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  • Type:Project
  • Chapters:5
  • Pages:62
  • Format:Microsoft Word
(Mathematics Project Topics & Materials)




This study is aimed at determining the optimal quantity of raw materials to be ordered for and when best to make the order. It also aimed in determing the completion time in the producer of paint. A case study of Aka paint industry limited was taken. ­To complete these, data was collected from the company and the project network was drawn. Mathematical models such as economic lot size model were used in determing the optimal quality of the raw materials to be kept on inventory. Programme evaluation and review technique (PERT) and critical path method (CPM) were used in estimating the completion time and expected duration respectively. The optimum quantifies for the various raw materials were calculated with their inventory length. Also, the minimum and the expected duration of the production were obtained.  An optimum quantity of 12, 409 buckets 9,475 bags and 70, 372kg were obtained from water, dolomite and chemicals respectively and their inventory lengths were found to be I year for each item. Also, a total completion time for 59 days and expected duration of 84 days of the production were obtained. 


Title page        -      -      -      -      -      -      -     -      i

Certification     -      -      -      -      -      -      -     -      ii

Dedication       -      -      -      -      -      -      -     -      iii

Acknowledgements -      -      -      -      -      -      -     iv

Abstract   -      -      -      -      -      -      -      -     -      vi

Table of contents     -      -      -      -      -      -     -      vii


1.0 Introduction      -      -      -      -      -      -     -      1

1.1 Brief history of Aka paint (nig) limited       -     -      3

1.2 Inventory problem     -      -      -      -      -     -      5

1.3 The need for an inventory-      -      -      -      -     5

1.4 Inventory cost   -      -      -      -      -      -     -      6

1.5 Inventory control system   -      -      -      -     -      7

1.6 Problem of study       -      -      -      -      -     -      9

1.7 Motivation aims and objective of network

 analysis in production planning       -      `-    -     -      11

1.8 Cost and network basic definitions     -      -     -      13

1.9 Decision problem in inventory control       -     -      13

1.10 Definition of terms   -      -      -      -      -     -      14

1.11 Decision problem in network analysis      -     -      16

1.12 Network terminology       -      -      -      -     -      17

1.13 Scope of study-      -      -      -      -      -      -     19

1.14 Limitations of the study  -      -      -      -      -     20


2.0 Literature reviews     -      -      -      -      -     -      21


3.0 Study methodology and data collection     -     -      32

3.1 Study methodology    -      -      -      -      -     -      32

3.2 Data collection and persecution-      -      -      -     38

3.3  Data collection 1       -      -      -      -      -     -      39


4.0 Data analysis and interpretation        -      -     -      48

4.1 Data analysis     -      -      -      -      -      -     -      48

4.2 Calculate of minimum and expected duration

 of network analysis        -      -      -      -      -     -      48

4.3 Calculation of optimal quantity of raw materials       56

4.4 Interpretation           -      -      -      -      -     -      59


5.0 Conclusion and recommendation       -      -     -      61

5.1 Conclusion         -      -      -      -      -      -     -      61

5.2 Recommendation       -      -      -      -      -     -      63

        Bibliography     -      -      -      -      -      -     -      65



The development of any firm more especially in production depends to a very great extent on the development and utilization of raw materials. Because of increased techniques and advanced in technology organizations ensure steady production and supply of their goods by storing certain quantities of raw materials as buffer against unprecedented short fall in their supplies.

Certain stocks of finished goods are maintained in order to meet up with unforeseen demand or short - notice orders. Inventory is referred to as the stock of raw materials finished goods and work- in progress. The best planned and managed enterprises survive and efficiency of a company’s operation is directly related to the inventory situation existing within it.

Inventory control enables organization to determine when it is necessary to stock physical goods or commodities for the purpose of specified periods of time. Amount of inventory results to high capital costs, high operating cost and decreased production efficiency when too much space is used while insufficient inventory leads to inability of the firm to meet up with the demand for its product and in severe case leads to shut downs if there occurs a drop or half in supply of raw materials.

According to Oxford Advanced learner’s dictionary, network is a system of broadcasting stations that link up to broadcast the same programs of the same time. Network analysis is a family of related techniques developed to aid management in planning and control of projects scheduling and coordinating various inter - related activities that define a project. In a production of specified duration, network analysis is inter - relationship of the various jobs, or tasks, which make up the overall and obvious identify the critical paths of the production.


This Industry was developed through the inspiration of Nze B.C Onuoha. He engaged in car selling and paint making business. Due to his real to reduce human suffering, manufacturing in the year 1994 as a limited liability company. It is located at Enyiogugu in Aboh Mbaise. It has three depots located at 139 Wetheral Road Owerri, opposite Timber market Oguta Road Mgbidi and 45 Aba Owerri Road Aba, Abia State respectively. In 1994, the European commission came and help to introduced the company.

The official opening of the company took place in 1995. the objects clause as stated in the memorandum of association of the company is to produce, sale, import, distribute paints other chemical related items. The company has four major department namely production/ quality control department personnel department, account department and sales/ marketing department.


v Essentially for local Nigeria market – replacement and original equipment

vExports of car paints.


- Emulsion paints

- Texcote paints

- Gloss paints

- Car paints

To produce these products several raw materials are needed and in different proportions. Some of the raw materials in puts includes methyl ethyl ketone (MEK) toluene resin, petrol, kerosene, ethylene glycol, etc, these products yield different levels of profit to the company and how to make profits as large possible is mystifying to management.

Furthermore, the scarcity of some of these raw materials limits the flexibility of management in production. Other restricting factor as interview disclosed are labour time and demand for the products.


An inventory problem is one which seeks to determine when it is necessary to stock physical goods or commodities for the purpose of satisfying demand over a specified period of time

This type of problem aims at knowing how much of the commodity order for and when to make the order. An over stock requires higher invested capital per unit time but less frequent occurrence of shortages and placement of orders. Whereas an under stock decreases the invested capital per unit time but increase the frequency ordering as well as the risk of running out of stock.


The inventory of a company can be described as the totality of stocks of various kinds which include raw materials, partly finished goods and materials, subassemblies, office and workshop supplies and finished goods.

The fundamental reason for inventory is that it is physically impossible and economically impracticable for each stock item to arrive exactly when it is needed other reasons are

vAnticipating normal demand

vTaking advantage of bulk- purchase discounts.

vMeeting emergency shortages due to some unforeseen circumstance like strikes breakdown of the firm’s plant or vehicle

vAbsorbing wastage and unpredictable fluctuation etc.


(a) Purchase or manufacturing cost :- This is per unit cost of buying or making a unit of production. This includes transportation, clerical and administrative costs associated with the physical movement of bought goods. The unit price of the commodity decreases as the ordered quantity increases.

(b) Holding or carring cost :- This is the cost of carrying item in storage of inventory until it is sold or used. This include

(i) Interest on capital invested in the stock

(ii) Storage costs or changes (rent lighting heating air conditioning etc)

(iii) Insurance security

(iv) Stores staffing equipment maintaince and running costs. Holding cost increase with the level of inventory.

(c) Shortage or penalty or stock out cost :- These are the cost associated with running out of stock. These include

(i) Cost contribution through the best sale called by the stock out

(ii) Loss of future sales because consumers goes elsewhere

(iii) Loss of consumers good will

(d) Setup cost :- This is the cost of placing an order for a commodity from an outside vendor, which is independent of the number of units ordered for


The general objective of inventory control is to keep stock level so that the combined costs are at a minimum. This could be achieved with factors via

- When to order

- How many to order

The two major systems of establishing these are

(a) Re-order level system

(b) Periodic review system

(a) The Re-order level system is also known as two- bin system its features are

(i) A predetermined re-order level is set fro each item

(ii) The replenishment order quantity is invariably the EOQ (i.e the Economic Order Quantity)

(iii) When the stock level falls to the re- order level, replenishment is issued

(iv) The minimum level is calculated so the management would be warned when demand is above average and accordingly the butter stock is utilized  

(b) Periodic review system this is sometimes called the costant circle system. Its features are

(i) Stock levels for all parts are revived at fixed intervals e.g every week

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Type Project
Department Mathematics
Project ID MTH0033
Price ₦3,000 ($9)
Chapters 5 Chapters
No of Pages 62 Pages
Format Microsoft Word

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    Type Project
    Department Mathematics
    Project ID MTH0033
    Price ₦3,000 ($9)
    Chapters 5 Chapters
    No of Pages 62 Pages
    Format Microsoft Word

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