CA FINAL AMA Written notes-MT Educare

AMA-Notes

Contents 0.

INTRODCUCITON TO AMA................................. ................ ................................... ................................... ................................... ................................... ................................. ................ 6

1.

LEARNING CURVE................................ CURVE............... .................................. ................................... ................................... ................................... .................................... ................................. ............... 7

1.1.

Logarithm and Anti-Logarithm Anti-Logari thm ................................... .................. .................................. ................................... .................................... ................................... ........................ ....... 7

1.2.

Introduction Introducti on to Learning Curve .................................. ................. .................................. ................................... .................................... ................................... ........................ ....... 7

1.3.

Learning Curve formula ................................... .................. ................................... ................................... ................................... ................................... ................................... .................... 8

2.

LINEAR PROGRAMMING.................... PROGRAMMING..................................... ................................... ................................... ................................... ................................... ............................... .............. 25

2.1.

Learning Objectives Objective s ................................... .................. .................................. ................................... ................................... .................................. ................................... .......................... ........ 25

2.2.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 25

2.3.

Maximization Maximizatio n Linear Programming Problem (LPP)........................ (LPP)....... ................................... .................................... .................................. ................ 26

2.3.1.

Graphical Approach ................................... .................. ................................... ................................... ................................... ................................... ................................... ...................... 26

2.3.2.

Simplex Method .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 27

2.3.3.

Steps in solving a maximization maximizati on problem using Simplex Method .................................. ................. ............................... .............. 31

2.4.

Minimization Linear Programming Problem (LPP) ................................. ................ ................................... ................................... ......................... ........ 32

2.4.1.

Graphical Approach ................................... .................. ................................... ................................... ................................... ................................... ................................... ...................... 33

2.4.2.

Simplex Method .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 34

2.5.

Infeasible Infeasibl e Solution .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 36

2.6.

Unbounded Solution .................................... .................. ................................... .................................. ................................... ................................... ................................... ....................... ..... 37

2.7.

Multiple Optimal Solution .................................. ................. ................................... ................................... ................................... ................................... ............................... .............. 39

2.8.

Degeneracy Degenerac y .................................. ................. ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 40

2.9.

Interpretation Interpre tation of final simplex table .................................. ................ ................................... ................................... .................................... .................................. ................ 42

2.10.

Primal and Dual .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 42

2.10.1.

Conversion of Primal to Dual .................................. ................. .................................. ................................... .................................... ................................... ...................... ..... 42

2.10.2.

Interpretation Interpret ation of dual problem and Comparison of simplex tables ................................... .................. ............................ ........... 46

2.11.

Formulation types............................ types........... .................................. ................................... ................................... .................................. ................................... ................................ .............. 50

3.

ASSIGNMENT PROBLEMS ................................. ................ ................................... ................................... ................................... ................................... .................................. ................. 56

3.1.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 56

3.2.

Minimization Minimization balanced assignment problem – Hungarian Method ................................................. 56

3.3.

Maximization balanced assignment problem – Hungarian Method ................................................ 58

3.4.

Minimization unbalanced assignment problem – Hungarian Method & Degeneracy .................. 59

3.5.

Maximization unbalanced unbalanced assignment problem – Hungarian Method ............................................ 63

3.6.

Multiple Optimal Solution .................................. ................. ................................... ................................... ................................... ................................... ............................... .............. 69

4.

TRANSPORTATION ................................. ................ .................................. ................................... ................................... .................................. ................................... ............................. ........... 76

E M Reddy

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AMA-Notes 4.1.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 76

4.2.

Minimization Balanced .................................. ................. ................................... ................................... ................................... ................................... ................................... ...................... 76

4.2.1.

Northwest Corner Method ................................. ................ ................................... ................................... ................................... ................................... ............................ ........... 76

4.2.2.

Least Cost Method .................................... .................. ................................... .................................. ................................... ................................... ................................... ....................... ..... 77

4.2.3.

Vogel’s approximation method  method  .......................................................................................................... 77

4.3.

Minimization Balanced - Degeneracy Degenerac y.................................. ................ ................................... ................................... .................................... ............................... ............. 79

4.4.

Maximization Maximizati on Unbalanced and Improvement Improvem ent through Looping .................................. ................. ................................... ...................... 81

4.5.

Multiple Optimal Solution .................................. ................. ................................... ................................... ................................... ................................... ............................... .............. 87

4.6.

Formulation ................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 92

5.

STANDARD COSTING or VARIANCE ANALYSIS: .................................. ................. ................................... ................................... ....................... ...... 101

5.1.

Learning Objectives Objective s ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 101

5.2.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... .................... ... 101

5.3.

Understanding Understandi ng Standard Cost .................................. ................. ................................... ................................... ................................... ................................... ....................... ...... 102

5.4.

Cost Variances Variance s ................................... .................. .................................. ................................... ................................... ................................... .................................... ................................ .............. 103

5.4.1.

Material Cost Variances – Single Raw Material Input .................................................................. 103

5.4.2.

Material Cost Variances – Mix of Raw Materials ........................................................................... 105

5.4.3.

Labour Variances – without mix ...................................................................................................... 109

5.4.4.

Labour Variances – with mix ............................................................................................................ 109

5.4.5.

Labour Variance – Idle time .............................................................................................................. 111

5.4.6.

Variable Overhead Variances .................................. ................. .................................. ................................... .................................... ................................... .................... ... 112

5.4.7.

Fixed Overhead Variances – With Calendar .................................................................................. 114

5.4.8.

Fixed Overhead Variances – Without Calendar ............................................................................. 118

5.4.9.

Cost Variances Reconciliation Reconciliati on .................................. ................. .................................. ................................... .................................... ................................... .................... ... 120

5.5.

Marginal Costing vs. Absorption Costing .................................. ................. ................................... ................................... ................................... ..................... ... 124

5.6.

Sales Variances .................................. ................. .................................. ................................... ................................... ................................... .................................... ................................ .............. 127

5.7.

Types of Reconciliation Reconcilia tion Problems .................................. ................ ................................... ................................... .................................... ................................... ................. 132

5.7.1.

Standard Reconciliation Reconcilia tion Statement Statemen t .................................. ................ ................................... ................................... .................................... ............................. ........... 132

5.8.

Concept of Standard Profit .................................. ................. ................................... ................................... ................................... ................................... ............................. ............ 138

5.9.

Reconciliation Reconcili ation with Work in Progress ................................. ............... ................................... .................................. ................................... .............................. ............ 140

5.10.

Opportunity Cost Method of Reconciliation Reconciliat ion ................................... .................. ................................... ................................... ............................. ............ 146

5.11.

Planning Variance vs. Operating Variance ................................... .................. ................................... ................................... ................................ ............... 154

5.12.

Planning vs. Operating Variance – Market Size and Market Share Variance ............................ 163

5.13.

Balance Score Card Method of Reconciliation Reconciliat ion ................................. ................ ................................... ................................... ............................. ............ 166

5.14.

Miscellaneous Miscellaneous Concepts – Standard Costing Ratios ...................................................................... 171

E M Reddy

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AMA-Notes 4.1.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 76

4.2.

Minimization Balanced .................................. ................. ................................... ................................... ................................... ................................... ................................... ...................... 76

4.2.1.

Northwest Corner Method ................................. ................ ................................... ................................... ................................... ................................... ............................ ........... 76

4.2.2.

Least Cost Method .................................... .................. ................................... .................................. ................................... ................................... ................................... ....................... ..... 77

4.2.3.

Vogel’s approximation method  method  .......................................................................................................... 77

4.3.

Minimization Balanced - Degeneracy Degenerac y.................................. ................ ................................... ................................... .................................... ............................... ............. 79

4.4.

Maximization Maximizati on Unbalanced and Improvement Improvem ent through Looping .................................. ................. ................................... ...................... 81

4.5.

Multiple Optimal Solution .................................. ................. ................................... ................................... ................................... ................................... ............................... .............. 87

4.6.

Formulation ................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 92

5.

STANDARD COSTING or VARIANCE ANALYSIS: .................................. ................. ................................... ................................... ....................... ...... 101

5.1.

Learning Objectives Objective s ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 101

5.2.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... .................... ... 101

5.3.

Understanding Understandi ng Standard Cost .................................. ................. ................................... ................................... ................................... ................................... ....................... ...... 102

5.4.

Cost Variances Variance s ................................... .................. .................................. ................................... ................................... ................................... .................................... ................................ .............. 103

5.4.1.

Material Cost Variances – Single Raw Material Input .................................................................. 103

5.4.2.

Material Cost Variances – Mix of Raw Materials ........................................................................... 105

5.4.3.

Labour Variances – without mix ...................................................................................................... 109

5.4.4.

Labour Variances – with mix ............................................................................................................ 109

5.4.5.

Labour Variance – Idle time .............................................................................................................. 111

5.4.6.

Variable Overhead Variances .................................. ................. .................................. ................................... .................................... ................................... .................... ... 112

5.4.7.

Fixed Overhead Variances – With Calendar .................................................................................. 114

5.4.8.

Fixed Overhead Variances – Without Calendar ............................................................................. 118

5.4.9.

Cost Variances Reconciliation Reconciliati on .................................. ................. .................................. ................................... .................................... ................................... .................... ... 120

5.5.

Marginal Costing vs. Absorption Costing .................................. ................. ................................... ................................... ................................... ..................... ... 124

5.6.

Sales Variances .................................. ................. .................................. ................................... ................................... ................................... .................................... ................................ .............. 127

5.7.

Types of Reconciliation Reconcilia tion Problems .................................. ................ ................................... ................................... .................................... ................................... ................. 132

5.7.1.

Standard Reconciliation Reconcilia tion Statement Statemen t .................................. ................ ................................... ................................... .................................... ............................. ........... 132

5.8.

Concept of Standard Profit .................................. ................. ................................... ................................... ................................... ................................... ............................. ............ 138

5.9.

Reconciliation Reconcili ation with Work in Progress ................................. ............... ................................... .................................. ................................... .............................. ............ 140

5.10.

Opportunity Cost Method of Reconciliation Reconciliat ion ................................... .................. ................................... ................................... ............................. ............ 146

5.11.

Planning Variance vs. Operating Variance ................................... .................. ................................... ................................... ................................ ............... 154

5.12.

Planning vs. Operating Variance – Market Size and Market Share Variance ............................ 163

5.13.

Balance Score Card Method of Reconciliation Reconciliat ion ................................. ................ ................................... ................................... ............................. ............ 166

5.14.

Miscellaneous Miscellaneous Concepts – Standard Costing Ratios ...................................................................... 171

E M Reddy

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AMA-Notes 5.15.

Partial Plan vs. Single Plan ................................. ................ ................................... ................................... ................................... ................................... .......................... ......... 175

5.16.

Reverse Working Problems ................................... .................. ................................... ................................... ................................... ................................... ....................... ...... 191

5.17.

Investigation Investigati on of Variances .................................. ................. ................................... ................................... ................................... ................................... .......................... ......... 196

6.

RELEVANT COSTING .................................... .................. ................................... .................................. ................................... ................................... ................................... ..................... ... 199

6.1.

Learning Objectives Objective s ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 199

6.2.

Relevant Cost of Materials .................................. ................. ................................... ................................... ................................... ................................... ............................. ............ 199

6.3.

Relevant Cost of Labour ................................... .................. ................................... ................................... ................................... ................................... ................................ ............... 201

6.4.

Relevant Cost of Overheads ................................... .................. ................................... ................................... ................................... ................................... .......................... ......... 202

6.5.

Comprehensive Comprehe nsive Problems ................................... .................. ................................... ................................... ................................... ................................... ............................. ............ 203

6.6.

Limiting Factor and Relevant Costing ................................. ............... ................................... .................................. ................................... .............................. ............ 208

6.7.

Joint product and Relevant Costing .................................. ................ ................................... ................................... .................................... ................................ .............. 211

6.8.

Relevant Costing under Uncertainty Uncertaint y ................................... ................. ................................... ................................... .................................... ............................. ........... 214

7.

MARGINAL COSTING ................................... ................. ................................... .................................. ................................... ................................... ................................... ..................... ... 220

7.1.

Learning Objectives Objective s ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 220

7.2.

Basics in Marginal Costing .................................. ................. ................................... ................................... ................................... ................................... ............................. ............ 220

7.2.1.

Income Statement .................................. ................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 221

7.2.2.

PV Ratio ................................... .................. ................................... ................................... .................................. ................................... .................................... ................................... .................... ... 221

7.2.3.

Breakeven Breakeve n Point .................................. ................. .................................. ................................... ................................... ................................... .................................... .......................... ........ 221

7.2.4.

Margin of Safety .................................. ................. .................................. ................................... ................................... ................................... .................................... .......................... ........ 221

7.2.5.

Profit ................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... .......................... ......... 222

7.3.

Issues in the concept of Break-even Break-ev en point ................................. ............... ................................... .................................. ................................... ........................ ...... 222

7.3.1.

Multiple break-even break-ev en points (Step fixed cost) ................................... .................. ................................... ................................... ............................. ............ 222

7.3.2.

Break-even Break-ev en point with semi-variable semi-var iable cost .................................. ................. ................................... ................................... ................................... .................. 227

7.3.3.

Marginal Costing (vs.) Absorption Costing Break-even Break-ev en point ................................... .................. ................................... .................. 229

7.3.4.

Break-even Break-ev en point with two products .................................. ................ ................................... .................................. ................................... ........................... ......... 234

7.4.

Indifference Indiffer ence Point ................................... .................. .................................. ................................... ................................... ................................... .................................... .......................... ........ 235

7.4.1.

Introduction to Indifference Indifferenc e point ................................. ............... ................................... ................................... .................................... ................................ .............. 235

7.4.2.

Indifference Indiffer ence point as a state of demand .................................. ................. ................................... ................................... ................................... ..................... ... 237

7.4.3.

Limiting Factor and Indifference Indifferenc e Point ................................. ............... ................................... .................................. ................................... ........................ ...... 240

7.4.4.

Understanding Understandin g how to analyze a semi-variable semi-va riable cost .................................. ................ .................................... ................................... ................. 244

7.5.

Limiting Factor Problems ................................. ................ ................................... ................................... ................................... ................................... ................................ ............... 249

7.5.1.

Basic Limiting factor allocation problems problem s .................................. ................. ................................... ................................... ................................... .................. 249

7.5.2.

Limiting factor in Make or Buy Situation ................................... .................. ................................... ................................... ................................... .................. 251

7.5.3.

Multiple Limiting factors in Make or Buy Situation ................................... ................. .................................... ................................... ................. 258

E M Reddy

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AMA-Notes 7.5.4.

Limiting factor with Specific Fixed Cost ................................. ................ ................................... ................................... ................................... ..................... ... 262

7.6.

Shut down (or) Continue decisions ................................... ................. ................................... ................................... .................................... ................................ .............. 268

7.7.

Differential Differen tial Costing ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 270

8.

SIMULATION ................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... .................... ... 279

9.

MATERIALS REQUIREMENT PLANNING (MRP) ................................. ................ ................................... ................................... .......................... ......... 289

9.1.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... .................... ... 289

9.2.

Planning Order Release ................................. ................ ................................... ................................... ................................... ................................... ................................... .................. 289

9.3.

Construction Constructi on of Product Tree ................................. ................ ................................... ................................... ................................... ................................... .......................... ......... 291

9.4.

Preparation Preparat ion of MRP ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 292

9.5.

Preparation Preparat ion of MRP with safety stock ................................. ............... ................................... .................................. ................................... .............................. ............ 292

9.6.

Material Purchase Budget and Economic Order Quantity [EOQ]................................. ................ ................................... .................. 293

10.

NETWORK ANALYSIS ................................. ................ ................................... ................................... ................................... ................................... ................................... .................. 296

10.1.

Learning Objectives Objective s .................................. ................ ................................... .................................. ................................... ................................... ................................... ..................... ... 296

10.2.

Introduction ................................... .................. .................................. ................................... ................................... ................................... .................................... ................................ .............. 296

10.3.

Understanding Understandin g some basic terms used in Network ................................... ................. .................................... ................................... ................. 296

10.3.1.

Activities & Events ................................... ................. ................................... .................................. ................................... ................................... ................................... ..................... ... 296

10.3.2.

Errors in Networking ................................. ................ ................................... ................................... ................................... ................................... ................................... .................. 297

10.3.2.1.

Looping Error .................................. ................. .................................. ................................... ................................... ................................... .................................... .......................... ........ 297

10.3.2.2.

Dangling Error ................................... .................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 298

10.3.2.3.

Mistake in Preceding, Precedin g, Succeeding relationship relationshi p ................................. ................ ................................... ................................... ....................... ...... 298

10.3.3.

Conventions in Network Drawing ................................... ................. ................................... ................................... .................................... ............................. ........... 299

10.4.

Floats, Forward Pass, Backward Pass and Critical Path ................................. ................ ................................... .............................. ............ 299

10.5.

Network Crashing .................................... .................. ................................... .................................. ................................... ................................... ................................... ..................... ... 303

10.6.

Program Evaluation Review Technique .................................. ................. ................................... ................................... ................................... ..................... ... 310

10.7.

Resource Allocation .................................. ................ ................................... .................................. ................................... ................................... ................................... ..................... ... 314

10.8.

Resource Leveling (or) Resource Smoothing ................................... .................. ................................... ................................... ............................. ............ 316

10.9.

Understanding Understandin g to draw a network & use dummy activities activiti es ................................... .................. ................................... ..................... ... 320

10.10.

Network Updation ................................... ................. ................................... .................................. ................................... ................................... ................................... ..................... ... 330

11.

TRANSFER PRICING .................................. ................ ................................... .................................. ................................... ................................... ................................... ..................... ... 332

11.1.

Introduction ................................... .................. .................................. ................................... ................................... ................................... .................................... ................................ .............. 332

11.2.

Transfer Price - Variable Cost .................................. ................. .................................. ................................... .................................... ................................... .................... ... 332

11.3.

Transfer Price – Specific Fixed Cost ................................................................................................. 339

11.4.

Linear Programming Method of Transfer Price fixation ................................ ............... ................................... .............................. ............ 342

11.5.

Limiting Factor and Transfer Pricing .................................. ................ ................................... .................................. ................................... ........................... ......... 347

E M Reddy

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AMA-Notes 11.6.

Multi-Division range fixations ................................. ................ .................................. ................................... .................................... ................................... .................... ... 352

11.7.

Lump Sum Consideration Considerat ion Method .................................. ................ ................................... ................................... .................................... ............................. ........... 354

11.8.

Transfer Pricing Fixation Chart .................................. ................ ................................... ................................... .................................... ................................... ................. 358

12.

PRICING ................................... .................. ................................... ................................... ................................... ................................... ................................... ................................... ....................... ...... 360

12.1.

Pricing Using Calculus.................................. ................. ................................... ................................... ................................... ................................... ................................ ............... 360

12.2.

Pricing Under Uncertainty and Expected Value of Perfect Information (EVPI) .................. ....................... ..... 364

12.3.

ROI (Return on Investment) Pricing ................................... ................. ................................... .................................. ................................... ........................... ......... 367

13.

DEVELOPMENTS IN COST ACCOUNTING (STRAGETIC COST MANAGEMENT ................ 368

13.1.

Learning Objectives Objective s .................................. ................ ................................... .................................. ................................... ................................... ................................... ..................... ... 368

13.2.

Through Put Costing .................................. ................. ................................... ................................... ................................... ................................... ................................... .................. 368

13.3.

Theory of Constraints ................................. ................ ................................... ................................... ................................... ................................... ................................... .................. 370

13.3.1.

Theory of Constraints Measures (TOC Measures) ................................... ................. .................................... ................................... .................... ... 373

13.4.

Just-in-Time Just-in-T ime System (JIT) ................................. ................ ................................... ................................... ................................... ................................... ............................. ............ 377

13.5.

Backflush Costing .................................. ................. .................................. ................................... ................................... .................................. ................................... ........................ ...... 381

13.5.1.

Backflush Costing – Version 1 .......................................................................................................... 381

13.5.2.

Backflush Costing – Version 2 .......................................................................................................... 382

13.5.3.

Backflush Costing – Version 3 .......................................................................................................... 383

13.6.

Total Quality Management (TQM) .................................. ................ ................................... ................................... .................................... ............................. ........... 387

13.7.

Life Cycle Costing (LCC) ................................. ................ ................................... ................................... ................................... ................................... ............................. ............ 393

13.8.

Target Costing .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................. ........... 395

13.9.

Activity Based Costing (ABC) .................................. ................. .................................. ................................... .................................... ................................... .................... ... 400

13.9.1.

Activity Based Costing (ABC) - Introduction .................................. ................. ................................... ................................... ............................. ............ 400

13.9.2.

Activity Based Costing (ABC) & Target Costing .................................. ................. ................................... ................................... ....................... ...... 412

13.9.3.

Activity Based Costing (ABC) with Variance Analysis ................................ ............... ................................... ................................. ............... 417

E M Reddy

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AMA-Notes

Contents 0.

INTRODCUCITON TO AMA................................. ................ ................................... ................................... ................................... ................................... ................................. ................ 6

1.

LEARNING CURVE................................ CURVE............... .................................. ................................... ................................... ................................... .................................... ................................. ............... 7

1.1.

Logarithm and Anti-Logarithm Anti-Logari thm ................................... .................. .................................. ................................... .................................... ................................... ........................ ....... 7

1.2.

Introduction Introducti on to Learning Curve .................................. ................. .................................. ................................... .................................... ................................... ........................ ....... 7

1.3.

Learning Curve formula ................................... .................. ................................... ................................... ................................... ................................... ................................... .................... 8

2.

LINEAR PROGRAMMING.................... PROGRAMMING..................................... ................................... ................................... ................................... ................................... ............................... .............. 25

2.1.

Learning Objectives Objective s ................................... .................. .................................. ................................... ................................... .................................. ................................... .......................... ........ 25

2.2.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 25

2.3.

Maximization Maximizatio n Linear Programming Problem (LPP)........................ (LPP)....... ................................... .................................... .................................. ................ 26

2.3.1.

Graphical Approach ................................... .................. ................................... ................................... ................................... ................................... ................................... ...................... 26

2.3.2.

Simplex Method .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 27

2.3.3.

Steps in solving a maximization maximizati on problem using Simplex Method .................................. ................. ............................... .............. 31

2.4.

Minimization Linear Programming Problem (LPP) ................................. ................ ................................... ................................... ......................... ........ 32

2.4.1.

Graphical Approach ................................... .................. ................................... ................................... ................................... ................................... ................................... ...................... 33

2.4.2.

Simplex Method .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 34

2.5.

Infeasible Infeasibl e Solution .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 36

2.6.

Unbounded Solution .................................... .................. ................................... .................................. ................................... ................................... ................................... ....................... ..... 37

2.7.

Multiple Optimal Solution .................................. ................. ................................... ................................... ................................... ................................... ............................... .............. 39

2.8.

Degeneracy Degenerac y .................................. ................. ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 40

2.9.

Interpretation Interpre tation of final simplex table .................................. ................ ................................... ................................... .................................... .................................. ................ 42

2.10.

Primal and Dual .................................. ................. .................................. ................................... ................................... ................................... .................................... ............................ .......... 42

2.10.1.

Conversion of Primal to Dual .................................. ................. .................................. ................................... .................................... ................................... ...................... ..... 42

2.10.2.

Interpretation Interpret ation of dual problem and Comparison of simplex tables ................................... .................. ............................ ........... 46

2.11.

Formulation types............................ types........... .................................. ................................... ................................... .................................. ................................... ................................ .............. 50

3.

ASSIGNMENT PROBLEMS ................................. ................ ................................... ................................... ................................... ................................... .................................. ................. 56

3.1.

Introduction Introducti on................................. ................ ................................... ................................... .................................. ................................... .................................... ................................... ...................... ..... 56

3.2.

Minimization Minimization balanced assignment problem – Hungarian Method ................................................. 56

3.3.

Maximization balanced assignment problem – Hungarian Method ................................................ 58

3.4.

Minimization unbalanced assignment problem – Hungarian Method & Degeneracy .................. 59

3.5.

Maximization unbalanced unbalanced assignment problem – Hungarian Method ............................................ 63

3.6.

Multiple Optimal Solution .................................. ................. ................................... ................................... ................................... ................................... ............................... .............. 69

4.

TRANSPORTATION ................................. ................ .................................. ................................... ................................... .................................. ................................... ............................. ........... 76

E M Reddy

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