(MCA-315) Computer Basaed Optimization Technique

Babu Banarasi Das National Institute of Technology and Management Department of Computer Applications Course Outline & Lecture Delivery Schedule Masters of Computer Applications (MCA) NEW Syllabus (Affiliated to G. B. Technical University, Lucknow.) III Semester MCA-315: Computer Based Optimization Techniques

A. Introduction: The optimization techniques are basically belongs to “Operations Research”. This new science comes into existence in military context. During World War II, military management called on scientists from various disciplines and organized them into teams to assist in solving strategic and tactical problems i.e. to discuss, evolve and suggest ways and means to improve the execution of various military projects. By their joint effort, experience and deliberations they suggested certain approaches that showed remarkable progress

B. Objective: The main objective of the paper is to provide understanding of various techniques and methods related to several topics of OR like L.P.P.; I.P.P.; Non linear programming; Assignment problem; Transportation; Transshipment; Routing problem etc. C. Students Performance Evaluation Scheme: External Semester Examination Internal Performance Assessment  3 Sessional Tests  Attendance  Teacher Assessment Based on Assignments, Seminars, Group Discusions & Class Participation D. Reading:

: : : : :

100 Marks 50 Marks 30 Marks 10 Marks 10 Marks

I-Text: T1 S. D. Sharma, “Operation Research” T2 Kanti Swaroop & Man Mohan, “Operation Research” II-Reference: R1 V. K. Kapoor, “Operation Research” R2 D. S. Cheema, “Operation Research” R3 B.S. Goel & S.K.Mittal, “Operation Research” R4 Frederick S. Hillier,Gerald J. Lieberman, “Operation Research” R5 R.K.Gupta, “Operation Research”

E. LECTURE DELIVERY SCHEDULE:

Lecture Session No.

Topic (Unit I ) Inventory Management

1

2

3 4

5

6 7 8

9

10 11 12 13

Inventory Control Introduction Types of Inventories Inventory Decisions Definition of Average Inventory Deterministic Inventory Models Models without Shortage Economic Order Quantity (EOQ) Models with Shortage Multi-Item Deterministic Inventory Models Concept of Price-Break EOQ Problems With One Price Break EOQ Problems With Two Price Break Stochastic Models

T1 Ch – 20 679-686

T1 Ch – 20 687- 706 T1 Ch – 20 711-719 T1 Ch – 20 720-727 T1 Ch – 20 734-770

Replacement Problems Concept of Replacement Problems T1 Ch – 22 796-809 Replacement Problems with constant Money value Concept of Present Worth Factor T1 Ch – 22 804-807 Replacement Problems with variable Money value How to Select a Best Machine. T1 Ch – 22 810-816 Group Replacement Vs Individual Replacement (Unit II) Linear Programming Problem and Integer Programming Problem Introduction to Linear Programming Problem. Components of L.P.P.  Objective Function  Constraints  Non Negative Restrictions Formulation of L.P.P. Examples on the formulation. Graphical method for solving L.P.P. Difference between Bounded and UnBounded Solutions Examples on the graphical method. Examples on graphical method in exceptional cases Various Definitions  Slack variables  Surplus variables  Normal solution  Feasible solution  Basic solution

T1 Ch – 3 53-65

T1 Ch – 3 65-76 T1 Ch – 3 77-81 T1 Ch – 3 82-89 T1 Ch – 3 91-93

14 15 16 17 18 19 20

21 22 23

24 25 26 27

28

29

 Basic feasible solution  Optimum solution  Unbounded solution Degeneracy etc. Simplex Method Computational procedure for Simplex method Examples on simplex method Concept of Artificial Variables Two – Phase Method Big – M Method. Disadvantage of BIG-M over 2-Phase method. Examples on Two – Phase & Big – M. Concept of Revised Simplex method. Examples on Revised Simplex method Concept of Duality Definition of Primal & Dual Problems Conversion of Primal to Dual Dual Simplex Computational procedure for Dual Simplex method Examples on Dual Simplex method Difference between Simplex & Dual Simplex Method Sensitivity Analysis Change in the Coefficient of the Objective Function Change in the component b’i of Vector (b) Change in the component aij of Matrix (A) (Unit III) Integer Programming Problem Gomory Cutting Plane method All Integer I.P.P. and Mixed Integer I.P.P. Examples on above methods Branch & Bound Method Transportation and Assignment Problem Transportation Problem Matrix Form of Transportation Problem Methods to Find IBFS  North-West corner rule method & Examples  Row Minimum method & Examples  Column Minimum method & Examples  Matrix Minimum method & Examples 

Vogel’s Approximation method to get the initial basic solution & based examples

T1 Ch – 5 117-120 T1 Ch – 5 121-130 T1 Ch – 5 131-134 T2 Ch – 3 T1 Ch – 5 138-142 T1 Ch – 5 143-146 T1 Ch – 6 168-200 T2 Ch – 3 T1 Ch – 7 T2 Ch – 4 202-220 T1, Ch – 8 236-238 T1 Ch – 8 239-245 T1 Ch – 9 248-268

T1 Ch – 10 276-288 T1 Ch – 10 289-293 T1 Ch – 10 294-300 T1 Ch – 12 356-360

T1 Ch – 12 361-366

T1 Ch – 12 366-370

30

Formation of Loops in Transportation Problem

T1 Ch – 12 362

31 32 33

Degeneracy in Transportation Problem Optimum solution for transportation problem using U-V method. Examples on optimum solution

T1 Ch – 12 398-400 T1 Ch – 12 373-376 T1 Ch – 12 377-380

34 35 36

37 38 39

40 41

42 43 44 45 46 47 48

49

50 51

52

53

Transshipment Problem. Examples on Transshipment Problem. Introduction to Assignment Problem Algorithm for Hungarian method. Examples on Hungarian method Maximization case & Unbalanced Assignment problem. Examples on above. (Unit IV) Non Linear Programming Problem Definition of Non-Linear Programming Problem Formulation of Non-Linear Programming Problem Canonical Form of NLPP Geometrical Interpretation of KT- Conditions Determination of KT Points Concept of Lagrangian Function Kuhn-Tucker conditions Statement and Examples Graphical Solution & Examples Quadratic Programming Problem. Wolfe’s method for Quadratic Programming Problem Examples on Wolfe’s Method (QPP). Definition of Convex & Concave Functions Convex Programming Problem. Introduction to Dynamic Programming Bellman’s Principle of Optimality of Dynamic Programming Solution to problem with Finite No. of Stages Minimum Path Problem and its Examples Multistage Decision Problem. Mathematical Formulation of Multistage Model Solution of L.P.P. as a Dynamic Programming Problem. (Unit V) Queuing Theory Introduction to Queues. Basic Elements of Queuing Models  Arrival Pattern  Service Pattern  Queue Discipline  Customer Behaviour Definition of Steady and Transient States Symbols & Notation used Traffic Intensity or Utilization Factor Pure Birth Process or Poisson Process Derivation of Arrival Distribution Properties of Poisson Process of arrivals Memory-less Distribution or Exponential Distribution Derivation of Inter-Arrival Time Distribution Role of Poisson and Exponential Distribution Markovian Property of Inter-Arrival Time Derivation of Service Time Distribution

T1 Ch – 12 429-430 T1 Ch – 12 431-432 T1 Ch – 11 305-325 T1 Ch – 11 326-330 T1 Ch – 11 331-340 T1 Ch – 28 1057-1060 T1 Ch – 28 1061-1063 T1 Ch – 27 1042- 1049 T1 Ch – 29 1064-1067 T1 Ch – 29 1068-1070 T1 Ch – 4 104-110 T1 Ch – 33 1107-1109 T1 Ch – 33 1110-1112 T1 Ch – 33 1133-1134 T1 Ch – 33 1141-1144 T1 Ch – 23 836-838

T1 Ch – 23 839-840 T1 Ch – 23 840-843 T1 Ch – 23 845-846 T1 Ch – 23 846-847

54 55 56

Erlang Distribution Kendall’s Notations for Queuing models Birth-Death Model Derivation of Steady-State Equations Examples on Poisson Queues.

T1 Ch – 23 849-851 T1 Ch – 23 853-857 T1 Ch – 23 861-873