LECTURES
IN
OPERATIONS PLANNING
AND
CONTROL
Prepared by:
MARLUNA LIM URUBIO, Ph. D
Introduction to Operations Planning and Control
Production
=
Factories / Machines / Assembly
From
Production
Management
Manufacturing management which involves
methods/techniques in factory operation.
Whereas,
Operations
Management
Responsible for management of production
systems either for creation of goods or
providing services.
Ex.
For service oriented company, it involves
managing
food service, providing medical
services, housekeeping
etc.
Ex. Managing a factory that involves decisions
on raw
materials, equipment, etc.
Functions within Business Organizations
Operations
Marketing
Finance
Functions overlap and they do not exist independently, but
they interact to achieve the goals and objective of the
organization.
Marketing
-
includes promotion/selling of goods
( demand = supply )
Finance
ensuring funds are available for production
requirement as well as product/ service
promotions.
includes budgeting, analysis of investment
proposal, sales, allocation of funds.
Operation/Production
production of goods, services
it consists of all activities that
are directly related to producing goods or
providing service.
Industrial
Engineering
Maintenance
Purchasing
Operations
Public
Relations
Accounting
Personnel
Accounting – provides data for cost of labor, materials, overhead, scraps,
downtime, inventory
Purchasing – procurement of raw materials
Personnel
–recruitment, training of personnel, labor relations, health,
safety
Public Relations
– building/maintaining image of the organization
(sports fest/cultural events/tours of facilities, etc.)
Industrial Engineering
– productivity/ quality improvement
Maintenance
– general maintenance and repair of equipment
and facilities
Operations Management Function
Main: guide the system thru decision making, especially day today
operating decisions
1. Designing and operating production systems

System design – decisions on system capacity, location of
facilities, arrangement of department, acquisition of
equipment
 usually involves decision that are for long-term
use

System Operation- decision on management of personnel,
inventory planning and control, scheduling, project
management, quality control
Note:
System design essentially determines many of the
parameters of system operation.
PRODUCTIVITY
Productivity is one of the primary concern and responsibility of a
manager, that is to achieve productive use of the organization’s resource.
is an index that measures output ( goods or service ) relative to
the input ( labor, materials, energy and other resources ).
PRODUCTIVITY =
OUTPUT
INPUT
Productivity growth is the increase in productivity from 1 period to the next
relative to the productivity in the preceding period.
Productivity Growth =
Current Period Prod – Previous period Prod
Previous Period Prod
Multifactor Productivity =
Quality of production at standard price
labor cost+ material cost + overhead
Classsifying Production Systems
1. Mass Production –there is large volume of standardized
products/goods, produced by low skilled or semi skilled workers, using
highly specialized and expensive equipment.
2. Lean production - uses minimal amount of resource to produce high
volume of high quality goods with some variety.
3. Craft Production - uses highly skilled workers using simple, flexible
tools to produce small quantities of customized goods
Efficiency
-
getting the most out of a fixed set of resources
Profitability efficiency if a
company or industry generates
earnings.
Profitability is expressed in terms of
several popular number that measure
one of two generic types of
performance “HOW MUCH THEY MAKE
WITH WHAT THEY’VE GOT? “
and
“ HOW MUCH THEY MAKE
FROM WHAT THEY TAKE IN?
“
PRODUCTIVITY
 Increase in output per
work hour or time
expended

Labor productivity
measures output per hour
of labor

Multifactor productivity
measures output per unit
of combined input which
consist of labor and
capital and in some cases,
intermediate outputs
TO ATTAIN PRODUCTIVITY, INDUSTRIAL ENGINEERS MUST
Maximize Profit
Integration of
MAN
MACHINE
MATERIALS
METHODS
THROUGH
EFFECTIVE and
EFFICIENT MEANS
SAMPLE PROBLEM:
Given
:
Solution
:
output produced
Labor hours
-
1,000 pcs
250 hrs
Productivity = units produced/ labor hours
= 1,000 pcs / 250 hours
= 4 pcs / hour
Multifactor Productivity
= output / labor + materials + Energy + Capital + Misc.
Sample Problem:
Collins Title Company has a staff of 4 each working 8 hours per day for a payroll
cost of USD 640/day and overhead expenses of USD 400/day. The company
recently purchased a computerized title search system that will allow processing
of 14 titles/day. Although the staff, their work hours and pay will be the same, the
overhead expenses are now USD 800/day.
Given:
Output
Labor cost
Overhead
No. of Staff
Available hours
:
:
:
:
:
8 titles / day
USD 640/day
USD 400/day
4
8 hours
New output
New Overhead Cost
:
:
14 titles/day
USD 800/day
Labor Productivity ( old system )
=
8 titles/ 4 8 = 0.125 titles/labor-hr
Labor Productivity ( new system )
=
14 titles/ 4 8 = 0.4375 titles/labor-hr
Solution:
Multifactor Productivity ( old system ) =
=
8 titles/ USD 640 + USD 400
0.0077 titles / dollar
Multifactor Productivity ( new system ) =
=
14 titles/ USD 640 + USD 800
0.0097 titles / dollar
Productivity Measures are useful to the following:
1. To track performance over time
2. To determine what has changed and then devise means of improving
productivity in the subsequent periods.
3. To judge the performance of an entire industry or the productivity of a
country as a whole.
Factors that Affect Productivity:
1. Methods ( Simple? Complicated ? )
Example: Bombing of IC in Helium Gas or FC 84
2. Capital
Example: From manual packing to automated packing but
requires capital investment for auto packer
3. Quality
Example: will it be 100% inspection which is time
consuming or just random sampling?
4. Technology
Example: Embroidery which used to be manual can now
be programmed
5. Management
Example: A supportive management will boost morale of
employees
6. Raw Materials
Example: Will production be able to work if RM do not
come on time?
7. Equipment
Example: What will be the output if the machines are too
old and experience downtime?
8. Working Condition/Environment
Example: Will one produce more if the work area is too
hot?
SAMPLE PROBLEMS FOR PRODUCTIVITY
A company that processes fruits and vegetables is able to produce 400 cases
of canned peaches in one half hour with four workers. What is the labor
productivity?
Solution :
Labor productivity = Quality Produced / Labors Hours
=400 cases (4 workers x 1/2 hours / workers)
=200 cases per labor hour
A wrapping paper company produced 2,000 rolls of paper one day. Standard
price is $ 1/roll. Labor cost was $ 160, material cost was $ 50, and overhead
was $ 320. Determine the multifactor productivity.
Multifactor productivity = Quality produced at standard price/Labor cost + Material
cost + Overhead
= 2,000 rolls x $ 1/ $160+ $ 50 + $320
= 3.77 rolls output per dollars
Sample Problem
A. Find the productivity if four workers installed 720 square yards of
carpeting in eight hours.
B. Compute for the productivity of a machine which produced 68 usable
pieces in two hours.
Solution:
A) Productivity = yards of carpeting install
Labors Hours worked
= 720 square yard
4 workers x8 hours / worker
= 720 yards
32 Hours
=22.5 yards/ hours
B) Productivity = Usable Pieces
Production Time
= 68 Pieces
2 hours
= 34 pieces/ hours
Sample Problem
Determine the multifactor productivity for the combined input of the labor and
the machine time using the following data:
Input:
Labor: $ 1,000
Materials: $ 520
Overheads: $ 2,000
Solution:
Multifactor Productivity = Output / Labor + Materials + Overheads
= 1,760 Units / $ 1,000 + $ 520 + $ 2,000
= 0.50 units
Sample Problem
Collins Little Company has a stuff of 4, each working 8 hours per day (for a
payroll cost of $ 640 / day) and overhead expenses of $ 400 / day. Collins
processes and closes on 8 titles each day. The company recently purchased a
computerized title search system that will allow the processing of 14 titles per
day. Although the staff, their works hours, and pay will be same, the overheads
expenses are now $ 800 per day.
Solution:
Labor productivity with the old system:
= 8 titles per day/ 32 labor hours = 0.25 titles per hour
Labor productivity with the new system:
=14 titles per day/ 32 labor hours = 0.44 title per labor hours
Multifactor productivity with the old system:
=8 titles per day / 640 + 400 = 0.0077 titles per dollars
Multifactor productivity with the new system:
=14 titles per day / 640 + 800 = 0.0097 titles per dollars
Sample Problem
At Modem Lumber, Inc., Art Binley, a president and a producer of an apple
crates sold to growers, has been able, with his current equipment, to produces
400 crates per 100 logs. He currently purchases 100 logs per day, and each
logs required 3 labor hours to process. He believes that he can hire a
professional buyer who can buy a better quality log at the same cost. If this is
the case, he increases his production to 260 crates per 100 logs. His labor
hours will increase by 8 hours per day. What will be the impact on productivity
(measured in crates per labor –hour) if the buyers is hired?
Solution:
a) Current labor productivity = 240 crates / 100 logs (3 hours pert log)
= 240/ 300
= 0.8 create per labor hour
b) Labor productivity with buyer = 260 crates / 100 logs (3 hours per logs) + 8
hours
= 260 / 308
= 0.844 crates per labor hours
Sample Problem
Art Binley has decided to look at his productivity from a multi factor (total
factor productivity) perspective (to solve problem n0.5). To do so, he has
determined his labor, capital, energy, material usage and decided to use
dollars as the common denominator. His total labor hours are now 300 per day
and will increase to 308 per day. His capital and energy cost will remain
constant at $350 and $150 per day, respectively. Material costs for the 100 logs
per day are $1000 and will remain the same. Because he will pay an average of
$10 per hour (with fringes), Binley determine his productivity increase as
follows:
Solution:
Current System
Buyer
Labor:
Material:
Capital:
Energy:
150
System with Professional
300 hrs at $ 10 = $ 3,000
100 logs/day
1,000
350
Total Cost:
4,500
$ 4,500
Productivity of current system:
system:
=240 crate/ 4,500 = 0.0533
308 hrs at $ 10 = $ 3,080
1,000
350
150
$
Productivity of proposed
= 260 crates/ 4,580 = 0.0567
Sample Problem
Calculate the productivity for the following operations:
a) Three employees processed 600 insurance policies last week. They 8 hours
per day, 5 days per week.
b) A team of workers made 400 units of product, which is valued by its
standard cost of $10 each (before markups for other expenses and profit).
That accounting department reported that for this job the actual cost were $
400 per labor, $1000 for materials and 4300 for overhead:
Solution:
a) Labor productivity = Policies processed
Employee, hours
= 600 policies
3 (40)
= 5 policies per hours
b) Multifactor productivity =
Quality at standard cost
Labor + Materials + Overheads
= 400units ($10/units)
$400 + $1000 + $ 3000
= $4000
$1700
=2.35
Sample Problem
Student tuition at Boering University is $ 100 per semester credit hours. The
states supplement school revenue by matching student tuition, dollars per
dollars. Average class size for typical three credit course is 50 students. Labor
costs are $4000 per class, material costs are $20 per student, and overhead
cost are $25,000 per class.
Find:
a) What is the multifactor productivity ratio?
b) If instructors work an average, what is the labor productivity ratio?
Solution:
a) Value of Output = ( 50 student )x (3 credit hours) x ($ 100 tuition + $ 100 state
support)
class
student
credit hours
= $ 30,000 per class
Value of Output = Labor + Materials + Overheads
= $ 4000 + ($20 per student x 50 students) + $25,000
Class
= $ 30,000 per class
Multifactor productivity = Output/ Input
= $ 30,000 / class
$ 30,000/ class
= 1.00
b) Labor productivity is the ratio of the value of output to the labor hours. The value
of output is the same as in part (a), or $ 30,000 per class, so
Labor hours of input = 14 hours x 16 week
weeks
weeks
= 224hours per class
Labor productivity
= Output/ Input
= $ 30,000 per class
224 hours per class
= $ 133.93 per hours
Sample Problem
A division of Miller chemicals produces water purification crystals for
swimming pools. The major inputs used in the production process are labor,
raw materials, and energy. The spreadsheets in the figure shown that amount
of output produced and input used for 1994 and 1995. By dividing the pounds
of the crystals produced by each input individually, we obtain the [partial
productivity measured shown in a columns D through F.
An example of multifactor productivity measure is output per non labor dollar.
For 1994 we have
= 100,000
$ 5,000 + $ 30,000
=2.86 lb/ non labor dollar
For 1995 we have
=150,00
$ 6,000 + $ 40,000
=3.261 lb/ non labor dollars
A
1
2
3
4
5
B
Miller Chemicals
Outputs
Pounds of crystal
C
D
1994
1995
100,000
150,000
E
F
1994
1994
Productivity
6 Inputs
measure
5
5.357
Output direct labor
7 Direct labor hours 20,000
28,000 hour
0.556 0.429
Output direct labor
8 Direct labor cost $180,000 $350,000 dollar
0.286 0.3745
Energy used
9 (kWh)
350,000 400,000 Output/kilowatt-hour
20
25
10 Energy cost
$5,000
$6,000 Output/energy dollar 0.8333 0.811
Raw material
Output/lb or raw
11 used (lb)
120,000 185,000 material
3.333
3.75
Output/raw material
12 Raw material cost $30,000 $40,000 dollar
13
For 1994:
Total productivity = 100,000
$ 180,000 + $ 5,000 = $ 30,000
=0.47 lb/ dollar
For 1995
Total productivity = 150,000
$ 350,000 + $ 6,000 + $ 40,000
=0.38 lb / dollar
DECISION PROCESS
Decision making can be done using the following :
1. Decision Tree
2. Forecasting
3. Capacity Planning
DECISION TREES
Decision Trees
- schematic representation of the alternatives available to a
decision maker and the possible consequences. This is composed of a
number of nodes that have branches emanating from the stem.
NOTE:
Square nodes denote decision point and circular node denotes chance
events.
Decision trees are read from left to right.
Example of a Decision Tree
Left
Right
Decision Point
Chance Events
3 Basic Categories in Decision Making:
 Certainty
It means that relevant parameters such as cost, capacity and
demand have known values.
 Risk
It means that certain parameters have probabilistic outcomes.
 Uncertainty
It means that it is impossible to assess the likelihood of various
possible future events.
4 Possible Decision Criteria Under Uncertainty:
1. Maximin determines the worst possible pay off for each
alternative and choosing the best among the worst.
2. Maximax determines the best possible payoff and choose the
best alternative from among the best.
3. Laplace determines the average payoff for each alternative
and choose the alternative with the best average.
Decision Making Under Risk
Expected monetary value criterion ( EMV )
where the alternative with
the highest expected value is
selected.
Expected Value of Perfect Information ( EVPI )difference between the
expected payoff with perfect
information and the expected
payoff under risk.
FORECASTING
Forecast
- statement about the future ( weather, demand, sales, etc )
Example:
How much food should be prepared for the party?
How many visitors will the venue accommodate?
Will the person get the job?
Basis of Forecast:
1. Current factors or condition
2. Past experience in similar situation
Forecasting / Forecasts are basis for the following:
1. Capacity Planning
2. Budgeting
3. Sales Planning
4. Productions Inventory Planning
5. Manpower Planning
6. Purchasing Planning
Other uses of Forecasting:
1. Predict Profits
2. Revenues
3. Costs
4. Productivity Changes
5. Prices and availability of energy and raw materials
6. Interest Rater
7. Movement of key economic indications
8. Prices of stocks and bonds
Elements of Good Forecast:
1. Timely
2. Reliable
3. Accurate
4. Expressed in meaningful units
Elements of Good Forecast:
5. Be in writing
6. Be simple and easy to understand
Factors in Developing Useful Forecasts
1. Expertise
2. Judgment
3. Technical Expertise
6 Basic Steps in Forecasting:
1. Determine the purpose of the forecast
2. Establish time horizon
3. Select forecasting technique
4. Gather and analyze relevant data
5. Prepare the forecast
6. Monitor the forecast
Approaches to Forecasts
1. Judgmental Forecast - rely on analysis of subjective inputs obtained from
sources like surveys, sales staff, marketing executive and panel of
experts.
2. Historical Data/Time Series - attempts to project past experience into
future. Assumption is that future will be like past.
3. Associative Model
- uses equations that can be used to predict future
demand. Example demand of paint might be related to variables such 3.
Associative Models- use equations that can be used to predict future
demand. Example demand of paint might be related to variables such as
price/ gallon etc.
Approaches to Forecasting
1. Qualitative- consists of subjective inputs
2. Quantitative- Involves the use of historical data as basis
Forecast Based on Judgment and Opinions
1. Executive Opinions
2. Sales force Opinions- sales staff or customer service opinion is believed to
be a good source of information.
3. Consumer Surveys- the advantage is the ability to tap information that might
be available. However, surveys can be expensive and time consuming.
4. Delphi Method- involves circulating a series of questionnaire among
individuals who posses the knowledge and ability to contribute
meaningfully. Responses are kept anonymous which tends to
encourage honest responses.
Forecasts Based on Time Series Data
Time Series is a time ordered sequence of observation taken at regular
intervals over a period of time.
Some Common Behaviors that Appear in Plotting Data
1. Trend- refers to a long term upward or downward movement.
Example: population shifts, cultural changes
2. Seasonality-refers to short-term regular variations related to time.
Example: restaurants and hotels are fully booked during Valentines Day
while malls are peak during Christmas season.
3. Cycles- wavelike variations of more than 1 year duration. These are often
related to a variety of economic and political conditions.
4. Irregular Variations- are due to unusual circumstances such as severe
weather conditions, strikes, etc. These are not typical behavior.
5. Random Variations- are residual variations that remain after all other
behavior have been accounted for.
Three Techniques for Averaging
1. Moving average
2. Weighted moving average
3. Exponential smoothing
Moving Average
Given:
Period
1
2
3
4
5
Demand( in pcs )
42
40
43
40
41
To Find: Forecast for period 6 ( F6 ), using 3 period MA( moving average)
Solution:
MA
=
F6
=
43+40+41
3
= 41.33 units ≈ 42 units
If F6 becomes actual demand:
F7
using MA
=
40+41+42
3
= 41 units
Weighted Moving Average
Given:
Find:
Weights are as follows: 0.4, 0.3, 0.2, 0.1
Period
1
2
3
4
5
Solution:
Demand
42
40
43
40
41
Forecast for Period 6
F6
=
Weights
0.1
0.2
0.3
0.4
0.6(41)+0.3(40)+0.2(43)+0.1(40) =
41pcs
Exponential Smoothing
CAPACITY PLANNING
Capacity planning refers to the upper limit or ceiling on the load that an
operating unit can handle.
It enables manager to quantify production capability.
3 Basic Questions in Capacity Planning:
 What kind of capacity is needed?
 How much is needed?
 When is it needed?
Importance of Capacity Decision:
 capacity decisions have impact on the ability of the organization to meet
future demands
 it affects operating costs
 it is a major determinant of initial cost
 it affects competitiveness
 it affects the ease of management
2 Useful Definitions of Capacity
 Design capacity
attained.
-
the maximum output that can possibly be
 Effective capacity the maximum possible outputs given a
product mix, scheduling difficulties, machine maintenance, quality
factors, etc.
2 Measures of System Effectiveness:
 Efficiency is the rate of actual output to effective capacity.
 Utilization is the ratio of actual output to design capacity.
Efficiency
=
Actual Output
Effective capacity
Utilization
=
Actual Output
Design Capacity
Determinants of Effective Capacity:
1.
2.
3.
4.
5.
6.
Facilities
Product or Service
Processes quality
Human Consideration
training
Operations schedule
External Forces
product standards
Aggregate Planning
It is an intermediate range capacity planning that covers a time horizon of 2 –
12 months.
3 Levels of Capacity Decisions in an Organization:
1. Long term relate to product and service selection, facility size
and location, equipment decision, lay out of facilities.
2. Intermediate term and inventories.
3. Short term equipment.
relate to general level of employment, output
consists
scheduling
of
jobs,
workers
and
IMPORTANCE OF AGGREGATE PLANNING:
It helps synchronize flow throughout the supply chain, it affects costs,
equipment, utilization, employment levels and customer satisfaction.
Demand Options in Aggregate Planning:




Pricing
Promotion
Back Order
New Demand
Capacity Options in Aggregate Planning:
1.
2.
3.
4.
5.
Hire and Lay off workers
Overtime/slack time
Part time workers
Inventories
Subcontracting
Strategies for Meeting Demand:
1.
2.
3.
4.
Maintain a level workforce
Maintain a steady output rate
Match demand period by period
Use a combination of options
General Procedure for Aggregate Planning consists of the following:
1.
2.
3.
4.
Determine demand for each period.
Determine capacities for each period.
Identify policies that are pertinent.
Determine units costs of regular time, overtime, subcon, holding of
inventories, back orders , layoffs, etc.
5. Develop alternative plans and compute cost for each.
6. Select the alternative that satisfies objectives.
Some basic questions in capacity planning are the following:
1. What kind of capacity is needed?
Depends on the products and services that management intends to
produce or provide.
2. How much is needed?
3. When it is needed?
Forecast is key units to answer the question.
CAPACITY DECISIONS ARE STRATEGIC
For a number of reasons, capacity decisions are among the most fundamental of all
the design decisions that managers must make. In fact, capacity decisions can be
critical for an organization:
1. Capacity decisions have a real impact on the ability of the organization to
meet future demands for products and services; capacity essentially limits the
rate of output possible. Having capacity to satisfy demand can allow a
company to take advantage of tremendous opportunities.]
2. Capacity decisions affect operating costs. Ideally, capacity and demand
requirements will be matched, which will tend to minimize operating costs. In
practice, this is not always achieved because actual demand either differs
from expected demand or trends to vary. In such cases, a decision might be
made to attempt to balance the costs of over-and under capacity.
3. Capacity usually a major determinant of initial cost. Typically, the greater the
capacity of a productive unit, the greater its cost. This does not necessarily
imply a one-for-one-relationship; larger units tend to cost proportionately less
than smaller units.
4. Capacity decisions often involved long-term commitment of resources and the
fact that once they are implemented, it may be difficult or impossible to modify
those decisions without incurring major cost.
5. Capacity decision can affect competitiveness. If a firm has excess
capacity, or can quickly add capacity that may serve as a barrier to entry
other firms. Then too, capacity can affect delivery speed which can be
competitive advantage.
6. Capacity can affect the ease of the management, having appropriate
capacity makes management easier then when the capacity is
mismatched.
7. Globalization has increased the importance and the compellability of the
capacity decisions, Fur-flung supply chains and distant markets add to the
uncertainty about capacity needs.
8. Because capacity decisions often involve substantial financial and other
resources, it is necessary to plan for them far in advance.
DEFINING AND MEASURING CAPACITY
Capacity often refers to an upper limit on the rate of output.
Two useful definitions of capacity:
1. Design capacity: the maximum output rate or service capacity an
operation, process, or facility is designed for.
2. Effective capacity: Design capacity minus allowances such as personal
time, maintenance, and scrap.
-
Actual output cannot exceed effective capacity and is often less
because of machine breakdowns, absenteeism, shortages of
materials, and equality problems as well as factors that are outside the
control of the operating managers.
-
Efficiency is the ratio of actual output to effective capacity
-
Capacity utilization is the ratio of actual output to design capacity.
FORMULA TO REMEMBER IN CAPACITY PLANNING:
Efficiency= actual output
Effective capacity
Utilization = actual output
Design Capacity
Business
Auto manufacturing
Steel mill
Oil refinery
Farming
Inputs
Outputs
Labor hours, machine per
Number of cars per shift
hours
Furnace size
Tons of steel per day
Refinery size
Gallons of fuel per day
Bushels of grains per
Number of acres, number
acre per year gallons milk
of cows
per day
Restaurant
Number of tables, sitting
capacity
Theater
Number of seats
Retail sails
Square feet of floor
space
Number of milk served
per day
Number of tickets per
performance
Revenue generated per
day
DETERMINANTS OF EFFECTIVE CAPACITY
Facilities
- Design of facilities, including size and provision for expansions is key.
Location factors, such as transportation costs, distance to market,
labor supply, energy sources, and room for expansion are also
important. Likewise the layout of the work area often determines how
smoothly work can be performed, and environmental factors such as
heating, lighting, and ventilation also play a significant role in
determining whether personnel can perform effectively or whether they
must struggle to overcome poor design characteristics.
Product and services factors
- in general the more the output is uniform, the more opportunities there
are for standardization of methods and materials, which leads to a
greater capacity. The particular mix of products or services rendered
also must be considered since different items will have different rates
of output.
Process factors
- The quantity capability of the process is an obvious determinant of
capacity. A more subtle determinant is the influence of output quality.
Human factors
- the task that make up a job, the variety of activities involved, and the
training, skill, and experience required to perform a job all have impact
on the potential and actual output. In addition, employee motivation
has a very relationship to capacity, as do absenteeism and labor turnover.
Operational factors
- Scheduling problems occurs when an organization has differences in
equipment, capabilities among alternative pieces of equipment or
differences in job requirements. Inventory stocking decisions, late
deliveries, purchasing requirements, acceptability of purchased
materials and parts, quality inspection and control procedures also can
have an impact on effective capacity.
Supply chain factors
- Must be taken into account capacity planning if substantial capacity
changes are involved. Key question include: What impact will the
changes have on the suppliers, warehousing, transportation, and
distributors? If capacity will be increased, will these elements of the
supply chain be able to handle increase? Conversely, if the capacity
decreased, what impact will be loss in business have on these
elements of the supply chain?
External factors
- Product standards, especially minimum quality performance standards,
can restrict management’s option for increasing and using capacity.
STRATEGY FORMULATION
An organization typically bases its capacity strategy on assumptions and
predictions about long-term demand patterns, technological changes, and the
behavior of its competitors. These typically involve: (1) the growth rate and
variability of demand (2) the costs of building and operating facilities of various
sizes (3) the rate direction of technological innovation (4) the likely behavior of
the competitors, and (5) availability of capital and other inputs.
Key decisions of capacity planning relate to:
1. The amount of capacity needed
2. The timing of changes.
3. The need to maintain balance through out the system.
4. The extent of flexibility of facilities and the workforce.

Capacity cushion – extra demand intended to offset uncertainty.
STEPS IN THE CAPACITY PLANNING PROCESS
1. Estimate future capacity requirements.
2. Evaluate existing capacity and facilities and identify gaps.
3. Identify alternatives for meeting requirements.
4. Conduct financial analyses of each alternative.
5. Asses key qualitative issues for each alternative.
6. Select one alternative to pursue.
7. Implement the selected alternative.
8. Monitor results.
Determining Capacity Requirements
Capacity Planning Decisions involves;
a. Long- term considerations- relate to overall level capacity.
b. Short term considerations- relate to probable variations in capacity
requirements
Factors/ reasons why companies buy product or services
1.
2.
3.
4.
5.
6.
Available capacity
Expertise
Quality considerations
The nature of Demand
Cost
Risk
Developing Capacity Alternatives
1. Design flexibility into systems
Example: Expand restaurant in the original design or remodel an existing
structure.
Factors to be considered are layout of equipment, location, equipment ,
production planning, scheduling, and inventory policies.
1. Take stage of life cycle into account
Example
INTRODUCTION
GROWTH
MATURITY
Third generation
mobile phones
Portable DVD
Players
Personal Computers Typewriters
E-conferencing
Email
Faxes
All-in-one racing skin- Breathable synthetic
Cotton t-shirts
suits
fabrics
iris-based personal
Smart cards
Credit cards
identity cards
DECLINE
Handwritten
letters
Shell Suits
Cheque books
3. Take a “big picture” approach to capacity changes
Example: A restaurant increases the number of chairs and tables, there’s a
probable increase in demand of parking and maintenance.
4. Prepare to deal with capacity “chunks” – developing capacity alternatives
may result to shortage or excess
Example: The desired number of units per hour is150, machines used for this
operation are able to produce 100 units per hour each. One machine would be
50 units short to its desired number, but two machines will have an excess
capacity of 50 units
5. Attempt to smooth out capacity requirements – The demand for the
product/service changes occasionally. Expanding it may result to unevenness.
Example: When the storm came there’s an increase in demand on water, not like
on normal days. Adding a water station would reduce the burden of heavy
demands but it would add cost on other times
6. Identify the optimal operating level
Ideal level: cost per unit is lowest for that production unit
Output rate < Optimal level: increase in output rate will result in decrease in
average unit costs
Output rate > Optimal level: average units costs would become increasingly
larger
Figure.1 Production units have an optimal rate output for minimum cost
Average per unit
Minimum cost
0
optimal rate Rate of output
Reasons for economies scale include;
a. Fixed costs are spread over more units, reducing the
fixed cost per unit.
b. Construction cost increase at a decreasing rate with
respect to the size of the facilities to be built.
c. Processing costs decrease as output rate increase
because operations become more standardize which
reduces unit costs.
Reasons for diseconomies scale include;
a. Distribution costs increase due to traffic congestion and shipping from
one large centralized facility instead of several smaller, decentralized
facilities.
b. Complexity increases costs; control and communication become more
problematic.
c. Inflexibility can be an issue.
d. Additional levels of bureaucracy exist, slowing decision making and
approvals for changes.
3 Important Factors in Planning Service Capacity
The need to be near customers.
Convenience for costumers is important aspect of service and
service must be located near the costumers.
Ex. Drug Store, were located near the hospitals.
The inability to store services.
The degree of volatility of demand.
Presents problems for capacity planners. Tends to higher the service
than the goods not only in the timing of demands, but also in the
amount of time required to service individual costumers.
Evaluating Alternatives
An organization needs to examine alternatives for future capacity from a
number of perspectives. Most obvious are economic considerations:

Will an alternative be economically feasible?





How much will it cost?
How soon can we have it?
What will operating and maintenance costs be?
What will its useful life be?
Will it be compatible with present personnel and operations?
IMPORTANT FACTORS IN EXAMINING ALTERNATIVES
1) Possible negative public opinion – any option that could disrupt lives
and property is bound to generate hostile reactions.
2) Construction of new facilities – may necessitate moving personnel to a
new location.
3) Embracing new technologies – may mean restraining some people and
terminating some jobs.
4) Relocation – can cause unfavorable reactions, particularly if a town is
about to lose a major employer.
5) Community pressure – may arise if the presence of the company is
viewed unfavorably by noise, traffic and pollution.
TECHNIQUES USED FOR EVALUATING CAPACITY ALTERNATIVES
1)
2)
3)
4)
Cost-Volume Analysis
Financial Analysis
Decision Theory
Waiting-Line Analysis
Cost Volume Analysis – focuses on relationships between cost, revenue, and
volume of output. The purpose of this analysis is to estimate the income of an
organization under different operating conditions. It is particularly a useful tool for
comparing capacity alternatives. Use of the technique requires identification of all
costs related to the production of a given product. These costs are then
designated as fixed costs or variable costs. Fixed costs tend to remain constant
regardless of volume of output.
Examples of Fixed Costs
1)
2)
3)
4)
Rental costs
Property taxes
Equipment costs
Heating and Cooling Expenses
5) Administrative Costs
On the other hand, Variable costs vary directly with volume of output.
The Two (2) Major components of Variable Costs
1) Materials
2) Labor Costs
The total cost associated with a given volume of output is equal to the sum
of the fixed cost and the variable cost per unit times volume. Revenue per
unit, like variable cost per unit, is assumed to be the same regardless of
the quantity output. Hence, we could have the following formulas for
solving problems related with Cost-Volume:
Where:
TC
VC
TR
= FC + VC
=QxV
=RxQ
FC
VC
v
TC
TR
R
Q
QBEP
P
= Fixed Cost
= Total Variable Cost
= Variable Cost per Unit
= Total Cost
= Total Revenue
= Revenue per unit
= Quantity or Volume of Output
= Break Even Quantity
= Profit
Total Profit can be computed using the formula:
P = TR-TC = R x Q – (FC + v x Q)
Rearranging terms, we could have:
P = Q(R – v) – FC
The required volume, Q, needed to generate a specified profit is:
Q = (P + FC)/(R-v)
A special case of this is the volume of output needed for total revenue to equal
total cost. This is the Break-Even Point. We could compute it using the formula:
QBEP = FC/(R-v)
SAMPLE PROBLEMS:
The owner of Old-Fashioned Berry Pies, S. Simon is contemplating
adding new line of pies, which will require leasing new equipment for a
monthly payment of $6000. Variable costs would be $2.00 per pie and pies
would retail for $7.00 each.
a)
b)
c)
d)
How many pies must be sold in order to break even?
What would the profit (loss) be if 1000 pies are made and sold in a month?
How many pies must be sold to realize a profit of $4000?
If 2000 can be sold, and a profit target is $5000, what price should be
charged per pie?
Given:
FC = $6000
VC = $2.00 per pie
Rev = $7.00 per pie
Solution:
a.) QBEP = FC/(Rev – VC) = ($6000)/($7 - $2) = 1200 pies per month
b.) For Q = 1000, P = Q(R – v) – FC = 1000($7 - $2) - $6000 = $1000
c.) P = $4000; Q = ($4000 + $6000)/($7 - $2) = 2000 pies
d.) Profit = Q(R – v) – FC
$5000 = 2000 (R - $2) - $6000
R = $7.50
SAMPLE PROBLEM # 2:
A manager has the option of purchasing one, two, or three machines.
Fixed costs and Potential Volumes are as follows:
Number of Machines
Total Annual Fixed Costs
1
2
3
$ 9600
$ 15000
$ 20000
Corresponding Range of
Output
0 to 300
301 to 600
601 to 900
Variable Cost is $10 per unit, and revenue is $40 per unit:
a) Determine the break even point for each range
b) If projected annual demand is between 580 and 600 units, how many
machines should the manager purchase?
SOLUTIONS:
a.) For one machine;
QBEP = ($9600)/($40 per unit - $10 per unit) = 320units not in range
For two machines = ($15000)/($40 per unit - $10 per unit) = 500 units
For three machines = ($20000)/($40 per unit - $10 per unit) = 666.67 units
b.)
Comparing the projected range of demand to the two ranges for which
a break even point occurs, you can see that the break even point is
500, which is in the range 301 to 600.
Cost-Volume Analysis can be a valuable tool for comparing capacity
alternatives if certain assumptions are satisfied:
1) One product is involved
2) Everything produced can be sold
3) The variable cost per unit is the same regardless of the volume
4) fixed costs do not change with volume changes, or they step
changes
5) The revenue per unit is the same regardless of volume
6) Revenue per unit exceeds variable cost per unit
FINANCIAL ANALYSIS – a common approach is to use this to rank various
investment proposals.
Cash Flow – refers to the difference between the cash received from sales
(of goods or services) and other sources, and the cash outflow for labor,
materials, overhead and taxes.
Present Value – expresses in current value the sum of all future cash flows
of an investment proposal.
THE THREE (3) MOST COMMONLY USED METHODS OF
FINANCIAL ANALYSIS ARE PAYBACK, PRESENT VALUE AND
INTERNAL RATE OF RETURN.
Payback – is a crude but widely used method that focuses on the length of
time it will take for an investment to return its original cost.
Present Value – summarizes the initial cost of an investment, its estimated
annual cash flows, and any expected salvage value in a single value cslled
the equivalent current value.
Internal Rate of Return – summarizes the initial cost, expected annual cash
flows, and estimated future salvage values of an investment proposal in an
equivalent interest rate.
DECISION THEORY
- is a helpful tool for financial comparison of alternatives under
conditions of risk and uncertainty. It is suited to capacity decisions
and to a wide range of other decisions mangers must take.
WAITING-LINE ANALYSIS
- is useful in helping managers choose a capacity level that will be
cost effective through balancing the cost of having customers wait with the
cost of providing additional capacity. It can be an aid in the determination of
the expected costs for various levels of service capacity.
SUMMARY
Capacity – refers to a system’s potential for producing goods or delivering services
over a specified time interval.
Capacity decisions – are important because capacity is a ceiling on output and a
major determinant of operating costs.
Capacity planning decision - is one of the most important decisions that managers
make. The capacity decision is strategic and long – term in nature, often involving a
significant initial investment of capital.
Capacity planning is particularly difficult in cases where returns will accrue over a
lengthy period and risk is a major consideration.
FACTORS THAT CAN INTERFERE EFFECTIVE CAPACITY:






Facilities Design and layout
Human factors
Product/service design
Equipment failures
Scheduling problems
Quality considerations
Capacity planning – involves Long - term and Short - term considerations.
Long- term considerations – relate to the overall level of capacity.
Short – term considerations – relate to variations in capacity requirements due to
seasonal, random, and irregular fluctuations in demand.
Program Evaluation and Review Technique / Critical Path Method
(P E R T C P M)
Advantages of using PERT / CPM
1. This shows the graphical display of project activities.
2. This shows an estimate of how long the project will take.
3. This serves as an indication of which activities are most critical to
timely project completion.
4. This serves as an indication of how long any activity can be delayed
without lengthening the project.
Precedence Diagram
2 Ways of Constructing a Diagram
1. AOA or Activity – on Arrow
A
B
C
2. AON or Activity on Node
A
Sample Problem :
Precedes
a
c
d
b/e
B
C
Activity
Time
a
b
c
d
e
f
6 wks
10 wks
5 wks
4 wks
9 wks
2 wks
Crash Time Cost/day to Crash
6
8
4
1
1
1
Php 500
Php 300
Php 700
Php 600
Php 800
Php 200
B = 10
A= 6
F=2
E=9
C=5
D=4
Find :
Solution:
1.
2.
The CPM
Improve the completion time by doing the necessary
crashing if applicable.
1. Determine the CPM
ABF =
6 + 10 + 2 = 18
CDEF =
5 + 4 + 9 + 2 = 20
Longest path is CDEF, therefore, this is the CPM
2. Rank the CPM activities in order of lowest crashing cost and determine the
number of days each can be crashed.
Activity
F
D
C
E
C D E F
Cost
Php 500
Php 600
Php 700
Php 800
5 + 4 + 9 + 2 = 20
Days Available for Crashing
1
1
4
1
Time
2
4
5
9
Critical Path
Choose the lowest crashing cost which is f, therefore, 5 + 4 +9 + 1 = 19 days
1 day can still be crashed , 5 + 3 + 9 + 1 = 18 days, New Cost is + Php 1,100.
INVENTORY MANAGEMENT
Introduction to Inventory Management
Inventory is a stock or store of goods. It includes raw materials or stock
incoming suppliers.
Two types of Demand:
1.
Dependent Demand
These are items that are typically subassemblies or component parts that
will be used in the production of a final or finished product.
 Subassemblies and component a part is derived from the number of
finished units that will be produced.
Example: Demand for wheels for new cars.
2.
Independent Demand
These are items that are the finished goods or other end items. These
items are sold or at least shipped out rather than used in making another
product.
The Nature and Importance of Inventories
TYPES OF INVENTORIES
 Raw materials and purchased parts
 Partially completed goods
 Finished-goods inventories or merchandise
 Replacement parts, tools, and suppliers
 Goods-in-transit to warehouses or customers
Functions of Inventory
1. To meet anticipated customer demand. These inventories are referred to
as anticipation stocks because they are held to satisfy planned or expected
demand.
2. To smooth production requirements. Firms that experience seasonal
patterns in demand often build up inventories during off-season to meet
overly high requirements during certain seasonal periods. Companies that
process fresh fruits and vegetable deal with seasonal inventories.
3. To decouple operations. The buffers permit other operations to continue
temporarily while the problem is resolved. Firms have used buffers of raw
materials to insulate production from disruptions in deliveries from suppliers,
and finished goods inventory to buffer sales operations from manufacturing
disruptions.
4. To protect against stock-outs. Delayed deliveries and unexpected
increases in demand increase the risk of shortages. The risk of shortages can
be reduced by holding safety stocks, which are stocks in excess of
anticipated demand.
5. To take advantage of order cycles. Inventory storage enables a firm to buy
and produce in economic lot sixes without having to try to match purchases or
production with demand requirements in short run.
6. To hedge against price increase. The ability to store extra goods also
allows a firm to take advantage of price discounts for large orders.
7. To permit operations. Production operations take a certain amount of time
means that there will generally be some work-in-process inventory.
Inadequate control of inventories can result into two categories:
1. Under stocking
results in missed deliveries, lot sales, dissatisfied
customers and production bottlenecks
2. Overstocking unnecessarily ties up funds that might be more productive
Two Main Concerns of Inventory Management
1. Level of customer service to have the right goods, in sufficient quantities, in
the right place, and at the right time.
2. Cost of ordering and carrying inventories.
Objectives of Inventory Management
General
To achieve satisfactory levels of customer service while keeping inventory
costs within reasonable bounds.
Specific
 Decision maker tries to achieve a balance in stocking
 Fundamental decision must be made related to the timing and size of
orders
Requirements for Effective Inventory Management
To be effective, management must have the following:
1. A system to keep track of the inventory on the hand on order.
2. A reliable forecast of demand that includes an indication of possible forecast
error.
3. Knowledge of lead times and lead time variability.
4. Reasonable estimates of inventory holding costs, ordering costs, and
shortage costs.
5. A classification system for inventory items.
Inventory Counting Systems
Inventory counting systems can be either
1.
periodic
2.
perpetual.
Periodic System
This is a physical count of items in inventory is made at periodic intervals (e.g.
weekly, monthly) in order to decide how much to order of each item.
Advantage
Orders for many items occur at the same time, which can result in economies in
processing and shipping orders
Disadvantages
1. Lack of control between reviews.
2. The need to protect against shortages between review periods by carrying
extra stock.
3. The need to make a decision on order quantities at each review.
Major users:
Supermarkets, discounts stores, and department stores.
Universal Product Code (UPC) bar code printed on a label that has information
about the item to which it is attached.
Bar coding represents an important development for other sectors of business
besides retailing. In manufacturing, bar codes attached to parts, subassemblies, and
finished goods greatly facilitate counting and monitoring activities.
Perpetual Inventory System (also known as a continual system)
This keeps track of removals from inventory on a continuous basis, so the system
can provide information on the current level of inventory for each item.
Advantages
1. The control provided by the continuous monitoring of inventory withdrawals.
2. The fixed-order quantity; management can identify an economic order size.
Disadvantage
1. The added cost of record keeping.
Two-bin-system is two containers of inventory; reorder when the first is empty. The
advantage of this system is that there is no need to record each withdrawal from
inventory; the disadvantage is that the reorder card may not be turned in for a variety
of reasons.
Demand Forecast and Lead time Information
Managers need to know the extent to which demand and lead time might
vary; the greater the potential variability, the greater the need for additional stock to
reduce the risk of a shortage between deliveries.
Lead time is time interval between ordering and receiving the order.
Cost Information
Three Basic Costs
1. Holding or Carrying Cost is costs to carry an item in inventory for a length of
time usually a year. Cost includes interest, insurance, taxes, depreciation,
obsolescence, deterioration, spoilage, pilferage, breakage, etc.
2. Ordering Cost is cost of ordering and receiving inventory. These include
determining how much is needed, preparing invoices, inspecting goods upon
arrival for quality and quantity, and moving the goods to temporary storage.
3. Storage Cost is cost resulting when demand exceeds the supply of inventory
on hand. These costs can include the opportunity cost of not making a sale,
loss of customer goodwill, late charges, and similar costs.
Classification System
An important aspect of inventory management is that items held in inventory
are not of equal importance in terms of dollars invested, profit potential, sales or
usage volume, or stock-out penalties.
Example:
A producer of electrical equipment might have electric generators, coils of
wire, and miscellaneous nuts and bolts among the items carried in inventory. It would
be unrealistic to devote equal attention to each of these items.
A-B-C Approach classifies inventory items according to some measure of
importance, usually annual dollar usage, and then allocates control efforts
accordingly.
Three Classes of Items Used:
A (very important)
B ( moderately important)
C ( least important)
A-B-C Concept
High
Annual dollarVolume of items
Low
Few

Number of Items
Many
A typical A-B-C breakdown in relative annual dollar value of items and
number of items by category
Cycle Counting is a physical count of items in inventory. The purpose of cycle
counting is to reduce discrepancies between the amounts indicated by inventory
records and the actual quantities of inventory on hand.
The key questions concerning cycle counting for management are:
1. How much accuracy is needed?
2. When should cycle counting be performed?
3. Who should do it?
Economic Order Quantity Models
Economic Order Quantity (EOQ) is the order size that minimizes total cost.
EOQ models identify the optimal order quantity in terms of minimizing the sum of
certain annual costs that vary with order size.
Three (3) Order Size
1. The economic order quantity model.
2. The economic order quantity model with non instantaneous delivery.
3. The quantity discount model.
Basic Economic Order Quantity (EOQ) Model
EOQ models identify the optimal order quantity in terms of minimizing the sum of
certain annual costs that vary with order size.
Inventory Cycles begins with the receipt of an order of Q units, which are withdrawn
at instant rate over time. When the quantity on the hand is just sufficient to satisfy
demand during lead time, an order for Q units is submitted to the supplier.
Assumption of the Basic EOQ Model
1. Only one product is involved.
2. Annual demand requirements are known.
3. Demand is spread evenly throughout the year so that the demand rate is
reasonably constant.
4. Lead time does not vary.
5. Each order is received in a single delivery.
6. There are quantity discounts.
Annual Carrying Cost is computed by multiplying the average amount of inventory
hand by the cost to carry one unit for one year. The average inventory is simply half
of the order quantity.
Annual Carrying Cost = Q H
2
where:
Q = Order quantity in units
H = Holding (carrying) cost per unit
Carrying Cost, Ordering Cost, and Total Cost curve
A. Carrying costs are linearly
related to order size.
Annual
Q H
2
Cost
Order Quantity
B. Ordering costs are inversely
and nonlinearly related to
Annual
Cost
D S
Q
order size
Order Quantity
C. The total-cost curve is
U-shaped
Annual
Coast
TC= Q H + D S
2
Q
Order Quantity
Annual Ordering Cost is a function of the number of orders per year and the
ordering cost per order.
Annual Ordering Cost = D S
Q
where:
D = Demand, usually in unit per year
S = Ordering cost
Total Annual Cost is associated with carrying and ordering inventory when Q unit
are ordered each time.
TC = Annual Carrying Cost + Annual Ordering Cost
TC = Q H + D S
2
Q
The length of an order cycle (Ex. The time between orders) is:
Length of Order Cycle = Qо
D
EOQ with Non instantaneous Replenishment
When a firm is both a producer and a user or deliveries are spread over time,
inventories tend to build up gradually instead of instantaneously.
If usage production (or delivery) rates are equal, there will be no inventory buildup
since all output will be used immediately and the issue of lot size doesn’t come up. In
the more typical case, the production or delivery rate exceeds the usage rate. In the
production case, production occurs over only a portion of each cycle because the
production rate is greater than the usage rate, and usage occurs over the entire
cycle.
Equations:
TCmin = Carrying cost + setup cost
Where
= (Imax / 2) H + ( D/ Q0)S
Imax = Maximum inventory
Q0 = √2DS/H √p/ p – u
Where
P = Production or delivery rate
u = usage rate
Example:
A toy manufacturer uses 48000 rubber wheels per year for its popular
dump truck series. The firm makes its own wheels, which it can produce at a
rate of 800 per day. The toy trucks are assembled uniformly over the entire
year. Carrying cost is $1 per wheel a year. Setup cost for production run of the
wheels is $45. The firm operates 240 days per year. Determine each of the
following.
a. Optimal run size
b. Minimal total annual cost for carrying and setup
c. Cycle time for the optimal run size
Solution:
D = 48000 wheels per year
S = $ 45
H = $1 per wheel per year
P = 800 wheels per day
U = 48000 wheels per 240 days, or 200 wheels per day
a. Q0 = √2DS/H √p/ p – u = √2(48000)45/1 √800 /(800 – 200)
= 2400 wheels
b. TCmin = Carrying cost + setup cost = (Imax / 2) H + ( D/ Q0)S
Imax = 1800 wheels
TC = (1800/2) * 1 + (48000/2400) *45 = $1800
c. Cycle time = 2400/ 200 = 12 days
d. run time = 2400/ 800 = 3 days
Quantity Discounts are price reductions for large orders offered to customers
to induce them to buy in large quantities. If quantity discounts are offered, the
customer must weigh the potential benefits of reduced purchase price and
fewer orders that will result from buying in large quantities against the
increase in carrying costs caused by higher average inventories
TC = carrying cost + Ordering cost + Purchasing Cost
= (Q/2)H + (D/Q)s + PD
where:
P = Unit price
Cost
TC with PD
TC without PD
PD
EDQ
* Adding PD doesn’t change the EOQ
Quantity
TC @ 2.00 each
TC @ 1.70 each
TC @ 1.40 each
PD @ 2.00
PD @ 1.70
PD @ 1.40
45
70
Quantity
* The total cost curve with quantity discounts is composed of a portion of the total
cost curve for each price
Example:
The maintenance department of a large hospital uses about 816 cases
of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per
case a year, and the new schedule indicates that orders of less than 50 cases
will cost $20 per case, 50 to 79 will cost $18 per case, 80 to 99 cases will cost
$17 per case, and larger orders will cost $16 per case. Determine the optimal
order quantity and total cost.
Solution:
D= 816 cases per year
Range
S = $12
H = $4 per year
Price
1 to 49
$20
50 to 79
18
80 to 99
17
100 or more
16
EDQ = √2DS/H= √ 2(816)12 /4 = 70 cases
TC70 = Carrying cost + Order cost + Purchase cost
= (Q/2) H
+ (D/Q0)
+PD
= (70/2) 4
+ (816/70)12 +18(816) = $14968
TC80 = $14154
TC100 = $13354
When to Reorder with EOQ Ordering
Reorder Point it occurs when the quantity on hand drops to a predetermined
amount. That amount generally includes expected demand during lead time and
perhaps an extra cushion of stock, which serves to reduce the probability of
experiencing a stock out during lead time.
4 Determinants of the Reorder Point Quantity:
1. The rate of demand
2. The length of lead time
3. The extent of demand and/or lead time variability
4. The degree of stock out risk acceptable to management
If demand and lead time are both constant , the reorder point is
simply
ROP = d*LT
where:
d = Demand per day or week
LT = Lead time in days or weeks
Example:
Tingly Two – a Day vitamins which are delivered to his home by a
routman seven days after an order is called in. At what point should tingly
telephone his order in?
Usage = 2 per day
Lead time = 7 days
ROP = Usage * Lead time
= 2 vitamins per day * 7 days = 14 vitamins
Tingly should reorder when 14 vitamin tablets are left
Safety stock is when variability is present in demand or lead time, the
possibility that actual demand will exceed expected demand created.
Consequently, it is very necessary to carry additional inventory.
ROP = Expected demand during lead time + Safety stock
Service Level
Because it costs money to hold safety stock, a manager must carefully weigh
the cost of carrying safety stock against the reduction in stock – out risk it provides,
since the service level increases as the risk of stock out decreases.
The probability that demand will not exceed supply during lead time
Service Level = 100% - stock out risk
The amount of safety sock that is appropriate for a given situation
depends on the following factors:
1. The average demand rate and the average demand time.
2. Demand and time variability.
3. The desired service level.
 For a given order cycle service level, the greater the variability in either
demand rate or lead time, the greater the amount of safety stock that will be
needed to achieve that service level.
 Several models will be described that can be used in cases when variability is
present. The first model can be used if an estimate of expected demand
during lead time and its standard deviation are available.
Reorder Point Formula
ROP = Expected demand during lead time + zσdLT
where:
z = Number of standard variations
σdLT = The standard deviation of lead time demand
The ROP Based on normal distribution of lead time demand:
Risk of a
stock out
Service Level
(Probability of no
Blackout)
Expected Demand
ROP quantity.
Safety stock
0
z
Example:
Suppose a manager of a construction supply house determined from
historical records that the lead time demand for sand averages 50 tons. In
addition, suppose the manager determined that demand during lead time could
be described by a normal distribution that has a mean of 50 tons and a
standard deviation of 5 tons. Answer these questions assuming that the
manager is willing to accept a stock – out risk of no more than 3 percent.
a. What value of z is appropriate?
b. How much safety stock should be held?
c. What reorder point should be used?
Expected lead time demand = 50 tons
σdLT = 5 tons
Risk = 3%
Solution:
a. from z table, using a service level of 1 - .03 = .9700, you obtain a value of z =
+ 1.88
b. Safety stock = zσdLT
=1.88(5)
=9.40 tons
c. ROP = expected time of demand + safety stock
= 50 + 9.40
= 59.40 tons.
If only demand is available, then σdLT = √LTσd, and the reorder point is
ROP = đ * LT + z √LTσd
where:
đ = Average daily or weekly demand
σd = standard deviation of demand per day or week
LT = Lead time in days or weeks
Shortages and Service Levels
The ROP computation does not reveal the expected amount of shortage for a
given lead time service level. The expected number of units can, however, be very
useful to a manager. This quantity can easily be determined from the same
information used to compute the ROP, with one additional piece of information.
(Table 11 – 3; Operation Production Management Fifth Edition by William
Stevenson).
Formula:
E(n) = E(z)σdLT
where:
E(n) = Expected number of units short per order cycle
E(z) = Standard number of units short obtained from table 11 – 3
σdLT = Standard deviation of lead time demand
Example:
Suppose the standard deviation of lead time demand is known to be 20
units. Lead time demand is approximately normal
a. For a lead time service level of 90%, determine the expected number of units
short o any order cycle.
b. What lead time service would an expected shortage of 20 units imply?
Solution:
a. Lead time service level = .90. From table 11 – 3 (Stevenson), E(z) = 0.048.
E(n) = 0.048(20 units) = 0.96, or about 1 unit
b. For the case where E(n) =2, you must solve for E(z) and then use table 11 – 3
(Stevenson) to determine the lead time service level that implies. Thus, E(n) = E(z)
σdLT, so E(z) = E(n) / σdLT = 2/20 = .100. From table 11 – 3, this implies a service
level of approximately 81.5 percent (interpolating).
Fixed-Order interval Model
The Annual service level and the lead time service level can be related using the
following formula:
SL annual
=
1 - E (N)
D
Using the previous formula:
E (N)
=
E (π) D/Q
=
E(z) σdLT D/Q
Thus,
SL annual
=
1 - E(z) σdLT
Q
How Much to Order: Fixed-Order-Interval Model
Fixed-Order-Interval (FOI) model is used when orders must be placed at fixed time
intervals (weekly, twice a month, etc.). The question to be answered at each order
point is:
How much should be ordered for the next (fixed) interval?
Fixed-interval recorder, requires only periodic checks of inventory levels.
Determining the Amount to Order
Both the demand rate and lead time are constant, the fixed-interval model
and the fixed-quantity model function identically. In the fixed-quantity arrangement,
orders are triggered by a quantity (ROP), while in the fixed-interval arrangement
orders are triggered by a time.
Order size in the fixed-interval model is determined by the following computation:
Expected demand
Amount
=
to order
during protection
+
interval
=
d(OI + LT)
where: OI
A
+
Safety
- Amount on hand
stock
at recorder time
zσd(OI+LT)^ ½ -
A
=
Order interval (length of time between orders)
=
Amount on hand at recorder time
As in previous models, we assume that demand during the protection interval is
normally distributed.
The SINGLE – PERIOD MODEL
Single-period is used to handle ordering of perishable (fresh, fruits, vegetables,
seafood, cut flowers) and items that have a limited useful life (newspaper,
magazines, spare parts for specialized equipment. The period for spare parts is the
life of the equipment, assuming that the parts cannot be used for other equipment.)
Shortage cost includes a charge for loss of customer goodwill as well as opportunity
cost of lost sales. Shortage cost is simply unrealized profit.
C shortage = Cs = Revenue per unit – Cost per unit
The shortage or stock out relates to an item used in production or to spare part for a
machine, then shortage cost refers to the actual cost of lost production.
Excess cost pertains to items left over at the end of the period. In effect, excess
cost the difference between purchase costs and salvage value. That is,
C excess = C s = Original cost per unit – Salvage value per unit
The goal of the single-period model is to identify the order quantity, or stocking that
will minimize the long run excess and shortage costs.
Ce
Cs
Service level
Se
Quantity
So = Optimum Stoking quantity
Continuous Stoking Levels
The concept of identifying an optimal stocking level is perhaps easiest to
visualize when demand is uniform. The service level is the probability that demand
will not exceed the stocking level and computation of the service level is the key to
determining the optimal stocking level.
Service level =
Where
Cs
C + Cs
Cs = Shortage cost per unit
Ce = Excess cost per unit
Example
Sweet cider is delivered weekly to Cindy’s Cider bar. Demand varies
uniformly between 300 liters and 500 liters per week. Cindy pays 20 cents per
liter for the cider and charge 80 cents per liter for it. Unsold cider has no
salvage value and cannot be carried over into the next week due to spoilage.
Find the optimal stocking level and its stock out risk for that quantity;
Ce = Cost per unit – Salvage value per unit
= $0.20
- $0
= $0.20 per unit
Cs = Revenue per unit – Cost per unit
= $0.80
- $0.20
= $0.60 per unit
SL =
Cs
Cs+ Ce
=
$0.60
= .75
$0.60+$0.20
So = 300 + 0.75(500- 300) = 450 liters
75%
300
450
500
Stock out risk is 1.00 - .75 = .25
Discrete Stocking Levels
Then stocking levels are discrete rather than continuous, the service level
computed using the ratio Cs/( Cs + Ce) usually does not coincide with a feasible
stocking level.
Example
Historical records on the use of spare parts for several large hydraulics
presses are to serve as an estimate of usage for spares of a newly installed
press. Stock out cots involves downtime expenses and special ordering costs.
There average $4,200 per unit short rates cost $800 each, and unused parts
have zero salvage. Determine the optimal level.
0
1
Cs
Cs + Ce
2
3
4
5
6
7
8 stoking
level
Number of spares used
0
1
2
3
4 or more
Cs = $4.20
SL =
Relative Frequency
.20
.40
.30
.10
.00
1.00
Cumulative Frequency
.20
.60
.90
1.00
Ce = $800
Cs
Cs+ Ce
=
$ 4,200
= .84
$ 4,200+$ 800
Operations Strategy
Inventories are necessary part of doing business, but having too much
inventory is not good. One reason is that inventories tend to hide problems; they
make it easier to live a problem rather than eliminate them. Another reason is that
inventories are costly maintain.
Revised
CC
CC
Qlo
Qo
OC
Revised (increased) carrying costs results in a smaller EOQ
Revised
CC
Improve
OC
CC
QIIo
Qlo
Qo
OC
Reductions in both ordering/setup cost and carrying cost results in much smaller lot
sizes.