Unit 14

5

Control Function in

Production ManagementUNIT 14 CONTROL FUNCTION IN PRODUCTION MANAGEMENT

Structure 14.1 Introduction

Objectives

14.2 Control Function in Production Management

14.3 Inventory Control 14.3.1 Inventory 14.3.2 Inventory Control in Services

14.4 Economic Order Quantity Model

14.5 Safety Stock 14.5.1 The Probability Approach 14.5.2 Fixed-order Quantity Model with Safety Stock

14.6 ABC Inventory Control

14.7 Process Control and Acceptance Sampling 14.7.1 Process Control with Attribute Measurement 14.7.2 Process Control with Variable Measurement

14.7.3 Method for Constructing X and R Charts 14.7.4 Acceptance Sampling

14.8 Summary

14.9 Key Words

14.1 INTRODUCTION

Production management is defined as the management of an organization’s production system, which converts inputs into the organization’s products and services. A production system takes inputs such as raw materials, personnel, machines, buildings, technology, cash, information, and other resources and converts them into outputs, such as products and services. This process is the predominant step in the production management. In companies that manufacture goods, the production activities that create goods are usually quite oblivious. For instance, we can watch the creation of a tangible product such as Sony television set or a Tata truck. When referring to such activity, we tend to use the term production management. This unit will deal with the control functions related to production management, Inventory planning, Economic order quantity and Safety stock. The objectives of this unit are detailed as follows.

Objectives After studying this unit, you should be able to understand

• control functions of production management and various decisions taken by designers,

• inventory control policy followed by the firms,

• significance of economic order quantity,

• establishment of safety stock level, and

• ABC classification of materials.

6

Control & Measurement of Production Management 14.2 CONTROL FUNCTION IN PRODUCTION

MANAGEMENT

Production is the creation of goods and services. The role placed by production management is the heart of any industry. The Production that takes place when your cheque s processed at your bank, or when a patient is taken care of in a hospital is called operations. The product that is produced may take some unusual forms, such as placing machine readable marks on paper, filling an empty seat on an airplane, or prescribing medicine. Such a task accompanied by firms is known as service organization. The basic functions of the management performed by the good managers are as follows.

Planning

Managers determine objectives and goals for organization and develop programs, policies, and procedures that will help organizations in attaining them. Managers also determine subordinate plans for every department, group and individual.

Organizing

Managers develop a structure of individuals, groups, departments, and divisions to achieve objectives.

Staffing

Managers determine personnel requirements, including the best way to recruit, train, retain, and terminate employees for achieving objectives.

Leading

Managers lead, supervise, and motivate personnel to achieve objectives.

Controlling

Managers develop the standards and communication networks necessary to ensure that the enterprise is pursuing appropriate plans and achieving objectives.

There are six major factors which have significant impact on production management. These are as follows :

(a) Reality of global competition.

(b) Improvement in quality, customer service, and cost challenges.

(c) Rapid expansion of advanced production technology.

(d) Continued growth in the service sector.

(e) Scarcity of production resources.

(f) Increase in demand of innovative products.

Above mentioned factors affect the operations managers in the sense of not providing protection to country’s border from foreign imports. Day-by-day competition is increasing and to withstand in such a competitive environment, companies must take a commitment to customer responsiveness and continuous improvement towards the goal of quickly developing innovative products.

A production system model is illustrated in Figure 14.1. Inputs are classified into three categories viz. external, market and primary resources. External inputs generally are informational in character and are inclined more towards providing knowledge about conditions outside the production system to operations managers. In spirit similar to external, market inputs are inclined towards informational character. Information regarding product design, competition and other aspects of the market is necessary. In contrast to this, primary resources are referred as those inputs that directly support the production and delivery of goods and services. The output directly obtained from production system may be either in tangible or

7

Control Function in

Production Managementintangible form. Outputs such as automobiles, hair dryers, calculators, clothes, cakes, soap are daily manufactured in enormous amount and are known as tangible goods while the intangible outputs are those which pour from production system like education, health service, public service and transportation facility.

Feedback Information

Inputs Conversión Subsystem

Output

External

Legal/Political Social Economic

Market Competition Product Information Customer Desires

Primary Resources Materials and Supplies Personnel Capital and Capital Goods Utilities

Physical (Manufacturing, Mining)

Locational Services (Transportaron) Exchange Services (Retailing/Wholeseling) Storage Services (Warehousing) Other Services (Insurance, Finance, Utilities, Real Estate, Health, Bussiness Service, and Personal Service) Government Services (Local, State, Federal)

Direct outputs Products

Services

Indirect Outputs Taxes

Wages and Salaries Technological developments Enviornmental Impact

Employee Impact Societal Impact

Control Subsystem

Figure 14.1 : A Production System Model

The task of production management and its working is controlled and governed by various factors and schemes. Usually, operation managers are in very hasty situation as their decision plays a vital role in deciding the progress of a firm. Their decision falls into three categories namely strategic decision, operating decision and control decision.

Strategic Decision

These decisions are related to products, processes and facilities. They carry a strategic importance and have a long-term significance for the organization. These decisions are so important that people from every sector get together and study the business opportunities carefully and finally arrive at a decision that put the organization in the best position for achieving its long-term goals. Examples of such a planning decision are :

• Deciding on the launch of a new-product development project.

• Deciding on the design of a production process for a new product.

• Deciding the need of new factories and where to locate them.

• Deciding how to allocate scarce raw materials, utilities, production capacity, and personnel among new and existing business opportunities.

Operating Decisions

The decision related to planning production to achieve the desired demand. The main function of operations is to take the orders generated by marketing function for products and services from customers and deliver products and services in such a way that there are satisfied customers at reasonable costs. Examples of such a planning are as follows (Figure 14.2) :

8

Control & Measurement of Production Management

• Deciding what products and quantity of each item to be included in next month’s production schedule.

• Deciding the quantity of finished goods inventory to carry for each product.

• Deciding whether increase production capacity next month on the basis of working overtime or giving subcontract of production to suppliers.

• Deciding the details of a plan for purchasing raw materials to support next month’s production schedule.

Error!

Enviornmental Analysis Identify the threats, opportunities, weaknesses and strengths. Understand the environment,

customers, industry and competitors.

Determine corporate mission

State the reasons for the firm’s existence and identify the value it creates

Form a strategy price, design or volume flexibility, quality, quick

deliverBuild a competitive advantage, such as low

roduct lines. y, dependability, after-the-sale services, broad p

Implement Main Strategy and Form Functional Area Strategies

Service Distribution Promotion Price Channels of distribution Product positioning

Leverage Cost of capital Working capital Receivables Payables Financial control

Decisions Simple Options Quality Define customer expectations with performance measures Product Customized or standarized Process Facility size, technology Location Near supplier or near customer Layout Work cells or assembly line Human resource Specialized or enriched jobs Procurement Single or multiple source suppliers Inventory When to reorder; how much to keep on hand Scheduling Stable or fluctuating production rate Reliability and Repair as required or preventive Maintenance maintenance

Figure 14.2 : Developing Overall Strategy

Control Decision These decisions are pertaining to the variety of problems arising in operations, mainly it handle planning and controlling operations. Decisions concerning with day to day activities of worker’s, quality of products and services, production and overhead costs and maintenance of machines come in the category of control decisions. Operation managers get engaged in planning, analyzing, and controlling activities so that poor work performance and inferior product quality do not interfere with the profitable operation of the production system. Examples of this type of decision are as follows :

• Deciding the frequency of performing preventive maintenance on a key piece of product machinery.

9

Control Function in

Production Management• Deciding the steps to be taken for the department’s failure to meet the

planned labour cost target.

• Developing labour cost standards for a revised product design that is about to go into production.

• Deciding what the new quality control acceptance criteria should be for a product that has a change in design.

The day-to-day decisions about workers, product quality, and production machinery, when taken together, may be the most pervasive aspect of an operation manager’s job.

SAQ 1 (a) What are the basic functions performed by the managers in a firm?

(b) Elaborate the need of strategic and controlling decision taken by managers.

14.3 INVENTORY CONTROL

You know that inventory is one of the most expensive assets of most of the companies, representing as much as 40% of total invested capital. Operation managers at these firms and around the globe have long recognized that having good control over inventory is crucial. On one hand, a firm tries to reduce costs by reducing on hand inventory levels. On the other hand, customers become dissatisfied when an item is frequently out of stock. Thus, companies must strike a balance between inventory investment and customer service levels. As you would expect, cost minimization is a major factor in obtaining this delicate balance.

14.3.1 Inventory The word inventory resembles the stock of any item or resources used in an organization. An inventory system is the set of policies and controls that monitors levels of inventory and determines what level should be maintained, when stock should be replenished and how large orders should be. The prime motive of inventory analysis in manufacturing and stock keeping services is to satisfy the following needs :

(a) When items should be ordered, and

(b) How large the order should be.

Most of the firms are engaged in longer-term relationships with vendors to supply their needs for the entire year. The inventory purposes are discussed in next subsection.

Purposes of Inventory

Inventories kept by all firms are due to following reasons :

(a) interdependence between operations.

(b) variation in product demand.

(c) flexibility in production scheduling.

(d) variation in raw material delivery time.

Due to above reasons, all firms have more inclination towards inventory. There are various costs associated with inventory and are given as follows :

10


Holding Cost

It includes the cost for storage facilities, handling, insurance, pilferage, breakage, obsolescence, depreciation, taxes and the opportunity cost of capital. This implies that high holding costs tend to favour low inventory levels and frequent replenishment.

Setup (or Production Change Cost)

Manufacturing of a product require the necessary materials, arranging specific equipment setups, filling out the required papers, appropriately changing time and materials and moving out previous stock of materials. This all contributes to the setup cost.

Ordering Cost

These costs refer to the managerial and administrative costs to prepare the purchase or production order, transportation cost, receiving and inspection cost.

Shortage Costs

When the stock of an item gets exhausted, an order for that item must either wait until the stock is replenished or be canceled. These cost accounts for the shortage cost. This is of two types (i) Lost scale, and (b) Back orders.

Besides costs, the timing of these orders is a critical factor that has impact over inventory cost. There are two ways of classifying inventory systems viz. fixed-order quantity models (known as Economic order quantity and Q-model) and fixed-time period models (also known as periodic system and P-model). The main distinction between these two models is that Q-models are “event triggered” whereas P-model are “time-triggered”. The key differences between them are tabulated in Table 14.1. A brief discussion on Q-model is detailed now in coming paragraphs.

Table 14.1 : Differences between Q-model and P-model

Feature Q-model or Fixed Order Quantity Model

P-model or Fixed-time Period Model

Order quantity Q-constant (same amount ordered each time)

Q-variable (varies each time order is placed)

When to place order R-when inventory position drops to the reorder level

T-when the review period arrives

Size of inventory Less than fixed-time period model

Larger than fixed-order quantity model

Record keeping Each time a withdrawal or addition is made

Counted only at review period

Types of Item A class B and C class

14.3.2 Inventory Control in Services To demonstrate the way in which inventory control is done in service organizations, we have selected two areas to describe: a departmental store and an automobile service agency.

Department Store Inventory Policy

Stock keeping unit (SKU) is the common term used to identify an inventory item. It identifies each item, its manufacturer and its cost. The number of SKUs becomes large even for small departments. For example, if bed sheets carried in domestic items departments are obtained from three manufacturers in three quality levels, three sizes and four colours. Altogether there are 3 × 3 × 3 × 4 = 108 items. For

11

Control Function in

Production Managementsuch large numbers individual economic order quantities cannot be calculated for each item by hand. Purchasing of housewares is generally done from distributors rather than from manufacturers. Distributor handles products from various manufacturers and has the advantage of fewer orders and faster shipping time. Moreover, the distributor’s sales personnel may visit the housewares weekly and count all the items they supply to this department. Then, in line with the replenishment level that has been established by the buyer, the distributor’s salesperson places orders for the buyers. This saves the department time in counting inventory and placing orders. The lead time for receipt of stock from a housewares distributor is two or three days. The safety stock, therefore, is quite low, and the buyer establishes the replenishment level so as to supply only enough items for two to three day lead time, plus expected during the period until the distributor’s salesperson’s next visit.

Maintaining Parts Inventory of Automobile Repair Shop A firm in the automobile service business purchases most of its parts supplied from a small number of distributors. Franchised new car-dealers purchase the great bulk of their supplies from the auto manufacturer. A dealer’s demand for auto parts originates primarily from the general public and other departments of the agency, such as the service department or body shop. For this case, problem is to determine the order quantities for the several thousand items carried. Most of the dealers order their inventory by computers and software packages. For both manual and computerized systems, an ABC classification works well. Expensive and high-turnover supplies are counted and ordered frequently; low-cost items are ordered in large quantities at infrequent intervals. The drawback associated with frequent order placement is the extensive amount of time needed to physically put the items on the shelves and log them in. The computer output provides a useful reference file, identifying the item, cost, order size and the number of units on hand. The output itself constitutes the purchase order and is sent to the distributor or factory supply house. This simple procedure is attractive because once the forecast weighting is selected; all that needs to be done is to input the number of units of each item on hand. Thus, negligible computation is involved and very little preparation is needed to send the order out.

SAQ 2 (a) What are the main reasons for controlling inventory? (b) What kind of policy or procedure would you recommend to manage the

inventory operation in a department store? What advantages and disadvantages does your system have vis-a-vis for the department store inventory operation described in this section?

14.4 ECONOMIC ORDER QUANTITY MODEL

The two important decisions pertaining to controlling the inventory of a raw material are when to place an order and how much order to order. F. W. Harris developed a rule for determining the optimal number of units of an item to purchase if several fundamental assumptions are satisfied. This proposed model is referred as the Basic Economic Order Quantity (EOQ) Model.

In more concise manner, it can be concluded that there exists for every material held in inventory an optimal order quantity where total annual stocking costs are at a minimum.

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There exist certain assumptions for the basic EOQ model that are summarized as follows :


(a) The item’s price or cost (p) is independent of the quantity ordered.

(b) The demand for or usage of the item follows a relatively constant rate of D units per unit time.

(c) C0 is a fixed cost that is used for executing an order that is independent of the quantity ordered (Q).

(d) There exists a proportional relationship between holding cost for inventories and Quantity stored.

(e) Whenever a demand arises in the market, it should be fulfilled. No shortages are allowed.

(f) Lead time is known with certainty and is a constant quantity. It is referred to that time from when an order is placed until it gets delivered.

(g) All items ordered are delivered at the same time, there are not split deliveries.

The definitions of variables and list of cost formulas are given in Table 14.2.

Table 14.2 : List of Variable Definitions and Cost Formulas

Variable Definitions

D = annual demand for a material (units per year)

Q = quantity of material ordered at each order point (units per order)

C = cost of one unit of the material

S = average cost of completing an order for a material (Rs. per year)

TC = Total annual cost

H = Annual holding and storage cost per unit of average inventory (Rs. unit per year)

R = Reorder point L = Lead time

Cost Formulas

Annual holding cost = Average inventory level × carrying cost = (Q/2) H

Annual ordering cost = Orders per year × ordering cost = (D/Q) S

Total annual stocking cost = Annual carrying cost + Annual ordering cost = (Q/2) H + (D/Q) S

Total annual cost = Annual purchase cost + Annual ordering cost + Annual holding cost TC = DC + (D/Q) S + (Q/2) H

These cost relationships are shown in Figures 14.3 and 14.4. The order quantity (Qopt) at which total cost is minimum can be visualized from Figure 14.4. It tells that the total cost is minimal at the point where the slope of the curve is zero. With the help of calculus, we take the derivate of total cost with respect to zero and set this equal to zero. The calculations involved in this are shown below. To illustrate the above formula of economic order quantity model, we had taken an example. These will demonstrate the use of the formula derived.

2

D QTC DC S HQ

⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

. . . (14.1)

13

Control Function in

Production Management20

2dTC DS HdQ Q

⎛ ⎞−= + +⎜ ⎟

⎝ ⎠ . . . (14.2)

opt2DSQ

H= . . . (14.3)

Accordingly, reorder point is given by

R dL=

where d is average daily demand (constant) and L is the lead time in days.

Error!

L L L

Q QQ

Q - Model

Inventory on Hand

Time

R

Figure 14.3 : Basic Economic Order Quantity Model

Ordering Costs

Order Quantity (Q)

C o s t

Annual Cost ofItems (DC)

Total Cost

QOPT

Holding Costs

Figure 14.4 : Annual Product Costs Based on Size of the Order

Example 14.1

Find the economic order quantity and the reorder point. Given

Annual demand (D) = 2,000 units

Average daily demand (d) = 2,000/365

Ordering cost (S) = Rs. 4.2 per order

Holding cost (H) = Rs. 1.75 per unit per year

14

Lead time (L) = 5 days Control & Measurement of Production Management

Cost per unit (C) = Rs. 10.75

What quantity should be ordered?

Solution

The optimal order quantity is

opt2DSQ

H=

2(2,000) (4.2) 9600 97.95 units1.75

= = =

The reorder point is

2000 (5) 27.39 units365

R dL= = =

Rounding to the nearest unit, the inventory policy is as follows : When the inventory position drops to 28, place an order for 97 more.

The total annual cost will be

2

D QTC DC S HQ

⎛ ⎞ ⎛ ⎞= + +⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠

2000 97= 2000 (10.75) + (5) + (1.75)97 2

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

= Rs. 21687.875

SAQ 3 (a) What are the assumptions of the EOQ model?

(b) What are the main differences between fixed-order quantity model and fixed time period model?

(c) How sensitive is EOQ to variations in demand or costs?

14.5 SAFETY STOCK

The model developed earlier has assumption of constant demand and that is also known in advance. In most of the situations demand varies daily. Thus, there arises a need of maintaining a safety stock that provides some level of protection against stock outs. Safety stock can be defined as the amount of inventory carried in addition to the expected demand. For the normal distribution case, it can be measured as mean. To demonstrate the meaning of its definition, let us assume our average yearly demand is 1000 units and we expect next year to be the same. Now in case next year we carry 1100 units then we have 100 units of safety stock.

Safety stock can be determined from different criteria. The most common used approach followed by a firm is that simply state that a certain number of weeks of supply be kept in safety stock. The probability approach is also among one of the common approaches followed by industries.

15

Control Function in

Production Management14.5.1 The Probability Approach The key principle over which it is based is that this approach considers only the probability of running out of stock, not how many units we are short of. For determining the probability of stocking out over the time period, a simple plot of normal distribution for the expected demand is drawn and noted down the amount we have on hand lies on the curve. The situation will be clearer by the following example. Say we expect demand to be 100 units over the next month and standard deviation of it is known to us and it is 20. Now, if we go into the month with just 100 units, we know that our probability of stocking out is 50 per cent. Half of the months we would expect demand to be greater than 100 units; half of the months we would expect it to be less than 100 units.

Taking this further, if we ordered a month’s worth of inventory of 100 units at a time and received it at the beginning of the month, over the long run we would expect to run out of inventory in six months of the year.

14.5.2 Fixed-order Quantity Model with Safety Stock Inventory level is perpetually monitored by the fixed-order quantity system and it places a new order when stock reaches some level R. During Lead time between the time an order is placed and the time it is received, there is danger of stockout in the model. It is shown in Figure 14.5 that an order is placed when the inventory position drops to the reorder point, R. During this lead time L, a range of demands is possible.

Figure 14.5 : Fixed-order Quantity Model with Safety Stock

Time

Num

ber o

f Uni

ts o

n H

and

O

B

R

Q

L Stock Out

Safety Stock

Range of Demand

The main difference lying between a fixed-order quantity model where demand is known and one where demand is uncertain is in computing the re-order point. The amount of order quantity remains same in both cases. The uncertainty element is taken into account in the safety stock. The reorder point is given by

LR dL z= + σ

where d = Average daily demand,

z = Number of standard deviations for a specified service probability, and

σL = Standard deviation of usage during lead time.

The term Lzσ accounts for the amount of safety stock. The positive sign of safety stock indicates that its effect is to place a reorder is sooner.

Computation of d , σL and z

Demand arising during the replenishment lead time is helpful in estimating the expected use of inventory from the time an order is placed to when it is received. For example, if a 30-day period was used to calculate d, then a simple average would be

16


30

1 1

30

n

i ii i

d dd

n= == =∑ ∑

Where n is the number of days. The standard deviation of the daily demand is given by

2

1

( )n

ii

d

d d

n=

−

σ =∑

302

1

( )

30

ii

d d=

−

=∑

Since dσ refers to one day and if lead time extends over several days, we can use the statistical premise that the standard deviation of a series of independent occurrences is equal to the square root of the sum of the variances. Mathematically, it can be written as

2 2 2 21 2 3 . . .s nσ = σ + σ + σ + σ

Afterwards we need to find z, the number of standard deviations of safety stock. Let our probability of not stocking out during the lead time is to be 0.90. The z-value corresponding to 90 per cent probability of not stocking out is 1.52. The standard deviation for 5 days is then calculated as

2 2 2 2 210 10 10 10 10 22.36sσ = + + + + =

Now, the safety stock is calculated as follows

1.52 22.36 33.9872LSS z= σ = × =

Now two examples are given that will demonstrate and differentiate the variation in demand in terms of standard deviation.

Example 14.2 : Economic Order Quantity Consider an economic order quantity case where annual demand D = 500 units, economic order quantity Q = 100 units, the desired probability of not stocking out P = 0.95, the standard deviation of demand during lead time Lσ = 20 units, and Lead time L = 12 days. Determine the reorder point. Assume that demand is over a 250 = workday year.

Solution

d in above example is

500 2250

d = = and lead time is 12 days.

From the equation,

2(12) (20)LR dL z z= + σ = +

Since, in this case z is 1.64. Substituting this value of z, we get

R = 2 (12) + 1.64 (20) = 24 + 32.8 = 56.8 units

This shows that when the stock on hand gets down to 56 units, order 100 more.

Example 14.3 : Order Quantity and Reorder Point

17

Control Function in

Production ManagementDaily demand for a certain product manufactured by ABC company is normally distributed with a mean of 30 and standard deviation of 5. The source of supply is reliable and maintains a constant lead time of 6 days. The cost of placing the order is Rs. 8.5 and annual holding cost are Rs. 0.75 per unit. There are no stockout costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over the entire 365 days of the year. Find the order quantity and reorder point to satisfy a 95 per cent probability of not stocking out during the lead time.

Solution

For this problem, we will first calculate the order quantity Q as well as the reorder point R. Given data are

d = 30 S = Rs. 8.5 dσ = 5 H = Rs. 0.75 D = 30 (365) L = 6

The optimal order quantity is

opt2 2(30) (3.65) (8.5) 248200 498.1967 units

0.75DSQH

= = = =

For computing the reorder point, we need to calculate the amount of product used during the lead time and add this to the safety stock.

The standard deviation of demand during the lead time of six days is calculated from the variance of the individual days. Since each day’s demand is independent

2 2

1

6(5) 12.2474i

L

d di=

σ = σ = =∑

Since, z is 1.64,

30(6) 1.64 (12.2474) 200.0857 unitsLR dL z= + σ = + =

To summarize the policy derived in this example, an order for 498 units is placed whenever the number of units remaining in inventory drops to 200 units.

Obtaining actual order, setup, carrying and shortage costs is difficult. For example, Figure 14.6 compares the ordering costs that are assumed linear to the real case where every addition of a staff person causes a step increase in cost. Most of the inventory systems are affected by two major problems viz. maintaining adequate control over each inventory item, and ensuring that accurate records of stock on hand are kept.

Error! Assumption Reality

Figure 14.6 : Cost to Place Orders Versus the Number of Orders Placed : Linear Assumption and Normal Reality

SAQ 4 (a) Does the production model or the standard EOQ model yield a higher EOQ

if set up cand holding costs are the same?

(b) What happens to total inventory costs and EOQ if inventory holding costs per unit increases?

Number of Orders

Ordering Costs

Number of Orders

18


(c) What is safety stock? Briefly explain its probability aspect?

(d) How the Economic order Quantity Model with safety stock differs from normal one?

14.6 ABC INVENTORY CONTROL

Maintenance of inventory through counting, placing orders, receiving stock, and so on takes personnel time and costs money. Since, these resources are available in limited capacity, so it is necessary to use the available resources for controlling inventory in best possible way. Any inventory system must specify when an order is to be placed for an item and how many units are required to be ordered. Most inventory control situations involve so many items that it is not practical to model and give treatment to each item. To get around this problem, the ABC classification scheme divides inventory items into three groupings : high value (A), moderate value (B), and low value (C). Usage is a measure of importance; an item low in cost but high in volume can be more important than a high-cost item with low volume.

14.6.1 ABC Classification of Materials Owing to the large number of materials while production at many manufacturing plants, needs of classifying materials arises. This can be achieved on the basis of annual usage. There are lot many schemes for classifying materials, among them one such scheme is ABC method. It is based on the idea that only a small percentage of materials represent the majority of inventory value.

If classification of items in inventory is listed on the basis of annual usage, the list shows that a small number of items account for a large usage value and that a large number of items account for a small usage value. Example in Table 14.3 illustrates this relationship.

Table 14.3 : Annual Usage of Inventory by Value

Item Number Annual Usage in Rs.

Percentage of Total Value in %

22 95.000 40.8 68 75000 32.1 27 25.000 10.7 03 15.000 6.4 82 13.000 5.6 54 7.500 3.2 36 1.500 0.6 19 800 0.3 23 425 0.2 41 225 0.1

Total Rs. 233,450 100.0%

The ABC approach divides this list into three categories by value : A items constitute roughly the top 15% of the items, B items the next 35%, and C items the last 50%. From observation, it appears that the list in Table 14.3 may be meaningfully grouped with A including 20%, B including 30%, and C including 50%. These point show clear delineations between sections. The result of this segmentation is shown in Table 14.4.

Table 14.4 : ABC Grouping of Inventory Items

Classification Item Number Annual Usage Percentage of

19

Control Function in

Production Managements in Rs. Total A 22,68 170,000 72.9 B 27,03,82 53,000 22.7 C 54, 36, 19, 23, 41 10,450 4.4

The objective of classifying items into groups is to establish the appropriate degree of control over each item. Figure 14.7 illustrates the fundamental aspect of ABC method. Following observations can be made from Figure 14.7.

(a) The inventory portion and inventory value captured by the A materials constitutes only 20% and 75% respectively.

(b) Class B of materials represents 30% of the materials in inventory and 20% of the inventory value.

(c) Similarly Class C of materials represents 50% of the inventory material and only 5% of inventory value.

On account of the above classification, following inference can be made that with the increase in inventory value of a material, extent of analysis also rises. Ordinarily, Class A materials would be analyzed extensively as compared to the Class C of the materials. The implementation of this classification requires an intelligent decision and judgment that is based on under mentioned points. Materials Critical to Production

Large inventories are justified because of the effects of these materials as they are capable of break down the entire production lines.

Materials having Short Span of Lives For such materials, small inventories are suitable because these materials may be subject to very fast obsolescence or deterioration.

Very Large and Bulky Materials Small inventories are justified for such materials because of the large space occupied by them.

Materials with Highly Erratic Lead Times Materials having unpredictable demand require large order quantities and order points.

Valuable Materials Subject to Pilferage For reducing the risk of loss, small inventories are appropriate.

Standard Packaging, Shipping Container, or Vehicle Size If order size departs from norm, quantities other than Economic order quantity are suitable for them.

0

20

40

60

80

100

120

0 3 5 8 10 20 30 40 50 60 70 80 90 100

Figure 14.7 : Fundamental Aspect of ABC Method

SAQ 5 (a) Why is it desirable to classify items into groups, as the ABC classification

does?

20

(b) Differentiate between the Classes A, B and C of inventory planning. Control & Measurement of Production Management

(c) List five intelligent decision necessary before implementing ABC classification scheme.

14.7 PROCESS CONTROL AND ACCEPTANCE SAMPLING

Process control is concerned with monitoring quality while the product or service is being produced. The main objectives of process control plan are to provide timely information on whether currently produced items are meeting design specifications and to detect shifts in the process that future products may not meet specifications. Statistical process control (SPC) involves testing a random sample of output from a process to determine whether the process is producing items within a pre-selected range. All the components have quality characteristics that are measurable, such as the diameter or weight of a part. Attributes are quality characteristics that are classified as either good or bad, or functioning or malfunctioning. For example, a lawnmover either runs or it doesn’t; it attains a certain level of torque and horsepower or it does not. This type of measurement is known as sampling by attributes. Alternatively, a lawnmower’s torque and horsepower can be measured as an amount of deviation from a set of standard. This type of measurement is known as measurement by variables. In the following discussion, some standard approaches to control sampling are described.

14.7.1 Process Control with Attribute Measurement Measurement by attributes implies that samples are taken on the basis of single decision i.e. item is either good or bad. Since, the answer would be yes or no, we can use simple statistics to create p chart with an upper control limit (UCL) or lower control limit (LCL). We can draw these control limits on a graph and then plot the fraction defective of each individual sample tested. Hence, following mathematical equations can be used to determine the UCL or LCL.

Total number of defects from all samplesNumber of samples Sample size

p =×

. . . (14.4)

(1 )p

p psn−

= . . . (14.5)

pUCL p z s= + . . . (14.6)

pLCL p z s= − . . . (14.7)

where, p is the fraction defective, sp is the standard deviation, n is the sample size and z is the number of standard deviations for specific confidence. Example 14.4

ABC insurance company wants to design a control chart to monitor whether insurance claim forms are being completed correctly. The company intends to use the chart to see if improvements in the design of the form are effective. To start the process the company collected data on the number of incorrect completed forms over the past 10 days. The insurance company processes thousands of these forms each day, and due to the high cost of inspecting each form, only a small

21

Control Function in

Production Managementrepresentative sample was collected each day. The data and analysis are given in Table 14.5.

Solution

To construct the control chart, first calculate the overall fraction defective from all samples. This sets the centerline for the control chart.

91 0.030333000

p = =

Next calculate the sample standard deviation :

0.03033 (1 0.03033) 0.0099300ps −

= =

Finally calculate the upper and lower control limits. For z = 3, we have

3 0.03033 3 (0.00990) 0.06004pUCL p s= + = + =

3 0.03033 3 (0.00990) 0.00063pLCL p s= − = − =

Table 14.5 : Insurance Company Claim Form

Sample Number Inspected Number of Forms Completed Incorrectly Fraction Defective

1 300 10 0.0333

2 300 8 0.02667

3 300 9 0.03

4 300 13 0.04333

5 300 7 0.02333

6 300 7 0.02333

7 300 6 0.02

8 300 11 0.03667

9 300 12 0.004

10 300 8 0.02667

Total 3000 91 0.03033

Sample standard deviation 0.00099

14.7.2 Process Control with Variable Measurements In attribute sampling, we determine whether something is good or bad, fit or does not fit, etc. In variable sampling, we measure the actual weight, volume, number of inches, or other variable measurement. Based on the measurements, we develop control charts to determine the acceptability or rejection of the process. There are four main issues to address in creating a control chart viz. the size of the samples, number of samples, frequency of samples and control limits.

Size of Samples

For industrial application in process control involving the measurement of variables, it is preferable to keep the sample size small. There are two main reasons. First, the sample needs to be taken within a reasonable length of time; otherwise, the process might change while the samples are taken. Second, larger the sample, the more it costs to take.

Number of Samples

22

Once the chart has been set up, each sample taken can be compared to the chart and a decision can be made about whether the process is acceptable or not.


Frequency of Samples

It depends on the trade-off between the cost of sampling and the benefit of adjusting the system. Usually, it is best to start off with frequent sampling of a process and taper off as confidence in the process builds.

Control Limits

Standard practice in statistical process control for variables is to set control limits i.e. three standard deviations above the mean and three standard deviations below. This implies that 99.7% of the sample means are expected to fall within these control limits. Thus, if one sample mean falls outside this wide band, we have strong evidence that the process is out of control.

14.7.3 Method for Constructing X and R Charts For a known value of standard deviation of the process distribution, the X chart may be defined as

and x xx xUCL X zs LCL X zs= + = − . . . (14.8)

where, xssn

= = standard deviation of sample means,

s = standard deviation of the process distribution,

n = sample size,

X = average of sample means or a target value set for the process, and

z = number of standard deviations for a specific confidence level (z = 3).

An X chart is simply a plot of the means of the samples that were taken from a process, whereas, R chart is a plot of the range within each sample. The range is the difference between the highest and the lowest numbers in that sample. Mathematically, it can be defined as :

1

n

ii

X

Xn

==∑

. . . (14.9)

where, X is the mean of the sample, i is the item number and n is the total number of items in the sample.

1

m

jj

X

Xm

==∑

. . . (14.10)

where, j is the sample number, m is the total number of samples, Rj is the difference between the highest and lowest measurements in the sample and R is the average of the measurement differences R for all the samples, or

1

m

jj

R

Rm

==∑

. . . (14.11)

Thus, upper and lower control limits can be defined as

Upper control limit for 2X X A R= + . . . (14.12)

23

Control Function in

Production ManagementLower control limit for 2X X A R= − . . . (14.13)

Upper control limit for 4R D R= . . . (14.14)

Lower control limit for 3R D R= . . . (14.15)

14.7.4 Acceptance Sampling Acceptance sampling is performed on goods that already exist to determine what percentage of products conforms to specifications. These products may be items received from another company and evaluated by the receiving department, or they may be components that have passed through a processing step and are evaluated by company personnel either in production or later in the warehousing function.

Acceptance sampling is executed through a sampling plan. In this section we illustrate the planning procedures for a single sampling plan, i.e. a plan in which the quality is determined from the evaluation of one sample. A single sampling plan is defined by n and c where n is the number of units in the sample and c is the acceptance number. The size of n may vary from one up to all the items in the lot from which it is drawn. The acceptance number c denotes the maximum number of defective items that can be found in the sample before the lot is rejected. Values for n and c are determined by the interaction of four factors i.e. AQL, α, LTPD and β that quantify the objectives of the product’s producer and its consumer.

The objective of the producer is to ensure that the sampling plan has a low probability of rejecting good lots. Lots are defined as high quality if they contain no more than a specified level of defectives and are known as acceptable quality level (AQL). Lots are defined as low quality if the percentage of defectives is greater than a specified amount and is termed as lot tolerance percent defective (LTPD). The probability associated with rejecting a high-quality lot is denoted by the letter α and is termed as producer’s risk. The probability associated with accepting a low-quality lot is denoted by letter β, known as consumer’s risk. The selection of particular values for AQL, α, LTPD and β is an economic decision based on a cost trade-off or more typically on company policy.

Example 14.5

ABC industries manufactures X-band radar scanners used to detect speed traps. The printed circuit boards in the scanners are purchased from an outside vendor. The vendor produces the boards to an AQL of 2% defectives and is willing to run a 5% risk α of having lots of this level or fewer defectives rejected. The company considers lots of 8% or more defectives (LTPD) unacceptable and wants to ensure that it will accept such poor quality lots not more than 10% of the time (β). A large shipment has just been delivered. What values of n and c should be selected to determine the quality of this lot?

Solution

It is given in the problem that

AQL = 0.02, α = 0.05, LTPD = 0.08 and β = 0.1. We can use table 14.6 to calculate c and n.

Thus, the appropriate sampling plan is C = 4 and n = 100. Up to four defects found in the lot, the lot will be accepted.

Table 14.6 shows various acceptance numbers C. Corresponding to the particular C values, sample size is constant.

Table 14.6 : Data for Deriving a Single Sampling Plan (Derived from Poisson Cumulative Table with α = 0.05 and β = 0.10)

C np0.95np0.10

np0.10/np0.95

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0 0.051 2.30 45.10

1 0.355 3.89 10.96

2 0.818 5.32 6.50

3 1.366 6.68 4.89

4 1.970 7.99 4.06

5 2.613 9.28 3.55

6 3.285 10.53 3.21

7 3.981 11.77 2.96

8 4.695 12.99 2.77

In the present case LTPD/AQL = 4.

If you look at the Table 14.6, ratio 0.10

0.95

n

npp

is 4.06 when C = 4 which is nearby to

the ratio of LTPD/AQL.

0.10 7.99n p =

0.08 7.99n × =

100n ≈

SAQ 6 (a) Discuss the differences between p-charts and X and R charts.

(b) Describe the trade-off between achieving a zero AQL (acceptable quality level) and a positive AQL.

14.8 SUMMARY

Controlling is a sub system of the production system where a portion of the output is monitored for feedback signals to provide corrective action, if required. The management and control of inventory is a common problem to all types of organisations. Inventory control refers to the planning for optimum quantities of materials at all stages in the production cycle and envolving techniques which would ensure the availability of planned inventories.

Quality control assure that resulting product will perform its intended function. Therefore, it is concerned with the prevention of defects so that items may be made right at the first time. To achieve this several activities are required to performed. Inspection and control of raw materials ensure that they meet specification. Statistical quality control (SQC) attempts to evaluate machines, materials by observing capabilities and trends in variation so that continual analysis and production may be made to the desired quality level.

25

Control Function in

Production Management14.9 KEY WORDS

Production Management : Activities that transform resources into goods and services.

Inventory : It is a stored resource that is used to satisfy a current or future need.

Safety Stock : It can be termed as an extra stock possessed by a firm.

Acceptance Quality : The term AQL refers to the level of quality of a Level (AQL) product that is judged by the consumer to be good in terms of the percentage of defective items.

Producers Risk (α) : This refers to the productivity that lots of the acceptable quality level will not be accepted.

Lot Tolerance Percent : This refers a small properties of bad components Defective (LTPD) some what larger than AQL in a lot such that the lots having more than this proportion of defectives components have a small probability of getting accepted.

Manufacture’s Risk : It is the small probability of a batch being good or even better than AQL but yielding a bad sample and thus getting rejected.

Purchaser’s Risk : It is the probability of a lot being bad or even worse that limiting quality but yielding a good sample and thus getting accepted.

Sample : A sample may be defined as the number of items or component parts drawn from a lot, batch or population.

Control Charts : Control charts is a (day-to-day) graphical presentation of the collected information. It detects variations in the processing and warns if there is any departure from the specified tolerance limit.

Operating Characteristic : It describes in graphical form the probabilities Curve (OC Curve) associated with accepting lots of varying quality for a particular sampling plan.

Re-order Point : The level of inventory at which an order is placed is defined as re-order point.

Lead Time : The time period between placement of an order and arrival of the materials is known as lead time.

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Unit 14