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Chapter 9. Capacity and Aggregate Planning . To Accompany Russell and Taylor, Operations Management, 4th Edition ,  2003 Prentice-Hall, Inc. All rights reserved. Web Links. http://myphliputil.pearsoncmg.com/student/bp_russell_opsmgmt_4/09web.html. Capacity Planning.

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chapter 9

Chapter 9

Capacity and Aggregate Planning

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

web links
Web Links
  • http://myphliputil.pearsoncmg.com/student/bp_russell_opsmgmt_4/09web.html
capacity planning
Capacity Planning
  • Establishes overall level of productive resources
  • Affects lead time responsiveness, cost & competitiveness
  • Determines when and how much to increase capacity
the following have much to say about capacity
The following have much to say about capacity
  • Goldratt--Theory of Constraints
    • Internal vs. External
  • Senge--Wonder Tech and Peoples Express Air
the issue of time
The Issue of Time
  • Long-range capacity planning
    • time horizon of 3 to 10 years
    • Physical plant expansion
  • Medium-range capacity planning
    • time horizon of 6 months to 3 years
    • Aggregate production planning fits here
    • This is labor planning
  • Short-range capacity planning
    • time horizon of 0 to 6 months/material planning fits here
    • Also called Capacity Requirements Planning
how much to increase capacity depends on
How much to increase capacity depends on
  • 1) the volume and certainty of anticipated demand,
  • 2) the strategic objectives in terms of growth, customer service, and competition, and
  • 3) the costs of expansion and operation.
capacity expansion
Capacity Expansion
  • Volume & certainty of anticipated demand
  • Strategic objectives for growth
  • Costs of expansion & operation
  • Incremental or one-step expansion
capacity expansion strategies1

(a) Capacity lead strategy

(b) Capacity lag strategy

Capacity

Demand

Units

Units

Demand

Capacity

Time

Time

(c) Average capacity strategy

(d) Incremental vs. one-step expansion

One-step expansion

Capacity

Units

Units

Incremental

expansion

Demand

Demand

Time

Time

Capacity Expansion Strategies

Figure 9.1

best operating levels1

Average cost per room

Best operating

level

Economies of scale

Diseconomies of scale

250 500 1000

# Rooms

Best Operating Levels

Figure 9.2

aggregate production planning app
Aggregate Production Planning (APP)
  • Matches market demand to company resources
  • Plans production 6 months to 12 months in advance
  • Expresses demand, resources, and capacity in general terms
  • Develops a strategy for economically meeting demand
  • Establishes a company-wide game plan for allocating resources
inputs and outputs to app1

Capacity

Constraints

Strategic

Objectives

Company

Policies

Aggregate

Production

Planning

Demand

Forecasts

Financial

Constraints

Size of

Workforce

Production

per month

(in units or $)

Inventory

Levels

Units or dollars

subcontracted,

backordered, or lost

Inputs and Outputs to APP

Figure 9.3

adjusting capacity to meet demand
Adjusting Capacity to Meet Demand

Producing at a constant rate and using inventory to absorb fluctuations in demand (level production)

Hiring and firing workers to match demand (chase demand)

Maintaining resources for high demand levels

Increase or decrease working hours (overtime and undertime)

Subcontracting work to other firms

Using part-time workers

Providing the service or product at a later time period (backordering)

strategy details
Strategy Details
  • Level production - produce at constant rate & use inventory as needed to meet demand
  • Chase demand - change workforce levels so that production matches demand
  • Maintaining resources for high demand levels - ensures high levels of customer service
strategy details1
Strategy Details
  • Overtime & undertime - common when demand fluctuations are not extreme
  • Subcontracting - useful if supplier meets quality & time requirements
  • Part-time workers - feasible for unskilled jobs or if labor pool exists
  • Backordering - only works if customer is willing to wait for product/services
level production1

Demand

Production

Units

Time

Level Production

Figure 9.4 (a)

chase demand

Demand

Production

Units

Time

Chase Demand

Figure 9.4 (b)

app using pure strategies

QUARTER SALES FORECAST (LB)

Spring 80,000

Summer 50,000

Fall 120,000

Winter 150,000

APP Using Pure Strategies

Hiring cost = $100 per worker

Firing cost = $500 per worker

Inventory carrying cost = $0.50 pound per quarter

Production per employee = 1,000 pounds per quarter

Beginning work force = 100 workers

Example 9.1

app using pure strategies1

QUARTER SALES FORECAST (LB)

Spring 80,000

Summer 50,000

Fall 120,000

Winter 150,000

Level production

(50,000 + 120,000 + 150,000 + 80,000)

4

= 100,000 pounds

APP Using Pure Strategies

Hiring cost = $100 per worker

Firing cost = $500 per worker

Inventory carrying cost = $0.50 pound per quarter

Production per employee = 1,000 pounds per quarter

Beginning work force = 100 workers

Example 9.1

level production strategy

SALES PRODUCTION

QUARTER FORECAST PLAN INVENTORY

Spring 80,000 100,000 20,000

Summer 50,000 100,000 70,000

Fall 120,000 100,000 50,000

Winter 150,000 100,000 0

400,000 140,000

Cost = 140,000 pounds x 0.50 per pound = $70,000

Level Production Strategy

Example 9.1

chase demand strategy

SALES PRODUCTION WORKERS WORKERS WORKERS

QUARTER FORECAST PLAN NEEDED HIRED FIRED

Spring 80,000 80,000 80 0 20

Summer 50,000 50,000 50 0 30

Fall 120,000 120,000 120 70 0

Winter 150,000 150,000 150 30 0

100 50

Chase Demand Strategy

Cost = (100 workers hired x $100) + (50 workers fired x $500)

= $10,000 + 25,000 = $35,000

Example 9.1

app using mixed strategies

MONTH DEMAND (CASES) MONTH DEMAND (CASES)

January 1000 July 500

February 400 August 500

March 400 September 1000

April 400 October 1500

May 400 November 2500

June 400 December 3000

APP Using Mixed Strategies

Production per employee = 100 cases per month

Wage rate = $10 per case for regular production

= $15 per case for overtime

= $25 for subcontracting

Hiring cost = $1000 per worker

Firing cost = $500 per worker

Inventory carrying cost = $1.00 case per month

Beginning work force = 10 workers

Example 9.2

app by linear programming
APP by Linear Programming

Minimize Z = $100 (H1 + H2 + H3 + H4)

+ $500 (F1 + F2 + F3 + F4)

+ $0.50 (I1 + I2 + I3 + I4)

Subject to

P1 - I1 = 80,000 (1)

Demand I1 + P2 - I2 = 50,000 (2)

constraints I2 + P3 - I3 = 120,000 (3)

I3 + P4 - I4 = 150,000 (4)

Production 1000 W1 = P1 (5)

constraints 1000 W2 = P2 (6)

1000 W3 = P3 (7)

1000 W4 = P4 (8)

100 + H1 - F1 = W1 (9)

Work force W1 + H2 - F2 = W2 (10)

constraints W2 + H3 - F3 = W3 (11)

W3 + H4 - F4 = W4 (12)

where

Ht = # hired for period t

Ft = # fired for period t

It = inventory at end

of period t

Pt = units produced

in periodt

Wt = workforce size

for periodt

Example 9.3

app by the transportation method

EXPECTED REGULAR OVERTIME SUBCONTRACT

QUARTER DEMAND CAPACITY CAPACITY CAPACITY

1 900 1000 100 500

2 1500 1200 150 500

3 1600 1300 200 500

4 3000 1300 200 500

Regular production cost per unit $20

Overtime production cost per unit $25

Subcontracting cost per unit $28

Inventory holding cost per unit per period $3

Beginning inventory 300 units

APP by the Transportation Method

Example 9.4

the transportation tableau

PERIOD OF USE

Unused

PERIOD OF PRODUCTION 1 2 3 4 Capacity Capacity

1

2

3

4

Beginning 0 3 6 9

Inventory 300 — — — 300

Regular 600 300 100 — 1000

Overtime 100 100

Subcontract 500

Regular 1200 — — 1200

Overtime 150 150

Subcontract 250 250 500

Regular 1300 — 1300

Overtime 200 — 200

Subcontract 500 500

Regular 1300 1300

Overtime 200 200

Subcontract 500 500

Demand 900 1500 1600 3000 250

20 23 26 29

25 28 31 34

28 31 34 37

20 23 26

25 28 31

28 31 34

20 23

25 28

28 31

20

25

28

The Transportation Tableau

Table 9.2

burruss production plan

REGULAR SUB- ENDING

PERIOD DEMAND PRODUCTION OVERTIME CONTRACT INVENTORY

1 900 1000 100 0 500

2 1500 1200 150 250 600

3 1600 1300 200 500 1000

4 3000 1300 200 500 0

Total 7000 4800 650 1250 2100

Burruss’ Production Plan

Table 9.3

other quantitative techniques
Other Quantitative Techniques
  • Linear decision rule (LDR)
  • Search decision rule (SDR)
  • Management coefficients model
demand management
Demand Management
  • Shift demand into other periods
    • Incentives, sales promotions, advertising campaigns
  • Offer product or services with countercyclical demand patterns
  • Partnering with suppliers to reduce information distortion along the supply chain
hierarchical planning process1

Production Planning

Capacity Planning

Resource Level

Items

Aggregate production plan

Resource requirements plan

Product lines or families

Plants

Master production schedule

Rough-cut capacity plan

Critical work centers

Individual products

Material requirements plan

Capacity requirements plan

All work centers

Components

Shop floor schedule

Input/ output control

Manufacturing operations

Individual machines

Hierarchical Planning Process

Figure 9.5

available to promise

PERIOD

ON-HAND = 50 1 2 3 4 5 6

PERIOD

ON-HAND = 50 1 2 3 4 5 6

Forecast 100 100 100 100 100 100

Customer orders

Master production schedule 200 200 200

Available to promise

Forecast 100 100 100 100 100 100

Customer orders 90 120 130 70 20 10

Master production schedule 200 200 200

Available to promise 40 0 170

Available-to-Promise

ATP in period 1 = (50 + 200) - (90 + 120) = 40

ATP in period 3 = 200 - (130 + 70) = 0

ATP in period 5 = 200 - (20 + 10) = 170

Example 9.5

available to promise2

Product Request

Is an alternative product available at an alternate location?

Yes

Yes

Is the product available at this location?

Available-to-promise

No

No

Allocate inventory

Capable-to-promise date

Yes

Is an alternative product available at this location?

Available-to-promise

Is the customer willing to wait for the product?

No

Yes

Allocate inventory

Revise master schedule

Is this product available at a different location?

Yes

No

Trigger production

Lose sale

No

Available-to-Promise

Figure 9.6

aggregate planning for services
Aggregate Planning for Services

Most services can’t be inventoried

Demand for services is difficult to predict

Capacity is also difficult to predict

Service capacity must be provided at the appropriate place and time

Labor is usually the most constraining resource for services

yield management

Cu

Cu + Co

P(n < x) 

Yield Management

where

n = number of no-shows

x = number of rooms or seats overbooked

Cu = cost of underbooking; i.e., lost sale

Co = cost of overbooking; i.e., replacement cost

P = probability

yield management1
Yield Management

NO-SHOWS PROBABILITY

0 .15 1 .25

2 .30

3 .30

Example 9.4

yield management2

NO-SHOWS PROBABILITY P(N < X)

0 .15 .00

1 .25 .15

2 .30 .40

3 .30 .70

.517

Expected number of no shows

0(.15) + 1(.25) + 2(.30) + 3(.30) = 1.75

Optimal probability of no-shows

P(n < x)  = = .517

Cu

Cu + Co

75

75 + 70

Yield Management

Example 9.4

yield management3

NO-SHOWS PROBABILITY P(N < X)

0 .15 .00

1 .25 .15

2 .30 .40

3 .30 .70

Cost of overbooking

[2(.15) + 1(.25)]$70 = $38.50 Cost of bumping customers

(.30)$75 = $22.50 Lost revenue from no-shows

$61.00 Total cost of overbooking by

2 rooms

.517

Expected number of no shows

0(.15) + 1(.25) + 2(.30) + 3(.30) = 1.75

Optimal probability of no-shows

P(n < x)  = = .517

Expected savings = ($131.225 - $61) = $70.25 a night

Cu

Cu + Co

75

75 + 70

Yield Management

Example 9.4