1964. An IP model where ships have different kinds of holds and a certain mix of materiel has to be moved and ships have different costs.
Danskin, J.M., "Linear programming in the face of uncertainty," in H.A. Antosiewicz (ed), Proceedings of the Second Symposium in Linear Programming, vol. 2., NBS and USAF Washington D.C., 1955. He shows where expected values get one in trouble when calculating the optimal bomb load for an aircraft. Stochastic programming is necessary. An early good example.
Dantzig, G.B., "Programming interdependent activities, II, mathematical model," Econometrica, vol. 17, pp. 200-211, 1949. Original paper of the general statement of the linear programming model. Shows connection with Koopmans' transportation model, Stigler's diet model and Leontief's I/O model.
Dantzig, G.B., "Maximization of linear function of variables subject to linear inequalities," in Activity Analysis of Production and Allocation (T.C. Koopmans ed.), Wiley, NY 1951. The original paper. It includes a time model that is a military manpower scheduling model.
Dantzig, G.B., "Application of the simplex method to a transportation problem," (pp. 359-373) in Activity Analysis of Production and Allocation (T.C. Koopmans ed.), Wiley, NY, 1951. Dantzig, G.B., "A Comment on Edie's 'Traffic Delays at Toll Booths,'" Operations Research, vol. 2, no. 3, 1954. Develops the personnel scheduling LP using the set covering model.
Dantzig, G.B., "Linear programming under uncertainty," Management Science, vol. 1, 1955, pp. 197-206. Two stage stochastic programming. Uses expected value in the objective function.
Dantzig, G.B., "Optimal solution of a dynamic Leontief model with substitution," Econometrica, vol. 23, no. 3, July 1955, pp. 295-302. Formulates I/O model with multiple activities for production of each item. Presents the properties of the model and an algorithm for solving it that is based on the simplex algorithm. Classic paper on linking Leontief matrices into larger model and solving the system.
Dantzig, G.B., "Recent advances in linear programming," Management Science, vol.2, no.2, Jan. 1956, pp. 131-144. Shows how to formulate a priority scheduling problem for sequencing jobs on a computer as a transportation problem by using Orden's transshipment model. Credits Charnes and Lemke with separable programming. Looks at uncertainty combinatorics from the perspective of LP solutions that are integer and large systems.
Dantzig, G.B., "On the status of multistage linear programming problems," Management Science, vol.6, no. 1, 1959. Algorithm focus. Looks at special cases such as dynamic Leontief systems. First clear statement of LP with inventory balances instead of cumulative coefficients in a triangular structure.
Dantzig, G.B., "A machine job scheduling model," Management Science, vol. 6, 1960, pp. 191-196. Generates columns that represent potential timings for doing each of the steps in a job sequence. For each time period and each machine, there is a constraint with a capacity of 1.
Dantzig, G.B., "On the shortest route through a network," Management Science, vol.6, no.2, Jan. 1960, pp. 187-190.
A simple adjacency algorithm, virtually the same as what is taught now. No LP.
Dantzig, G.B., and D.R. Fulkerson, "Minimizing the number of tankers to meet a fixed schedule," Naval Research Logistics Quarterly, vol. 1, 1954, pp. 217-222. This is a problem of routing tankers to various pickup and discharge points over time. They take what was formulated as an integer program and then show how to reformulate it as a transportation model. It can be thought of as a netform model.
Dantzig, G.B. and D.L Johnson, "Maximum payloads per unit time delivered through an air network," Operations Research, vol. 12, no. 2, 1964. The longest segment determines the amount of fuel needed and this takes from the freight capacity. An extension of the shortest route algorithm.
Dantzig, G.B., and S. Johnson, "A production smoothing problem," in H.A. Antosiewicz (ed), Proceedings of the Second Symposium in Linear Programming, vol. 2., NBS and USAF Washington D.C., 1955. Dantzig, G.B., S. Johnson, and W. White, "A linear programming approach to the chemical equilibrium problem," Management Science, vol. 5, no. 1, 1958. Chemical equilibrium problem expressed in the form of minimizing the free energy using a piece-wise linear approximation to the free energy function. Uses Charnes/Lemke separable programming.
Dantzig, G.B., and J.H. Ramser, "The truck dispatching problem," Management Science, vol. 6, no. 1, 1959. Extension of traveling salesman problem. An IP.
Davidson, D. and P. Suppes, "Experimental measure of utility by using a linear programming model, (abstract), Econometrica, vol. 24, no. 2, April, 1956. They use linear programming to find the indifference zone in a set of samples of choices made by subjects. They then partition the decision space using this information.
Debeau, D.E., "Linear programming isn't always the answer," Operations Research, vol. 5 pp. 429-437, 1957. In steel making the scrap is not uniform and messes up LP blends based on averages. Does not provide an alternative.
Dines, L.L., "System of linear inequalities," Annals of Mathematics, 2, 20, pp. 191, (1918-1919). Dorfman, R., "Mathematical or 'linear,' programming: A nonmathematical exposition," American Economic Review, vol 43, no. 5, part 1, pp. 797-625, 1953.
Still the best overview. It presents the first graphical view--the standard one used in the text books. Connects with the economic equilibrium literature (p. 822) and input/output literature as precursors and notes their different purposes.
Dorn, W.S., and H.J. Greenberg, "Linear programming and plastic limit analysis of structures," Quarterly Journal of Applied Mathematics, vol. 15, no. 2, pp. 155-167, July, 1957. Presents the plastic collapse model in Charnes and Greenberg with variations.
Dzielinski, B.P. and R.E. Gomory, "Optimal programming of lot sizes, inventory and labor allocations," Management Science, vol. 11, no. 9, pp. 874-890, July 1965. Uses decomposition to solve Manne's economic lot scheduling LP.
Eckstein, O., "The input-output system - Its nature and use" in Economic Activity Analysis, Ed. O. Morgenstern, John Wiley and Sons, 1954. Eisenmann, K., "The trim problem," Management Science, vol. 3, April, 1957, pp. 279284. The original specification of the trim problem. No decomposition, just enumeration. A set covering model.
Eisemann, K., "Generalized stepping stone method for the machine loading problem," Management Science, vol. 11, no. 1, 1964. The model is the generalized transportation model with one coefficient per activity different from 1.
Eisemann, K., and J.R. Lourie, "The machine loading problem," IBM Corporation Publication, 1960. Eisemann, K. and W.M. Young, "Study of a textile mill with the aid of linear programming," in R.R. Crane, and C.W. Churchman (eds.), Management Technology, 1960. Elmaghraby, S., "A note on production scheduling by the use of the transportation method," Operations Research, vol. 5, pp. 565-566, 1957. The same model as the Bowman model, evidently invented simultaneously.
Elmaghraby, S. "An approach to linear programming under uncertainty," Operations Research, vol. 7, 1959, pp. 208-216. RHS deterministic, calculate expected value in the objective function.
Elmaghraby, S., "Allocation under uncertainty when the demand has continuous D.F.," Management Science, vol. 6, pp. 270-294, 1959.
Includes a shortage and inventory cost and minimizes expected losses.
Engel, J.F. and M. Warshaw, "Allocating advertizing dollars by linear programming," Journal of Advertizing Research, vol. 5, pp. 42-48, 1964. Good attack on using LP in media selection. Examples with actual data.
Enke, S., "Equilibrium among spatially separated markets: Solution by electric analogue," Econometrica, vol. 19, Jan. 1951, pp. 40-47. Builds a model that could use analog computers for solving. No LP references. This paper was referenced by Samuelson as the one that made him think about the relationship between LP and economic equilibria.
Erickson, V., and P. Randolph, "An application of linear programming to the assignment of materials handling equipment," Industrial Engineering, vol. 8, no. 6, pp. 386-388, Nov-Dec., 1957. Uses assignment model to allocate equipment to products.
Evans, J., "A single-commodity transformation for certain multicommodity networks," Operations Research, vol. 26, no. 4, pp. 673-680, July-August 1976. Constructs an equivalence between the two models when the multicommodity model meets certain conditions. Office of Naval Research supported research at Kaiser Steel. Used ratios for blending restrictions for determining furnace charge. Tried sequencing but failed because of setups, etc.
Fabian, T., "A linear programming model of integrated iron and steel production," Management Science, vol.4, no. 4, 1958, pp. 415-449. Detailed description of an integrated steel mill. Relates the steps in the steelmaking process to variables and equations in an LP. Many blending constraints Good description of a process that is no longer used in steel making--open hearth furnaces.
Fabian, T. "Blast furnace production planning--A linear programming example," Management Science, vol. 14, no. 2 pp. B-1 -B-27, October 1967. A detailed description of a blast furnace and an LP formulation.
Farrell, M.J., "An application of activity analysis to the theory of the firm," Econometrica, vol. 22, no. 3, pp. 291-302, July, 1954. Uses a single period model with long run elasticities to show that the oligopoly price is too high when calculated with short run elasticities.
Ferguson, A.R., and Dantzig, G.B., "The problem of routing aircraft," Aeronautical Engineering Review, vol. 14, no. 4, 1956. Ferguson, A.R., and Dantzig, G.B., "The allocation of aircraft to routes- An example of linear programming under uncertain demand," Management Science, vol. 3, no. 1, 1956. Assigning aircraft to routes using the transportation model. Formulates a maximize revenue objective function with a discrete probability distribution for demands. Solved with a variant of transportation algorithm.
Fetter, R.B., "A linear programming model for long range capacity planning," Management Science, vol. 7, no. 4, 1961. Addresses capacity issues, focusses on leasing, uses spot market to deal with uncertainty.
Fisher, W. D., and L. W. Shruben, "Linear programming applied to feed mixing under different pricing conditions," Journal of Farm Economics, Nov. 1953, vol. 35, no. 4, pp. 471-483. Introduces piecewise linear approximation to isoquants.
Fite, W. L., "Maximization of return from limited resources," Journal of the Society for Industrial and Applied Mathematics, Dec. 1953, vol. 1, no. 2, pp. 73-90. Theoretical paper, no references to LP. General model can be used for spatial analysis.
Fitzpatrick, G.R., J. Bracken, M.J. O'Brien, L.G. Wentling, and J.C, Whiton, "Programming the procurement of airlift and sealift forces: a linear programming model for analysis of the least-cost mix of strategic deployment systems," Naval Research Logistics Quarterly, vol. 14, pp. 241-255, 1967. Model to determine equipment mix and positioning to prepare for regional wars.
Flood, M. M., "On the Hitchcock-distribution problem," Pacific Journal of Mathematics, vol. 3, no. 2, 1953. An algorithm for solving the model.
Flood, M. M., "Application of transportation theory to scheduling a military tanker fleet," Operations Research, vol. 2, no. 2, 1954. "Supply" empty tankers from oil demand points to supply points. Reverse of normal formulation, however, this was original view by Koopmans, since Koopmans focused on moving empties.
Flood, M. M., "The traveling salesman problem," Operations Research, vol. 4, pp. 61-75, 1955.
Ford, L.R., "Network Flow Theory," The RAND Corporation, Paper P-923, 1956. Ford, L.R., and D.R. Fulkerson, "A simple algorithm for finding maximal network flows and an application to the Hitchcock problem," Canadian Journal of Mathematics, vol. 9, 1957, pp. 210-218. Formulates maximum flow network problem as an LP then presents an alternative algorithm.
Foulkes, J., "Linear programming and structural design," in Antosiewicz, H.A., Second Symposium on Linear Programming, National Bureau of Standards, Washington, Jan 2729, 1955. Develops a model of a plastic hinge of a structure using LP.
Fox, K.A., "A spatial equilibrium model of the livestock-feed economy in the United States," Econometrica, Oct. 1953, vol. 21, no. 4, pp. 547-566. Algorithm very much like the Jones and Saigal homotopy algorithm. Uses model to forecast equilibrium prices.
Fox, K., "Discussion: Activity analysis: An agricultural marketing tool," Journal of Farm Economics, Dec. 1955, vol. 37, no. 5, pp. 1261-1263. Comments on the survey paper by French.
Fox, K. A., and R.C. Taeuber, "Spatial equilibrium models of the livestock-feed economy," The American Economic Review, Sept. 1955, vol. 45, no. 4, pp. 584-608. Mentions transportation model without a reference. Uses fixed regional price differences to compute the equilibrium.
Franklin, A.D. and E. Koenigsberg, "Computed school assignments in a large district," Operations Research, vol. 21, 1974, pp. 295-297. Uses the blending model to achieve racial balance. Not applied because of the politics.
French, C.E., "Activity analysis: An agricultural marketing tool," Journal of Farm Economics, Dec. 1955, vol. 37, no. 5, pp. 1236-1248. Survey with more potentially real applications rather than actual applications. No Dantzig reference, which is common in the agriculture literature.
Freund, R.J., "The introduction of risk into a programming model," Econometrica, vol. 24, no. 3, July 1956, pp. 253-263. Adds an expected utility component to the objective function.
Fulkerson, D.R. and G.B. Dantzig, "Computation of Maximal Flows in Networks," Naval Research Logistics Quarterly, vol. 2, no. 4, 1955, pp. 277-283. Uses the LP formulation of the maximal flow problem to derive a solution algorithm.
Gainen, L., "Linear programming in bid evaluations," in Antosiewicz, H.A., Second Symposium on Linear Programming, National Bureau of Standards, Washington, Jan 2729, 1955. The first bidding models. Starts out with the transportation model and winds up with integer programs to meet bid conditionals--"and," "or," and hinge bidding. Not a covering model.
Gainen, L., D. Honig, and E.D. Stanley, "Linear programming in bid evaluation," Naval Research Logistics Quarterly, vol. 1, pp. 48-52, 1954. Gale, D., "Linear programming and the theory of games," in T.C. Koopmans (ed), Activity Analysis of Production and Allocation, John Wiley and Sons, Inc., NY 1951. Garvin, W., H.W. Crandall, J.B. John and R.A. Spellman, "Applications of linear programming in the oil industry," Management Science, vol. 3, no.4, July 1957, pp. 407430. They model the decrease in the marginal contribution of TEL to octane, recognize nonlinearities in cut points, and describe distribution planning and routing problems.
Gilmore, P.C., and R.E. Gomory, "A linear programming approach to the cutting stock problem--part II," Operations Research, Nov.- Dec., 1963, pp. 863-887. Shows knapsack problem for generating cuts, extends beyond paper industry, alternative objectives.
Goldman, T., "Efficient transportation and industrial location," Papers and Proceedings of the Regional Science Association, vol. 4, 1958. Goldstein, L., "The problem of contract awards," in A. Orden and L. Goldstein (eds) Symposium on Linear Inequalities, Project SCOOP #10, Planning Research Division, Directorate of Management Analysis Service, Comptroller, USAF, Washington D.C., April 1952, pp. 147-154. Covering constraints and different kinds of capacity limits on the suppliers.
Gray, P. and C. Cullinan-James, "Applied optimization--A survey," Interfaces, vol. 6, no. 3, pp. 24-41, May 1976 Covers a short, then current time span.
Greenberg, H.J., and W. Prager, "Limit design of beams and frames," Transactions of the American Society of Civil Engineers, vol. 117, pp. 477 ff. 1952.
Presents the equations for plastic collapse. No LP, but the equations define the constraints for what is probably in the Charnes and Greenberg LP.
Greene, J.H., K. Chattoo, C.R. Hicks, and C.B. Cox, "Linear programming in the packing industry," Journal of Industrial Engineering, vol. 10, no.5, Sept-Oct 1959, pp. 364-372. A simple product mix: smoking hams etc. versus selling fresh meat. More like a transport model with side constraints.
Guiget, R., "The programming of electric equipment considered from the point of view of applied economics," Economique Appliquee, vol. 1, 1951. Gunther, P. "Use of linear programming in capital budgeting," Operations Research, vol. 3, pp. 219-224, 1955. A letter to the editor using a home economics example to explain LP and duality.
Haley, K.B., "The solid transportation problem," Operations Research, vol. 10, no. 4, 1962. 3-dimensional extension of transportation model. A mathematical artifact rather than driven by real modeling needs.
Halmos, P. R., and H. E. Vaughan, "The marriage problem," American Journal of Mathematics, vol. 72, no. 1, Jan. 1950, pp. 214-215. A matching problem, defined before the assignment problem.
Hansmann, F. "A linear programming approach to production and employment scheduling," in R.R. Crane, and C.W. Churchman (eds.), Management Technology, 1960. Hansmann, F., and S.W. Hess, "A linear programming approach to production and employment scheduling," Management Technology, January 1960. Harrison, J.O., jr., "Linear programming and operations research," in J.F.M. McCloskey and F.N. Trefethen (eds.) Operations Research for Management, pp. 217-237, Baltimore, 1954. Heady, E.O., "Simplified presentation and logical aspects of linear programming technique," Journal of Farm Economics, Dec. 1954, vol. 36, no. 5, pp. 1035-1048. An explanatory paper. Compares to budgeting the approach taken before agricultural economists knew of LP. A major proponent of using LP in agriculture.
Heller, I., "On linear programs equivalent to the transportation problem," SIAM, vol. 12, no. 1, pp. 31-42, March, 1964. Looks at mathematically equivalent models and shows how to transform them into transportation models.
Henderson, J.M., "Efficiency and pricing in the coal industry," Review of Economics and Statistics, vol. 38, Feb., 1956. Uses model to compare LP solutions with market outcomes for 1947, 1949, and 1951 to examine the efficiency of the industry. This was a period of steep decline in the industry. Actual costs 13-25% higher than LP solution. Notes UMW work sharing, long-term contracts etc.
Henderson, J.M., "A short-run model of the coal industry," Review of Economics and Statistics, vol. 37, Nov., 1955. Spatial model of US coal. Capacities of mines and demands are taken as fixed--a short run model. Looks at royalties to mines from duals. Only one coal type and rank, unlike current models.
Henderson, J.M., "The utilization of agricultural land: A regional approach," Papers and Proceedings of the Regional Science Association, vol. 3, 1957. Henderson, J.M., The Efficiency of the Coal Industry, Harvard University Press, Cambridge, MA, 1958. The above papers combined into a book.
Henderson, A., and R. Schlaifer, "Mathematical programming," Harvard Business Review, May-June 1954, pp. 94-100. Expository article with several good case studies from HJ Heinz for teaching. One model involves process selection. Does production planning with overtime and inventories.
Herrmann, C.C. and J.F. Magee, "Operations research for management," Harvard Business Review, vol. 31, no. 4, July-August 1953, pp. 100-112. Excellent description of the field. Shows how broadly the field was defined.
Heselden, G.P.M., and S. Vajda, "Linear programming of an airlift," in Vajda, S., A. Land, G. Morton, Brown, E.M.L. Beale, and Prinz, eds., Conference on Linear Programming, May 1954, Ferranti, London, 1955. Model of the air supply of a fixed quantity during a period of several weeks. Minimizes the training and utilization of crews. An example and not a specific application, used to test ideas.
Heyman, J., "Plastic design of plane frames for minimum weight," Structural Engineer, vol. 31, pp. 125-129, 1953. Heyman, J., "Plastic design of beams and plane frames for minimum material consumption," Quarterly Applied Mathematics, vol. 8, no. 4, pp. 373-380, 1951.
Sets up a set of linear inequalities to define beams in a structure. Uses a method of Dines (Ann. Math. (2), 191 (1918-1919) to solve.
Hildreth, R. J., "Discussion: Integrating crop and livestock activities in farm management analysis," Journal of Farm Economics, Dec. 1955, vol. 37, no. 5, pp. 1263-165. A discussant report of Swanson, Fox, Babbar et al.
Hildreth, C.G., "Economic implications of some cotton fertilizer experiments," Econometrica, Jan. 1955, vol. 23, no. 1, pp. 88-98. Uses experimental data directly in LP rather than fit a function, ie. data are extreme points.
Hildreth, C.G., and S. Reiter, "On the choice of a crop rotation plan," Activity Analysis of Production and Allocation, Proceedings of the Conference on Linear Programming held in Chicago, Illinois 20-24 June 1949, T.C. Koopmans (ed), NY, pp. 177-188. Crop tour formulated as a mix of outputs, not traveling salesman.
Hirschleifer, J. "On the economics of transfer pricing," Journal of Business of the University of Chicago, vol. 29, pp. 172-184, 1956. No LP but the problem should be viewed as an LP.
Hirschleifer, J. "The Economics of the Divisionalized Firm," Journal of Business of the University of Chicago, vol. 30, pp. 96-108, 1957. No LP. Precursor to the decomposition literature on organizations.
Hitchcock, F.L., "The distribution of a product from several sources to numerous localities," Journal of Mathematical Physics, vol. 20, 1941, pp. 224-230. Original paper on transportation problem. Has no references.
Hoffman, A.J. and W. Jacobs, "Smooth patterns of production," Management Science, vol. 1, no. 1, 1954. Includes a cost of increasing production in a production planning model.
Hoffman, A.J. and H.M. Markowitz, "A note on the shortest path, assignment and transportation problems," Naval Research Logistics Quarterly, vol. 1, no. 1, 1954. Uses a sequence shortest path problems to solve the assignment and transportation problems.
Holley, L., "A dynamic model: I. Principles of model structure," Econometrica, vol. 20, pp. 616-642, 1952 A paper on input/output modeling. Uses LP ideas of Dantzig to make multiperiod and develop prices.
Hood, W.C., "Linear Programming and the Theory of the Firm," Canadian Journal of Economics and Political Science, vol. 18, pp. 208-212, 1952. A review of Dorfman's book. Thoughtful.
Hood, W.C., "Linear programming and the firm," Cambridge Journal of Economics, vol. 18, 1952. Isbell, J.R. and W. H. Marlow, "On an industrial programming problem of Kantorovich," Management Science, vol. 8, 1961, pp. 13-17. An application of the K-T conditions to the original nonlinear programming model of Kantorovich, which is to maximize a prespecified mix of outputs.
Isard, W. "General interregional equilibrium," Papers and Proceedings of the Regional Science Association, vol. 3, 1957. Isard, W., and D. Ostroff, "The existence of a competitive interregional equilibrium," Papers and Proceedings of the Regional Science Association, vol. 4, 1958. Jacobs, W., "The caterer problem," Naval Research Logistics Quarterly, vol. 1., no. 2, 1954. Has inventory balances in formulation, characterizes the optimal solution. Model for repair and acquisition.
Jacobs, W. "Military applications of linear programming," in Antosiewicz, H.A., Second Symposium on Linear Programming, National Bureau of Standards, Washington, Jan 2729, 1955. Includes absolute value objective functions and attributes the idea to Dantzig. Uses the transportation model for sortie allocation. For training over time, a dynamic model that connects to dynamic Leontief systems.
Jewell, W.S., "Warehousing and distribution of a seasonal product," Naval Research Logistics Quarterly, vol. 4, no.1, March 1957, pp. 29-34. Uses transshipment formulation of multiperiod production/distribution of a single product.
Johnson, S.M., "Sequential production planning over time at minimum cost," Management Science, vol. 3, no. 4, 1957.
Shows how the Bowman production planning model can be solved immediately without resorting to the transportation algorithm.
Kalaba, R.E., and M. Juncosa, "Optimal design and utilization of communication networks," Management Science, vol. 3, no. 1, 1956, pp. 33-44. Optimal routing (max flow) with multiple sources, switch capacities, destinations and link demands. Adds capacity activities for design problem.
Kantorovitch, L., "On the translocation of masses, Management Science, vol. 5, no. 1, 1958/(1942-in russian). Gives conditions for min-cost transportation flow pattern. Translation of the original paper.
Kantorovich, L., "Mathematical methods of organizing and planning production," Leningrad University, 1939. Translated into English Management Science, vol. 6, pp. 366-422, 1960. Translation of original 1939 paper.
Karush, W., "On a class of min-cost problems," Management Science, vol. 2, 1958, pp. 136-153. Builds on Modigliani and Hohn work with linear decision rule kinds of models. Knows of math programming but tries to extend calculus-based approaches.
Karush, W. and A. Vaszonyi, "Mathematical programming and service scheduling," Management Science, vol. 3, pp. 140-148, January, 1957. Extension of Modigliani-Hohn production smoothing model. Formulates the mathematical program and then uses DP rather than LP to solve.
Karush, W. and A. Vaszonyi, "Mathematical programming and employment scheduling," Naval Research Logistics Quarterly, vol. 5, December, 1957. Workforce planning model with costs to changing number of employees. Includes overtime. Addresses planning horizon issues.
Katzman, I., "Solving feed problems through linear programming," Journal of Farm Economics, May 1956, vol. 38, no. 2., pp. 420-429. Covers models probably used at Armour. Blending to make food products, feedmix using amino acids in constraints.
Kav, E., and G. Morton, "Linear programming--an application of swarf recovery," Metalworking Production, December 30, 1955. Kawaratani, T.K., R.J. Ullman, and G.B. Dantzig, "Computing tetraethyl-lead requirements in a linear programming format," Operations Research, vol. 8, no. 1, JanFeb 1960. Simplifies of TEL formulation in Garvin et al. (1957).
Kelley, J.E., jr., "A dynamic transportation model," Naval Research Logistics Quarterly, vol. 2, no. 3, pp. 175-180, Sept, 1955. Shows how to convert a model of military tanker routing to a transportation problem.
Kelley, J.E., "An application of linear programming to curve fitting," Journal of Industrial and Applied Mathematics, vol. 6 pp. 15-22, 1958. Shows that curve fitting with the max deviation norm is an LP.
Kelley, J.E., jr., "Critical-path planning and scheduling: mathematical basis," Operations Research, vol. 9, no. 3, 1961. Connects CPM with linear programming. Only link to LP literature a paper by Gass on parametric programming and another by Ford and Fulkerson on network flows.
Kelley, J.E., jr., "The cutting-plane method for solving convex programs," SIAM Journal of Industrial and Applied Mathematics, vol. 8, no. 4, pp. 703-712, Dec. 1960. Outer approximation to the feasible region with LP subproblem.
Kennington, J.L., "A survey of linear cost multicommodity network flows," Operations Research, vol. 26, No. 2, pp. 209-236, March-April, 1978. A detailed survey.
King, R. A., "Use of economic models: Some applications of activity analysis in agricultural economics," Journal of Farm Economics, Dec 1953, vol. 35, no. 5, pp. 823833. Covers feedmix and product mix.
King, R. A., C.E. Bishop and J. G. Sutherland, "Programming resource use and capital investment in agriculture," Management Science, Jan. 1957, vol. 3, no. 2, pp. 173-184. Introduces a risk constraint and gets a "portfolio" of crops. The constraint works with the sum of the variances on the returns. An excellent paper that is part of the start of the LP finance literature.
Knight, U.G.W., "The logical design of electrical networks using linear programming methods," Institute of Electrical Engineers, Proceedings, vol. 107, no. 33, 1960. Uses LP to model the design of electrical networks.
Koch, A.R. and M.M. Snodgrass, "Linear programming applied to location of and product flow determination in the tomato processing industry" Papers and Proceedings of the Regional Science Association, vol. 5, 1959. Uses the transportation model for economic analysis of interregional issues in tomato processing. Uses the model to predict interregional shifts of economic activity. An interesting micro-economic market analysis.
Koenigsberg, E., "Some industrial applications of linear programming," Operational Research Quarterly, vol. 12, no. 2, 1961. A plywood product mix model, one on transportation of grain and grain products, and one on fermentation. No references.
Koopmans, T.C., "Optimum utilization of the transportation system," Econometrica (supplement), vol. 17, 1949. Presents a series of conditions for an efficient transportation market using marginal analysis. Shows they are met in shipping because of competitive market. Raises issue of rail monopolies. Notes inefficient movement of raw materials to Northeast US. Start of location theory.
Koopmans, T.C., "Analysis of production as an efficient combination of activities," in Activity Analysis of Production and Allocation, Proceedings of the Conference on Linear Programming held in Chicago, Illinois 20-24 June 1949, T.C. Koopmans (ed), NY, pp. 222-259, 1951. Koopmans, T.C. and M. Beckmann, "Assignment problems and the location of economic activity," Econometrica, vol. 25, 1957, pp. 52-76. They are developing a theory of locating indivisible resources. They use the assignment model, then general LP w/o integer restrictions, they use the quadratic assignment model, game theory and prices from duals. They admit that they do not succeed. First public statement of quadratic assignment problem(?).
Koopmans, T.C., and S. Reiter, "A model of transportation," in Activity Analysis of Production and Allocation, Proceedings of the Conference on Linear Programming held in Chicago, Illinois 20-24 June 1949, T.C. Koopmans (ed), NY, pp. 222-259. Analyzes tours for freighters. Can't really solve because an IP.
Klahr, C.N., "Multiple objectives in mathematical programming," Operations Research, vol. 6, no. 6, pp. 849-855, Nov-Dec. 1958. Decides against weighted averages of objectives. Defines a partition of "subobjective space."
Kuhn, H.W., "A note on Prager's transportation problem," Journal of Mathematical Physics, vol. 36, no. 2, July 1957, pp. 107-111. Criticizes Prager's use of physical equilibrium models to explain LP by analogy. States that LP involves optimization not equilibrium. A narrow view of the subject that illustrates the problem of thinking becoming too channeled.
Laderman, J., L. Gleiberman, and J.F. Egan, "Vessel allocation by linear programming," Naval Research Logistics Quarterly, vol. 13, pp. 315-320, 1966. A capacity planning model, so not the same as Dantzig and Fulkerson. Does not address sequencing. Evidently, customers not sensitive to time in this case.
Lawler, E.L., "The quadratic assignment problem," Management Science, vol. 19, 1963, pp. 586-599. Presents an equivalent LP formulation to the quadratic assignment model.
Lawrence, J.R. and A.D.J. Flowerdew, "Economic models for production planning," Operational Research Quarterly, vol. 14, no. 1, pp. 11-29, 1963. Blast furnace model, integrated steelworks through slab does not link to rolling mill. Planned link with simulations, based on Fabian work, no other references.
Lee, A.S. and J.S. Aronofsky, "Linear programming for scheduling crude oil production," Transactions of the American Institute of Petroleum Engineers, vol. 213, pp. 389 ff. Lefeber, L. "General equilibrium analysis of production, transportation, and the choice of industrial location" Papers and Proceedings of the Regional Science Association, vol. 4, 1958. Lomax, K.S., "Allocation and programming in modern economics," Manchester Statistical Society, 1952. Lorie, J.H. and L.J. Savage, "Three problems in rationing capital," The Journal of Business, vol. 28, no. 4, pp. 229-239, October, 1955. Lagrange multiplier search. A precursor to Everett's GLM. No math programming references.
Loucks, D.P., C. S. Revelle, and W. R. Lynn, "Linear programming models for water pollution control," Management Science, vol. 14, no. 4, pp. B-166-B-181, December, 1967
Two LP models to meet dissolved oxygen standards at minimum cost.
Louwes, S.L., J.C.G. Boot and S. Wage, "A quadratic programming approach to the problem of the optimal use of milk in the Netherlands, Journal of Farm Economics, vol. 45, 1963, pp. 309-317. Mix of optimization and equilibrium. Problem of surplus milk.
MacKenzie, H.C., "The linear programming approach to production planning," Scottish Journal of Political Economy, vol. 4, pp. 29-45, 1956. An expository article explaining LP to economists. Surveys then-existent models.
MacKenzie, H.C. and T.E. Godsell, "Linear programming and the cost of pig-fattening rations," Journal of Agricultural Economics, January, 1956. Manne, A.S., "A linear programming model of the US petroleum refining industry," Econometrica, vol. 26, no. 1, 1958, pp. 67-106. (Also appeared as an abstract in Econometrica, vol. 23, no. 3, 1955, pp. 337). Process model of the industry. It is part of an I/O project to model the whole economy. See Markowitz (1954).
Manne, A.S., "A Note on the Modigliani-Hohn production smoothing model," Management Science, vol. 3, no. 4, pp. 371-379, July, 1957. Uses a piece-wise linearization of the quadratic functions in the Modigliani-Hohn model, then shows equivalent to the transportation model.
Manne, A.S. "Programming economic lot sizes," Management Science, vol. 4, no. 2, pp. 115-135, January, 1958. Introduces multiproduct production scheduling model. An IP but notes that few noninteger variables in the solution. Therefore, roundable.
Manne, A.S., "On the job scheduling problem," Operations Research, vol. 8, 1960, pp. 219-223. Minimizes makespan sequence using IP.
Manne, A.S., "Linear programming and sequential decisions," Management Science, vol. 6, pp. 259-269, 1960. Formulates the infinite horizon Markov inventory problem as an LP. Received after Howard's presentation where he lays out the bulk of the ideas.
Markowitz, H., "Portfolio Selection," The Journal of Finance, vol. 17, no, 1, March 1952.
The original portfolio paper. Has no LP references. A precursor paper.
Markowitz, H.M., "Concepts and computing procedures for certain Xij programming problems," in H.A. Antosiewicz (ed), Proceedings of the Second Symposium in Linear Programming, vol. 2., NBS and USAF Washington D.C., 1955, pp. 509-565. Contains the result that transportation duals connected by the basis move simultaneously. Develops a specialized version of the simplex algorithm for generalized transportation problems using the tree structure.
Markowitz, H.M., "Industry-wide, multi-industry, and economy-wide process analysis," in Barna, T. ed., The Structural Interdependence of the Economy, Proceedings of an International Conference on Input-Output Analysis, pp. 121-150, 1954. Lays out project to build process models of the different sectors in the US economy. Discusses the Manne refinery model. Shows piecewise linear approximation to the nonlinear function for TEL in the refinery model. Examines issues of nonconvexities and problem size. The starting point for getting beyond I/O in economic modeling of multiple industries.
Marshak, J., "Elements for a theory of teams," Management Science, vol. 1, pp. 127-137, 1955. Group decisionmaking with each person doing different areas and common rewards for a joint result, no individual incentives. Information issues (cost and availability) and use of rules of thumb. A good introduction.
Martin, A.D. "Mathematical programming of portfolio selections," Management Science, vol. 1, no. 2, pp. 152-166, Jan., 1955. Presents Markowitz model as a mathematical program and a solution procedure for the quadratic program.
Mass, P., and R. Gibrat, "Applications of linear programming in the electric power industry," Management Science, vol.3, no.1, Jan 1957, pp. 149-166. Early representation of the load duration curve for capturing instantaneous fluctuations in demand. Uses vertical slices.
McCorkle, C. O. Jr., "Linear programming as a tool in farm management analysis," Journal of Farm Economics, Dec. 1955, vol. 37, no. 5, pp. 1222-1235. Only potential applications. Page 1230 time model relevant, a growth model with internal cash flow generated being reinvested.
McGuire, C.B., "Some team models of a sales organization," Management Science, vol. 7, no. 1, pp. 101-130, 1961. Marshak team theory.
Meyer, M., "Applying linear programming to the design of ultimate pit limits," Management Science, vol. 16, no. 2, pp. 121-135, October 1969. Copes with boundaries using triangles and other geometric forms.
Modigliani, F., and F.B. Hohn, "Production planning over time and the nature of expectations and the planning horizon," Econometrica, vol. 23, pp. 46-66, 1955. A model with which they try to characterize the optimal solution without solving as an LP. A focus on planning horizon issues. Misses the opportunity to have inventory variable, use cumulative production and demand instead.
Moore, F.T., "Regional economic reaction paths," American Economic Review, vol. 45, May, 1955. Regional input-output models for Utah and California. Converts California model to LP to examine dynamic growth from 1954 to 1960.
Morton, G., "Notes on linear programming," Economica, vol. 18, pp. 397-411, 1951. Survey of early LP's (transportation and diet) and theory from an economist's perspective.
Morton, G., "Application of linear programming to commercial airline operations," (abstract), Econometrica, vol. 21, no. 1, p. 193, Jan., 1953. An abstract where the author mentions building a model for British European Airways to determine the pattern and timing of flights. No model specification.
Morton, G. and A.H. Land, "A contribution to the traveling salesman problem," Journal of the Royal Statistical Society, vol. 17, pp. 185-194, 1955. They add subtour elimination constraints to the LP formulation.
Murphy, F.H., and V. Panchanadam (1995), "Understanding the Relationships among Linear Programming Problems and Models through an Examination of the Early Papers on Model Formulation," working paper, Temple University. Naslund, B., and Whinston A., "A model of multi-period investment under uncertainty," Management Science, vol. 8, no. 2, Jan. 1962, pp. 184-200. Applies chance-constrained programming to portfolio problem. With probability constraints derives demand curves for investments.
Nordbotten, S., "Allocation in stratified sampling by means of linear programming," Skandinavia Aktuarietidskrift, vol. 39, pp. 1-6, 1956. Orden, A., "The transshipment problem," Management Science, vol. 2, no.3, April 1956, pp. 276-285. Shows equivalence of transshipment problem and transportation problem.
Orden, A., "Survey of research on mathematical solutions of programming problems," Management Science, vol, 1, pp. 170-172, 1954. A short presentation that ties together mathematical programming, dynamic programming and the work of Wald in statistical decision theory.
Orgler, Y., "An unequal-period model for cash management decisions," Management Science, vol. 16, pp. B77-92, 1969. Orr, E.W., "A synthesis of theories of location, of transport rates and of spatial price equilibrium," Papers and Proceedings of the Regional Science Association, vol. 3, 1957. Paull, A.E., "Linear programming: A key to optimum newsprint production," Pulp and Paper Magazine of Canada, vol. 57, pp. 85-90, 1956. Implemented the transportation and trim models at Abitibi Paper Co. Says very successful. Refers to books and Henderson and Schlaifer article.
Paull, A.E. and J. R. Walter, "The trim problem - An application of linear programming to the manufacture of newsprint paper," Econometrica, vol. 23, no. 3, July 1955, (abstract). Authors at paper company. See Eisenmann.
Percus, J., and L. Quinto, "The application of linear programming to competitive bond bidding," Econometrica, vol. 24, no. 4, pp. 413-428, 1956. Important first LP application to finance. Only agriculture references. Minimizes "net interest cost" to borrower to make a winning bid on bonds.
Peterson, G.A., "Selection of maximum profit combinations of livestock enterprises and crop rotations," Journal of Farm Economics, vol. 37, pp. 546-554, August 1955. Two stage model. The first is crops, the second is livestock.
Plaxico, J.S., "Discussion: Linear programming as a tool in farm management analysis," Journal of Farm Economics, Dec. 1955, vol. 37, no. 5, pp. 1258-1261. Prager, W., "Limit analysis design," Journal of the American Concrete Institute, vol. 25, no. 4, Sept., 1953.
Uses geometric reasoning for the design of beams, then recognizes that when the problem becomes large, linear programming is necessary.
Prager, W., "On the role of congestion in transportation problems," Zeitschr. angew. Math. Mech., vol. 35, pp. 264-268, 1955. Prager, W., "On the caterer problem," Management Science, vol. 3, 1956, pp. 15-23. Shows the caterer problem of Jacobs is a transportation problem. Includes, without saying, the relationship between transportation and transshipment models.
Prager, W.W., "A generalization of Hitchcock's transportation problem," Journal of Mathematical Physics, vol. 36, no. 2, July 1957, pp. 99-106. Uses analogies to physical equilibrium systems. Kuhn attacks on grounds that LP is "optimization."
Prager, W. "On warehousing problems," Operations Research, vol. 5, no. 4, pp. 504-512, Aug., 1957. Shows that the warehousing problem of Charnes and Cooper is a transportation model. Done independently from Dantzig.
Radner, R., "The linear team: An example of linear programming under uncertainty," in H.A. Antosiewicz (ed.), Proceedings of the second symposium in linear programming, vol. 2, NBS and USAF, Washington D.C., 1955. Team members are willing to jointly optimize (no agency problem). However, they do not have the same information to make jointly optimal decisions. Uses LP to find decision rules for coordination.
Radner, R., "The application of linear programming to team decision problems," Management Science, vol. 5, no. 2, pp. 143-150, January, 1959. Continuation of using LP's for team decision problems.
Rapoport, L.A. and W.P. Drews, "Mathematical approach to long-range planning," Harvard Business Review, vol. 40, no. 3, pp. 75-87, 1962. Uses integrated oil company example to tie in LP modeling to corporate decisionmaking. Excellent record of the early literature.
Rhode, F.V., Bibliography on linear programming, Operations Research, Feb. 1957. Rosander, A.C., "The use of linear programming to improve the quality of decisions," Industrial Quality Control, vol. 12, pp. 11-16, 1956.
A tutorial with a focus on examples. Tries a model for allocating audits in the IRS, where he worked. No implementation.
Roy, A.D., "Safety first and the holding of assets," Econometrica, vol. 20, pp. 431-449, 1952. Allocation based on variance reduction using an approximation formula and a Lagrangian on a budget constraint.
Salveson, M.E., "A mathematical theory of production: planning and scheduling," Industrial Engineering, pp. 3-6&21, February, 1953. Background on early scheduling literature, description of the early information concerns, formulates a model, recognizes an IP and difficult to solve.
Salveson, M.E., "Mathematical methods in management programming," Industrial Engineering, pp. 9-15, March, 1954. A tutorial using a production planning model. A good description of what can and cannot be represented. Lists extensions and variations.
Salveson, M.E., "A problem in optimal machine loading," Management Science, vol. 2, no. 3, April 1956, pp. 232-260. Formulates a problem to assign parts to machines to maximize the production of the third of 3 products. A strange goal.
Salveson, M.E. "The assembly line balancing problem," in H.A. Antosiewicz (ed.), Proceedings of the second symposium in linear programming, vol. 2, NBS and USAF, Washington D.C., 1955. Formulates the IP to solve the balancing problem.
Samuelson, P.A., "Spatial price equilibrium and linear programming," American Economic Review, vol. XLII, June 1952, 283-303. Demonstrates the equivalence of the spatial economic equilibrium and the LP solution that maximizes social welfare.
Samuelson, P.A., "Linear programming and economic theory," in H.A. Antosiewicz (ed.), Proceedings of the second symposium in linear programming, vol. 2, NBS and USAF, Washington D.C., 1955. Connects with 1930's economics, welfare economics, I/O, military, games, statistical decision theory, pure math of inequalities, economic theory of arbitrage, speculation, location rationing. Discusses theoretical development of existence of equilibria.
Schell, E.D. "Distribution of a product by several properties," in H.A. Antosiewicz (ed.), Proceedings of the second symposium in linear programming, vol. 2, NBS and USAF, Washington D.C., 1955. Purely mathematical extension of the transportation model to 3 dimensions.
Schwan, H.T., "Practical linear programming applications," Industrial Quality Control, vol. 12, pp. 408, 1956. An expository article describing LP to a quality control audience.
Sengupta, J.K., G. Tintner, and B. Morrison, "Stochastic linear programming with applications to economic models," Economica, vol. 30, 1963, pp. 262-275. Relates "wait and see" formulation with "here and now" formulation.
Shapley, L.S., "Complements and substitutes in the optimal assignment problem," RM 2240, The RAND Corporation, August, 1958. Sharpe, W.F., "A linear programming algorithm for mutual fund portfolio selection," Management Science, vol. 13, no. 7, pp. 499-310, March, 1967. Reformulates Markowitz model as a parametric linear program using a linear approximation to the quadratic objective function.
Smith, J.W., "A plan to allocate and procure electronic sets by the use of linear programming techniques and analytical methods of assigning values to qualitative factors," Naval Research Logistics Quarterly," vol. 3, pp. 151-162, 1956. Uses weights for differences in suitability of radios to be allocated to ships during overhaul. A transportation model (really assignment).
Smith, L.W., "Current status of the industrial use of linear programming," Management Science, vol. 2, no. 2, pp. 156-158, 1956. A panel noted 20 examples of which 1/2 had made an important contribution to decisions. Describes "brute force school' which wants faster machines to solve larger models versus the Charnes and Cooper school, which looks for special structure.
Smith, S.B., "Planning transistor production by linear programming," Operations Research, vol. 13, pp. 132-139, 1965. Presents an interesting formulation that increased yields.
Smith, V.E., "Linear programming models for determination of palatable diet," Journal of Farm Economics, vol. 41, no. 2, May 1959, pp. 272-283.
Uses bounds to achieve palatability for humans (not good).
Solow, R., "On the structure of linear models," Econometrica, vol. 20, no. 1, Jan. 1952, pp. 29-46. Explores the math of I/O models. No mention of LP but solution has many of the same computational problems.
Soyster, H., "Mathematical Programming and Evaluations of Freight Shipment Systems, Part 1: Applications," Naval Research Logistics Quarterly, vol. 1, pp. 237-242, 1954. Describes the situation at the Union Railroad. Charnes and Miller (1954) describe the solution method for a crew scheduling situation at the railroad.
Srinivason, V., "A transshipment model for cash management decisions," Management Science, vol. 20, 1974, pp. 1350-1363. A good model for managing a cash "inventory." Earlier papers by Baumol etc. hung up on the word "inventory" and tried EOQ models. Orgler was first in seeing this.
Stasch, S., "Linear programming and space-time considerations in media selection," Journal of Advertising Research, vol. 5, pp. 40-46, 1965. A weak extension that did nothing to respond to problems raised by Engel and Warshaw.
Stevens, B. H., "An interregional linear programming model," Journal of Regional Science, vol. 1, summer, 1958. Interregional equilibrium for the location of economic activities. Interesting use of duals to understand economic rents, both location and quality of resources.
Stigler, G.J., "The cost of subsistence," Journal of Farm Economics, vol. 27, 1945, pp. 303-314. Diet problem. No references. According to Dantzig, Cornfield first did this formulation in 1941.
Swanson, E.R., "Integrating crop and livestock activities in farm management activity analysis," Journal of Farm Economics, vol. 37, no. 5, December 1955, pp. 1249-1258. 2 period 2 stage production process.
Swanson, E.R., "Application of programming analysis to corn belt farms," Journal of Farm Economics, May 1956, vol. 38, no. 2, pp. 408-419.
Does an example production plan for a farm. Proposes a set of plans to avoid solving LP's for each farm
Swanson, E.R., and K. Fox, "The Selection of Livestock Enterprises by Activity Analysis," Journal of Farm Economics, vol. 36, 1954, pp. 78-86. Product mix model, grains, fodder and livestock. Can purchase or sell grains and fodder.
Swanson, E.R., Linear programming approach to the solution of practical problems in farm management and micro-agricultural economics," Journal of Farm Economics, vol., 42, pp. 386-392, 1960. Reports on actual implementations of LP to develop farm plans. Reports on a feed-mix application.
Swanson, L.W., and J.G. Woodruff, "A sequential approach to the feed-mix problem," Operations Research, vol. 12, no. 1, 1964. Used dual to shrink the problem and sequenced a series of models to minimize pivots and get the best from advanced bases.
Szwarc, W., "The transportation problem with stochastic demand," Management Science, vol. 11, no. 1, pp. 33-50, September, 1964. The objective function is a combination of minimizing cost and expected deviations.
Taylor, R.J., and S.P. Thompson, "On a certain problem in linear programming," Naval Research Logistics Quarterly, vol. 5, pp. 171-187, 1958. A military model that was classified and they could not describe. They develop a special solution procedure.
Thompson, D.M., and G.L. Thompson, "A bibliography of game theory," in Tucker, A.W. and R.D. Luce (eds.), Contributions to the Theory of Games, IV, Annals of Mathematics Studies No. 40, Princeton University Press, 1959. Thomas, J., "Linear programming models for production-advertising decisions," Management Science, vol. 17, no. 8, pp. B-475-B-485, April, 1971. Incorporates a demand curve based on advertising for production smoothing.
Thorndike, R.L., "The problem of classification of personnel," Psychometrika, vol. 15, 1950, pp. 215-235. Poses personnel assignment problem. Presents a heuristic solution. Precursor paper like Stiglitz.
Tintner, G., "Stochastic linear programming with applications to agricultural economics," in Antosiewicz, H.A., Second Symposium on Linear Programming, National Bureau of Standards, Washington, Jan 27-29, 1955 Calculates approximations to the distribution of the max. Uses actual agriculture data.
Tintner, G., "Programmazione linear stocastica con appliazioni a problem di economica agraria," Giornale degli Economisti e Annali di Economica, Lugio-Agosto, pp. 299-317, 1955. Italian translation of above article.
Tintner, G., "A note on stochastic linear programming," Econometrica, vol. 28, no. 2, pp. 490-495, 1960. Presents passive (only have the distribution approximated in objective function) and active (decision variables have amounts that result from random outcome).
van de Panne, C. and W. Popp, "Minimum-cost cattle feed under probabilistic protein constraints," Management Science, vol. 9, pp. 405-430, 1963. Deals with the problem that the protein levels in feeds are random.
van Slyke, R.M., "Monte Carlo methods and the PERT problem," Operations Research, vol. 11, no. 5, Sept/Oct 1963. Simulates to look at the effect of uncertainty on the critical path.
Vidale, M.L., "A graphical solution of the transportation problem," Operations Research, vol. 4, no. 2, 1956, pp. 193-203. Constructs level sets and shows how they define boundaries in a truly spatial transportation problem.
Vienott, A.F. and H.M. Wagner, "Optimal capacity scheduling-I and II," Operations Research, vol. 10, 1962, pp. 518-546. Shows that many problems can be represented as transshipment problems, including capacity scheduling, equipment replacement, lot sizing, product assortment batch queuing, labor-force planning and multi-commodity warehouse decisions.
Votaw, D.F., jr., "Methods of solving some personnel classification problems," Psychometrika, vol. 17, pp. 255-266, 1952.
Shows that the Thorndike model for the assignment of people to jobs is the transportation model. Did this research for airforce. The start of the military manpower-planning models.
Votaw, D.F., "Programming under conditions of uncertainty," in H.A. Antosiewicz (ed.), Proceedings of the second symposium in linear programming, vol. 2, NBS and USAF, Washington D.C., 1955, pp. 187-196. Treats uncertainty analogues to the assignment problem. Not really LP but many LP refs.
Votaw, D.F., and A. Orden, "The personnel assignment problem," in Alex Orden and Leon Goldstein (eds) Symposium on linear inequalities, project SCOOP #10, Planning Research Division, Directorate of Management Analysis Service, Comptroller, USAF, Washington D.C., April 1952, pp. 155-163. They use the transportation problem and maximize the min score of persons for jobs. Do not know Hungarian method.
Wagner, H.M., "A supplementary bibliography on linear programming, Operations Research, vol. 5, pp. 555-563, 1957. This bibliography has an more of an economics slant. It is a supplement to Rhode.
Wagner, H.M., "A linear programming solution to the dynamic Leontief type models," Management Science, vol. 3, 1957, pp. 234-254. (Also, published in 1954, Report No. RM-1343, Santa Monica, The Rand Corporation) Solves large multiperiod I/O growth model. Notes connection to corporate models with one output property.
Wagner, H.M., "On the distribution of solutions in linear programming problems," Journal of American Statistical Association, vol. 53, 1958, pp. 161-163. Shows there is a problem with Babbar paper.
Wagner, H.M., "On a class of capacitated transportation problems," Management Science, vol. 5, no. 3, 1959. Shows how to convert certain kinds of constraints that cut across arcs into a pure transshipment formulation.
Wagner, H.M., "An integer linear-programming model for machine scheduling," Naval Research Logistics Quarterly, vol. 6, pp. 131-140, 1959. Formulates sequencing problem as an IP.
Wagner, H. M., Linear programming techniques for regression analysis," Journal of the American Statistical Association, vol. 54, no. 285, Mar, 1959. Formulates the regression problem as minimizing the sum of absolute deviations and maximum deviations. Connects with Charnes, Cooper, and Ferguson.
Waugh, F. V., "Minimum-cost dairy feed (An application of linear programming), Journal of Farm Economics, Aug 1951, vol. 33, no. 3, pp. 299-310. No reference to Stigler, probably a reinvention. References Dantzig and Koopmans. Looks for a simple solution procedure.
Waugh, F. V., "Applicability of recent developments in methodology to agricultural economics," Journal of Farm Economics, Dec 1953, vol. 35, no. 5, pp. 692-706. A survey with a good poem on the need for applicability. Most references include here.
Waugh, F.V., "Alligation, forerunner of LP," Journal of Farm Economics, vol. 40, 1958, pp. 89-101. Shows connection to alligation, an old method of arithmetic.
Weston, J. and W. Barenek, "Programming investment portfolio construction," Analysts Journal, vol. 11, pp. 51-55, 1955. Explains Markowitz model for securities analysts. Mentions the importance of operations research for solving the quadratic programming problem.
Williams, A.C., "A stochastic transportation problem," Operations Research, vol. 11, 1963, pp. 759-770. Minimizes expected cost, shows convexity of problem.
Williams, H.P., "The formulation of mathematical programming models," Omega, vol. 3, no. 5, pp. 551-556, 1975. Lays out some important aspects for making formulation a science. Treats usability and numerical stability.
White, W.B., S.M. Johnson, and G.B. Dantzig, "Chemical equilibrium in complex mixtures," Journal of Chemical Physics, vol. 28, no. 5, May, 1958. Companion paper to Dantzig, Johnson, and White. Uses separable programming.
Whitin, T., "Classical theory, Graham's theory and linear programming in International Trade," Quarterly Journal of Economics, vol. 67, pp. 520-544, 1953.
Uses LP to reformulate a model of international trade and then shows the impact on Graham's conclusions.
Williams, N. "An application of linear programming to the selection of raw materials," Applied Statistics, vol. 4, pp. 22-31, 1955. An explanation of LP through a feedmix problem to statisticians.
Wolfe, P. and G.B. Dantzig, " Linear programming in Markov chains," Operations Research, vol. 10, 1962, pp. 702-710. Formulates an LP to solve the infinite horizon DP over a finite-state Markov chain using decomposition. Follows Manne paper.
Zierer, T.K., W.A. Mitchell, and T.R. White, "Practical applications of linear programming to Shell's distribution problems," Interfaces, vol. 6, no. 4, pp. 13-26, August, 1976. Describes use of LP to integrated production and distribution of oil. With first model found that different refineries shipped different products to same location in violation of the reality of he physical flows. They tried IP but model too big. They noted that what they were shipping was a product slate, not products. Reformulated model works well.
BOOKS
Antosiewicz, H.A., Second Symposium on Linear Programming, National Bureau of Standards, Washington, Jan 27-29, 1955. Aronofsky, J.S., J.M. Dutton, and M.T. Tayyabkhan, Managerial Planning with Linear Programming in Process Industry Operations, Wiley, New York, 1978. Arrow, K., L. Hurwicz, and H. Uzawa, Studies in Linear and Non- Linear Programming, Stanford University Press, Stanford, CA, 1958. Batchelor, J.H., Operations Research--An Annotated Bibliography, St. Louis University Press, St. Louis, 1960. Beckman, M.J., C.B. McGuire, and C.B. Winsten, Studies in the Economics of Transportation, Yale University Press, New Haven, 1956. Boden, M.A. (1990), The Creative Mind, Myths and Mechanisms, Basic Books, NY, NY.
Charnes, A. and W.W. Cooper, Management Models and Industrial Application of Linear Programming, vols. I&II, McGraw Hill, 1961. Important early work, excellent bibliography.
Charnes, A., W.W. Cooper, and A. Henderson, An Introduction to Linear Programming, Wiley, NY 1953.
Earliest book. 75 pages.
Churchman, C.W., R.L. Ackoff, and E.L. Arnoff, Introduction to Operations Research, John Wiley, 1957. Dorfman, R., Application of Linear Programming to the Theory of the Firm, Berkley and LA: University of California Press, 1951. Dorfman, R., P.A. Samuelson, and R.M. Solow, Linear Programming and Economic Analysis, McGraw-Hill, NY, 1958. Ferguson, R.O. and L.F. Sargent, Linear Programming: Fundamentals and Applications, McGraw-Hill, NY, 1958. Ford, L.R., and D.R. Fulkerson, Flows in Networks, Princeton University Press, Princeton, NJ, 1962. Goldschmidt, H.O., Financial Planning in Industry, H.E. Stenfert Kroese N.V. Leiden, Holland, 1956. Hadley, G. Linear Programming, Addison Wesley, Reading MA, 1962. Heady, E.O., and W. Candler, Linear Programming Methods, Iowa State College Press, Ames, IA, 1958. Emphasis on agricultural applications.
Holt, C.C., F. Modigliani, J. Muth, and H.A. Simon, Planning Production, Inventory and Workforce, Prentice Hall, Englewood Cliffs, NJ, 1960. Isard, W., Location and Space Economy, Wiley, NY, 1956. Isard, W., Methods of Regional Analysis: An Introduction to Regional Science, Wiley, NY, 1960. Has a chapter entitled "Interregional linear programming."
Kirchmayer, L.K. Economic Operation of Power Systems, Wiley, NY, 1958. Koopmans, T.C., Activity Analysis of Production and Allocation, Proceedings of the Conference on Linear Programming held in Chicago, Illinois 20-24, June 1949, NY. Lefeber, L., Allocation in Space, North-Holland, 1959(?). Leontief, W.W., The Structure of the American Economy, 1919-1939, Oxford University Press, NY 1951. Magee, J.F., Production Planning and Inventory Control, McGraw- Hill, NY, 1958. Manne, A.S., Scheduling of Petroleum Refinery Operations, Harvard University Press, 1956. Manne, A.S., and H.M. Markowitz, Studies in Process Analysis,Economy-wide Production Capabilities, Wiley, NY, 1963. A 1961 conference where LP models are used to represent the whole sector of an economy. Covers refining, food and agriculture, metals and metalworking, Mexican economy.
Markowitz, H. Portfolio Selection: Efficient Diversification of Investment, Cowles Commission Monograph No. 16, Wiley, NY, 1959.
Morgenstern, O., ed. Economic Activity Analysis, Wiley, NY, 1954. Riley, V., and S. Gass, Linear Programming and Associated Techniques, A Comprehensive Bibliography of Linear, Nonlinear, and Dynamic Programming, Johns Hopkins Press, Baltimore, 1958. Symonds, G.H., Linear Programming: The Solution of Refinery Problems, Esso Standard Oil Co. NY, 1955. Vajda, S., Theory of Games and Linear Programming, Wiley & Sons, NY 1956. Vajda, S., Readings in Mathematical Programming, 2nd edition, Wiley, NY, 1962. A collection of model descriptions. Covers most of the common models and then some. A good reference for constructing homework problems.
Vajda, S., A. Land, G. Morton, Brown, E.M.L. Beale, and Prinz, Conference on Linear Programming, May 1954, Ferranti, London, 1955. Vazsonyi, A., Scientific Programming in Business and Industry, Wiley, NY, 1958.
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