4. Operations Management PERT & CPM

4. Production Planning & Control

&

Introduction to Production

Planning & Control (PPC)

Inputs from L C Jhamb

PPC - defined

• Production is “manufacturing of goods and / or services”

• Planning is “the series of related & co-ordinated activities –demand management, aggregate sales & operations planning, process planning, materials management (incl. MRP & Inventory control), Operations scheduling, and others; designed to

systematize in advance the manufacturing efforts. Planning aims to utilize resources most effectively, to provide the right goods, at the right time, in the right quantity”

• Control is “the review of work progress, make corrections where required; thus

ensuring that the actual is as per plan. Control includes activities such as dispatching, progressing & expediting”

• Overall PPC is thus:

– Planning production in advance – Setting the “run-rate” for each item

– Fixing starting & end dates for each item

– Authorizing shop floor activity by release of production orders – Follow-up, inspect & expedite to stay on course (as per plan)

Objectives of PPC

• Meet targets of production, as aligned with demand, with available resources

• Provide resources (men, material, machines) of the right quantity, quality at right time.

• Optimum scheduling of facilities

• To achieve balanced flow of production, with co-ordination between all departments

• Ensure conformance to delivery commitments, and make sales aware of any potential difficulties

• Inform all concerned, especially management, well in time, re: difficulties which may crop up

Regular (essential) Functions of PPC

(IMP) ORDER PREPARATION: includes preparation of work orders, converting them to shop

orders & auxiliary orders, release of such orders to appropriate entities

MATERIAL CONTROL: includes making material estimates, indenting, purchasing,

follow-up, allocating material to shop orders

PROCESS PLANNING (or ROUTING): includes method of manufacture, operations & their

sequences, machine & tool requirements for each activity, defining requirements of supporting equipment – i.e. jigs & fixtures, measuring instruments, …

TOOLS CONTROL: estimating requirement & specifications of tools (e.g. cutting tools), jigs

& fixtures, measuring instruments,. Replenishment of non – consumable tools due to wear & tear (e.g. allen keys, spanners, ..)

SCHEDULING: fixing calendar dates of various operations for various job-orders,

committing delivery dates to sales & despatch schedules

DISPATCHING: preparation & distribution of shop orders & manufacturing instructions;

assigning responsibilities to appropriate persons; authorizing them to perform the work at respective work-centres as per the predefined schedule; authorize them to draw the

necessary resources (tools, consumables, material, etc);

PROGRESSING: recording progress of work & comparing with plan

Optional Functions of PPC

(IMP)

COST ESTIMATION: pre-production cost estimates used for budgeting, pricing &

profitability management. Alternatively this could the responsibility of Costing dept. or Industrial Engineering

WORK MEASUREMENT: to estimate the time taken by a qualified worker to perform a

task, under given conditions, and at the desired level of performance. Techniques like time & methods study, work sampling, etc. Alternatively this could the responsibility of

Industrial Engineering

SUB-CONTRACT: outsourcing work for various reasons! Alternatively this could the responsibility of Materials / Purchase depts.

CAPACITY PLANNING: Estimation of requirements of men & machines to meet the firms

planned level of business over the short / medium & long term. Alternatively this could the responsibility of the Engineering dept.

DEMAND MANAGEMENT: making projections of demand for various products, which can

become a basis for production planning. Various demand forecasting techniques are used to forecast demand. For the medium term (6-18 months) an “Aggregate Sales & Operations plan” is prepared. Thereon a firm schedule is created (Master Production Schedule).

The Order Preparation process – a block diagram

MANUFACTURING METHODS

Order Acceptance (OA) Receive Sales Program Entry of OA into the system

(say ERP)

Raise Work Order

Convert Work order into Shop Order

Shop order – part A

Prepare Production Program

Check on-hand availability

Issue Shop orders

Produced to stock

Produced to order

• Demand Management

• Qualitative Forecasting Methods

• Simple & Weighted Moving Average Forecasts • Exponential Smoothing

• Simple Linear Regression • Web-Based Forecasting

Demand Management

A B(4) C(2) D(2) E(1) D(3) F(2) Dependent Demand: Raw Materials, Component parts, Sub-assemblies, etc. Independent Demand: Finished Goods

Independent Demand:

What a firm can do to manage it?

• Can take an active role to influence demand

• Can take a passive role and simply respond

Types of Forecasts

• Qualitative (Judgmental)

• Quantitative

–

Time Series Analysis

–

Causal Relationships

–

Simulation

Components of Demand

• Average demand for a period of time

• Trend

• Seasonal element

• Cyclical elements

• Random variation

• Autocorrelation

Finding Components of Demand

1 2 3 4 x x x xx xx xx_x x x x xxx xx xx x x_x x x x xx xx x x x xx x x x x x x x x x x x x

S

al

es

Seasonal variation Seasonal variation Linear Trend Linear Trend

Qualitative Methods

Grass Roots Market Research Panel Consensus Executive Judgment Historical analogy Delphi Method Qualitative Methods

Delphi Method

l. Choose the experts to participate representing a variety of knowledgeable people in different areas

2. Through a questionnaire (or E-mail), obtain forecasts (and any premises or qualifications for the forecasts) from all participants

3. Summarize the results and redistribute them to the participants along with appropriate new questions

4. Summarize again, refining forecasts and conditions, and again develop new questions

5. Repeat Step 4 as necessary and distribute the final results to all participants

Time Series Analysis

• Time series forecasting models try to predict

the future based on past data

• You can pick models based on:

1. Time horizon to forecast 2. Data availability

3. Accuracy required

4. Size of forecasting budget

Simple Moving Average Formula

F =

A + A

+ A +...+A

n

t t-1 t-2 t-3 t-n

• The simple moving average model assumes an average is a good

estimator of future behavior

• The formula for the simple moving average is:

F_t = Forecast for the coming period N = Number of periods to be averaged

Simple Moving Average Problem (1)

Week Demand 1 650 2 678 3 720 4 785 5 859 6 920 7 850 8 758 9 892 10 920 11 789

F =

A + A

+ A +...+A

n

t t-1 t-2 t-3 t-n

Question: What are the

3-week and 6-3-week moving

average forecasts for

demand?

Assume you only have 3

weeks and 6 weeks of

actual demand data for the

respective forecasts

Question: What are the

3-week and 6-3-week moving

average forecasts for

demand?

Assume you only have 3

weeks and 6 weeks of

actual demand data for the

respective forecasts

Week Demand 3-Week

6-Week

1

650

2

678

3

720

4

785

682.67

5

859

727.67

6

920

788.00

7

850

854.67

768.67

8

758

876.33

802.00

9

892

842.67

815.33

10

920

833.33

844.00

11

789

856.67

866.50

12

844

867.00

854.83

F₄=(650+678+720)/3 =682.67 F₇=(650+678+720 +785+859+920)/6 =768.67

500 600 700 800 900 1000 1 2 3 4 5 6 7 8 9 10 11 12 W e e k D em an d Demand 3-W eek 6-W eek

Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example

Plotting the moving averages and comparing them shows how the lines smooth out to reveal the overall upward trend in this example

Note how the 3-Week is

smoother than the Demand,

Note how the 3-Week is

smoother than the Demand,

Simple Moving Average Problem (2) Data

Week Demand 1 820 2 775 3 680 4 655 5 620 6 600

Question: What is the 3

week moving average

forecast for this data?

Assume you only have 3

weeks and 5 weeks of

actual demand data

for the respective

forecasts

Question: What is the 3

week moving average

forecast for this data?

Assume you only have 3

weeks and 5 weeks of

actual demand data

for the respective

forecasts

Simple Moving Average Problem (2)

Solution

Week Demand

3-Week

5-Week

1

820

2

775

3

680

4

655

758.33

5

620

703.33

6

600

651.67

710.00

7

575

625.00

666.00

F₄=(820+775+680)/3 =758.33 F₆=(820+775+680 +655+620)/5 =710.00

Weighted Moving Average Formula

F = w A + w A

_{t 1 t-1 2 t-2}

+ w A +. ..+w A

_{3 t-3 n t-n}

w = 1

_i

n

∑

While the moving average formula implies an equal

weight being placed on each value that is being averaged,

the weighted moving average permits an unequal

weighting on prior time periods

While the moving average formula implies an equal

weight being placed on each value that is being averaged,

the weighted moving average permits an unequal

weighting on prior time periods

w_t = weight given to time period “t” w_t = weight given to time period “t”

The formula for the moving average is:

Weighted Moving Average Problem (1)

Data

Weights:

t-1

.5

t-2

.3

t-3

.2

Week Demand 1 650 2 678 3 720 4

Question: Given the weekly demand and weights, what is the forecast for the 4th _{period or Week 4?}

Question: Given the weekly demand and weights, what is the forecast for the 4th _{period or Week 4?}

Note that the weights place more emphasis on the most recent data, that is time period “t-1”

Note that the weights place more emphasis on the most recent data, that is time period “t-1”

Weighted Moving Average Problem (1)

Solution

Week Demand Forecast

1

650

2

678

3

720

Weighted Moving Average Problem (2) Data

Weights:

t-1

.7

t-2

.2

t-3

.1

Week Demand 1 820 2 775 3 680 4 655

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?

Question: Given the weekly demand information and weights, what is the weighted moving average forecast of the 5th period or week?

Weighted Moving Average Problem (2)

Solution

W eek Demand Forecast

1

820

2

775

3

680

4

655

5

672

F = (0.1)(755)+(0.2)(680)+(0.7)(655)= 672

Exponential Smoothing Model

• Premise: The most recent observations might

have the highest predictive value

• Therefore, we should give more weight to the

F

_t

= F

_t-1

+

α

(A

_t-1

- F

_t-1

)

F

_t

= F

_t-1

+

α

(A

_t-1

- F

_t-1

)

constant

smoothing

Alpha

period

e

past t tim

in the

occurance

Actual

A

period

past time

1

in

alue

Forecast v

F

period

t time

coming

for the

lue

Forcast va

F

:

Where

1 -t 1 -t t

=

=

=

=

α

Exponential Smoothing Problem (1) Data

Week Demand 1 820 2 775 3 680 4 655 5 750 6 802 7 798 8 689 9 775

Question: Given the weekly

demand data, what are

the exponential

smoothing forecasts for

periods 2-10 using

α

=0.10 and

α

=0.60?

Assume F

₁

=D

₁

Question: Given the weekly

demand data, what are

the exponential

smoothing forecasts for

periods 2-10 using

α

=0.10 and

α

=0.60?

Week

Demand

0.1

0.6

1

820

820.00

820.00

2

775

820.00

820.00

3

680

815.50

793.00

4

655

801.95

725.20

5

750

787.26

683.08

6

802

783.53

723.23

7

798

785.38

770.49

8

689

786.64

787.00

9

775

776.88

728.20

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

Answer: The respective alphas columns denote the forecast values. Note that you can only forecast one time period into the future.

Exponential Smoothing Problem (1)

Plotting

5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 2 3 4 5 6 7 8 9 1 0 W e e k De m an d D e m a n d 0 .1 0 .6

Note how that the smaller alpha results in a smoother line in this example

Note how that the smaller alpha results in a smoother line in this example

Exponential Smoothing Problem (2)

Data

Question: What are the

exponential smoothing

forecasts for periods 2-5

using a =0.5?

Assume F

₁

=D

₁

Question: What are the

exponential smoothing

forecasts for periods 2-5

using a =0.5?

Assume F

₁

=D

₁

Week Demand

1

820

2

775

3

680

4

655

5

Exponential Smoothing Problem (2)

Solution

Week Demand

0.5

1

820

820.00

2

775

820.00

3

680

797.50

4

655

738.75

F₁=820+(0.5)(820-820)=820 _F 3=820+(0.5)(775-820)=797.75

The MAD Statistic to Determine

Forecasting Error

MAD =

A - F

n

t t t=1 n

∑

1 M AD 0.8 standard deviation

_{1 standard deviation 1.25 M AD}

≈

_≈

• The ideal MAD is zero which would mean

there is no forecasting error

• The larger the MAD, the less the

MAD Problem Data

Month

Sales

Forecast

1

220

n/a

2

250

255

3

210

205

4

300

320

Question: What is the MAD value given

the forecast values in the table below?

Question: What is the MAD value given

the forecast values in the table below?

MAD Problem Solution

MAD = A - F n = 40 4 = 10 t t t=1 n

∑

Month Sales Forecast Abs Error

1 220 n/a 2 250 255 5 3 210 205 5 4 300 320 20 5 325 315 10 40

Note that by itself, the MAD only lets us know the mean error in a set of forecasts Note that by itself, the MAD only lets us know the mean error in a set of forecasts

Tracking Signal Formula

• The Tracking Signal or TS is a measure that

indicates whether the forecast average is keeping pace with any genuine upward or downward

changes in demand.

• Depending on the number of MAD’s selected, the TS

can be used like a quality control chart indicating when the model is generating too much error in its forecasts.

• The TS formula is:

TS =

RSFE

MAD

=

Running su m of forec ast errors

Mean absol ute deviat ion

Simple Linear Regression Model

Y

_t

= a + bx

0 1 2 3 4 5 x (Time) Y

The simple linear regression model seeks to fit a line

through various data over time

The simple linear regression model seeks to fit a line

through various data over time

Is the linear regression model

Is the linear regression model a

Yt is the regressed forecast value or dependent

variable in the model, a is the intercept value of the the regression line, and b is similar to the slope of the regression line. However, since it is calculated with the variability of the data in mind, its formulation is not as straight forward as our usual notion of slope.

Simple Linear Regression Formulas for

Calculating

“a” and “b”

a = y - bx

b =

xy - n(y)(x)

x - n(x

2 2

∑

Simple Linear Regression Problem Data

Week

Sales

1

150

2

157

3

162

4

166

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

Question: Given the data below, what is the simple linear regression model that can be used to predict sales in future weeks?

Week Week*Week

Sales Week*Sales

1

1

150

150

2

4

157

314

3

9

162

486

4

16

166

664

5

25

177

885

3

55

162.4

2499

Average

Sum Average

Sum

b = xy - n(y)(x) x - n(x = 2499 - 5(162.4)(3) = 2 2

∑

∑

) 55 5 9− ( ) = 63 10 6.3

Answer: First, using the linear regression formulas, we can compute “a” and “b”

Answer: First, using the linear regression formulas, we can compute “a” and “b”

Y

_t

= 143.5 + 6.3x

180 135 140 145 150 155 160 165 170 175 1 2 3 4 5 S al e s Sales Forecast

The resulting regression model is:

Now if we plot the regression generated forecasts against the actual sales we obtain the following chart:

Web-Based Forecasting: CPFR

• Collaborative Planning, Forecasting, and Replenishment

(CPFR) a Web-based tool used to coordinate demand

forecasting, production and purchase planning, and inventory replenishment between supply chain trading partners.

• Used to integrate the multi-tier or n-Tier supply chain,

including manufacturers, distributors and retailers.

• CPFR’s objective is to exchange selected internal information

to provide for a reliable, longer term future views of demand in the supply chain.

Web-Based Forecasting:

Steps in CPFR

• 1. Creation of a front-end partnership

agreement

• 2. Joint business planning

• 3. Development of demand forecasts

• 4. Sharing forecasts

Question Bowl

Which of the following is a classification of a basic type of forecasting?

a. Transportation method b. Simulation

c. Linear programming d. All of the above

e. None of the above

Answer: b. Simulation (There are four types

Question Bowl

Which of the following is an example of a

“Qualitative” type of forecasting technique or model?

a. Grass roots

b. Market research c. Panel consensus d. All of the above e. None of the above

Question Bowl

Which of the following is an example of a “Time Series Analysis” type of forecasting technique or model?

a. Simulation

b. Exponential smoothing c. Panel consensus

d. All of the above e. None of the above

Answer: b. Exponential smoothing (Also includes Simple Moving Average, Weighted Moving Average, Regression Analysis, Box Jenkins, Shiskin Time Series, and Trend Projections.)

Question Bowl

Which of the following is a reason why a firm should choose a particular forecasting model?

a. Time horizon to forecast b. Data availability

c. Accuracy required

d. Size of forecasting budget e. All of the above

Question Bowl

Which of the following are ways to choose weights in a Weighted Moving Average

forecasting model? a. Cost

b. Experience

c. Trial and error

d. Only b and c above e. None of the above

Question Bowl

Which of the following are reasons why the Exponential Smoothing model has been a well accepted forecasting methodology? a. It is accurate

b. It is easy to use

c. Computer storage requirements are small d. All of the above

e. None of the above

Question Bowl

The value for alpha or α must be between which of the following when used in an Exponential Smoothing model?

a. 1 to 10 b. 1 to 2 c. 0 to 1 d. -1 to 1

e. Any number at all

Question Bowl

Which of the following are sources of error in forecasts?

a. Bias

b. Random

c. Employing the wrong trend line d. All of the above

Question Bowl

Which of the following would be the “best” MAD values in an analysis of the accuracy of a

forecasting model? a. 1000 b. 100 c. 10 d. 1 e. 0

Answer: e. 0

Question Bowl

If a Least Squares model is: Y=25+5x, and x is equal to 10, what is the forecast value using this model?

a. 100 b. 75 c. 50 d. 25

e. None of the above

Question Bowl

Which of the following are examples of seasonal variation?

a. Additive

b. Least squares

c. Standard error of the estimate d. Decomposition

e. None of the above

Answer: a. Additive (The other type is of seasonal variation is Multiplicative.)

• Sales and Operations Planning

• The Aggregate Operations Plan

• Examples: Chase and Level

strategies

Master scheduling

Material requirements planning

Order scheduling

Weekly workforce and customer scheduling Process planning

Strategic capacity planning

Sales and operations (aggregate) planning

Long range Intermediate range Short Manufacturing Services Exhibit 14.1 Exhibit 14.1

Sales plan Aggregate operations plan Forecasting

& demand management

Sales and Operations Planning Activities

• Long-range planning

– Greater than one year planning horizon – Usually performed in annual increments

• Medium-range planning

– Six to eighteen months

– Usually with weekly, monthly or quarterly increments

• Short-range planning

– One day to less than six months

The Aggregate Operations Plan

• Main purpose: Specify the optimal combination of

– production rate (units completed per unit of time) – workforce level (number of workers)

– inventory on hand (inventory carried from previous

period)

• Product group or broad category (Aggregation) • This planning is done over an intermediate-range

Balancing Aggregate Demand

and Aggregate Production Capacity

0 2000 4000 6000 8000 10000

Jan Feb Mar Apr May Jun 4500 5500 7000 10000 8000 6000 2000 4000 6000 8000 10000 4500 4000 9000 8000 4000 6000

Suppose the figure to the right represents forecast demand in units

Suppose the figure to the right represents forecast demand in units

Now suppose this

lower figure represents the aggregate capacity of the company to

meet demand

Now suppose this

lower figure represents the aggregate capacity of the company to

meet demand

What we want to do is balance out the

production rate,

workforce levels, and

What we want to do is balance out the

production rate,

Required Inputs to the Production Planning

System

Planning for production External capacity Competitors’ behavior Raw material availability Market demand Economic conditions Current physical Current workforce Inventory levels Activities required External to firm Internal to firm

Key Strategies for Meeting Demand

• Chase

• Level

Aggregate Planning Examples: Unit Demand

and Cost Data

Materials Rs5/unit

Holding costs Rs1/unit per mo.

Marginal cost of stockout Rs1.25/unit per mo. Hiring and training cost Rs200/worker

Layoff costs Rs250/worker

Labor hours required .15 hrs/unit Straight time labor cost Rs8/hour Beginning inventory 250 units

Suppose we have the following unit demand and cost information:

Suppose we have the following unit demand and cost information:

Demand/mo Jan Feb Mar Apr May Jun 4500 5500 7000 10000 8000 6000

Jan F eb M ar A pr M ay Jun

D ay s /m o 22 19 21 21 22 20

H rs /w ork er/m o 159.5 137.75 152.25 152.25 159.5 145

Productive hours/worker/day 7.25 Paid straight hrs/day 8

Demand/mo Jan Feb Mar Apr May Jun

4500 5500 7000 10000 8000 6000

Given the demand and cost information below, what

are the aggregate hours/worker/month, units/worker, and dollars/worker?

Given the demand and cost information below, what

are the aggregate hours/worker/month, units/worker, and dollars/worker? 7.25x2 2 7.25x0.15=48.33 & 84.33x22=1063.33 22x8hrsxRs8=Rs1 408

Cut-and-Try Example: Determining Straight Labor Costs and Output

Chase Strategy

(Hiring & Firing to meet demand)

Jan Days/mo 22 Hrs/worker/mo 159.5 Units/worker 1,063.33 Rs/worker 1,408 Jan Demand 4,500 Beg. inv. 250 Net req. 4,250 Req. workers 3.997 Hired Fired 3

Lets assume our current workforce is 7 workers.

Lets assume our current workforce is 7 workers.

First, calculate net requirements for production, or 4500-250=4250 units

Then, calculate number of workers needed to produce the net

requirements, or

4250/1063.33=3.997 or 4 workers Finally, determine the number of workers to hire/fire. In this case we

Jan Feb Mar Apr May Jun

Days/mo 22 19 21 21 22 20

Hrs/worker/mo 159.5 137.75 152.25 152.25 159.5 145 Units/worker 1,063 918 1,015 1,015 1,063 967 Rs/worker 1,408 1,216 1,344 1,344 1,408 1,280

Jan Feb Mar Apr May Jun

Demand 4,500 5,500 7,000 10,000 8,000 6,000 Beg. inv. 250 Net req. 4,250 5,500 7,000 10,000 8,000 6,000 Req. workers 3.997 5.989 6.897 9.852 7.524 6.207 Hired 2 1 3 Fired 3 2 1

Below are the complete calculations for the remaining months in the six month planning horizon

Below are the complete calculations for the remaining months in the six month planning horizon

Jan F eb M ar A pr M ay Jun Dem and 4,500 5,500 7,000 10,000 8,000 6,000 B eg. inv. 250

Net req. 4,250 5,500 7,000 10,000 8,000 6,000 Req. work ers 3.997 5.989 6.897 9.852 7.524 6.207

Hired 2 1 3

F ired 3 2 1

W ork forc e 4 6 7 10 8 7

E nding inventory 0 0 0 0 0 0

Jan F eb M ar A pr M ay Jun Cos ts

M aterial 21,250.00 27,500.00 35,000.00 50,000.00 40,000.0030,000.00 203,750.00 Labor 5,627.59 7,282.76 9,268.97 13,241.38 10,593.10 7,944.83 53,958.62

Hiring c os t 400.00 200.00 600.00 1,200.00

F iring c os t 750.00 500.00 250.00 1,500.00

Below are the complete calculations for the remaining months in the six month planning horizon with the other costs included

Level Workforce Strategy (Surplus and

Shortage Allowed)

Jan Demand 4,500 Beg. inv. 250 Net req. 4,250 W orkers 6 P roduction 6,380 Ending inventory 2,130 Surplus 2,130

Lets take the same problem as before but this time use the Level Workforce strategy

Lets take the same problem as before but this time use the Level Workforce strategy

This time we will seek to use a workforce level of 6 workers This time we will seek to use a workforce level of 6 workers

Jan

Feb

Mar

Apr

May

Jun

Demand

4,500

5,500

7,000

10,000

8,000

6,000

Beg. inv.

250

2,130

2,140

1,230

-2,680

-1,300

Net req.

4,250

3,370

4,860

8,770

10,680

7,300

Workers

6

6

6

6

6

6

Production

6,380

5,510

6,090

6,090

6,380

5,800

Ending inventory

2,130

2,140

1,230

-2,680

-1,300

-1,500

Surplus

2,130

2,140

1,230

Shortage

Note, if we recalculate this sheet with 7 workers

2,680

1,300

1,500

we would have a surplus

Note, if we recalculate this sheet with 7 workers

we would have a surplus

Below are the complete calculations for the remaining months in the six month planning horizon

Below are the complete calculations for the remaining months in the six month planning horizon

Jan Feb Mar Apr May Jun 4,500 5,500 7,000 10,000 8,000 6,000 250 2,130 10 -910 -3,910 -1,620 4,250 3,370 4,860 8,770 10,680 7,300 6 6 6 6 6 6 6,380 5,510 6,090 6,090 6,380 5,800 2,130 2,140 1,230 -2,680 -1,300 -1,500 2,130 2,140 1,230 2,680 1,300 1,500 Jan Feb Mar Apr May Jun

8,448.00 7,296.00 8,064.00 8,064.00 8,448.00 7,680.00 48,000.00 31,900.00 27,550.00 30,450.00 30,450.00 31,900.00 29,000.00 181,250.00 2,130.00 2,140.00 1,230.00 5,500.00 3,350.00 1,625.00 1,875.00 6,850.00

Below are the complete calculations for the remaining

months in the six month planning horizon with the

other costs included

Below are the complete calculations for the remaining

months in the six month planning horizon with the

other costs included

Note, total costs under this strategy are less than Chase at

Rs260.408.62

Note, total costs under this strategy are less than Chase at Rs260.408.62 Labor Material Storage Stockout

Question Bowl

Sales and Operations Planning activities

are usually conducted during which

planning time horizon?

a. Long-range

b. Intermediate-range

c. Short-range

d. Really short-range

e. None of the above

Answer: b.

Intermediate-range

(i.e., 6 to 18 months)

Question Bowl

Which of the following are Production Planning Strategies can involve trade-offs among the

workforce size, work hours, inventory, and backlogs? a. Chase strategy

b. Stable workforce-variable work hours c. Level strategy

d. All of the above

Question Bowl

Which of the following are considered “relevant costs” in the Aggregate Production Plan?

a. Costs associated with changes in the production rate

b. Inventory holding costs c. Backordering costs

d. Basic production costs e. All of the above

Question Bowl

Which of the following Aggregate Planning Techniques can be performed using simple spreadsheets?

a. Cut-and-try

b. Linear programming c. Transportation method d. All of the above

e. None of the above

Answer: a. Cut-and-try (The other two involve more complex computational effort than simple spreadsheets.)

Question Bowl

Which of the following methods can be used to allocate the right type of capacity to the right type of customer at the right price and in time to

maximize revenue? a. Cut-and-try

b. Yield management

c. Transportation method d. All of the above

e. None of the above

Answer: b. Yield

management

Question Bowl

From an operational perspective Yield Management is most effective as a capacity technique, when

which of the following happens?

a. Demand can not be segmented by customer b. Variable costs are high

c. Fixed costs are low

d. Demand is highly variable

e. All of the above

Answer: d. Demand is

4c. Inventory Control

• Inventory System Defined • Inventory Costs

• Independent vs. Dependent Demand • Single-Period Inventory Model

• Multi-Period Inventory Models: Basic Fixed-Order

Quantity Models

• Multi-Period Inventory Models: Basic Fixed-Time

Period Model

• Miscellaneous Systems and Issues

Inventory System

• Inventory is the stock of any item or resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process

• An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

Purposes of Inventory

1. To maintain independence of operations 2. To meet variation in product demand

3. To allow flexibility in production scheduling 4. To provide a safeguard for variation in raw

material delivery time

5. To take advantage of economic purchase-order size

Inventory Costs

• Holding (or carrying) costs

– Costs for storage, handling, insurance, etc • Setup (or production change) costs

– Costs for arranging specific equipment

setups, etc

• Ordering costs

– Costs of someone placing an order, etc • Shortage costs

E(1 )

Independent vs. Dependent Demand

Independent Demand (Demand for the final end-product or demand not related to other items)

Dependent Demand (Derived demand items for component parts, subassemblies, Finished product

Inventory Systems

• Single-Period Inventory Model

– One time purchasing decision (Example:

vendor selling t-shirts at a football game)

– Seeks to balance the costs of inventory

overstock and under stock

• Multi-Period Inventory Models – Fixed-Order Quantity Models

• Event triggered (Example: running out of

stock)

– Fixed-Time Period Models

Single-Period Inventory Model

u

o

u

C

C

C

P

+

≤

estimated

under

demand

of

unit

per

Cost

C

estimated

over

demand

of

unit

per

Cost

C

:

Where

u o

=

=

This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu

This model states that we should continue to increase the size of the inventory so long as the probability of selling the last unit added is equal to or greater than the ratio of: Cu/Co+Cu

Single Period Model Example

• Our college basketball team is playing in a tournament game this weekend. Based on our past experience we sell on average 2,400 shirts with a standard deviation of 350. We make Rs100 on every shirt we sell at the

game, but lose Rs50 on every shirt not sold. How many shirts should we make for the game?

C_u = Rs100 and C_o = Rs50; P ≤ 100 / (100 + 50) = .667

Z_.667 = .432 (use NORMSDIST(.667) or Appendix E) therefore we need 2,400 + .432(350) = 2,551 shirts

Multi-Period Models:

Fixed-Order Quantity Model Model

Assumptions (Part 1)

• Demand for the product is constant and

uniform throughout the period

• Lead time (time from ordering to receipt) is

constant

Multi-Period Models:

Fixed-Order Quantity Model Model Assumptions

(Part 2)

• Inventory holding cost is based on

average inventory

• Ordering or setup costs are constant

• All demands for the product will be

Basic Fixed-Order Quantity Model and

Reorder Point Behavior

R = Reorder point L _L Q Q Q R Time Number of units on hand

1. You receive an order quantity Q.

2. Your start using

them up over time. 3. When you reach down to a level of inventory of R, you place your next Q 4. The cycle then repeats.

Cost Minimization Goal

Ordering Costs Holding Costs C O S T Annual Cost of Items (DC) Total Cost By adding the item, holding, and ordering costs

together, we determine the total cost curve, which in turn is used to find the Q_opt inventory order point that minimizes total costs

By adding the item, holding, and ordering costs

together, we determine the total cost curve, which in turn is used to find the Q_opt inventory order point that minimizes total costs

Basic Fixed-Order Quantity (EOQ)

Model Formula

H

2

Q

+

S

Q

D

+

DC

=

TC

Total Annual = Cost Annual Purchase Cost Annual Ordering Cost Annual Holding Cost + + TC=Total annual cost D =Demand

C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory TC=Total annual cost

D =Demand

C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory

Deriving the EOQ

Using calculus, we take the first derivative of the

total cost function with respect to Q, and set the

derivative (slope) equal to zero, solving for the

optimized (cost minimized) value of Q

_opt

Using calculus, we take the first derivative of the

total cost function with respect to Q, and set the

derivative (slope) equal to zero, solving for the

optimized (cost minimized) value of Q

_opt

Q =

2DS

H

=

2(Annual Demand)(Order or Setup Cost)

Annual Holding Cost

OPT

Reorder p oint, R = d L

_

d = average daily demand (constant)

_

We also need a reorder point to tell us when to We also need a reorder point to tell us when to

EOQ Example (1) Problem Data

Annual Demand = 1,000 units

Days per year considered in average

daily demand = 365

Cost to place an order = Rs10

Holding cost per unit per year = Rs2.50

Lead time = 7 days

Cost per unit = Rs15

Given the information below, what are the EOQ and reorder point?

Given the information below, what are the EOQ and reorder point?

EOQ Example (1) Solution

Q = 2DS H = 2(1,000 )( 10) 2.50 = 89.443 un its or OPT 90 units d = 1,000 unit s / year

365 days / year = 2.74 unit s / day

Reorder p oint, R = d L = 2.74units / day (7days ) = 19.18 or _ 20 units

In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90

EOQ Example (2) Problem Data

Annual Demand = 10,000 units

Days per year considered in average daily

demand = 365

Cost to place an order = Rs10

Holding cost per unit per year = 10% of cost

per unit

Lead time = 10 days

Cost per unit = Rs15

Determine the economic order quantity

and the reorder point given the following…

Determine the economic order quantity

EOQ Example (2) Solution

Q = 2DS H = 2(10,000 ) (10) 1.50 = 365.148 un its, or OPT 366 units d = 10,000 uni ts / year

365 days / year = 27.397 uni ts / day

R = d L = 27.397 uni ts / day (10 da ys) = 273.97 or _ 274 units

Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.

Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.

Fixed-Time Period Model with Safety

Stock Formula

order) on items (includes level inventory current = I time lead and review over the demand of deviation standard = y probabilit service specified a for deviations standard of number the = z demand daily average forecast = d days in time lead = L reviews between days of number the = T ordered be to quantitiy = q : Where I Z + L) + (T d = q L + T L + T σ σ

q = Average demand + Safety stock – Inventory currently on hand

Multi-Period Models: Fixed-Time Period Model: Determining the Value of σ _T+L

( )

σ σ σ σ σ T+L d i 1 T+L d T+L d 2 =

Since each day is independent and is constant, = (T + L)

i

2

=

∑

• The standard deviation of a sequence of

random events equals the square root of the sum of the variances

Example of the Fixed-Time Period Model

Average daily demand for a product is

20 units. The review period is 30 days,

and lead time is 10 days. Management

has set a policy of satisfying 96 percent

of demand from items in stock. At the

beginning of the review period there are

200 units in inventory. The daily

Given the information below, how many units

should be ordered?

Given the information below, how many units

should be ordered?

Example of the Fixed-Time Period Model:

Solution (Part 1)

(

)( )

σ

_T+L

_{= (T + L)}

σ

_d2

_{= 30 + 10 4 = 25.298}

2

The value for “z” is found by using the Excel

NORMSINV function, or as we will do here, using

Appendix D. By adding 0.5 to all the values in

Appendix D and finding the value in the table that

comes closest to the service probability, the “z”

value can be read by adding the column heading

label to the row label.

Example of the Fixed-Time Period Model:

Solution (Part 2)

or

644.272,

=

200

-44.272

800

=

q

200

-

298)

(1.75)(25.

+

10)

+

20(30

=

q

I

Z

+

L)

+

(T

d

=

q

_T+L

units

645

+

σ

So, to satisfy 96 percent of the demand,

you should place an order of 645 units at

Price-Break Model Formula

Cost

Holding

Annual

Cost)

Setup

or

der

Demand)(Or

2(Annual

=

iC

2DS

=

Q

_OPT

Based on the same assumptions as the EOQ model, the price-break model has a similar Q_opt formula:

i = percentage of unit cost attributed to carrying inventory C = cost per unit

Since “C” changes for each price-break, the formula above will have to be used with each price-break cost

Price-Break Example Problem Data

(Part 1)

A company has a chance to reduce their inventory

ordering costs by placing larger quantity orders using

the price-break order quantity schedule below. What

should their optimal order quantity be if this company

purchases this single inventory item with an e-mail

ordering cost of Rs4, a carrying cost rate of 2% of the

inventory cost of the item, and an annual demand of

10,000 units?

A company has a chance to reduce their inventory

ordering costs by placing larger quantity orders using

the price-break order quantity schedule below. What

should their optimal order quantity be if this company

purchases this single inventory item with an e-mail

ordering cost of Rs4, a carrying cost rate of 2% of the

inventory cost of the item, and an annual demand of

10,000 units?

Order Quantity(units) Price/unit(Rs) 0 to 2,499 Rs1.20

Price-Break Example Solution (Part 2)

units 1,826 = 0.02(1.20) 4) 2(10,000)( = iC 2DS = Q_OPT

Annual Demand (D)= 10,000 units Cost to place an order (S)= Rs4

First, plug data into formula for each price-break value of “C”

units 2,000 = 0.02(1.00) 4) 2(10,000)( = iC 2DS = Q_OPT 4) 2(10,000)( 2DS

Carrying cost % of total cost (i)= 2% Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, the Q_opt value is feasible

Interval from 2500-3999, the Q_opt value is not feasible

Interval from 4000 & more, the

Price-Break Example Solution (Part 3)

Since the feasible solution occurred in the first price-break, it means that all the other true Q_opt values occur at the beginnings of each price-break interval. Why?

Since the feasible solution occurred in the first price-break, it means that all the other true Q_opt values occur at the beginnings of each price-break interval. Why?

Total annual costs

So the candidates for the

price-breaks are 1826, 2500, and 4000 units

So the candidates for the

price-breaks are 1826, 2500, and 4000 units

Because the total annual cost function is a “u” shaped function

Because the total annual cost function is a “u” shaped function

Price-Break Example Solution (Part 4)

iC

2

Q

+

S

Q

D

+

DC

=

TC

Next, we plug the true Q_opt values into the total cost annual cost function to determine the total cost under each price-break TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = Rs12,043.82 TC(2500-3999)= Rs10,041 TC(4000&more)= Rs9,949.20 TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = Rs12,043.82 TC(2500-3999)= Rs10,041 TC(4000&more)= Rs9,949.20

Finally, we select the least costly Q_opt , which is this problem occurs in the 4000 & more interval. In

Maximum Inventory Level, M

Miscellaneous Systems:

Optional Replenishment System

M Actual Inventory Level, I

q = M - I

I

Miscellaneous Systems:

Bin Systems

Two-Bin System

Full

Empty

Order One Bin of

Inventory

One-Bin System

Order Enough to

Refill Bin

ABC Classification System

• Items kept in inventory are not of equal

importance in terms of:

– Rupees invested – profit potential

– sales or usage volume – stock-out penalties 0 30 60 30 60

A

B

C

% of Rs Value % of Use

So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B”

Inventory Accuracy and Cycle Counting

• Inventory accuracy

refers to how well

the inventory records agree with

physical count

• Cycle Counting

is a physical

inventory-taking technique in which

inventory is counted on a frequent

Question Bowl

The average cost of inventory in the

United States is which of the

following?

a. 10 to 15 percent of its cost

b. 15 to 20 percent of its cost

c. 20 to 25 percent of its cost

d. 25 to 30 percent of its cost

Question Bowl

Which of the following is a reason why firms keep a supply of inventory?

a. To maintain independence of operations b. To meet variation in product demand

c. To allow flexibility in production scheduling d. To take advantage of economic purchase

order size

e. All of the aboveAnswer: e. All of the above (Also can include to

provide a safeguard for variation in raw material delivery time.)

Question Bowl

An Inventory System should include policies that are related to which of the following?

a. How large inventory purchase orders should be b. Monitoring levels of inventory

c. Stating when stock should be replenished d. All of the above

e. None of the above

Question Bowl

Which of the following is an Inventory Cost item that is related to the managerial and clerical

costs to prepare a purchase or production order? a. Holding costs

b. Setup costs c. Carrying costs d. Shortage costs

e. None of the above

Answer: e. None of the

above (Correct answer

is Ordering Costs.)

Question Bowl

Which of the following is considered a Independent Demand inventory item? a. Bolts to a automobile manufacturer b. Timber to a home builder

c. Windows to a home builder

d. Containers of milk to a grocery store e. None of the above

Question Bowl

If you are marketing a more expensive

independent demand inventory item, which inventory model should you use?

a. Fixed-time period model b. Fixed-order quantity model c. Periodic system

d. Periodic review system

Question Bowl

If the annual demand for an inventory item is 5,000 units, the ordering costs are Rs100 per order, and the cost of holding a unit is stock for a year is Rs10, which of the following is approximately the Q_opt ?

a. 5,000 units b. Rs5,000 c. 500 units d. 316 units

e. None of the above

Answer: d. 316

units

(Sqrt[(2x1000x10

0)/10=316.2277)

Question Bowl

The basic logic behind the ABC Classification

system for inventory management is which of the following?

a. Two-bin logic b. One-bin logic c. Pareto principle d. All of the above e. None of the above

Question Bowl

A physical inventory-taking technique in which inventory is counted frequently

rather than once or twice a year is which of the following?

a. Cycle counting

b. Mathematical programming c. Pareto principle

d. ABC classification

e. Stockkeeping unit (SKU)

4d. Materials Requirements Planning

• Material Requirements Planning (MRP)

• MRP Logic and Product Structure Trees

• Time Fences

• MRP Example

• MRP II and Lot Sizing

Material Requirements Planning

• Materials requirements planning (MRP) is a means for determining the number of parts, components, and materials needed to produce a product

• MRP provides time scheduling information

specifying when each of the materials, parts, and components should be ordered or produced

• Dependent demand drives MRP • MRP is a software system

Example of MRP Logic and Product

Structure Tree

B(4)

E(1)

D(2)

C(2)

F(2)

D(3)

A

Product Structure Tree for Assembly A _{Lead Times} A 1 day B 2 days C 1 day D 3 days E 4 days F 1 day Total Unit Demand Day 10 50 A

Given the product structure tree for “A” and the lead time and demand information below, provide a materials requirements plan that defines the number of units of each component and when they will be needed

LT = 1 day

Day: 1 2 3 4 5 6 7 8 9 10

A Required 50

Order Placement 50

First, the number of units of “A” are scheduled

backwards to allow for their lead time. So, in the

materials requirement plan below, we have to place

an order for 50 units of “A” on the 9

th

day to receive

Next, we need to start scheduling the components that make up “A”. In the case of component “B” we need 4 B’s for each A. Since we need 50 A’s, that means 200 B’s. And again, we back the schedule up for the necessary 2 days of lead time.

Day: 1 2 3 4 5 6 7 8 9 10 A Required 50 Order Placement 50 B Required 20 200 Order Placement 20 200

B(4)

C(2)

A

Spares

LT = 2

4x50=200

Day: 1 2 3 4 5 6 7 8 9 10 A Required 50 LT=1 Order Placement 50 B Required 20 200 LT=2 Order Placement 20 200 C Required 100 LT=1 Order Placement 100 D Required 55 400 300 LT=3 Order Placement 55 400 300 E Required 20 200 LT=4 Order Placement 20 200 F Required 200 LT=1 Order Placement 200

B(4)

C(2)

A

40 + 15 spares Part D: Day 6

Finally, repeating the process for all components, we have the final materials requirements plan:

Master Production Schedule (MPS)

• Time-phased plan specifying how

many and when the firm plans to build

each end item

Aggregate Plan

(Product Groups)

Aggregate Plan

(Product Groups)

MPS

Types of Time Fences

• Frozen

– No schedule changes allowed within this

window

• Moderately Firm

– Specific changes allowed within product

groups as long as parts are available

• Flexible

– Significant variation allowed as long as overall