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A Simulation Tool for Dynamic Pricing

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A Simulation Tool for Dynamic Pricing

Summary/abstract
In a world where there is a constant need for sellers to make more money and similarly, for buyers to save money, there is often a disagreement about the appropriate price for a product. This is particularly notable in a market with a finite time horizon where sellers want all goods sold prior to the end of the horizon, making as much revenue as possible. But how can sellers be sure they are selling their products at the optimum price? The optimum price for a product is often determined by external factors, such as the amount of inventory sold on previous periods. The use of Dynamic Pricing will take such factors into account and use them to calculate a new price. However, the strategies used for Dynamic Pricing differ and are suitable to different markets. Should the wrong strategy be chosen, a loss in revenue could be the result.

To avoid this occurance, simulators are often built and used to assess the effect of a particular strategy on the market after an initial strategy and market analysis.

The purpose of this project is to build such a simulator for the West Yorkshire Playhouse to assess
whether a particular Dynamic Pricing strategy is suitable to the market after an initial analysis into the various strategies and the specified market. The project will assess if revenue increases compared
to historical data as a result of the Dynamic Pricing strategy chosen and if the amount of inventory remaining at the end of the horizon decreases if applicable.

Contents
1 Introduction 1
1.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Project Aim and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Minimum Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Deliverables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5 Project Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.5.1 Revisions to Project Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review 5
2.1 Markets and Auctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Finite and Infinite Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Auction Mechanisms in Markets . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 E-Markets and Dynamic Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Revenue Manangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Dynamic Pricing in Revenue Management . . . . . . . . . . . . . . . . . . . 7
2.3 Dynamic Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3.1 Full Planning Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Partial Planning Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Theoretical Studies on Dynamic Pricing . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Previous Simulation Studies on Dynamic Pricing . . . . . . . . . . . . . . . . . . . . 10
2.6 Buyer Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Dynamic Pricing Strategies 12
3.1 Dynamic Pricing Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1.1 Goal Directive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.1.2 Derivative Following . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.3 Myopically Optimal Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Fixed Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Unsuitable Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3.1 Delayed Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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3.3.2 Delayed Topicion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.3 Q Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.4 Game Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Simulation 20
4.1 Simulation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.1.1 Simulation vs Direct Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2 Simulation vs Mathematical Modelling . . . . . . . . . . . . . . . . . . . . . 21
4.1.3 The Management Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Simulation Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2.1 Simulation and Model Types . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.2 Time Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.3 Model Scope and Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 Model Conceptualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 Design 27
5.1 System Conceptualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.1 Entities, Attributes, Activities and Events . . . . . . . . . . . . . . . . . . . . 27
5.1.1.1 Ticket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.1.1.2 Buyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.1.1.3 Seller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1.2 Model Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.1.3 The Simulation Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2 Model Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.2 Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.2.3 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.2.4 Model Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.5 Dynamic Pricing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2.6 Implementation Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.2.6.1 Witness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
5.2.7 Design Revision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.3 Input Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6 Policy Use and Analysis 39
6.1 Simulated Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1.1 Fixed Pricing Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.1.2 Goal Directive Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
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6.1.3 Derivative Following Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2 Conclusion and Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
7 Project Evaluation 45
7.1 Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7.1.1 Project Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
7.1.2 The Simulation Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
7.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2.1 Project Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2.1.1 Minimum Requirements . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2.1.2 Usefulness and Accuracy of Dynamic Pricing Research . . . . . . . 48
7.2.1.3 Usefulness and Accuracy of Simulation Research . . . . . . . . . . 48
7.2.2 The Simulation Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.2.2.1 Model Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.2.2.2 Model Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.2.2.3 Usefulness and Accuracy of Data . . . . . . . . . . . . . . . . . . . 50
7.2.2.4 Conduction of Appropriate Tests . . . . . . . . . . . . . . . . . . . 50
7.2.2.5 Appropriate Presentation of Results . . . . . . . . . . . . . . . . . . 51
7.3 Evaluation Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7.4 Further Enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Bibliography 52
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