Unit 1: Introduction of Systems Approach (A) Introduction to System approach, Operations Research and Optimization Techniques, Applications of systems approach in Civil Engineering. (B) Introduction to Linear and Non linear programming methods (with reference to objective function, constraints), Graphical solutions to LP problems. (C) Local & Global optima, unimodal function, convex and concave function. (Chapter - 1) Unit 2 : Stochastic Programming (A) Sequencing- n jobs through 2, 3 and M machines. (B) Queuing Theory : elements of Queuing system and it's operating characteristics, waiting time and ideal time costs, Kendall's notation, classification of Queuing models, single channel Queuing theory : Model I (Single channel Poisson Arrival with exponential services times, Infinite population (M/M/1) : (FCFS). (C) Simulation : Monte Carlo Simulation. (Chapter - 2) Unit 3 : Linear programming (A) (A) The Transportation Model and its variants. (B) Assignment Model, and its variants. (Chapter - 3) Unit 4 : Linear programming (B) (A) Formulation of Linear optimization models for Civil engineering applications. The simplex method. (B) Method of Big M, Two phase method, duality. (Chapter - 4) Unit 5 : Nonlinear programming (A) Single variable unconstrained optimization : Sequential Search Techniques-Dichotomous, Fibonacci, Golden section. (B) Multivariable optimization without constraints - The gradient vector and Hessian Matrix, Gradient techniques, steepest ascent/decent technique, Newton's Method, (C) Multi variable optimization with equality constraints - Lagrange Multiplier Technique. (Chapter - 5) Unit 6 : Dynamic programming, Games Theory & Replacement Model (A) Multi stage decision processes, Principle of optimality, recursive equation, Applications of D.P. (B) Games Theory- 2 persons games theory, various definitions, application of games theory to construction Management (C) Replacement of items whose maintenance and repair cost increase with time, ignoring time value of money, (Chapter - 6)
