Monte Carlo simulation for analysis of the optimum value distribution in stochastic mathematical programs

This paper shows how simulation can be used to quickly solve an otherwise complex mathematical problem of derivation of the optimum value distribution function in stochastic mathematical programs. Two software packages (LINDO and UNIFIT II) are used along with a FORTRAN code in simulating and analyzing a given linear program with stochastic coefficients. Two previously analytically solved problems are resolved using simulation to show that simulation is indeed an effective method of solution.

[1]  Jerome Bracken,et al.  STATISTICAL DECISION ANALYSIS OF STOCHASTIC LINEAR PROGRAMMING PROBLEMS. , 1966 .

[2]  B. L. Foote,et al.  A procedure to rank bases by probability of being optimal using imbedded hyperspheres , 1975, Math. Program..

[3]  Bertil Naslund,et al.  A Model of Capital Budgeting Under Risk , 1966 .

[4]  Behram J. Hansotia,et al.  STOCHASTIC LINEAR PROGRAMMING WITH RECOURSE: A TUTORIAL* , 1980 .

[5]  I. M. Stancu-Minasian,et al.  Stochastic Programming: with Multiple Objective Functions , 1985 .

[6]  Marc J. Schniederjans,et al.  A stochastic linear programming model to improve automobile dealership operations , 1991, Comput. Oper. Res..

[7]  Hiroyuki Itami.  Expected Objective Value of a Stochastic Linear Program and the Degree of Uncertainty of Parameters , 1974 .

[8]  Behram Hansotia.  Technical Note - Some Special Cases of Stochastic Programs with Recourse , 1977, Oper. Res..

[9]  B. Bereanu,et al.  The continuity of the optimum in parametric programming and applications to stochastic programming , 1976 .

[10]  Moshe A. Pollatschek,et al.  The Probability Distribution Function of the Optimum of a 0-1 Linear Program with Randomly Distributed Coefficients of the Objective Function and the Right-Hand Side , 1975 .

[11]  M. A. Hanson.  ERRORS AND STOCHASTIC VARIATIONS IN LINEAR PROGRAMMING , 1960 .

[12]  Leen Stougie.  Design and analysis of algorithms for stochastic integer programming , 1987 .

[13]  András Prékopa,et al.  ON THE PROBABILITY DISTRIBUTION OF THE OPTIMUM OF A RANDOM LINEAR PROGRAM , 1966 .

[14]  On the distribution of the optimal value for a class of stochastic geometric programs , 1980 .

[15]  Harvey M. Wagner,et al.  On the Distribution of Solutions in Linear Programming Problems , 1958 .

[16]  Jati K. Sengupta,et al.  Stochastic Linear Programming with Applications to Economic Models , 1963 .

[17]  Bernard Bereanu,et al.  On stochastic linear programming. The laplace transform of the distribution of the optimum and applications , 1966 .

[18]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[19]  Hillel L. Kumin,et al.  A Method for the Solution of the Distribution Problem of Stochastic Linear Programming , 1974 .