Dantzig

Dantzig, J.A., Goldman, Y.E., Millar, N.C., Lacktis, J., Homsher, E. (1992). Reversal of the cross-bridge force-generating transition by photogeneration of phosphate in rabbit psoas muscle fibers. J. Physiol. 451,247-278. 

Ekins S, Kim RB, Leake BF, Dantzig AH, Schuetz E, Lan LB, Yasuda K, Shepard RL, Winter MA, Schuetz JD, Wikel JH, Wrighton SA. Three-... 

Snyder NJ, Tabas LB, Berry DM, Duckworth DC, Spry DO and Dantzig AH. Structure-activity relationship of carbacephalosporins and cephalosporins antibacterial activity and interaction with the intestinal proton-dependent dipeptide transport carrier of Caco-2 cells. Antimicrob Agents Chemother 1997 41 1649-57. 

Clocksin, W.F., and Mellish, C.S., Programming in Prolog. Springer-Verlag, Berlin (1984). Dantzig, G.B., Linear Programming and Extensions. Princeton University Press, Princeton, NJ, 1963. 

The technique is useful where the problem is to decide the optimum utilisation of resources. Many oil companies use linear programming to determine the optimum schedule of products to be produced from the crude oils available. Algorithms have been developed for the efficient solution of linear programming problems and the SIMPLEX algorithm, Dantzig (1963), is the most commonly used. 

Dantzig, G. B. (1963) Linear Programming and Extensions (Princeton University Press). 

Dantzig, A. H., Bergin, L., Uptake of cephalosporin, cephalexin, by a dipeptide transport carrier in the human intestinal cell line, Caco-2,... 

Yang, C. Y., A. H. Dantzig, and C. Pidgeon. Intestinal peptide transport systems and oral drug availability. Pharm. Res. 1999, 16, 1331-1343. 

Dantzig, A. H., et al. Association of intestinal peptide transport with a protein related to the cadherin superfamily. Science 1994, 264, 430— 433. 

White, W. B., S. M. Johnson and G. B. Dantzig, 1958, Chemical equilibrium in complex mixtures. Journal of Chemical Physics 28, 751-755. 

We now generalize the ideas illustrated earlier from 2 to n dimensions. Proofs of the following theorems may be found in Dantzig (1963). First a number of standard definitions are given. 

To explain the method, it is necessary to know how to go from one basic feasible solution (BFS) to another, how to identify an optimal BFS, and how to find a better BFS from a BFS that is not optimal. We consider these questions in the following two sections. The notation and approach used is that of Dantzig (1998). 

Two systems of equations are said to be equivalent if they have the same solution sets. Dantzig (1998) proved that the following operations transform a given linear system into an equivalent system ... 

In the following discussion we assume that, in the system of Equations (7.6)-(7.8), all lower bounds lj = 0, and all upper bounds Uj = +< >, that is, that the bounds become 0. This simplifies the exposition. The simplex method is readily extended to general bounds [see Dantzig (1998)]. Assume that the first m columns of the linear system (7.7) form a basis matrix B. Multiplying each column of (7.7) by B-1 yields a transformed (but equivalent) system in which the coefficients of the variables ( x,. . . , xm) are an identity matrix. Such a system is called canonical and has the form shown in Table 7.1. 

If, at some iteration, the basic feasible solution is degenerate, the possibility exists that/can remain constant for some number of subsequent iterations. It is then possible for a given set of basic variables to be repeated. An endless loop is then set up, the optimum is never attained, and the simplex algorithm is said to have cycled. Examples of cycling have been constructed [see Dantzig (1998), Chapter 10]. 

Pratt, S., Chen, V., Perry, W.I., 3rd, Starling, J.J. and Dantzig, A.H. (2006) Kinetic validation of the use of carboxydichlorofluorescein as a drug surrogate for MRP5-mediated transport. European Journal of Pharmaceutical Sciences, 27, 524—532. 

Consideration of the expected value of profit alone as the objective function, which is characteristic of the classical stochastic linear programs introduced by Dantzig (1955) and Beale (1955), is obviously inappropriate for moderate and high-risk decisions under uncertainty since most decision makers are risk averse in facing important decisions. The expected value objective ignores both the risk attribute of the decision maker and the distribution of the objective values. Hence, variance of each of the random price coefficients can be adopted as a viable risk measure of the objective function, which is the second major component of the MV approach adopted in Risk Model I. 

Dantzig, G.B. (1955) Linear programming under uncertainty. Management Science,... 

DANTZIG Cutinase-Defective Mutant o/Fusarium solani... 

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