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Studies in The Mathematical Theory of Inventory and Production2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Kenneth J.Arrow 著
出版社： Stanford University Press
ISBN：
出版时间：1958
标注页数：340页
文件大小：79MB
文件页数：351页
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图书目录

PART Ⅰ．INTRODUCTION1

1 Historical Background＆(Kenneth J．Arrow)3

INTRODUCTION3

THE TRANSACTION MOTIVE4

THE PRECAUTIONARY MOTIVE7

THE SPECULATIVE MOTIVE8

RISKS IN MULTI-PERIOD ANALYSIS13

CONCLUSION14

2 The Nature and Structure of Inventory Problems＆(Kenneth J．Arrow,Samuel Karlin,and Herbert Scarf)16

DECISION PROBLEMS16

INVENTORY AND PRODUCTION PROBLEMS18

COST AND REVENUE CONSIDERATIONS19

DEMAND23

DELIVERIES24

THE GENERAL STRUCTURE OF INVENTORY MODELS24

TYPES OF ANALYSIS30

3 Summaries＆(Kenneth J．Arrow,Samuel Karlin,and Herbert Scarf)37

CHAPTERS 4,5,AND 6:37

CHAPTER 7:41

CHAPTER 8:42

CHAPTER 9:44

CHAPTER 10:45

CHAPTER 11:46

CHAPTER 12:48

CHAPTER 13:48

CHAPTER 14:49

CHAPTER 15:52

CHAPTER 16:55

CHAPTER 17:56

PART Ⅱ．OPTIMAL POLICIES IN DETERMINISTIC INVENTORY PROCESSES59

4 Production over Time with Increasing Marginal Costs＆(Kenneth J．Arrow and Samuel Karlin)61

INTRODUCTION61

A CONSISTENCY REQUIREMENT62

BEGINNING A CONSTRUCTIVE SOLUTION63

THE CASE OF t0 < T64

THE CASE OF NO STORAGE COST66

EXAMPLES66

5 Smoothed Production Plans＆(Kenneth J．Arrow and Samuel Karlin)70

INTRODUCTION70

THE EVALUATION OF J(z)71

CONVENIENT TRANSFORMATIONS71

UPPER AND LOWER BOUNDS ON THE OPTIMAL POLICY72

THE CASE IN WHICH s(t) IS CONVEX74

THE CASE IN WHICH s(t) IS CONVEX-CONCAVE78

THE CASE IN WHICH s(t) IS CONCAVE-CONVEX82

THE CASE IN WHICH s(t) IS CONCAVE-CONVEX-CONCAVE83

THE GENERAL CASE83

6 Production Planning without Storage＆(Kenneth J．Arrow and Samuel Karlin)86

7 The Optimal Expansion of the Capacity of a Firm＆(Kenneth J．Arrow,Martin J．Beckmann,and Samuel Karlin)92

INTRODUCTION92

MATHEMATICAL FORMULATION94

DERIVATION OF ALGORITHM96

THE SOLUTION WHEN INITIAL CAPACITY IS SMALLER THAN INITIAL DEMAND100

DEMAND CONSTANT OVER INTERVALS102

SUMMARY OF THE ALGORITHM103

SOME ILLUSTRATIONS104

PART Ⅲ．OPTIMAL POLICIES IN STOCHASTIC INVENTORY PROCESSES107

8 One Stage Inventory Models with Uncertainty＆(Samuel Karlin)109

MODEL I WITH LINEAR ORDERING COST FUNCTIONS111

MODEL I WITH MORE GENERAL ORDERING COST FUNCTIONS118

MODEL Ⅱ．FIXED ORDERING LEVELS124

MODEL Ⅲ．RANDOM ORDERING LEVELS126

EXAMPLES OF THE STATIC INVENTORY MODEL131

9 Optimal Inventory Policy for the Arrow-Harris-Marschak Dynamic Model＆(Samuel Karlin)135

THE DYNAMIC MODEL WITH A LINEAR ORDERING COST137

THE DYNAMIC MODEL WITH A SET-UP COST142

DYNAMIC MODELS WITH A CONVEX ORDERING COST FUNCTION149

EXAMPLES152

10 Inventory Models of the Arrow-Harris-Marschak Type with Time Lag＆(Samuel Karlin and Herbert Scarf)155

PROOF OF THEOREMS 1 AND 2159

CHARACTERIZATIONS OF THE OPTIMAL POLICY FOR MODEL II162

SOLUTION OF ONE STAGE LAG,MODEL I169

THE ANALYSIS OF ＂SIMPLE＂ POLICIES IN AN INVENTORY MODEL WITH TIME LAG172

11 Optimal Policy for Hydroelectric Operations＆(John Gessford and Samuel Karlin)179

A HYDROELECTRIC MODEL WITH LINEAR COST FUNCTIONS180

A HYDROELECTRIC MODEL WITH A CONVEX COST FUNCTION194

12 A Min-Max Solution of an Inventory Problem＆(Herbert Scarf)201

INTRODUCTION201

THE MATHEMATICAL SOLUTION OF THE PROBLEM203

SOME OBSERVATIONS ON THE SOLUTION207

THE RESULT WITH SALVAGE VALUE209

13 On the Two-Bin Inventory Policy:An Application of the Arrow-Harris-Marschak Model＆(Martin J．Beckmann and Richard F．Muth)210

INTRODUCTION210

DISTRIBUTION OF DEMAND FOR SOME MACHINE REPAIR PARTS211

SOLUTION OF THE INVENTORY EQUATION FOR EXPONENTIALLY DISTRIBUTED DEMAND215

PART Ⅳ．OPERATING CHARACTERISTICS OF INVENTORY POLICIES221

14 Steady State Solutions＆(Samuel Karlin)223

INVENTORY MODEL WITH A LAG227

STATIONARY INVENTORY MODEL WITH (s,S) POLICIES229

THE EXISTENCE OF THE LIMITING DISTRIBUTION FOR (s,S) POLICIES234

INVENTORY MODEL WITH RANDOM SUPPLY237

INVENTORY MODEL WITH GENERAL RANDOM SUPPLY AND EXPONENTIAL DEMAND239

INVENTORY MODEL WITH RANDOM SUPPLY AND DEMAND DISTRIBUTION A MEMBER OF THE GAMMA FAMILY243

UNIQUENESS AND AVERAGE CONVERGENCE260

EXTENSIONS267

15 The Application of Renewal Theory to the Study of Inventory Policies＆(Samuel Karlin)270

SOME RESULTS CONCERNING RENEWAL PROCESSES272

A SIMPLE MODEL INVOLVING COMPARISON OF TWO PROCEDURES277

PROBABILITY EVALUATION OF LOSSES FOR ORDERING RULES WHICH ARE OF (s,S) TYPE280

AN INVENTORY MODEL WITH POISSON INPUT285

DISTRIBUTIONS RELATED TO RENEWAL PROCESSES288

16 Stationary Operating Characteristics of an Inventory Model with Time Lag＆(Herbert Scarf)298

THE CASE D = 1 (POISSON DEMAND)304

THE INFINITE MODEL WITH AN ARBITRARY INTERARRIVAL DISTRIBUTION AND A NEGATIVE EXPONENTIAL DISTRIBUTION FOR THE TIME LAG307

THE FINITE MODEL WITH AN ARBITRARY INTERARRIVAL DISTRIBUTION AND A NEGATIVE EXPONENTIAL DISTRIBUTION FOR THE TIME LAG311

A DETERMINATION OF CERTAIN AVERAGES316

17 Inventory Models and Related Stochastic Processes＆(Samuel Karlin and Herbert Scarf)319

INTRODUCTION319

THE DISTRIBUTION OF THE NUMBER OF OUTSTANDING ORDERS FOR GENERAL INPUT AND SERVICE DISTRIBUTIONS320

THE MAXIMUM TIME FOR SERVICE TO BE COMPLETED325

EXTENSIONS328

TRUNCATED MODEL WITH POISSON INPUT330

POISSON INPUT VARYING WITH TIME334

Bibliography of Inventory Theory337