Kishor N. Shedge

UNIT-I Linear Programming Q.1. Explain the properties of Liner Programming.          [4] Q.2. Answer the questions related to the model below:         [4] max.   3 x1 + 2 x2  st   2 x1 + 2 x2 ≤ 5  2 x1 + x2 ≤ 4  x1 + 2 x2 ≤ 4  x1, x2 ≥ 0  a. Use the graphical solution technique to find the optimal solution to the model.  b. Use the simplex algorithm to find the optimal solution to the model.  c. For which objective function coefficient value ranges of x1 and x2 does the solution remain optimal? d. Find the dual of the model. Q.3. what is the allowable range for the objective function coefficient of x2 in which current solution (basis) remains optimal? (Hint: Use the relation of Duality-Sensitivity) Q.4. Explain maximization and minimization models with example.    [4] Q.5. Explain mathematical model of single period production model.  [4] UNIT-II Du...

UNIT-I Linear Programming Q.1. Explain the properties of Liner Programming.                                                    [4] Q.2. Answer the questions related to the model below:                                             [4] max.    3 x1 + 2 x2 st         2 x1 + 2 x2 ≤ 5 2 x1 + x2 ≤ 4 x1 + 2 x2 ≤ 4 x1, x2 ≥ 0 a. Use the graphical solution technique to find the optimal solution to the model. b. Use the simplex algorithm to find the optimal solution to ...

Unit VI Decision Theory and Sensitivity Analysis Syllabus: Decision making under certainty, uncertainty and risk, sensitivity analysis, Goal programming formulation and algorithms – The weights method, The preemptive method. 6.1 Decision making under certainty, uncertainty and risk 6.2 Sensitivity analysis       Change in objective function co-efficients and effect on optimal solution Table 5.11: Sensitivity Analysis Table Output 6.3 Goal programming formulation and algorithms – The weights method, The preemptive method. Generally speaking, the objective of a business organization is to maximize profits and to minimize expenditure, loss and wastage. However, a company may not always attempt at profit maximization only. At times, a necessity may arise to pay atten...

Unit V Integer Programming Problem and Project Management Syllabus: Integer Programming Algorithms – B&B Algorithms, cutting plane algorithm, Gomory’s All-IPP Method, Project Management: Rules for drawing the network diagram, Application of CPM and PERT techniques in project planning and control; Crashing and resource leveling of operations Simulation and its uses in Queuing theory & Materials Management. 5.1 Integer Programming Algorithms – The ILP algorithms are based on exploiting the tremendous computational success of LP. The strategy of these algorithms involves three steps. 5.1.1 B&B Algorithms The first B&B algorithm was developed in 1960 by A. Land and G. Doig for the general mixed and pure ILP problem. Later, in 1965, E. Balas developed the additive algorithm for solving ILP problems with pure binary (zero or one) variables . The additive algorithm's computations were so simple (m...