Optimization and Inventory Management (eBook)

Contents 6
About the Editors 9
1 Economic Production Quantity (EPQ) Inventory Model for a Deteriorating Item with a Two-Level Trade Credit Policy and Allowable Shortages 10
1.1 Introduction 10
1.2 Suppositions and Notation 14
1.2.1 Suppositions 14
1.2.2 Notation 14
1.3 Inventory Model Formulation 15
1.4 Numerical Examples 23
1.5 Sensitivity Analysis 23
1.6 Conclusion 27
References 27
2 An Economic Order Quantity (EOQ) Inventory Model for a Deteriorating Item with Interval-Valued Inventory Costs, Price-Dependent Demand, Two-Level Credit Policy, and Shortages 29
2.1 Introduction 30
2.2 Suppositions and Notations 33
2.2.1 Suppositions 33
2.2.2 Notations 33
2.3 Mathematical Derivation of the Inventory Model 34
2.4 The Solution for Three Demand Functions 42
2.5 Numerical Examples 50
2.6 Sensitivity Analysis 50
2.7 Conclusion 59
References 60
3 Inventory Control Policies for Time-Dependent Deteriorating Item with Variable Demand and Two-Level Order Linked Trade Credit 62
3.1 Introduction 62
3.2 Notation and Assumptions 64
3.2.1 Notation 64
3.2.2 Assumptions 65
3.3 Mathematical Model 65
3.4 Numerical Examples with Sensitivity Analysis 69
3.4.1 Numerical Examples 69
3.4.2 Sensitivity Analysis 71
3.5 Conclusion 72
References 73
4 Inventory Modelling of Deteriorating Item and Preservation Technology with Advance Payment Scheme Under Quadratic Demand 75
4.1 Introduction 76
4.2 Notation and Assumptions 77
4.2.1 Notation 77
4.2.2 Assumptions 78
4.3 Mathematical Model 79
4.4 Numerical Example and Sensitivity Analysis 80
4.4.1 Numerical Example 80
4.4.2 Sensitivity Analysis for the Inventory Parameters 81
4.5 Conclusion 84
References 84
5 Dynamic Pricing, Advertisement Investment and Replenishment Model for Deteriorating Items 86
5.1 Introduction 87
5.2 Notation and Assumptions 88
5.2.1 Notation 88
5.2.2 Assumptions 88
5.3 Mathematical Model 89
5.4 Numerical Example and Sensitivity Analysis 92
5.5 Conclusion 95
References 96
6 A Production Reliable Model for Imperfect Items with Random Machine Breakdown Under Learning and Forgetting 98
6.1 Introduction 98
6.2 Assumptions and Notations 101
6.2.1 Assumptions 101
6.2.2 Notations 102
6.3 Mathematical Formulation of the Model 103
6.3.1 Crisp Model 103
6.3.2 Model Formulation with Learning and Forgetting in Setup Cost 109
6.3.3 Fuzzy Model Formulation 110
6.4 Optimal Solution Procedure 111
6.5 Numerical Examples 111
6.5.1 Crisp Model 112
6.5.2 Effect of Learning and Forgetting on Setup Cost 112
6.5.3 Fuzzy Model 112
6.6 Concavity of the Proposed Inventory System 115
6.7 Sensitivity Analysis 116
6.8 Effect of Inventory Parameters on Expected Average Profit (i = 1,2) 116
6.8.1 Effect of Inventory Parameters on Time T11 and Time T21 (i = 1,2) 117
6.8.2 Effect of Inventory Parameters on Time T12 and Time T22 (i = 1,2) 120
6.8.3 Effect of Inventory Parameters on Demand D1 and D2 (i = 1,2) 120
6.9 Conclusion 120
References 121
7 Inventory Policies with Development Cost for Imperfect Production and Price-Stock Reliability-Dependent Demand 123
7.1 Introduction 124
7.2 Notations and Assumptions 127
7.2.1 Notations 127
7.2.2 Assumptions 128
7.3 Mathematical Model Formulation 129
7.4 Numerical Example and Sensitivity Analysis 131
7.4.1 Numerical Example 131
7.4.2 Sensitivity Analysis of the Optimal Inventory Policy 132
7.5 Conclusion and Future Scope 137
References 138
8 Imperfect Quality Item Inventory Models Considering Carbon Emissions 141
8.1 Introduction and Related Literature 141
8.2 Low-Carbon EOQ Models for Imperfect Quality Items 143
8.2.1 Basic EOQ Model for Imperfect Quality Items Considering Carbon Emission 145
8.2.2 EOQ Model with Complete Backorder Considering Carbon Emission 147
8.2.3 Illustrative Examples 151
8.3 Low-Carbon Supply Chain Inventory Model for Imperfect Quality Items 152
8.3.1 Buyer’s Cost Function 153
8.3.2 Vendor’s Cost Function 155
8.3.3 Integrated Decision 158
8.3.4 Illustrative Example 159
8.4 Concluding Remarks 161
References 162
9 Non-instantaneous Deteriorating Model for Stock-Dependent Demand with Time-Varying Holding Cost and Random Decay Start Time 164
9.1 Introduction 164
9.2 Notations and Assumptions 166
9.2.1 Notations 166
9.2.2 Assumptions 167
9.3 Model Development 167
9.3.1 Different Costs for the Models 169
9.4 Total Cost of the Model and Solution Procedure 170
9.4.1 Case I: Fixed Holding Cost When t0 Is Known 170
9.4.2 Case II: Time-Varying Holding Cost and Known t0 171
9.4.3 Case III: Time-Dependent Holding Cost When t0 Is Random 173
9.5 Algorithm to Calculate Optimum Solution 175
9.6 Numerical Results 175
9.7 Sensitivity Analysis 177
9.7.1 Observation and Managerial Insights Based on Numerical Results and Sensitivity 178
9.8 Concluding Remarks 181
References 182
10 Stock-Dependent Inventory Model for Imperfect Items Under Permissible Delay in Payments 184
10.1 Introduction 185
10.2 Conclusion 196
References 196
11 Joint Effects of Carbon Emission, Deterioration, and Multi-stage Inspection Policy in an Integrated Inventory Model 198
11.1 Introduction 199
11.2 Problem Description 200
11.2.1 Problem Definition 200
11.2.2 Notation 201
11.2.3 Assumptions 201
11.3 Mathematical Model 202
11.3.1 Buyer’s Model 203
11.3.2 Vendor’s Model 204
11.3.3 Coordination Policy Between Vendor and Buyer 205
11.3.4 Solution Methodology 205
11.4 Numerical Experiment 207
11.5 Analysis Section 209
11.6 Sensitivity Analysis 209
11.7 Conclusions 210
References 210
12 A Note on “Inventory and Shelf-Space Optimization for Fresh Produce with Expiration Date Under Freshness-and-Stock-Dependent Demand Rate” 212
12.1 Introduction 212
12.2 Notations and Assumptions 214
12.2.1 Notations 214
12.2.2 Assumptions 215
12.3 Model Formulation 216
12.4 Numerical Examples 218
12.5 Sensitivity Analysis 219
12.6 Conclusion 220
References 220
13 EOQ Model Under Discounted Partial Advance—Partial Trade Credit Policy with Price-Dependent Demand 221
13.1 Introduction 221
13.2 Notations and Assumptions 223
13.3 The Model 224
13.3.1 Computation of Net 225
13.3.2 Analysis 227
13.4 Algorithm 229
13.4.1 Numerical Example 230
13.4.2 Sensitivity Analysis 231
13.4.3 Managerial Insights 233
13.5 Conclusion and Future Scope 235
Appendix 1 (Sufficiency Conditions) 235
Appendix 2 (Determinant of the Hessian Matrix) 236
References 238
14 Effects of Pre- and Post-Deterioration Price Discounts on Selling Price in Formulation of an Ordering Policy for an Inventory System: A Study 240
14.1 Introduction 240
14.2 Assumptions and Notations 241
14.3 Mathematical Formulation 242
14.4 Numerical Examples 248
14.5 Sensitivity Analysis 252
14.6 Conclusion 253
References 254
15 Efficient Supplier Selection: A Way to Better Inventory Control 256
15.1 Introduction 256
15.2 Supplier Selection: A Case Study 258
15.3 Sensitivity Analysis and Managerial Insights 272
15.4 Conclusion 278
References 279
16 Supply Chain Network Optimization Through Player Selection Using Multi-objective Genetic Algorithm 281
16.1 Introduction 281
16.2 Literature Review 282
16.3 Problem Description 283
16.4 Notations and Assumptions 284
16.4.1 Notations 284
16.4.2 Assumptions 285
16.5 Multi-echelon Inventory Model 286
16.6 Computational Algorithm 289
16.6.1 Multi-objective GA 289
16.6.2 3D-RadVis Visualization Technique 290
16.7 Numerical Example and Results 290
16.8 Conclusions 298
Appendix 298
References 315
17 Allocation of Order Amongst Available Suppliers Using Multi-objective Genetic Algorithm 316
17.1 Introduction 316
17.2 Notations and Assumptions 318
17.3 Mathematical Model 319
17.4 Algorithm 322
17.4.1 Multi-objective Genetic Algorithm 322
17.4.2 3D-RadVis Visualization Technique 323
17.5 Numerical Example 323
17.6 Conclusion 326
References 327
18 Some Studies on EPQ Model of Substitutable Products Under Imprecise Environment 329
18.1 Introduction 329
18.2 Mathematical Prerequisites 331
18.3 Assumptions and Notations 333
18.3.1 Assumptions 333
18.3.2 Notations 334
18.4 Model 1 : EPQ Model Having Substitution with the Constant Demand and Same Time Period 334
18.4.1 Model Formulation 334
18.5 Model 2 : EPQ Model Substitution Considering Shortage in One of the Items with Constant Demand and Same Time Period 337
18.5.1 Model Formulation 337
18.6 Different Types of Budget Constraints 341
18.7 Solution Methodology and Numerical Solution of Both the Models 343
18.8 Applications and Extensions of Proposed Model 344
18.9 Sensitivity Analysis and Discussion of Models 345
18.10 Conclusion and Future Work 356
References 356
19 An Effective MILP Model for Food Grain Inventory Transportation in India—A Heuristic Approach 359
19.1 Introduction 359
19.2 Literature Review 362
19.3 Problem Definition 363
19.4 Mathematical Model 364
19.5 Solution Methodology 365
19.6 Results and Discussion 367
19.7 Case Study 367
19.8 Conclusion 370
Appendix 1 370
Appendix 2 371
Appendix 3 372
References 373
20 Fuzzy Based Inventory Model with Credit Financing Under Learning Process 375
20.1 Introduction 376
20.2 Assumptions and Notations 377
20.2.1 Assumptions 378
20.2.2 Notations 378
20.3 Crisp Formulation Model 379
20.4 Fuzzy Methodology 382
20.4.1 Fuzzy Inventory Model 383
20.4.2 Derivation of  widetilde?1 ( Tc ) and  widetilde?2 ( Tc ) 383
20.4.3 Solution Procedure 384
20.4.4 Algorithm Procedure 385
20.5 Model Illustrated Examples 385
20.6 Sensitivity Analysis 385
20.6.1 Observations 385
20.7 Conclusion 387
References 388
21 A Fuzzy Two-Echelon Supply Chain Model for Deteriorating Items with Time Varying Holding Cost Involving Lead Time as a Decision Variable 389
21.1 Introduction 390
21.2 Assumptions and Notations 391
21.2.1 Notations 391
21.2.2 Assumptions 392
21.3 Mathematical Model 392
21.3.1 Retailer’s Model 392
21.3.2 Supplier’s Model 394
21.3.3 Fuzzy Model 397
21.4 Numerical Examples 398
21.5 Sensitivity Analysis 399
21.5.1 Observation 402
21.6 Conclusion 403
References 403
22 Transportation-Inventory Model for Electronic Markets Under Time Varying Demand, Retailer's Incentives and Product Exchange Scheme 405
22.1 Introduction 405
22.2 Literature Review 407
22.3 Mathematical Model 409
22.4 Model Formulation 410
22.5 Numerical Examples and Sensitivity Analysis 417
22.5.1 Numerical Problem 418
22.5.2 Sensitivity Analysis 419
22.6 Managerial Implications 420
22.7 Conclusion 421
References 421
23 Electronic Components’ Supply Chain Management of Electronic Industrial Development for Warehouse and Its Impact on the Environment Using Particle Swarm Optimization Algorithm 424
23.1 Introduction 425
23.2 Literature Review and Survey of Electronic Components’ Supply Chain Management 427
23.3 Related Works 429
23.3.1 Electronic Parts’ Supply Chain 429
23.3.2 Electronic Components Inventory Policy 430
23.3.3 Particle Swarm Optimization Algorithm 430
23.4 Model Design 431
23.4.1 Electronic Parts’ Supply Chain 431
23.4.2 Electronic Parts Model 432
23.4.3 Electronic Components Inventory Policy 433
23.5 Industrial Development and Its Impact on Environment 434
23.6 Simulation 435
23.6.1 Simulation Result 437
23.7 Conclusion 438
References 439
24 Interpretive Structural Modeling to Understand Factors Influencing Buying Behavior of Air Freshener 441
24.1 Introduction 442
24.2 Research Methodology 443
24.3 Case Study 445
24.4 Managerial Implications 451
24.5 Conclusion and Future Research Scope 453
References 453
25 Decision-Making with Temporal Association Rule Mining and Clustering in Supply Chains 455
25.1 Introduction 455
25.2 Background 457
25.3 Mathematical Model 459
25.4 Numerical Example 460
25.5 Conclusion and Future Scope 462
References 465