Operations management ii

Operations Management - II
Manimay Ghosh, Ph.D.

Road Map
 Inventory Control
 Material Requirement Planning
 Aggregate Planning
 Scheduling
 Quality Management and SPC
 Lean Manufacturing

Inventory
 Inventory: Stock of items held by the
organization

Goals in Operations w.r.t
Inventory
 Carrying the right amount of inventory and
ensuring that neither overstocking nor shortages
occur is the ultimate goal of inventory
management
 Keep the level of inventory in the supply chain
as low as possible
 Moving the inventory, in its continually changing
form, as fast as possible through the supply
chain for delivery to the final client

What is Inventory
Management?
 Inventory management encompasses
processes that ensures product availability
while reducing investment costs

Why do we need Inventory
Management?
 Largest (physical and financial sense) and
most difficult asset to manage for an
organization

Two Views of Inventory
 Pressure for high inventory
 Pressure for low inventory

Pressure for High Inventory
 To achieve economies of scale in production (cycle inventory)
 Immediate delivery not possible
 Crude oil, iron ore, coal can’t always be supplied on time
 To protect against unanticipated events (strikes, weather)
 To protect against price increases and take advantage of quantity
discount
 To satisfy periods of high seasonal demand
 Economies of scale offered by transportation companies
 One truck load or one ship load can reduce unit transportation cost
 Decoupling Inventory

Pressure for Low Inventory
 Holding costs
 Cost of coordinating production
 Quality issue
 Increased waste

Forms of Manufacturing
Inventories
 Manufacturing Inventory: Items that contribute to or
become part of a firm’s product.
 Raw material
 Physical inputs at the start of the production
process.
 Work-in-process
 Inventory between the start and end points of a product routine (yet
to become finished products)

Types of Manufacturing Inventory
(Work-in-process)

Manufacturing Inventory
 Finished goods
 End item ready to be sold at
the end of routine
 Maintenance / Repair /
Operating Supplies (MRO)
 Oil, lubricants, cotton waste,
wood dust
 Pens, papers, files, envelopes
 Pipeline or Transit Stock
 Inventory ordered but not yet
received

Service Inventory
 Inventory: Tangible goods to be sold and
the supplies necessary to administer the
services in various types of service
organizations (hospitals, banks)
Hospitals: (medicines, syringes, blood,
sutures, glucose bottles, bandages etc.)
Banks: brochures, pamphlets, currency notes,
coins

Levels of Inventory
 High Levels
Tying more financial capital
 High interest charges
 Low Levels
Stock outs
Lost sales

Goal of Materials Manager
 Optimal Level of Inventory
 Key Questions
What should be the size of order to the
supplier?
When should the order be placed?

Measures of Inventory
Management
 Inventory turnover
Costs of goods sold
--------------------------------------------------------
Average aggregate inventory value
 Cost of goods sold is finished goods valued at cost, not the
final sale price
 Average aggregate inventory value is the total value at
cost of all items (RM, WIP, Finished goods) being held in
inventory

Measures of Inventory
Management
 Days (or weeks) of inventory in hand
average aggregate value of inventory
= --------------------------------------------------
(cost of goods sold) / 365 days

Selective Control of Inventory
 FSN Classification
 Based on movement of inventory
 F: fast moving, S: slow moving, N: non-moving
 VED Classification
 Based on criticality of items
 V: Vital, E: essential, D: desirable
 ABC Classification
 Based on cost of items consumed

ABC Classification System
 ABC classification method divides inventory items into
three groups
 A items (high rupee volume)
 B items (moderate rupee volume)
 C items (low rupee volume)
Note: Rupee volume 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.

ABC Classification System
 In ABC analysis each class of inventory
requires different levels of inventory
monitoring and control – the higher the
value of the inventory, the tighter the
control

ABC Inventory Planning
 A items
 10 to 20% of # of items
 60 to 70% of annual rupee value of inventory
 Tight inventory control
 B items
 Represent 30% of # items and 15% of inventory value
 C items
 50 to 60% of # of items
 10 to 15% of annual rupee value of inventory
 Less stringent inventory control

Item No Annual Rupee Usage % of Total Value
22 95000 40.69
68 75000 32.13
27 25000 10.71
3 15000 6.43
82 13000 5.57
54 7500 3.21
36 1500 0.64
19 800 0.34
23 425 0.18
41 225 0.1
233,450 100%

Classification Item No. Annual Rupee Usage % of Total
A 22, 68 Rs 170,000 72.90%
B 27, 03, 82 53,000 22.7
C 54, 36, 19, 23, 41 10,450 4.4

Key Use of ABC Concepts
 Use in customer service
Focus on essential aspects
 Guide to cycle counting
Physical counting of items in inventory
 To avoid discrepancy indicated by inventory
records and actual quantities

ABC Analysis
 Annual Rupee Value Review Period
Rs >10,000 ≤30 days
Rs 3,000 – 10,000 ≤45 days
Rs 250 – 3,000 ≤90 days
<= Rs 250 ≤180 days
Experts recommend following accuracy:
A items: ±0.2%, B: ± 1%, C: ± 5%

Independent vs. Dependent
Demand
Independent demand
 Influenced by market conditions, i.e., originates outside the
system (say cars, bicycles, refrigerators, washing machines)
 Uncertain
Dependent demand
 Depends on demand of independent items, i.e., make up
independent demand products
 Known
 Example: Subassemblies, components parts

Independent Demand
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand
Independent demand is uncertain.
Dependent demand is certain.
Inventory

Managing Independent Demand
 This chapter focuses on managing
independent demand

Inventory Costs
 Types of costs
 Ordering costs (costs associated with placing an order and receiving
inventory, independent of order size). Assigned to entire batch
 Identification of sources of supply
 Price negotiation, purchase order generation
 Follow-up and receipt of materials
 Inspecting goods upon arrival for quality and quantity
 Stationery, postage, telephone and electricity bills
 Transportation costs
 Set-up Costs
 When a firm produces its own inventory, the cost of machine set-up
such as arranging tools, drawings, cleaning the machine, adjusting
the machine are all parts of set-up costs

Inventory Costs
Holding or Carrying costs (in warehouse)
 Cost of storage facilities (rent, if rented)
 Electricity
 Cost of capital tied up in inventory
 Material handling
 Interest charges
 Insurance and taxes
 Pilferage, scrap, & obsolescence
 Cost of personnel
 Software for maintaining inventory status

Inventory Costs
 Shortage Costs (or stock out costs)
Loss of profits
Loss of goodwill
Late charges

Basic Inventory Control
Systems
 Two types
 Fixed order quantity
model (Q – Model)
 Also known as Perpetual
system or Continuous
inventory System
 Event or quantity triggered
 Fixed time period model
(P-model)
 Also known as Periodic
Review System
 Time Triggered

Economic Order Quantity
(EOQ) Model
 Assumptions
 Annual demand for item is constant and uniform throughout
 Lead time is constant
 Price per unit of product constant
 Inventory holding cost is based on avg. inventory
 Ordering or set-up costs are constant
 Instantaneous replenishment
 There are no quantity discounts
 Inventory incurred no cost in transit

Q-Model
 Lead Time: Time between placing an
order and its receipt
 Reorder Point: The inventory level at
which a new order should be placed.

Q-Model
R
Time
L
Q
Inventory on hand
Demand Rate
Avg. Inventory
(Q/2)
Reorder Pt.
Order Placed
Order Receipt
L = Lead Time
R = Reorder Point
Time

Average Inventory Levels and
Number of Orders

Minimum Total Cost
The total cost curve reaches its
minimum where the carrying and
ordering costs are equal.
Q
2
H
D
Q
S=

Q Model
 Q opt=
2DS
H
Reorder Point, R = d×L
Where, d = average daily demand
L = Lead time in days
(constant demand, so no safety stock)
The square root formula is the EOQ, also referred as economic lot size
Q answers the “how much” question directly

When to Reorder with EOQ
 If demand and lead time are both
constant, the reorder point is
ROP = d X LT
where d = Demand rate (units per
day or week)
LT = Lead time in days or
weeks

Q-Model
 Optimal number of orders = D / Q
 Time between orders = Q / D

Fixed Order Quantity Model
(Q-model)
Total Annual Cost = Annual Purchase Cost + Annual
Ordering Cost + Annual Holding Cost
TC = PD + (D/Q)×S + (Q/2)×H
Where, TC = Total annual cost
D = Demand
P = Unit cost
Q = Quantity to be ordered
S = Ordering cost or set-up cost
R = reorder point
L = Lead Time
H = Annual holding or storing cost per unit of average
inventory

Q Model
 Item cost (P×D) is not a function of the order
quantity – there are no quantity discounts– so
the amount PD is constant. Therefore, the value
of Q that minimizes the equation is the value
that minimizes the sum of the ordering costs and
holding costs, called the total inventory cost or
total stock cost. This quantity is called Economic
Order Quantity (EOQ).

EOQ with Purchasing Cost
Adding purchasing cost does not change EOQ

Total Cost Curve Near EOQ
The Total Cost Curve is flat near EOQ

Little’s Law
Average Inventory
 Average Flow time = ----------------------------------------
Flow Rate (or Average demand)
The average amount of inventory in a system is equal to
the product of average demand and the average time a
unit is in the system

Observation
 If demand increases by a factor k, the optimal lot
size increases by factor √k. The number of
orders placed per year should also increase by a
factor √k. Flow time attributed to cycle inventory
should decrease by a factor of √k.

Production Order Quantity
Model or EPQ Model
 It is a variant of EOQ model
 Assumptions
Annual demand known
Usage rate constant
Usage occurs continually, but production
occurs periodically
Production rate constant
No quantity discounts

Production Order Quantity
Model

Production Order Quantity Model

Excessive Consumption During
Lead Time

Undue Stretching of Lead Time by
Supplier

When to Reorder with EOQ
 When variability is present in demand or
lead time, it creates the possibility that
actual demand will exceed expected
demand
 Therefore, it is necessary to carry safety
stock to avoid stock out

Safety Stock
 EOQ model assumed deterministic demand
 Demand in reality varies from day-to-day
 Probability of stock out during lead time
 Need to keep safety stock in addition to expected
demand
 To hedge against the possibility of stock out
 Amount of safety stock depends on
 Service Level
 Probability that inventory on hand during lead time
in sufficient to meet expected demand, i.e., the
probability that stock out will not occur.

Safety Stock Avoids Stock Out
Caused by Excessive Consumption

Safety Stock Avoids Stock Out by Undue
Stretching of LT by Suppliers

Fixed Order Qty Model With Safety
Stock

Service Level
 Probability that the demand will not
exceed supply during lead time
Example: Service level of 95% implies a probability of 95%
that demand will not exceed supply during lead time, and
probability of stock out is 5%
 Service Level = 100% - Stock out risk

Normal Distribution Curve During
Lead Time

© 2004 by Prentice Hall, Inc., Upper Saddle River, N.J.
07458 12-72
Probabilistic Models - When to
Order?
Reorder
Point
(ROP)
X
Safety Stock (SS)
Time
InventoryLevel
Lead Time
SS
ROP
Service
Level P(Stockout)
Place
order
Receive
order
Frequency

Reorder Point (ROP)
 If expected demand during lead time and its
standard deviation are available, then
 ROP = d×L + safety stock
 ROP = Expected demand during lead time + ZσdLT
Where, z = # standard deviations
σdLT = The standard deviation of demand during
lead time
ZσdLT = Safety Stock
Note: Smaller the risk manager is willing to accept, the greater the value of Z

Other Three Probabilistic
Models
1. Demand is variable, and LT constant
2. Lead time is variable, demand constant
3. Both lead time and demand are variable

Demand Variable and LT Constant

LT Variable and Demand Constant

Managing Inventory (Key
Learning)
 Inventory costs money, inventory hides problems
 Reduce inventory
 Reducing lot sizes (EOQ)
 Lowering order costs through E-bidding
 Reducing receiving costs
 Automated payment of invoices
 Examine holding cost. If understated, larger H will
reduce EOQ
 Reducing set-up costs
 Automation and process improvements

Managing Inventory (Key
Learning)
 Reduce safety stock
 Better forecasting models to reduce the unpredictability of
demand
 Collaborating Planning Forecasting and Replenishment
(CPFR)
 Reduce variability in demand by working with customers
 Reduce lead time
 Bringing suppliers close to the buyer, reduce throughput
time of suppliers
 Reliable method of transportation
 Faster method of transportation

Impact of Location on Inventory
(Key Learning)
 Questions related to inventory
How much to order?
When to order?
Where to stock inventories?
 Square Root Rule

Inventory Related to Number of
Locations

Managing Inventory
(Key Learning)
 Reduce number of locations
Major effort by many firms to reduce the
number of warehouses and distribution
centres
Substantial reduction in inventories due to
consolidation

Bar Code – 3 Litre Diet Coke
Manufacturer identification
number
Specific Item Number
Check digit

Quantity Discount Model
 Price reductions for large orders offered to
customers to induce them to buy in large
quantities
 TC = (Q/2)H + (D/Q)S + PD
Carrying Cost Ordering Cost Purchasing Cost

Advantages to Disadvantages
of Buyer on Discounts
 Advantages
 Reduces units cost of materials
 # of orders few, low ordering costs
 Low transportation costs
 Chances of stock out less
 Disadvantages
 High carrying costs
 High fund requirement
 Low stock turnover
 Deterioration of stocks

Advantages to Disadvantages
of Seller on Discounts
 Advantages
Clear glut in the inventory
Less carrying costs of inventories

Discount - Incremental
 In incremental discount increasing rates of
discounts are offered for higher range of
quantities purchased. Hence, under this
discount offer there shall be multiple unit
costs for the same item in a lot. The
ranges of quantity at which price changes
are called price breakers

Price Discount Model
 Two general cases
Carrying cost is constant (Rs 5 per unit per
year)
Carrying cost is a % of purchase price (say
20% of unit price)

Total Cost Curve with Constant Carrying
Cost
When carrying costs are constant, all curves have same minimum points at the
same quantity

Quantity Discounts
With Constant Carrying
Costs

Total Cost with Carrying Cost as
% of Unit Price
When carrying costs are % of unit price, minimum points don’t line up

Procedure for Determining Overall EOQ
when Carrying Costs are Constant
 Compute the common minimum point
 If the feasible minimum point is on the lowest price
range, that is the optimal quantity
 If the minimum point is in any other range, compute the
total cost for the minimum point and for the price breaks
of all lower unit costs. Compare the total costs; the
quantity (minimum point or price break) that yields the
lowest total cost is the optimal order quantity

Problems
 Carrying costs are constant

Determining Best Purchase Quantity when
Carrying Costs are % of Price
 Begin with lowest unit price, compute the minimum
points for each price range until you find a feasible
minimum point (i.e. until a minimum point falls in the
quantity range for its price)
 If the minimum point for the lowest unit price is feasible,
it is the optimal order quantity. If the minimum point is
not feasible in the lowest price range, compare the total
cost at the price breaks for all lower prices with the total
cost of the feasible minimum point. The quantity which
yields the lowest total cost is the optimum

Problems
 Carrying Costs are % of price

Total Annual Costs With
Quantity Discounts

Fixed Time Period Model
(P-Model) or Periodic Review System
 Inventory checked only at fixed intervals of time,
rather than on a continuous basis
 Time between orders is constant
 On-hand inventory is counted
 Only the amount necessary to bring the total
inventory up to a pre-specified target is ordered
(order size varies depending on on-hand
inventory)

Fixed Time Period Model
(P-Model) or Periodic Review System
Order Qty = Avg. demand + Safety Stock - Inventory on hand

P Model
 Advantages
 Practical approach if the inventory withdrawals can’t be closely
monitored
 Inventory counted only before the next review period
 Convenient administratively
 More appropriate for C-items
 Disadvantages
 No tally of inventory during review period
 Possibility of stock out
 Large amount of safety stock because need to protect against
shortages during order interval and lead time

Differences (Q vs. P Models)
 Q model
 Order Qty: Q fixed
 When order: ROP triggered
 Record keep: Each time
material withdrawn
 Size of Inv: Less than P
model
 Time to maintain: High
 If Higher than normal
demand – Shorter time
between orders
 Type of items: High priced,
critical, important items
 A items
 P model
 Order Qty: variable (varies
each time order is placed due
to demand variability)
 When order: Review period
(time triggered)
 Record keep: Counted only at
review period
 Administration: Easy
 Size of Inv.: Larger than Q
model
 Type of items: Retail, drugs
 Appropriate when large
number of items ordered
from same supplier
resulting in consolidation
and lower freight rates

Choosing Between Q and P
 Not an easy decision
Part science and part human judgment
It depends on variety of factors
 Total SKUs monitored
 Computerized or manual system
 ABC profile
 Strategic focus
 Cost minimization or customer service

Choosing Between Q and P
 P system
 The P system should be used when orders may be placed at specified
intervals
 Weekly order and delivery of FMCG products to a grocery store
 The P system is ideal when items are ordered from same supplier, and
delivered in same shipment
 Shipments can be consolidated resulting in lower freight rates
 Ordering for multiple products at the same time
 Provides scheduled replenishment and less record keeping
 Often used for inexpensive items
 Q system
 Often used for expensive items

Inventory Records and
Accuracy
 Inventory records differ from physical count
 Inventory accuracy refers to how closely they match
 How to keep up-to-date inventory records
 Keep store room locked
 Educating employees
 Putting fence up to ceiling around storage area to
prevent unauthorised access to pull items
clandestinely
 Cycle counting at regular intervals

Material Requirements
Planning (MRP)

MRP
 The logic for determining the number of
parts, components, and materials needed
to produce a product.
 It also provides a schedule specifying
when each of these materials, parts, and
components should be ordered and
produced

Demand
 Independent demand
 Influenced by market conditions, i.e., originates outside the
system (say cars, bicycles, refrigerators, washing machines)
 Uncertain
 Dependent demand
 Depends on demand of independent items, i.e., make up
independent demand products
 Known
 Example: Subassemblies, components parts

Demand

Demand Pattern for Independent
versus Dependent Items

Attribute Dependent
Demand
Independent
Demand
Nature of Demand No uncertainty Uncertainty
Goal Meet requirements
exactly
Meet demand for a
targeted service
level
Service Level 100% 100% difficult
Demand
occurrence
Often lumpy Often continuous
Estimation of
demand
By production
planning
By forecasting
How much to
order?
Known with
certainty
Estimate based on
past consumption
Key Differences: Dependent vs. Independent Demand

Material Requirements Planning (MRP)
 MRP is a technique that has been employed since the
1940s and 1950s.
 Joe Orlicky is known as the Father of MRP
 The use and application of MRP grew through the
1970s and 1980s as the power of computer hardware
and software increased.
 MRP gradually evolved into a broader system called
manufacturing resource planning (MRP II).

Material Requirements Planning
(MRP)
 MRP is a computerized inventory system
developed specifically to manage dependent
demand items
 MRP works backward from the due date using
lead times to determine when and how much to
order for
Subassemblies, component parts & raw
materials

MRP
 MRP begins with a schedule for finished goods
that is converted into a schedule of requirements
for subassemblies, component parts and raw
materials needed to produce the finished items in
the specified time frame
 MRP designed to answer the following questions
• What is needed ?
• How much is needed?
• When is it needed ?

MRP
 MRP thus works with finished products, or end items,
and their constituent parts, called lower level items
 According to one study, 80% of high performing
manufacturing plants have implemented MRP
 MRP works well for assembling complex discrete
products produced in batches
 Example: computers, consumer durables, furniture,
watches, trucks, generators, motors, machine tools

MRP
MPS
BOM MRP Inventory Records
Planned Order
Release
Work Order Purchase order
Rescheduling
Notices

Master Production Schedule
 A time table that specifies what (end item)
is to be made and when
 Time period used for planning is called a
time bucket
 MPS shows how many of each individual
item must be completed each period

Aggregate Production Plan and
MPS -- Amplifiers

How does MPS differ from AP-
Motors

Aggregate Production Plan - Cars
Hundai Motors:
Month # of Cars
Jan 10,000
Feb 12,000
Mar 8,000
April 11,000
May 7,000

Weeks
of
January
I II III IV Total
Santro 1,200 2,000 2,500 700 6,400
Accent 700 950 1,300 250 3,200
Sonata 100 50 200 50 400
2,000 3,000 4,000 1,000 10,000
MASTER PRODUCTION SCHEDULE

1. Master Production Schedule
(MPS)
 Master production schedule states
which end items are to be produced, when
these are needed, and in what quantities.
• Example: A master schedule for end item
X:
Comes from: customer orders, forecasts and orders from
warehouses to build up seasonal inventories, and
interplant transfers

2. Bill of Materials (BOM)
 A document that lists the components, their description,
sequence in which the product is created and the
quantity of each required to make one unit of a product
 Thus relationship between end items and lower level
items is described by the BOM
 It depicts exactly how a firm makes the item in the
master schedule
 Extremely important to have BOM correct to have
accurate material estimates

2. Bill of Materials (BOM)
 The BOM file is often called the product
structure file or product tree because it
shows how a product is put together

Assembly Diagram & Product
Structure Tree

Product Structure Tree of
Sub-Assembly

Product Structure Tree of Product
X With Levels
Visual description of the requirements in a bill of materials, where all
components are listed by levels
(Highest)
(Lowest)

Indented Parts List for Meter A and Meter B

A Product Structure Tree
Note: Restructuring the BOM so that multiple occurrences of a component all coincide
with the lowest level at which the component occurs

BOM & Product Structure Tree (An
Example)

Partial Bill
of Materials for a Bicycle

3. Inventory Record
 Third input in MRP
 It tells us about the status of inventory of an item
at present, or in a given interval of time in the
coming future
 On hand
 On Order (scheduled receipt)
 Lead time
 Lot size
 Low Level Code (LLC)

Outputs of MRP
(Primary Reports)
 Planned order receipt – A schedule indicating the
quantity that is planned to arrive at the beginning of a
period
 Planned Order release – Authorizes the execution of
planned orders (work order + purchase order). To
determine planned order release, count backward from
the planned order receipt using the lead time
 Order changes report – Changes to planned order,
including revisions for due dates or order quantities and
cancellation of orders

Outputs of MRP
(Secondary Reports)
 Performance control report – evaluate
system performance, deviations from
plans, missed deliveries, and stock outs
 Exception reports – attention to major
discrepancies such as late and overdue
orders, requirements for non-existence
parts, reporting errors

MRP Terminologies
 Gross Requirements: Total demand for an item during
each time period. For end items, these quantities are
shown in the master production schedule
 For components, these quantities are derived from the planned
order releases of their immediate parents
 Scheduled Receipts: Orders that have been released
and scheduled to be received from vendors by the
beginning of a period
 Projected On-Hand: The expected amount of inventory
that will be on hand at the beginning of each time period
(SR + Avl inv from last period)

MRP Terminologies
 Net requirements: The actual amount needed in each
time period
 Planned Order Receipts: The quantity expected to be
received from a vendor or in-house shop at the
beginning of the period in which it is shown. It is the
amount of an order that is required to meet a net
requirement in the period.
 Under lot-for-lot ordering, this quantity will equal net requirements.
Under lot-size ordering, this quantity may exceed net requirements. Any
excess is added to available inventory in the next time period.

MRP Terminologies
 Planned Order Release: Indicates a
planned amount to order in the beginning
of each time period; equals planned-order
receipts offset by lead time.

Format of MRP
Week Number 0 1 2 3 4 5 6 7 8
Item:
Gross requirements
Scheduled receipts
Projected on hand
Net requirements
Planned-order
receipts
Planned-order
releases

MRP Explosion
 The MRP process of determining
requirements for lower level items
(subassemblies, components, raw
materials) based on the master production
schedule

Planned Order Report
PERIOD
ITEM 1 2 3 4 5
A X1 X2 X3
B Y1 Y2
C Z1 Z2 Z3

Lot Sizing in MRP Systems
 Lot-for-lot (L4L)
Sets planned orders to exactly match
the net requirements. Eliminates
holding costs
 Economic order quantity (EOQ)
Balances setup and holding costs

Lot Sizing in MRP Systems
 Least total cost (LTC)
 Balances carrying cost and setup cost for various
lot sizes, and selects the one where they are most
nearly equal
 Least unit cost (LUC)
 Adds ordering and inventory carrying costs for
each trial lot size and divides by number of units
in each lot size, picking the lot size with the
lowest unit cost

Basic Data
 Cost per item: Rs 10
 Order cost: Rs 47
 Inventory carrying cost/week: 0.5% of unit cost
 Weekly net requirements:
1 2 3 4 5 6 7 8
50 60 70 60 95 75 60 55

Lot Size: EOQ
Rs171.05
77.05 94

Least Total Cost
Rs140.5046.5 94

Least Unit Cost
Rs153.5059.5 94

Lot Size Cost Comparisons
 L4L: Rs 376
 EOQ: Rs 171.05
 Least Total Cost: Rs 140.50
 Least Unit Cost: Rs 153.50
Preferred method: Least Total Cost

MRP and Capacity Planning
 MRP , as it was originally introduced, considered
only materials. MRP does not compare the
planned orders to the available capacity. Most
MRP plans assume infinite loading; that is an
infinite amount of capacity is available, which is
not realistic. Individual machines or work
centres may have capacity shortages and
backlogs of work to be completed
 We therefore need capacity planning.

Two Approaches to Capacity
Planning
 Rough-cut capacity planning
 Uses the MPS (end item) as the source of product
demand information
 Capacity determination at critical work centres
 Capacity Requirement Planning
 Completed at the component level rather than at the
end item level
 Uses planned order release from MRP
 Capacity determination at all work centres

Focused on critical
work centres

Capacity Requirements
Planning (CRP)
 CRP determines if all the work centres
involved have the capacity to implement
the MRP plan.
 A load profile compares weekly loads
needs against a profile of actual capacity.

Capacity
 Work center Effective Capacity/week (2 machines):
(# machines)×(# shifts)× (# of hours/shift)× (# days/week)×
(utilization)×(efficiency)
 Utilization: Time working / Time available
 Efficiency: Actual output / standard output
 Load: Standard hours of work assigned to a production facility
 Load % = (Load / Capacity)×100%

Scheduled Workload for a Work
Center
161.5
137.8
190.3
128.8
2m/c * 2 shifts/day * 10 hours/shift * 5 days/week * 85%(m/c Util) * 0.95 (m/c efficiency) =161.5 hrs/week

Capacity Levelling
 Work Overtime
 Selecting an alternative work center
 Subcontract
 Scheduling part of work of week 11 into
week 10
 Renegotiate due date

Safety Stock
 It would seem that an MRP inventory system should not require
safety stock. Practically, however, there may be exceptions.
Typically SS built-into projected on-hand inventory
Why is safety stock necessary?
 Two types of uncertainties are prevalent
A. The quantity of components received (soln: SS)
I. Poor quality may result in quantity loss
II. Reliability in supplier may result in quantity uncertainty
B. Timing of the receipts (solution: safety time)
A. Machine breakdowns, fluctuations in staffing

Updating MRP Schedules
 Updating MRP schedule is required because
 Customers may cancel or amend order
 Suppliers could default on supply
 Unexpected disruptions in manufacturing
 Two techniques of updating
 Regeneration, i.e., re plan the whole system (run MRP from
scratch, updated periodically, 100% replacement of the existing
information)
 Net change
 Instead of running the entire MRP system, schedules of
components pertaining to portions where changes have
happened are updated.
 Applies to sub-set of data as opposed to regeneration

MRP Dynamics - System
Nervousness
 MRP systems work best under conditions of reasonable
stability
 Frequent changes in an MRP system leads to major
changes in the order profiles for lower level
subassemblies or components creating havoc for
purchasing and production departments. This is called
system nervousness Two tools are helpful in reducing
system nervousness
 Time fences

Time Fences in MPSTime Fences in MPS
Period
“frozen”
(firm or
fixed)
“slushy”
somewhat
firm
“liquid”
(open)
1 2 3 4 5 6 7 8 9
Time Fences divide a scheduling time horizon into three
sections or phases, referred as frozen, slushy, and liquid.
Strict adherence to time fence policies and rules.

Pegging
 Tracing upward in the BOM from the
component to the parent item. By pegging
upward, the production planner can
determine the cause for the requirement
and make a judgement about the
necessary for a change in schedule

 Reduction in inventory
 Increased customer satisfaction due to
meeting delivery schedules
 Faster response to market changes
 Improved labor & equipment utilization
 Better inventory planning & scheduling
MRP Benefits

Benefits of MRP
 Ability to easily determine inventory
usage by backflushing
 Back flushing: Exploding an end item’s
bill of materials to determine the
quantities of the components that were
used to make the item.

MRP – Problems Encountered
 Data integrity is low
 Not frequent updates of databases when
changes takes place
 Uncertainties related to lead time and
quantity delivered

Requirements of Successful
MRP System
 Computer and necessary software
 Accurate and up-to-date
 Master schedules
 Bills of materials
 Inventory records
 User knowledge
 Management support

 Evolved from MRP in 1980s
 Didn’t replace or improve MRP. Rather expanded the scope
to include capacity requirements planning and to involve
other functional areas of the organization:
 Purchasing, Manufacturing, Marketing, Finance,
Logistics
 MRP II employed common database and an integrated
platform where sales, inventory, purchasing transactions
were updated in both inventory and accounting applications
Manufacturing Resource Planning
(MRP II)

MarketMarket
DemandDemand
ProductionProduction
planplan
Problems?Problems?
Rough-cutRough-cut
capacity planningcapacity planning
YesYes NoNo YesYesNoNo
FinanceFinance
MarketingMarketing
ManufacturingManufacturing
AdjustAdjust
production planproduction plan
MasterMaster
production scheduleproduction schedule
MRPMRP
CapacityCapacity
planningplanning
Problems?Problems?
RequirementsRequirements
schedulesschedules
AdjustmasterscheduleAdjustmasterschedule
An Overview of MRP II

Aggregate Sales and
Operations Planning

Aggregate Planning (or Sales
and Operations Planning)
 It is the process of planning the quantity and timing of
output over the intermediate time horizon (often 3-18
months) by adjusting the production rate,
employment, inventory, and other controllable
variables
 The term has been coined by companies to refer to
the process that helps companies keep demand and
supply in balance
 Minimize long-run costs of meeting forecasted
demand

Aggregate planning is a big picture approach to production
plan to meet the demand throughout the year or so.
It is not concerned with individual products, but with a single
aggregate product representing all products.
For example, in a TV manufacturing plant, the aggregate
planning does not go into all models and sizes. It only
deals with a single representative aggregate TV.
All models are lumped together and represent a single
product; hence the term aggregate planning.
Aggregate Planning

What does Aggregate Mean?
 Overall terms
 Product families or product lines rather than individual
products, thus the term aggregate
 In other words, one “collapses” a multi-product firm to
a single-product firm, the “product” being aggregate
units of production
 Big picture approach to planning
 Aggregate, for example # bicycles to be produced,
but would not identify bicycles by colour, size, type
etc.

Aggregation (Example)
 Suppose a bicycle manufacturer makes three models (Standard,
Deluxe, Sports)
 Time: Standard: 30 m/c hours, Deluxe: 60 m/c hours, Sports: 90 m/c
hours
 Thus manufacturing 1 deluxe model is equivalent to manufacturing
2 standard models. 1 sports model is equivalent to manufacturing 3
standard models from resource consumption perspective
 Thus a monthly demand of 1000 standard cycles, 500 deluxe, and
250 sports can be aggregated as 2750 standard models on the
basis of machine hours

Identifying Aggregate Units of
Production (Basic Data)
Family
Material
Cost/ Unit
($)
Revenue/
Unit ($)
Setup
Time/Ba
tch
(hour)
Average
Batch
Size
Production
Time/ Unit
(hour)
Net
Production
Time/Unit
(hour)
Percentage
Share of
Units Sold
A 15 54 8 50 5.60 5.76 10
B 7 30 6 150 3.00 3.04 25
C 9 39 8 100 3.80 3.88 20
D 12 49 10 50 4.80 5.00 10
E 9 36 6 100 3.60 3.66 20
F 13 48 5 75 4.30 4.37 15

Identifying Aggregate Units of
Production
Product
Family
Material cost/
Unit (Rs)
Revenue /
unit (Rs)
Prodn.
Time /unit
(includes
setup time)
% share of
units sold
A 15 54 5.76 10
B 7 30 3.04 25
C 9 39 3.88 20
D 12 49 5.00 10
E 9 36 3.66 20
F 13 48 4.37 15
Material cost / aggregate unit = 15*0.10+7*0.25+9*0.20+12*0.10+9*0.20+13*0.15 = Rs 10
Revenue / aggregate unit = 54*0.10+30*0.25+39*0.20+49*0.10+36*0.20+48*0.15 = Rs 40
Production time / agg. unit = 5.76*0.1+3.04*.25+3.88*0.20+5*0.1+3.66*0.20+4.37*0.15 = 4 hrs

Building a Rough Master
Production Schedule
 Disaggregate an aggregate plan
Family
Setup
Time/B
atch
(hour)
Average
Batch
Size
Production
Time/Unit
(hour)
Production
Quantity
Number
of
Setups
Setup
Time
(hours)
Production
Time
(hours)
A 8 50 5.60 258 5 40 1,445
B 6 150 3.00 646 4 24 1,938
C 8 100 3.80 517 5 40 1,965
D 10 50 4.80 258 5 50 1,238
E 6 100 3.60 517 5 30 1,861
F 5 75 4.30 387 5 25 1,664
2583

Aggregate Size: Worm Gear
Box (input shaft)
Size
(input
shaft)
Facing
(mins)
Turning
(mins)
Thread
Mill
(mins)
Key
way
(Mins)
HT
(mins)
Thread
Grind
(mins)
Cyl
Grind
(mins)
Total
(Hrs)
%
market
Share
400 5 20 20 2 480 15 15 9.28 15
500 5 22 25 3 480 20 20 9.58 25
600 6 23 27 4 480 25 25 9.83 20
700 7 25 30 5 480 30 30 10.11 6
800 8 30 32 6 480 35 35 10.43 15
1000 10 35 35 7 480 35 40 10.7 10
1200 12 38 40 8 480 40 40 10.96 9

Why Aggregate Planning?
 Provides for fully loaded facilities, thus
minimizing
Overloading and under loading
Minimizing cost over the planning period
 Adequate production capacity to meet
expected aggregate demand
Optimize balance between demand and
supply

Why Aggregate Planning?
 A plan for orderly and systematic change
of production capacity to meet peaks and
valleys of expected customer demand
 Getting the most output for the amount of
resources available, which is important in
times of scarce production resources

Steps in Aggregate Planning
1. Begin with sales forecast for each product that
indicates the quantities to be sold in each time
period (usually months, or quarters) over the
planning horizon (3-18 months)
2. Total all the individual product or service
forecast into one aggregate demand.

3. Determine capacities (regular time, OT,
subcontracting) for each period
4. Determine unit costs for regular time, OT,
subcontracting, holding inventories, back
orders, layoffs etc.
5. Identify company policy (chase, level, mixed)

6. Develop alternative plans and compute
cost for each
7. Select the best alternative that satisfies
company’s objectives

Strategies for Meeting Demand
 Proactive
Alter demand to match capacity
 Reactive
Alter capacity to match demand
 Mixed
Some of each

 Proactive strategies
Influencing Demand
 Offer discounts and promotions
Increase advertising in slack periods
Counter seasonal products
 Lawnmowers (summer) and snow-blowers (winter)

 Reactive Strategies
Changing inventory levels
Vary workforce size (hiring and lay-off)
Varying shifts
Varying working hours
Varying production through overtime or idle
time
Subcontracting

Inputs and Costs in AP
Decision Variable Costs
Varying work force size Hiring, training, firing costs
Using Overtime Overtime costs
Varying inventory levels Holding costs
Accepting back orders Back order costs
Subcontracting others Subcontracting costs

Outputs of Aggregate Planning
 Total cost of a plan
 Projected levels of
Inventory held
Output from
 Regular time, overtime
Employment
Subcontracting

Graphical Method
 Popular techniquePopular technique
 Easy to understand and useEasy to understand and use
 Trial-and-error approaches that doTrial-and-error approaches that do
not guarantee an optimal solutionnot guarantee an optimal solution
 Require only limited computationsRequire only limited computations

Graphical Method
Month Expected
Demand
Production
Days
Demand /
day
Avg. daily
demand
Jan 900 22 41 50
Feb 700 18 39 50
March 800 21 38 50
April 1200 21 57 50
May 1500 22 68 50
June 1100 20 55 50
6,200 124

Graphical Method
Note: Forecast differs from average demand

Aggregate Planning Techniques
 Two pure forms of aggregate planning
strategies
Level Production
Maintain constant workforce and
adjust inventory
Chase Demand
Hiring and Firing people

Aggregate Planning Techniques
 Mixed Strategy
 Combination of
 Overtime, under time, & subcontracting
 Part Time employees
 Hiring and firing
 Inventory
 Backordering
Note: When one alternative: Pure Strategy
When two or more are selected: Mixed strategies

Level Production Strategy
 It is an aggregate planning in which monthly production
is uniform
 Requires no overtime, no change in work force levels,
and no subcontracting
 Toyota and Nissan follow this strategy
 Finished goods inventory go up or down to buffer the
difference between demand and production
 Works when demand is stable

LEVEL PRODUCTION STRATEGY
Assume begin inventory: 2000

Chase Production Strategy
 It attempts to achieve output rates that match demand
forecast for that period.
 This strategy can be accomplished by:
 Vary workforce levels (hiring and firing)
 Service businesses use because they don’t have the
option to build inventory of their product

Chase vs. Level
Chase Approach
 Advantages
 Investment in inventory
is low
 Labor utilization in high
 Disadvantages
 The cost of adjusting
output rates and/or
workforce levels
Level Approach
 Advantages
 Stable output rates and
workforce
 Disadvantages
 Greater inventory costs
 Increased overtime and
idle time
 Resource utilizations vary
over time

Mixed Strategy
 For most firms, neither a chase strategy
nor a level strategy is likely to prove ideal,
so a combination of options must be
achieved to meet demand and minimize
cost
 More complex than pure ones but typically
yield a better strategy

Linear Programming
Approaches to AP
 Finds minimum cost solution related to
regular labour time, overtime,
subcontracting, caring inventory, and
costs associated with changing the size of
workforce

Mathematical Techniques to
Aggregate Planning
 Linear Programming
Optimal solutions
Cost minimization
Profit maximization
 Appropriate when cost and variable
relationships are linear
 Application in industry limited

Transportation Method
(An Example)

Total Costs
Period Demand Regular
Production
Overtime Subcontract End
Inventory
1 900 1000 100 0 500
2 1500 1200 150 250 600
3 1600 1300 200 500 1000
4 3000 1300 200 500 0
Total 7000 4800 650 1250 2100
Total Cost: 4800×$20+650×$25+1250×$28+2100×$3 = $153,550

Transportation Method
(Second Example – Prob 7)

Transportation Method: Cost of
Plan
 Period 1: 50($0)+300($50)+50($65)+50($80)=$22,250
 Period 2: 400($50)+50($65)+100($80)=$31,250
 Period 3: 50($81)+450($50)+50($65)+200($80)=$45,800
 Total Cost: $99,300

Simulation Models in AP
 Development of computerized model under
variety of conditions to find reasonably
acceptable solutions
 Advantages
 Lends itself to problems that are difficult to solve
mathematically
 Experimenting system behaviour without any risk
 Compresses time to understand system
 Understand system behaviour under wide range of
conditions

Simulation Models in AP
 Limitations
Simulation does not produce optimal
solutions, it merely indicates approximate
behaviour for a set of inputs
Simulations are based on models, and
models are only approximation of reality

Summary of Aggregate
Planning Techniques
Technique Solution
Approach
Characteristics
Spreadsheet Heuristic (trial and
error)
Intuitively appealing,
easy to understand,
solution not optimal
Linear Programming Optimizing Computerized
Simulation Heuristic (trial and
error)
Computerized
models can be
examined under
various scenarios

Scheduling
 Specifies when labour, equipment, and
facilities are needed to produce a product
or a service
 Scheduling deals with timing of
operations
 Scheduling occurs in every organization

Gantt Progress ChartGantt Progress Chart
Plymouth
Ford
Pontiac
Job 4/20 4/22 4/23 4/24 4/25 4/264/214/17 4/18 4/19
CurrentCurrent
datedate
Scheduled activity time
Actual progress
Start activity
Finish activity
Nonproductive time
Gantt Progress Chart for an Auto Parts Company

Gantt Workstation ChartGantt Workstation Chart
Gantt Workstation Chart for Hospital Operating Rooms

Dealing with the Problem Complexity
through Decomposition
Aggregate Planning
Master Production Scheduling
Materials Requirement Planning
Aggregate Unit
Demand
End Item (SKU)
Demand
Corporate Strategy
Capacity and Aggregate Production Plans
SKU-level Production Plans
Manufacturing
and Procurement
lead times
Component Production lots and due dates
Part process
plans
(Plan. Hor.: 1 year, Time Unit: 1 month)
(Plan. Hor.: a few months, Time Unit: 1 week)
(Plan. Horizon.: a few months, Time Unit: 1 week)
Shop floor-level Production Control
(Plan. Hor.: a day or a shift, Time Unit: real-time)

Reasons for Planning for Short-
Term
 Additional information becomes available
 Order cancellation, new orders, terms of existing orders
 Random occurrence of events
 Breakdown of machines, absenteeism, delays in raw material
supply, revision of job priorities
 Fine tune planning and decision making
 Focus on micro-resources
 Single machine, set of workers and so on
 Such focus is neither possible nor warranted in medium or lon-
term planning

Scheduling
 Scheduling takes place in
High-volume systems
Intermediate-volume systems
Low-volume systems

Scheduling
 Categorize scheduling techniques as
Forward scheduling
Backward scheduling

Scheduling Techniques
 Forward Scheduling
Refers to situation in which the system takes
an order and then schedules each operation
that must be completed forward
 Applications
 Hospitals and clinics
 Fine-dining restaurants
 Machine tool manufacturers
 For special machines

Backward Scheduling
 Backward Scheduling
Starts from some date in future (due date)
and then schedules the required operations in
reverse sequence
Applications
 Assembly programs in manufacturing
 Holding conferences
 Scheduling surgery
 Marriages

246
Forward Vs. Backward Scheduling
Start processing when order is received regardless of due date
Schedule the job’s last activity so it is finished right before the due date

Objectives of Scheduling
 Meeting customer due dates
 Minimizing job lateness
 Minimizing response time
 Minimizing time in system
 Maximizing machine or labour utilization

Job Shop Scheduling
 Job shop scheduling also known as production
control or shop floor control
 Responsibilities of production control dept. are
 Loading
 Sequencing
 Dispatching
 Monitoring
 Preparing various reports (scrap, performance,
rework)

Loading
 Loading is a capacity control technique
that decides which jobs to assign to which
work centers

Loading Work Centers
 Infinite loading
 Finite loading

Sequencing
 When more than one job is assigned to a
machine or activity, the operator needs to
know the order in which to process the
jobs. The process of prioritizing jobs is
called sequencing

Dispatching
 Administrative process of releasing of a work
order from the production planning department
to production authorizing processing of jobs
 Shop paperwork

Monitoring
 Maintaining progress on each job until
completed

Priority Rules for Job Sequencing
(n Jobs on One M/c)
 Single Dimension Rules
First Come First Served (FCFS)
Shortest Processing Time (SPT)
Earliest Due Date (EDD)
Longest Processing Time (LPT)
Smallest Critical Ratio

Performance measures
 Flow time: Length of time a job is at a particular
work station (Processing time + Transport time +
any waiting due to breakdown, parts non-
availability, quality problems etc.)
 Makespan: Total time needed to complete a
group of jobs. It is the time between start of the
first job in the group and the completion time of
the last job in the group

Performance Measures
 Job Tardiness is the difference between a
late job’s due date and its completion time

Metrics
 Average flow time per job
 Utilization
 Average job tardiness
 Average # jobs in the system (WIP)

Sequencing (An Example)
Job Processing
Time (days)
Job Due Date
A 6 8
B 2 6
C 8 18
D 3 15
E 9 23

FCFS Job Seq
(1)
Proc Time
(days)
(2)
Flow Time
(days)
(3)
Job Due
Date (4)
Job
Tardiness
(3) - (4)
A 6 0+6 = 6 8 0
B 2 6+2 = 8 6 2
C 8 8+8 = 16 18 0
D 3 16+3 = 19 15 4
E 9 19+9 = 28 23 5
TOTAL 28 77 11
AVG. 77/5 =15.4
days
11 / 5 = 2.2
days
FIRST COME FIRST SERVED (FCFS)

Metrics
 Avg. flow Time = Sum of total flow time / # jobs = 77 /5 =
15.4 days
 Utilization = Total proc. time / Sum of total flow time
28 / 77 = 36.4%
 Avg # jobs in system = Sum of flow time /
Total job processing time
77 days / 28 days = 2.75 jobs
 Avg job tardiness = Total late / # jobs = 11 / 5 = 2.2 days

SPT Job Seq
(1)
Proc Time
(2)
Flow Time
(3)
Job Due
Date
(4)
Job
Tardiness
(3-4)
B 2 0+2 =2 6 0
D 3 2+3=5 15 0
A 6 5+6 =11 8 3
C 8 11+18
=19
18 1
E 9 19+9 =28 23 5
Total 28 65 9
SMALLEST PROCESSING TIME (SPT)

SPT Metrics
 Avg. flow time = 65 / 5 = 13 days
 Utilization = 28 / 65 = 43.1%
 Avg. # jobs in the system = 65 / 28 = 2.32
jobs
 Avg job lateness = 9 / 5 = 1.8 days

EDD Job Seq
(1)
Proc Time
(2)
Flow Time
(3)
Job Due
Date
(4)
Job
Tardiness
(3-4)
B 2 2 6 0
A 6 8 8 0
D 3 11 15 0
C 8 19 18 1
E 9 28 23 5
TOTAL 28 68 6
EARLIEST DUE DATE (EDD)

LPT Job Seq Proc Time Flow Time Job Due
Date
Job
Tardiness
E 9 9 23 0
C 8 17 18 0
A 6 23 8 15
D 3 26 15 11
B 2 28 6 22
TOTAL 28 103 48
Longest Processing Time (LPT)

Sequencing
Rule
Avg. Flow
Time
Util. (%) Avg. #
jobs in
system
Average
tardiness
(days)
FCFS 15.4 36.4 2.75 2.2
SPT 13.0 43.1 2.32 1.8
EDD 13.6 41.2 2.43 1.2
LPT 20.6 27.2 3.68 9.6

Critical Ratio (CR)
Time Remaining until due date
CR = ----------------------------------
Workdays remaining
Due Date – Today’s Date
CR =-----------------------------
Workdays remaining (remaining processing time)

Critical Ratio (CR)
 If CR < 1.0, Job falling behind schedule
 If CR = 1.0, Job on schedule
 If CR > 1.0, Job ahead of schedule

Priority Rule (FCFS)
 Advantages
 For service systems
 Dominant priority rule
 Appear fair to
customers
 Simplicity
 Disadvantage
 Long jobs will tend to
delay other jobs

Priority Rule (EDD)
 Advantages
 Addresses due dates
 Intuitively appealing
 Minimizes tardiness
 Disadvantages
 Ignores processing
time
 Long waiting for other
jobs
 Shop congestion
 High In-process
inventories

Priority Rules (SPT)
 Advantages
 Lowest avg.
completion time
 Lower WIP
 Lower tardiness
 Better customer service
levels
 Lowest avg. # jobs in
the system
 Less congestion
 Ideal where shop is
highly congested
 Disadvantage
 Tend to make long
jobs wait
Solution- truncated
SPT

Sequencing
(n Jobs on 2 Machines)
 Johnson’s Rule
Objective is to minimize processing time for
sequencing a group of jobs through two work
centers
Developed by S M Johnson in 1954 for job
shop scheduling

Examples (2 work centres)
 A book binding operation where books
must first pass through binding before
going to trimming
 Finished products must pass through
inspection before packaging
 A medical clinic where patient goes for
registration and then consulting

Steps – Johnson’s Rule
1. All the jobs are to be listed, and the time that
each requires on a machine is to be shown. Set
up a one-dimensional matrix to represent the
desired sequence with the number of slots
equal to # of jobs
2. Select the job with the shortest activity time. If
the shortest time lies with the first machine, the
job is scheduled first. If the shortest time lies
with the second machine, schedule the job last.

Steps – Johnson’s Rule
3. Once a job is scheduled, eliminate it
4. Repeat steps 2 and 3 to the remaining jobs until all the
slots in the matrix have been filled or all jobs have
been sequenced
5. If a tie for the shortest processing time occurs in the
same work station, the competing two job sequences
need to be evaluated by comparing cumulative
processing times. The lowest cumulative processing
time would be the recommended sequence

Johnson’s Rule (Conditions)
 Job time (set up + proc time) must be known
for each work center
 All jobs follow same two-step sequence
 All units in a job must be completed at the first
work center before moving to second work
center

Johnson’s Rule
(An Example)
Jobs Work Center 1
(hrs)
Work Center 2
(hrs)
A 5 2
B 3 6
C 8 4
D 10 7
E 7 12

Johnson’s Rule
A
B A
B C A
B E D C A
1.
2.
3.
4.

Johnson’s Rule
Work Center 1
Work Center 2
3 7 10 8 5
6 12 7 4 2
B E D C A

Johnson’s Rule
Gantt Chart
Makespan – 35 hours

Johnson’s rule – 3 work centres
 Three work centres is an extension of the previous
model (2 work-centres)
 Examples
 A book binding operation where books pass through
printing and binding before going for trimming
 Finishing products, which pass through inspection,
painting, before going to packaging
 A medical centre where patients see a doctor, pass
onto x-ray, and then consult a specialist

 Johnson’s rule can be applied if either of
the following two criteria applies:
 The smallest time at the first processing operation is
at least as great as the largest duration on the second
processing operation
 The smallest duration on the third processing
operation is at least as great as the largest duration
on the second operation.

Beauty Products Pre-preparation
(hour)
Preparation
(hour)
Finishing
(hour)
Baby Blue 7 1 3
Virgin White 6 4 2
Shy Pink 8 5 4
Daring Purple 9 2 5
Sensuous Black 10 3 7
Minimum of 1st
operation, i.e., 6 >= maximum of second operation, i.e., 5
Therefore, Johnson’s rule can be applied

Beauty products Work centre 1
Operation time (hour)
Work centre 2
Operation time (hour)
Baby Blue (BB) 7+1 = 8 1+3 = 4
Virgin White (VW) 6+4 = 10 4+2 = 6
Shy Pink (SP) 8+5 = 13 5+4 = 9
Daring Purple (DP) 9+2 = 11 2+5 = 7
Sensuous Black (SB) 10+3 = 13 3+7 = 10
Apply Johnson’s rule with two work centres
Sequence: SB SP DP VW BB

Scheduling a Set Number of Jobs on
the Same no. of Machines
 Some work centres have enough of the right kinds of
machines to start all jobs at the same time
 Assignment Method (special case of transportation
method)
 There are n “things” to be distributed to n “destination”
 Each thing must be assigned to one and only one
destination
 Only one criteria can be used (min cost or max profit)

Assignment Method
Job A B C D E
I Rs 5 Rs 6 Rs 4 Rs 8 Rs 3
II Rs 6 Rs 4 Rs 9 Rs 8 Rs 5
III Rs 4 Rs 3 Rs 2 Rs 5 Rs 4
IV Rs 7 Rs 2 Rs 4 Rs 5 Rs 3
V Rs 3 Rs 6 Rs 4 Rs 5 Rs 5
Five jobs, 5 machines, Cost of each job given. Devise min cost assignment.

Shop Configuration
 Refers to the manner in which machines
are organized on the shop floor and the
flow pattern of the jobs utilizing these
machines
 Two alternative configurations
Flow shop
Job shop

Introduction-Elements of the Job Shop Scheduling Problems
An assembly line is a classic example of flow shop
 Every car goes through all the stations one by one in the same
sequences;
 Same tasks are performed on each car in each station;
 Its operations scheduling is simplified as assembly line balancing;
 An assembly balancing problem is to determine the number of stations
and to allocate tasks to each station.
Flow shop:
 Each of the n
jobs must be
processed
through the m
machines in the
same order.
 Each job is
processed
exactly once on
each machine.

A Pure Flow Shop
As there are n jobs, there are n! ways in which one can draw up
alternative schedules in the shop
In flow shop resources are organized one after another in the order the jobs are
processed
Since all jobs follow the same order of visiting machines, the scheduling function
Is essentially reduced to one of ordering the jobs in front of the first machine.

290
Job Shop
 Low volume job shop operations are
designed for flexibility
 Each product or service may have its own
routing (scheduling is much more difficult)
 Bottlenecks move around depending upon
the products being produced at any given
time

Introduction-Job Shop
A job shop is organized by machines which are grouped according to their
functions.

Introduction-Job Shop
Not all jobs are assumed to require exactly the same number of
operations, and some jobs may require multiple operations on a single
machine (Reentrant system, Job B twice in work center 3 ).
Each job may have a different required sequencing of operations.
No all-purpose solution algorithms for solving general job shop problems
;
Operations scheduling of shop floor usually means job shop scheduling;
Job A
Job B

Job Shop
Since there are n! ways of rank-ordering jobs in front of a machine and since
there are m machines in the shop, and all jobs are processed on all machines,
the number of alternatives that one can draw for a job shop is given by (n!)m
Job 1: 1-4-2-5-6
Job 2: 3-2-1-4-6-7
Job 3: 2-3-4-7-5-6

Scheduling n jobs on m machines
 Number of alternative schedules (n!)m
 Complex
 Likely solution - Simulation

Some Insights
 Bad news
Real world > 2 machines
Process times are not deterministic
Real world production scheduling problems
are hard
 Hard to find optimal solutions to realistic size
scheduling problems
 Far from exact science

Minimizing Scheduling
Difficulties
 Good News
Setting realistic due dates
Focus on bottlenecks
 Schedule this resource and propagate the
schedule to non-bottleneck resource

Bottleneck Scheduling
 Common approach
Simplify problem by breaking into pieces
 Scheduling bottleneck stations and then
propagating that schedule to non-bottleneck
stations

Case
 Old Oregon Wood Store

Video
 Scheduling – United Airlines

Minus-Cost Principle
Cost + Profit = Selling Price
Profit = Price – Cost

Toyota Production System
(Lean Manufacturing)
 Taiichi Ohno (1912-1990), Toyota
executive pioneered the concept
To do more and more with less and less
 Less human effort
 Less equipment
 Less time
 Less space
 Less capital

System for absolute elimination of waste
80% waste elimination
15% production system
5% kanban
Drive out waste so that all work adds value and satisfies
customer’s need

Lean Production
(Levels of Abstraction)
 Lean production has been described at
three levels
1. Philosophical perspective
A. Elimination of waste (Womack and
Jones,1996)
2. Implementation of tools and techniques
3. System design using three rules

What is Waste?
 Waste is defined as any activity that does
not add value to a product from
customer’s perspective
 Fujio Cho, Toyota’s president defined
“Anything other than the minimum amount of
equipment, materials, parts, and workers
essential for production”

Seven Categories of Muda
 Muda means Waste
1. Overproduction
2. Unnecessary Inventory
3. Transportation
4. Over Processing
5. Waiting
6. Unnecessary motion
7. Product Defects

The “Rocks in the Stream”
Concept
Production Problems

Lowering the “Water” Level
Production Problems
Inventory
Reductions
CRUNCH!

How Time is Spent by a Typical Part in a
Batch Production Machine Shop
Time on M/c
5%
Moving and Waiting
Time in
factory
Time on m/c
30% 70%
Cutting Loading, positioning,
gauging
95%

Class Exercise
 Students identify waste in their
organization

Wastes in IT Sector
 How long did you wait to start a scheduled
meeting?
 How many reports you created that nobody
read?
 How much time you waited for a decision from
your superior?
 How much rework you did while developing the
software?

Activities
 Value-added
Makes a product more complete
 Non-value-added
Does not add value in the customer’s eyes
and customer unwilling to pay
 Required non-value-added

Value-added Activity
 An activity that makes a product a more
complete product, in the eyes of the customer
 The value is defined from customer’s point of
view
 End result is the receipt of cash for our actions

Required Non-Value Added
Activity
 Activity for which the customer is likely to
pay
 We can change and improve the method
of performing these activities

Non-Value Added Activity
 The activity that consumes time and resources
but does not advance the product to a more
complete or finished state. Adds no value in
the customer’s eyes and that customer is
unwilling to pay for
 Seven categories of waste
 Overproduction, unnecessary motion, transport,
process, waiting, unnecessary motion

Basic Words
 Seven forms of waste composed of non-
value added activities, add cost
 The value added activities, generate
revenues

Conversion TimeConversion Time
Value-added
Start of production
for a single item
Components ofComponents of
Lead TimeLead Time
Components ofComponents of
Lead TimeLead Time
Nonvalue-added
Wait TimeWait Time Move TimeMove Time Down TimeDown Time
End of production
for a single item
Total Lead Time

Relationship Between SetupRelationship Between Setup
Times and Lead TimesTimes and Lead Times
Relationship Between SetupRelationship Between Setup
Times and Lead TimesTimes and Lead Times
LongLong
SetupSetup
TimesTimes
LargeLarge
BatchBatch
SizesSizes
LargeLarge
InventoryInventory
Longer Lead Times

Value Stream Mapping
 Process mapping tool that enables all
stakeholders of an organization to
visualize and understand a process
 To differentiate value from waste
 Eliminate waste
Chinese Proverb: “One picture is worth ten thousand words”

Value Stream Map
Walking and drawing the processing steps
(material and information) for one
product family from door to door in your
plant

Value Stream Mapping
To maximize value and eliminate waste
1. Form inter-disciplinary team
2. Mapping the current key process how it actually
operates
 Identify value added and non-value added activities
 Eliminate non value added activities using Kaizen
(continuous incremental improvement)
1. Develop future state value stream map

Takt Time
Available work time
per day
Takt Time = --------------------------------
Customer demand rate
per day

Ways to Eliminate NVAs
 Rearranging sequence
 Consolidating process steps
 Changing work methods
 Change type of equipment
 Redesigning forms and documents
 Improving operator training
 Eliminate unnecessary steps

 Multiple explanations for Toyota’s
success:
Elimination of waste
Using specific tools for production
Design Rules

Lean – Tools and Techniques
1. Pull Systems
2. Cellular Layout
3. Uniform Plant Loading (Heijunka)
4. Small lot sizes
5. Minimized set-up times
6. Kanban Systems
7. Quality at source (Poka-Yoke)
8. Flexible Resource
9. Total Productive maintenance
10. 5S

1. Continuous Flow
(One-piece flow)

1. Traditional vs. Lean
Approach

1. Pull vs. Push (Traditional)
 Pull Method: A method where customer demand
activates the production of service or item. Work
releases are authorised
 Push Method: A push method where the
production of the item begins in advance of
customer needs. Work releases are scheduled

Push vs. Pull
 Show Video
VTS_02_1.VOB

2. Cellular Layouts
 Cells group dissimilar machines to
process parts with similar shapes or
processing requirements

2. Cellular Layout
Process (Functional) LayoutProcess (Functional) Layout Group (Cellular) LayoutGroup (Cellular) Layout
Similar resources placed
together
Resources to produce similar
products placed together
T T T
M
M M T
M
SG CG CG
SG
D D D
D
T T T CG CG
T T T SG SG
M M D D D
M M D D D
A cluster
or cell

3. Uniform Plant Loading
(Heijunka)
Mixed model production

LEVELLED PRODUCTION
Levelled production means producing various models on the same production line to cater
the customer demand. See the following diagram. The various products are shown in the
form of different geometrical shapes. Assume they are different models of vehicles being
produced on the same production line.
Production leveling is done by finding the ratio of demand of various models. Instead of
producing batches of the same model, mix models are produced on the same production
line according to the ratio of their demand in the market.
This is how customers do not have to wait for long and throughout the month all the
customers are served equally well

Uniform Plant Loading (Maruti)

4. Small Lots
 Use lot sizes as small as possible
 Advantages
Average level of inventory less
Pass through the system faster
Quality problems are detected fast
Easier to schedule
 Disadvantage
Multiple set ups

5. Minimized Set up Times
 Small lot sizes to make mixed models
 Japanese workers: 800 T, time: 10 mins
 US workers time: 6 Hrs
 German workers time: 4 Hrs
 Set Ups
 Internal (Done when m/c is stopped); disruptive
 External (Done when m/c is running)
 Convert internal to external set ups
 Abolish the setup itself (uniform product design)
 Single Minute Exchange of Dies (SMED)

Video
 Internal and External set up
VTS_02_2.VOB

7. Quality at Source
 Emphasis on eliminating defects at their origination points
 Workers act as inspectors
 Jidoka (the authority of the workers to stop the line if quality problems
encountered)
 Andons or call lights
 Each worker given access to andons to seek help.
 Visual control of quality
 Poka-Yoke
 Are either warnings that signal existence of a problem or controls
that stop production until the problem is resolved
 Minimize human errors
 http://facultyweb.berry.edu/jgrout/everyday.html

Errors in Service
Service Error
Server Errors Customer Errors
(67%) (33%)

Classifying Service Poka-Yokes
Server Errors
Task:
Doing work incorrectly
Treatment:
Failure to listen to
customer
Tangible:
Errors in physical
elements of service (dirty
waiting rooms, unclear
bills)
Customer Errors
Preparation:
Failure to bring necessary
materials before the
encounter
Encounter:
Failure to follow system flow
Resolution:
Failure to signal service failure
Failure to execute post
encounter actions

8. Flexible Resource
 Multifunctional workers
 General purpose machines

9. Total Productive Maintenance
(TPM)
 Eliminating causes of machine failure
 Maximizing effectiveness of machine throughout
its entire life
 Involving everyone in all departments and at all
levels
 TPM develops a maintenance system
 Central to TPM is the concept of Overall
Equipment Effectiveness (OEE)

Overall Equipment
Effectiveness(OEE)
 OEE =
Availability Rate * Performance Rate * Quality Rate
 OEE captures six big losses which result
in reduced effectiveness of using an
equipment

OEE
 Availability: % of scheduled time that the
operation is available to operate. Often
referred to as Uptime.
 Performance: Speed at which the work
centre runs as a % of designed speed
 Quality: Good units produced as a % of
total units produced

OEE
 Can be applied to any individual work
centre or rolled up to department or plant
levels

10. 5 Elements of 5S
1. Sort: Remove all unnecessary material
and equipment
2. Straighten: Make it obvious where
things belong
3. Shine: Clean everything, inside and out
4. Standardize: Establish policies and
procedures to ensure 5S
5. Sustain: Training, daily activities
Note: Some add 6th
S for “safety”

4S: Place for Cleaning Supplies

 Multiple explanations for Toyota’s
success:
Elimination of waste
Using specific tools for production (SMED,
Poka Yoke)
Design Rules

TPS
 Spear and Bowen article

(Design Rules)
 Design Rules to design work processes
Activity
Connections
Pathways

Rule 1: Activity
 All work shall be highly specified as to
Content
Sequence
Timing
Outcome
Specified Tasks

Rule 2: Connections
 Every customer-supplier connection must
be direct and there must be an
unambiguous yes-or-no way to send
requests and receive responses
Streamlined communication

Rule 3: Pathways
 The pathway for every product and service
must be simple and direct
Simple process architecture

Rule 4: Scientific Problem Solving
 Any improvement must be made in
accordance with the scientific method,
under the guidance of a teacher, at the
lowest possible level in the organization
Hypothesis-driven problem solving

Backslide
What usually happens
Time
Improvement
Backslide
Backslide
“Actual”
If worked to the
new standards
Innovate
Innovate
Adapted from: Imai, “Kaizen”

Basic Structure and Flow of A3
Report

A3 Problem Solving: The Toyota Way

5 Whys Approach
 A workstation starved for work
Why starved? A pump failed
Why pump failed? It ran out of
lubricant
Why it ran out of lubricant? A leaky
gasket not detected
Why leaky gasket not detected?
Lack of training

Three Rules
 What kinds of wastes are eliminated?

Questions
 Do principles of lean production apply to
knowledge work?
 How can we extend the existing
framework of lean production to a new
context that differs substantially from that
in which lean was observed?

Video
 Gortrac – Process Improvement2

Video
 Flexible Manufacturing Strategy

History of Quality Management
 Rooted in Post-World war II Japan
 Japanese in an effort to build their nation adopted the US
manufacturing practices
 Embraced and suppported the work of two American
researchers: Joseph Juran (1904-2008) and W Edwards
Deming (1900-1993)
 Juran blamed the culture of the firm and management for
poor quality
 Deming developed SPC for industries
 Japanese industry leaders embraced the idea that efforts
to improve quality can actually reduce costs

History of Quality Management
 By 1970s and 1980s, US market was invaded by
Japanese electronic and automobile products
 Toyota was already using advanced quality management
system, and TPS became the international superstar of
manufacturing practice
 In late 1980s, Motorola developed the Six Sigma (SS)
approach, others (GE, Seagate, AlliedSignal) adopted
SS
 TQM, another well-known method adopted by industry

Performance and Conformance
 Successful quality management requires
managers to understand what constitutes
quality for the customer
 Firms need to identifying the needs of the
customers (internal or external) and
provide a product or service that will
satisfy or exceed their expectations

Performance and Conformance
 Different kinds of quality
 Performance quality
 Refers to the ability of the product to excel along one
or more performance dimensions (“attributes”)
 Conformance quality
 Because of inherent variability in production
processes, nothing is produced exactly according to
specifications. The degree of match between
specifications and the actual product or service is
what we call as conformance quality

Quality Article
 “Competing on eight dimensions of
quality” (Harvard Business Review, Nov-
Dec 1987) by David Garvin

Dimensions of Quality:
Manufactured Products
 Performance – primary product characteristics
 Features – secondary characteristics
 Reliability – How often does the product fail?
Consistency of performance
 Conformance to standards – meeting design
specifications
 Durability – How long the product lasts; its life span
before replacement
 Serviceability – ease of repair, speed of repair
 Aesthetics – sensory characteristics (sound, feel, look)
 Perceived Quality – past performance, reputation,
recognition

Article – Key Points
 Eight dimensions of quality
 Companies need not pursue all eight
dimensions
If pursued, products become costly
 Companies need to find what dimensions
customers care for and work on those
dimensions
Proper market research is key

Some Quality Issues in Recent
Times – Indian companies
 Safety features in Indian made passenger
vehicles
Five Indian made hatchbacks failed in New
Car Assessment Program (NCAP) Test
 Banning of Indian drugs in US for some Indian
pharmaceutical companies for poor
manufacturing practices
Ranbaxy, Wockhardt, RPG Life Sciences and
many

Quality Gurus
 Walter Shewart
 W. Edward Deming
 Joseph Juran
 Armand V. Feigenbaum
 Philip Crosby
 Kaoru Ishikawa
 Taguchi

Key Contributors to Quality
Management
Shewart Control Charts
Deming 14 points, special vs. common cause
variation
Juran Quality is fitness-for-use
Feigenbaum Customer defines quality
Crosby Quality is free, zero defects
Ishikawa Cause-and-effect diagrams
Taguchi Taguchi loss function
Ohno and Shingo Continuous improvement

Modern Definition of Quality
 Quality is inversely proportional to variability
Reduction of variability is the fundamental idea in quality
control.

Describing Variability
 Measures of variability (or spread out)
Range
Variance and the standard deviation
Stem-and-leaf plot
Histogram
Box Plot
Coefficient of variation

Quality Improvement
 Quality improvement is the reduction of
variability in processes and products

Describing Variability
 Stem-and-leaf display (Graphical display about a data
set)
 Shape
 Spread
 Central tendency
 Box Plot (Graphical Display)
 Central tendency
 Spread or variability
 Departure from symmetry
 Identification of outliers
 Histogram
 Same as above

Coefficient of Variation
 Coefficient of Variation, c = σ / µ
Where σ = standard deviation
µ = mean
 If c<0.75 , low variability
 If 0.75 <= c <=1.33, moderate variability
 If c >= 1.33, High variability

Approaches to Quality
Assurance
Acceptance
Sampling
Process Control
Continuous
Improvement
The least
progressive
The most
progressive
Inspection before/
After production
Inspection and
corrective action
during production
Quality built in
the process

Acceptance Sampling and
Process Control
TransformationInputs Output
Acceptance
Sampling
Process control
Acceptance
Sampling
Inspection before and after production often involves acceptance sampling
Procedures; monitoring during the production process is referred to as process
control

Acceptance Sampling
 In acceptance sampling, managers take
two key decisions
When in the process to conduct inspections
How rigorously to test
 Frequency of inspection
 How many products to test each time

When in the Process to Inspect?
 Raw materials and purchased parts
 Finished products
 Before a costly operation or where
significant value is added to the product
 Before an irreversible process
 Before a covering process

How Much to Inspect and How
Often?
 The amount of inspection can range from no inspection
whatsoever to inspection of each item.
 Low –cost, high volume items require less inspection
 High-cost, low volume items require intensive inspection
 Majority of the quality control applications lie somewhere
between the two
As a rule, operations with high proportion of human involvement necessitate
more inspection than mechanical operations

Costs of Quality
 Prevention Costs (costs associated with tasks intended to prevent
defects from occurring)
 Quality Planning (developing & implementing quality
management program)
 Process monitoring
 Training
 Purchasing better equipment that produces less variation
 Working with vendors to increase the quality of input materials
 Process redesign to reduce errors
 Quality data acquisition and analysis
 Quality improvement projects

Costs of Quality
 Appraisal Costs (assessing the condition of
materials and processes at various points in
process)
Inspection and testing of incoming materials
Product inspection and test at various stages
Maintaining accuracy of test equipment
(calibration)
Laboratory testing
Costs of quality estimated to be between 15%-20% of sales at most companies
Crosby

Cost of Quality
 Internal failure costs (defects discovered before shipment)
 Scrap
 Rework
 Process downtime
 Retest
 Failure analysis
 Disposition
 External failure costs (defects discovered after shipment)
 Customer complaint
 Warranty charges
 Liability costs
 Returned product/material
External and internal failure costs together accounted for 50%-80% of COQ
Juran

Quality Cost Trend Prediction
as a Function of Time

Cost of Quality
It is estimated that the cost to fix a problem at the customer end is about 5 times the
cost to fix a problem at the design stage

Cost of Quality
Ce + Ci + Ca + Cp
 Cost of Quality= --------------------------------------
Cb + Ce + Ci + Ca + Cp
Ce = External failure cost
Ci = Internal failure cost
Ca = appraisal cost
Cp = prevention cost
Cb = measured base production cost ( no costs for quality)

Consequences of Poor Quality
 Loss of business
 Liability
 Productivity
 Costs

Process Control
 Starts with measuring an important
variable. This can be a
Product attribute
 Diameter of a metal component, weight of a bag of
potato chip
Process Attribute
 Temperature in a restaurant’s oven, length of
waiting time in a ticket booth, pressure applied in a
molding process

Statistical Process Control
(SPC)
 A statistical process control involves testing a random
sample of output from a process to determine whether the
process is producing items within a pre-selected range
 SPC uses statistical tools to observe the performance of the
production process in order to detect significant variations
before they result in the production of a sub-standard article.
 SPC is about monitoring consistency and repeatability of a
process

Major Objectives of SPC
 Quickly detect the occurrence of
assignable causes of process so that
investigation of the process and corrective
action may be undertaken before non-
conforming units are manufactured
 Reducing variability in the process

Why Quality Problems?
 Variation due to two reasons
Common Cause or random variation
Assignable or Special cause or controllable
variation

Statistical Process Control Tools
(SPC)
 Variation in output is due to:
 Common causes (also known as natural variation)
 Inherent variation present in every process
 Causes may difficult to distinguish or wholly
unidentifiable
 Resulting degree of variation is minor
 Assignable causes (known as special variation)
 Variations due to specific causes
 A process subject to assignable variation is out of control

Statistical Process Control
Tools (SPC)
 Control (or in control or stable)
A process that exhibits only common cause
variation is said to be in control or stable
 A process is said to be out of control when
it exhibits assignable variation
Examples: less experienced worker has
replaced an experienced worker, machine
malfunctioning, change of machine settings

Common Cause & Assignable
Causes ( A Game)
 Writing “R” with right hand (one line)
 Writing “R” with left hand (one line)

Common Cause and Assignable
Cause Variation

Natural and Assignable Variation

Process Control: Three Types of Process Outputs

Relationship Between Population and Sampling
Distribution

Control Charts
 A control chart is a time ordered plot of sample statistics
 Sometimes called “the voice of the process”
 Graphical display of a quality characteristics (for example, level of
beer in each bottle in a bottling plant)
 Distinguish between random and non-random variability
 Chart contains a center line and two limits
 Upper control limit
 Lower control limit
 If the process is in control, all sample points will fall between them
 As long as points fall within control limits – the process is in
statistical control
 However, any point outside limits – investigate the assignable
causes

Control Charts
 If all the points plot inside the limits, but
behave in a nonrandom manner –
indication that process is out of control
and needs investigation

In Statistical Control
 A process that is operating with only
chance cause of variation present is said
to be in statistical control
 If the process is in control, all the plotted
points should have an essentially random
pattern

Reasons for Popularity of Control
Charts
 Proven technique for improving
productivity
 Effective in defect prevention
 Prevents unnecessary process adjustment
 Provides diagnostic information
 Provides information about process
capability

Statistical Process Control Tools
 Control Charts for variables (Characteristics that are expressed on a
numerical scale: density, weight, diameter, resistance, length, time, volume)
 X-bar Chart and R-Chart
 X-bar chart for process average
 R-chart for process variability
 Control Charts for attributes (characteristic that can’t be measured on a
numerical scale: smell of cologne acceptable or not acceptable, color of a
fabric acceptable or not)
 p-chart and c-chart
 p-charts for percent defective in a sample
 c-charts for counts (e.g. # of defects)

SPC Tools
 Control Charts for variables (X-chart, R-Chart)
Variables data are measured on continuous
scale
 Length
 Width
 Weight
 Voltage
 Viscosity
 Amount of time needed to complete a task

Mean Control Chart (x-bar
chart)
 A mean control chart or x-bar chart can be
computed in one of the two ways.
 Choice depends on what information is
available
If process standard (σ) is known from past
experience or historical data

chart)

chart)
 If the process standard deviation is not known, a
second approach is to use the sample range as
a measure of process variability. The
appropriate formulas for control limits are

R-Chart Control Limits
D3, D4 = constants that provide 3 standard deviations (3D3, D4 = constants that provide 3 standard deviations (3σσ) limits) limits
for a given sample sizefor a given sample size

X-bar Chart Limits
A2 = constant to provide three sigma limits for the sample meanA2 = constant to provide three sigma limits for the sample mean

Steps in developing X-bar and R-
chart
 Collect data on the variable measured (time, weight,
diameter). Collect at least 20-25 samples randomly.
Sample size should be of 4 to 5 units.
 Compute range for each sample, and average R-bar
 Calculate the UCL and LCL
 Plot the sample ranges. If all are in control process,
 Calculate UCL and LCL for x-bar chart
 Plot the sample means. If all are in control, process is in
statistical control.

Control Limits are Based on
Sampling Distribution

Zones for Identification of
Nonrandom Pattern

Pattern Recognition in Control
Charts
 Recognizing non-random patterns on the control
chart
One point plots outside 3σ limits
Two or three consecutive points plot beyond
2σ limits
Four out of 5 consecutive points plot at a
distance of 1σ or beyond from the centre line
Eight consecutive points on one side of centre
line

p-chart
 Control charts for attributes
 p-chart measures % defective items or proportion defective
items in a sample
Total # defects from all samples
 p-bar = ----------------------------------------
# samples × Sample size
 Appropriate when data consists of two categories of items
 Good or bad, pass or fail
 Examples: # bad light bulbs and good light bulbs in a given
lot
 # of bad glass bottles and good glass bottles

c-chart
 Appropriate when number of defects are counted
because not possible to compute proportion defective
 Examples
 Number of accidents per day
 Number of crimes committed in a month
 Blemishes on a desk
 Complaints in a day
 Typo errors in a chapter of the text book
 # customer invoice errors

C-chart Limits
C-bar = average no. of defects per unit = Total number of defects
No of samples

Process Capability
 Specifications: A range of values imposed by designers
of the product or service based on customer
requirements
 Control limits and based on production process, and they
reflect process variability
 Process variability: Natural or inherent variability in a
process due to randomness
 Process capability: The inherent variability of process
output relative to the variation allowed by the design
specifications

Measures of Process Capability
 Measures of Process Capability
 Process Capability Ratio
 Process Capability Index

Process Capability Ratio
 Cp = (Upper Spec – Lower Spec) / 6σ
 If Cp < 1, process range > tolerance range
 Process not capable of producing within design
specifications
 If Cp = 1, Tolerance range and process range are same
 If Cp > 1, Tolerance range > process range
 A desirable situation
 Ideally Cp > 1.33

Process Capability
 Cp does not take into account where the
process mean is located relative to the
specifications
 Cp simply measures the spread of the
specifications relative to the six sigma
spread in the process

Process Capability Index
Generally, if Cp = Cpk, the process is centered at the midpoint of the specifications
When Cpk < Cp, the process is off center

Operations management ii

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