Probabilistic inventory models

Presentation on theme: "Probabilistic inventory models"— Presentation transcript:

1 Probabilistic inventory models

2 Figure 16.1 Buffer stock, B, imposed on the classical EOQ model

3 Figure 16.2 Probability of running out of stock, P{z ≥ Kα} = α

4 Example 13-3-1 Demand: mean=100, SD=10 h=0.02, K=100, L=2,

5 Assumptions: Backlogged One outstanding order Stationary demand Ordering policy: At the reorder point R, order y. Decision variables: R, y

6 Figure 16.3 Probabilistic inventory model with shortage

7

8

9 Single-period models K: set up cost h: holding cost per unit
P: penalty cost per shortage unit f(D): pdf of demand y:oreder quantity

10

11 Figure 16.4 Holding and shortage inventory in a single-period model

12 example Demand: 300, SD=20 Pays 30 cents and sells 75 cents.
5 cents for left newspapers Holding and penalty costs: 25, 45

13 Figure 16.5 (s-S) optimal ordering policy in a single-period model with setup cost

14 Demand: uniform(0,10) Holding cost per unit: 0.5 Penalty cost:4.5 Setup cost: 25

15 Figure 16.6 s-S policy applied to Example 16.2-2

16 Multi period inventory models
-Backlog of demand is allowed -Zero-delivery lag: 0 lead time -discounted value of money: present value n periods and unfilled demand can be backlogged exactly one period

17 Infinite case

18 Prospect Theory: Daniel Kahneman
기준점: Adaptation level 물통 세개(찬, 더운, 보통온도) 민감도체감성: diminishing sensitivity , US $ 손실회피: 손해가 이득보다 크게 느껴짐 생각에 관한 생각(Thinking fast and slow)

19 Survivorship bias: 2차대전 중 비행기의 분석: 귀환한 비행기의 통계를 보니 날개, 동체, 엔진순으로 자국이 있음
성공한 사람의 특징 근로소득의 변화