Complete Chapter One
DETERMINISTIC INVENTORY MODEL AND ITS APPLICATION TO MOUKA FOAM INDUSTRY
DEPARTMENT OF MATHEMATICS
TABLE OF CONTENTS
Title page i
Table of Contents vii
1.0 Introduction: An Overview of Inventory Theory 1
Deterministic Inventory Models 3
Purpose of the Study 4
Scope of the Study 5
Organization of the Study 6
Some Basic Definitions 6
2.0 Introduction 9
2.1 Possible Application Areas of Inventory Theory 9
2.2 Importance of Inventory Theory to
Manufacturing Organization 11
2.3 Types of Inventory 13
2.4 Inventory Control and Management 15
2.5 Inventory Cost Concept 16
3.1 Deterministic Inventory Models 18
3.1.1 Shortages Not Permitted Model 19
3.1.2 Shortages Permitted Model 23
3.1.3 The EOQ Model with Non-Instantaneous Receipt 30
4.0 Introduction 34
4.1 Sources of Data 34
4.2 Data Analysis 36
CHAPTER FIVE: SUMMARY AND CONCLUSION
5.0 Summary 43
5.1 Conclusion 45
It is often necessary to keep inventory in order to meet with fluctuations in demand and also to avoid shortages that might lead to los of goodwill. Thus, most companies, to absorb certain fluctuations in demand strictly adhere to safety stock control. This approach could be the deterministic inventory which assumes that demand is known with certainty. The deterministic inventory model which reviews when to place an order or produce more goods was applied to a foam industry in this work. Empirical evidence therefore reveals that keeping inventory is an integral part of production and hence, production cannot be said to be completed until goods produced are bought by the final consumer.
1.0 INTRODUCTION: AN OVERVIEW OF INVENTORY THEORY
In most manufacturing process, production systems, the financial services industry, the economy, agriculture, it is a known fact that they maintain stock of goods and services for future sale or use. The practice of stocking goods for future use or sale is known as inventory.
It is a well known feature particularly with retailers, wholesalers and manufacturing companies. It is possible that the hotel manager will always make sure that a sizeable quantity of meat and fish is available in the freezer for use any time guests arrive.
Inventory theory is therefore concerned with mathematical and analytic techniques that help in making policy as to when to replenish the stock of goods available and in what quantity. In small firms, it is possible for the manager to keep track of inventory and make decisions. However, since this may not be feasible even in small firms, many companies have saved huge sums of money by using scientific inventory management. These scientific inventory management in particular are:
Formulate a mathematical model describing the behavior of the inventory system.
Derive an optimal inventory policy with respect to the model formulated.
Frequently use a computer system to maintain a record of the inventory level and to signal when and how much to replenish.
The maintenance of an optimal inventory policy occupies a significant slot in management policy decisions in many real life business situations this day. This is so because of the significant impact in the company, which a loss of goodwill engendered by a faulty inventory policy could have in terms of drop in patronage, revenue and customers loyalty.
The study of inventory enables us to formulate an optimal inventory policy which specifies:
The order or manufacturing quantity.
The time interval between one order and the next one.
The total minimum inventory cost.
The model formulation and the optimal inventory policy is done in such a way that (1) and (2) above gives us a minimum inventory cost which results in increased net income.
1.1 DETERMINISTIC INVENTORY MODELS
There are different models that exist in inventory problems. The type of model and its mathematical formulation is determined by the nature of demand and the lead time which is the time between when an order is placed and when it arrives.
These types of inventory models are concerned with inventory problems whereby the actual demand in the future is assumed to be known; we shall assume that the lead time for this models is instantaneous i.e. when an order is placed it arrives immediately. Demand, however, is usually of two types:
Random demand which is more common in practical situations. Demand in this case is uncertain but its behavior can still be likened to a certain pattern, also called as probability distributions such as normal, binomial etc. These models that operate with the assumption of random demand are known as stochastic inventory models.
Constant or known Demand.
1.2 PURPOSE OF THE STUDY
One major problem of most business organization is the determination of sufficient level of stocks of raw materials and other goods. To resolve this problem, management should adopt the techniques provided by inventory theory. The purpose of this study is to determine:
What will be the best quantity of an item to order each time an order is placed?
When should an order be placed?
What quantity of the item, if any, over the expected requirement should be held as safety stock in anticipation of variations in demand?
What quantity of item should be allowed to be backlogged or how much shortage should be allowed?
Should management take advantage of discount offer?
1.3 SCOPE OF THE STUDY
Inventory theory is a very wide area in operations research that has found useful and notable applications in various fields especially with research into stochastic inventory models.
This work however, is concerned with deterministic inventory models and how this model can be used in solving the problem of optimal stock keeping policy.
1.4 ORGANIZATION OF THE STUDY
This project work will be structured in five chapters. Chapter one is the introductory chapter, while chapter two will contain reviews of literature and some basic concepts of inventory theory. Chapter three will x-ray the methodological aspects and the theoretical aspects of inventory theory, chapter four is concerned with empirical investigation. Chapter five is the conclusion.
1.5 SOME BASIC DEFINITION
There are certain terms that will be used in the course of this project work. Below are the following definitions within the context of this work:
Safety Stock: This is stock which is kept by the company, it acts as a buffer against reasonably expected minimum usage i.e. sudden increase in the demand which may cause the company to run out of stock.
Stock: This refers to the total of all raw materials used in production, work-in-progress i.e. unfinished and also finished goods that are fully completed and ready for sale.
Lead Time or Procurement Time: This refers to the time between placing an order and the arrival of that order i.e. the time it takes for an order placed to be received.
Reorder Level: This is the level at which it becomes necessary to place an order for the new supply.
Holding/Carrying Cost: This is the cost which is incurred while stock is being held by the company. It consists of the cost of storage space, insurance, deterioration and the cost of adequate and accurate record keeping.
Ordering Cost: This is the cost involved in placing an order. It consists of clerical cost of preparing the purchase order and offer special processing and receiving cost that are related to the number of orders processed.
It has been established so far that organizations that purchase goods and services maintain stocks of this goods and services for future sale or use. Inventory theory was introduced in this chapter to simply provide us with operational techniques and tools for reaching an optimal stock keeping policy that aligns with overall objective of the organization.
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