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OPERATIONS RESEARCH (OR) COURSES
OPERATIONS RESEARCH (OR)
Definition and Scope of Operations Research: phases in Operation Research, models and their solutions, decision-making under uncertainty and risk, use of different criteria, sensitivity analysis. Transportation and assignment problems. Bellman’s principle of optimality, general formulation, computational methods and application of dynamic programming to LPP. Decision-making in the face of competition, two-person games, pure and mixed strategies, existence of solution and uniqueness of value in zero-sum games, finding solutions in 2x2, 2xm and mxn games. Analytical structure of inventory problems, EOQ formula of Harris, its sensitivity analysis and extensions allowing quantity discounts and shortages. Multi-item inventory subject to constraints. Models with random demand, the static risk model. P and Q- systems with constant and random lead times.
Queuing models – specification and effectiveness measures. Homogeneous discrete-time Markov chains, transition probability matrix, classification of states and ergodic theorems, homogeneous continuous-time Markov chains, Poisson process, elements of queuing theory, M/MI, M/M/K, G/M/l and M/G/1 queues. Steady-state solutions of M/M/1 and M/M/c models with associated distributions of queue-length and waiting time. M/G/1 queue and Pollazcek-Khinchine result. Sequencing and scheduling problems. 2-machine n-job and 3-machine n-job problems with identical machine sequence for all jobs Branch and Bound method for solving travelling salesman problem.
Replacement problems – Block and age replacement policies. PERT and CPM – basic concepts. Probability of project completion. Reliability concepts and measures, components and systems, coherent systems, reliability of coherent systems. Life-distributions, reliability function, hazard rate, common univariate life distributions – exponential, weibull, gamma, etc. Bivariate exponential distributions. Estimation of parameters and tests in these models. Notions of aging – IFR, IFRA, NBU, DMRL and NBUE classes and their duals. Loss of memory property of the exponential distribution. Reliability estimation based on failure times in variously censored life-tests and in tests with replacement of failed items. Stress-strength reliability and its estimation.
OR 201 : OPTIMIZATION MODELS
OR 201 : OPTIMIZATION MODELS
Modeling of allocation and control problems in industry and social systems. Framework and overview of optimization with examples of continuous and discrete optimization, unconstrained and constrained problems. Single stage and multi stage models. Formulations and equivalences. Examples from science, engineering and business. Linear programming. Geometry and algebra of the simplex method. Duality & sensitivity. Combinatorial optimization problems with emphasis on applications, notion of large feasible spaces and neighborhood solutions, representation of solution space, search tree, search techniques, branch and bound method. Examples of mixed-integer programming models. Use of binary variables in constraint modeling. Decision problems involving network flows, assignment models, transportation models, multi-stage flows.
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