An Optimal Inventory Control Of Raw Materials And Network Analysis Of Production Planning (a Case Study Of Aka Paint Nigeria Limited)

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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

(ii) If it becomes necessary, a replenishing order is issued.

(iii) The replenishment order quantity seeks to bring stock up to a predetermined level



- It permits ordering of goods in economic quantities

- It eliminates delays in production for lack of material

- It prevents large build up of non- essential goods

- It reduces losses because of inadequate inspection, material damages, obsolescence, waste etc.

- It provides an accurate base for cost accounting and financial accounting

- It provides a basis for effective production, planning and economical purchasing


The role of network in production planning:

The research system is an economic enterprise with input of the cost of a unit each of the product, raw materials, transport, bad road, lack of government encouragement, high cost of materials, high cost of tax and other limitations. The effect of decrease in productivity on the economy is phenomenal and the need for continuous productivity improvement in the manufacturing sector is no doubt a viable and indeed a necessary operation.

Although, there is the problem of the best and most serious way to generally improve productivity in various manufacturing firms with their varied operational, financial and corporate behaviour.

In this delay production implementation but achievement based on this delay frequently arises because of bad planning i.e the time needed to complete each activity or job is not properly estimated and assessed.

Network analysis helps in assessing the time required for completion of the activities, actions is taken to complete the production on or before the planned.



The word motivation is derived from a Latin word “ MOVERE” which means to move. While a motive is an inner forces that moves a person to believe or behave in a certain way, which enables a set of goal to be achieved.

The need for planning arises from the fact that man being economic is always trying to achieve best with whatever is available. “ The planning process within an organization is action and continuous, it has to be in order for the company to successfully meet the ever changing conditions both from within and without its own walls”,

The success management of large- scale production requires the managers to carefully set out objectives represent and evaluate then statement of different dynamics to be taken to achieve those objectives. It will help in planning events and coordinating various inter-related activities that define plan.

It is clear that network analysis is a powerful tool in the management of projects, particularly those consisting of large numbers of activities related in complex ways. This work is aimed at applying network analysis in representing and evaluate the plans of Aka paint Nigeria limited in the production of different sizes of paints.

Given that activities and the duration of each activity with the logical sequence that is, the inter-dependencies and precedence relationships among all the activities established, the objectives of this work therefore should be able to show the flowing

- Minimum duration of the production

- The critical and non-critical activities

- Probability of completing the project within a specified period.




(1) Least cost scheduling:- The process, which funds the least cost method of reducing the overall, project duration.

(2) Cost Scope:- average cost of shortening an activity by one time unit (day, week, mouth as appropriate)

(3) Normal Cost:- Cost associated with the minimum possible time for an activity. Resources used in most efficient manner

(4) Crash cost:- Cost associated with then minimum possible time for an activity. Crash cost because of extra wages, overtime premium, extra finality costs.

(5) Crash time:- the minimum possible time that an activity is planned to take.


There are a number of different decision problems in inventory management

(1) When should an order be placed?

(2) How much should be ordered?

(3) Which items should be carried in stock?

(4) What type of inventory control system should be used?

Number I and 2 are the classical question. Question 2 is concerned with the order quantity given that an order is placed. Question I is concerned with the timing of the order when should it be placed?

An inventory control is needed to make sure that the night amount is ordered at the right time. This system should keep accurate records, trigger order when needed, and track the flow of materials in and out of inventory.


- Lead or procurement time:- This is the period of time (in days, weeks, months etc) between ordering (internally or externally and replenishment i.e. when the goods are available for use.

- Demand:- This amount required by sales production etc this is expressed as rate of demand per week, month etc.

- Maximum stock:- This is the stock level selected as the maximum desirable which is used as an indicator to show when stock have risen too high.

- Physical stock:- This is the number of items physically in stock at a given time.

- Free stock:– This is the physical stock plus outstanding replenishment orders

- Butter stock (minimum stock or safety stock): This is the stock allowance to cover errors in forecasting the lead time or the demand during the lead time.

- Economic Order Quantity (EOQ): This is the calculated ordering quantity which minimizes the balance of cost between inventory holding cost and reorder costs.

- Economic Batch Quantity (EBQ): This is adapted EOQ which gives the size of the internal production run that minimized total inventory costs

- Inventory cycle:- This is the part of an inventory graph that regularly repeats itself

- Stock out being out of stock when a unit is required

- Re- Order quantity:- This is the amount of stock that is ordered when the reorder level a reached. It is normally the EOQ or EBQ.


There area number of decision problems in network analysis

(1) What are the major events and activities?

(2) Is there any relationship and inter dependence between the activities?

(3) What jobs or task must be completed before another one starts (i.e. precedence relationship)?

(4) What is the earliest possible and latest allowable time for the activities?

(5) What is the critical path like?

(6) What is the expected duration?

(7) Is there any probability of compulsory the project in less than or more than the set time?

Number I and 2 are classical network questions. Question 3 is all about immediate predecessors of the activities solutions to question 4 to y provides a decision rule, which specifies the time expected for the activities and the duration for the entire project. To make sure that the expected duration is met, a network analysis (using pert and CPM) is used.


(i) ACTIVITY:- This is a task that must be accomplished it is devoted by an error thus every activity must have a starting and finishing point.





Fig 1



EVENT: This takes place when start or furnish the work or an activity it is represented by a circle or node in a project network







Fig 2



(3) DANGLING: This occurs when an activity suddenly branches from an event (node) and then terminates in another event (node) but does not lead to any other event (node)

(4) MERGE EVENTS: This occurs when more than one activities enters into an event and one or more leave the event. 




 (5) Burst event (nodes) when some events have one or more entering activities generating a number of emerging activities such as event (nodes) are said to be burst events (nodes)

(6) DUMMY ACTIVITY: This is an activity introduced when two or more parallel independent activities have the same head and tail events it leads from the tail event to another event and then to the original head event. This activities does not consume time or resources. A dummy activity which is usually drawn with dotted line is assigned a zero completion time.


This work concentrates on optimal inventory control of raw materials used in paint production and the network analysis in the production planning. However, the study is limited to Aka point Nigeria limited. This system is automated and used to carry out sensitively analysis to be able to give solution to problems in section (1.4) and (1.6)



A number of limitation are expected from studies of this nature. However, some constraints, which includes resources, time and other academic demand inhabited the study. One of the major problem is time factor, the researcher is expected to complete the work within a given space of time so every thing has to be done to complete and submit the work within the given period. Also, there is the problem obtaining accurate data especially as regards the researcher as an information seeker who may eventually expose some top secret information therefore complete and accurate data is not given.

Finally, there is then problem of finance, this is always a major set back to project in this country. The student finances the project and so is often constrained by money.

Despite all these limitations, one tries to make the research work worth while.    



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