Approximate Dynamic Programming in Multi-location Inventory with Random Yield
- 주제(키워드) Approximate Dynamic Programming , Infinite Horizon Markov Decision Process , Random Yield , Value Function Iteration
- 발행기관 고려대학교 대학원
- 지도교수 정태수
- 발행년도 2021
- 학위수여년월 2021. 8
- 학위구분 박사
- 학과 대학원 산업공학과
- 원문페이지 106 p
- UCI I804:11009-000000251921
- DOI 10.23186/korea.000000251921.11009.0001243
- 본문언어 영어
초록/요약
In this paper, we propose Approximate Dynamic Programming (ADP) for the inventory control problem with random yield through intermediate locations. An infinite horizon Markov Decision Process (MDP) is used to model an inventory control problem where freight, subject to random shrinkage in transit, is transported from an origin to a destination through intermediate stages. In this dissertation we present the analytical methodology to translate the complicated value function with vector state variables as argument into the relevant function with a scalar value (sufficient statistic). Our approach shows for a related deterministic model that the pipeline inventory position is a sufficient statistic for determining the optimal order quantity. The value function iteration method is used to approximate the value function. We present and evaluate several related heuristics and our heuristic based on ADP.
more목차
Chapter 1: Introduction 1
1.1. Total Expected Discounted Cost Model 5
1.1.1. Markov Control Model 6
1.1.2. Infinite-horizon Model 7
1.1.3. Finite-horizon Model 9
1.2. Literature Review 13
1.3. Organization of the Thesis 19
Chapter 2: The Proposed Inventory Control Model 18
2.1. Problem Statement and Preliminaries 19
2.2. Deterministic Dynamic Programming Model 26
2.3. Deterministic Yield Model 27
2.4. Structural Analysis of Model 30
2.4.1. Sufficient Statistic T 30
2.4.2. Implication of v=v ̃+∆ 36
2.4.3. Properties of an Optimal Policy 46
Chapter 3: Approximate Dynamic Programming Approach 48
3.1. Approach I: Naïve Heuristic based on Inflation Rule (P_HIR ) 48
3.2. Approach II: Newsvendor Heuristic (P_HNV ) 50
3.3. Approach III: Approximate Dynamic Programming (P_ADP ) 53
3.3.1. Determination of value function approximation 58
3.3.2. Solution approach for deterministic optimization 58
3.3.3. Derivative for slope update 59
3.4. SPAR Projection for the Value Function 65
Chapter 4: Numerical Experiments 72
4.1. Performance Analysis 72
Chapter 5: Conclusion and Discussion 76
[References] 79
[Appendix A] 83
[Appendix B] 92
[Appendix C] 94
