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'ABSTRACT Shock models descrıbes the process of operatıon of a system subject to some form of damage or perturbatıon due to an ındıvıdual shock (stress) or series of shock (stress). The shock models can be applicable to several areas including inventory theory (Li and Kong, 2006). My work takes extracts from Yeh and Zhang (2004) δ-shock model which was generalized by Rangan and Tansu (2010) and applies it to inventory theory. Exponential demand arrival and constant demand arrival are considered, assuming the same kind of demand every time, inventory order level is also assumed to be constant. The replacement policy (T*) which refers to placing inventory orders at a particular time is applied to both models. For the exponential demand model optimal cost value and other related parameters are calculated for a range of demand arrival rate (λ) values. The constant model based on its mathematical expression is independent of demand arrival rate (λ). The aim of the study is to understand the behavior of optimal replacement time (T*) in relation to long run average cost and number of expected unmet demand in a cycle. Via aid of Matlab simulation, relevant data set is generated and discussed. The result of the simulation shows the kind of relationship that occurs amongst the given parameters for both exponential model and constant model. For the exponential distribution according to Poisson process, as the demand arrival rate increases the optimal replacement time (T*) decreases. Amongst inventory order (ί) of 0.05, the demand arrival rate of 1 has the smallest difference of E[C (T*)] and (M (T*)). For the constant model as the inventory order (ί) decrease the optimal time T* increases. As E[C (T*)] decreases M (T*) increases up to a point where the relationship changes and E[C(T*)] starts to increase and M(T*) also increases. Keywords: δ-shock, Demand, Inventory Order, Optimal replacement policy, Poisson process, Exponential distribution, Constant Distribution. '

1 CHAPTER 1

1 INTRODUCTION TO SHOCK MODELS

2 POISSON PROCESS

2 EXPONENTIAL DISTRIBUTION

4 CONSTANT DISTRIBUTION

4 LONG RUN AVERAGE COST

4 REPLACEMENTS POLICY

5 INVENTORY

6 BACKGROUND

6 CHAPTER 2

7 RENEWAL PROCESS

8 Mathematical express'on of the Process

10 Renewal reward process

10 SHOCK PROCESS CLASSIFICATION BASED ON SHOCK ARRIVAL DISTRIBUTION

11 Homogenous Poisson process

11 Non Homogenous Poisson process

12 Renewal process

12 Non-stationary birth process

12 TRADITIONAL SHOCK PROCESSES

13 Extreme shock

13369 Cumulative shock

13 ?- Shock model for a deteriorating system

18 Characteristics of the ?-shock model

18 ?-shock model va runs

20 CLASSIFICATION BASED ON DAMAGE DISTRIBUTION

20 Exponential model

20 Constant Model

22 REPLACEMENTS POLICY

25 Long run average cost per unit time

25 N→Policy

26 T→ Policy

27 Optimal replacement policy T*

28 APPLİCATION AREA

28 Inventory

29 Variability, uncertainty and Complexity in inventory managements

30 CHAPTER 3

30 INTRODUCTION

31 GENERAL ASSUMPTION

32 SPECIFIC MODELS

33 Model 1

35 Model 2

37 CHAPTER 4

37 EXPONENTIAL DEMAND DISTRIBUTUION MODEL

39 Graphical representations and interpretation for Table 4.1

46 CONSTANT DEMAND DISTRIBUTION MODEL

46 Graphical representation and interpretation of Table 4.2

48 CONCLUSION

48 Exponential Model

49 CONSTANT MODEL

50 ADVANTAGES OF APPLYGING ?-SHOCK MODELS TO INVENTORY

51 REFERENCES