Aggregate Planning

1
Chapter 16
Aggregate and Workforce Planning
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Aggregate Planning Issues

• Role of Aggregate Planning
• Long-term planning function
• Strategic preparation for tactical actions
• Over the next year or two What will be produced
  and when?
• Management Decisions to Consider
• Production Smoothing inventory build-ahead
• Product Mix Planning best use of resources
• Staffing hiring, firing, training
• Procurement supplier contracts for materials,
  components
• Sub-Contracting capacity vendoring
• Marketing promotional activities

3
Hierarchical Production Planning
FORECASTING
Marketing Parameters
Product/Process Parameters
CAPACITY/FACILITY PLANNING
WORKFORCE PLANNING
Labor Policies
Personnel Plan
Capacity Plan
AGGREGATE PLANNING
Aggregate Plan
Strategy
Customer Demands
WIP/QUOTA SETTING
Master Production Schedule
DEMAND MANAGEMENT
Tactics
SEQUENCING SCHEDULING
WIP Position
Work Schedule
REAL-TIME SIMULATION
SHOP FLOOR CONTROL
Work Forecast
Control
PRODUCTION TRACKING
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Basic Aggregate Planning

• Problem To project production over the planning
  horizon.
• Inputs
• Demand forecast (over planning horizon)
• Capacity constraints
• Unit profit
• Inventory carrying cost rate

5
A Simple AP Model
Notation
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A Simple AP Model (cont.)
summed over planning horizon
Formulation
sales revenue - holding cost
demand capacity inventory balance non-negativity
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A Simple Linear Programming Example - page 542
and 543
Data r 10 h 1 Io 0 ct 100, 100,
100, 120, 120, 120 dt 80, 100, 120, 140, 90,
140
Optimal Solution
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A Simple Linear Programming Example (cont.)

• Constraints
• Binding - an increase the constrained variable
  will increase the objective ( ie profit)
• Non Binding an increase will not increase the
  objective
• Interpretation
• Shadow prices increase objective by increased
  amount times shadow price as long as increase is
  less than or equal to Allowable increase
• Allowable increases is the amount of increase
  available until the shadow price no longer
  applies
• Allowable decrease is the amount of decrease
  until the shadow price no longer applies

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Common Encountered Situations - Product Mix
Planning

• Problem Determine most profitable mix over
  planning horizon
• Motivation for Study
• Linking marketing/promotion to operations
• Bottleneck identification.
• Inputs
• Demand forecast by product (family?) may be
  ranges
• Unit hour data
• Capacity constraints
• Unit profit by product
• Holding cost

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Basic Conceptual Formulation
Goal maximize profit subject to
production ? capacity, at all workstations in
all periods sales ? demand, for all
products in all periods
Note we will need some technical constraints to
ensure that variables represent reality.
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Product Mix Notation
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Product Mix Formulation
sales revenue - holding cost
demand capacity inventory balance non-negativity
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Product Mix (Goldratt) Example
Assumptions

• Two products, P and Q
• Constant weekly demand, cost, capacity, etc.
• Maximum capacity 2,400 minutes on each
  Workcenter
• Objective maximize weekly profit

Data
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A Cost Approach

• Unit Profit
• Product P 45
• Product Q 60
• Maximum Production of Q 50 units
• Remaining Capacity for Producing P
• 2400 - 10 (50) 1,900 minutes on Workcenter A
• 2400 - 30 (50) 900 minutes on Workcenter B
• 2400 - 5 (50) 2,150 minutes on Workcenter C
• 2400 - 5 (50) 2,150 minutes on Workcenter D
• Maximum Production of P 900/15 60 units
• Net Weekly Profit 45 ? 60 60 ? 50 -5,000
  700

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A Bottleneck Approach

• Identify the Bottleneck Bottleneck is Workcenter
  B, because
• 15 (100) 10 (50) 2,000 minutes on workcenter
  A
• 15 (100) 30 (50) 3,000 minutes on workcenter
  B
• 15 (100) 5 (50) 1,750 minutes on workcenter
  C
• 15 (100) 5 (50) 1,750 minutes on workcenter
  D
• Profit per Minute of Bottleneck Time used
• 45/15 3 per minute spent processing P
• 60/30 2 per minute spent processing Q
• Maximum Production of P 100 units
• Maximum Production time on bottleneck for Q
  2,400 (15100) 900 minutes
• Maximum Production of Q 900/3030 units
• Net Weekly Profit 45?100 60 ?30 -5,000
  1,300

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A Modified Example
Changes in processing times on workcenters B and
D.
Data
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A Bottleneck Approach

• Identifying the BottleneckWorkcenter B, because
• 15 (100) 10 (50) 2,000 minutes on workcenter
  A
• 15 (100) 35 (50) 3,250 minutes on workcenter
  B
• 15 (100) 5 (50) 1,750 minutes on workcenter
  C
• 25 (100) 14 (50) 3,200 minutes on workcenter
  D
• Bottleneck at B
• 45/15 3 per minute spent processing P
• 60/35 1.71 per minute spent processing Q
• Maximum Production of P2400/25 96 units
• Maximum Production of Q 0 units
• Net Weekly Profit 45?96 -5,000 -680

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A Bottleneck Approach (cont.)

• Bottleneck at D
• 45/25 1.80 per minute spent processing P
• 60/14 4.29 per minute spent processing Q
  so Q is more profitable than P
• Maximum Production of Q (Bottleneck at B)
  2400/35 68.57gt50, produce 50
• Available time on Bottleneck D for Product P
• 2400 - 14(50) 1,700 minutes on
  workcenter D
• Maximum Production of P 1700/25 68 units
• Net Weekly Profit 45?4360 ?50-5000 -65

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An Improvement Via Linear Programming Approach
Formulation
Solution
Net Weekly Profit Round solution down (still
feasible) to
To get 45 ?75 60 ?36 - 5,000 535.
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Workforce Planning

• Problem Determine most profitable production
  and hiring/firing policy over planning horizon.
  
• Inputs
• Demand forecast (assume single product for
  simplicity)
• Unit hour data
• Labor content data
• Capacity constraints
• Hiring/ firing costs
• Overtime costs
• Holding costs
• Unit profit

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Workforce Planning Notation
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Workforce Planning Notation (cont.)
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Workforce Planning Formulation
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Conclusions

• No single Aggregate Planning model is right for
  every situation
• Because AP uses long time horizons, precise data
  and intricate modeling are impractical
• Simplicity promotes understanding
• Linear programming is a useful AP tool
• Robustness matters more than precision
  unforseen events will need to be factored in

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Chapter 16

• Supplemental Material

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Extensions to Basic Product Mix Model
Other Resource Constraints
Notation
Constraint for Resource j
Utilization Matching Let q represent fraction of
rated capacity we are willing to run on resource
j.
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Extensions to Basic Product Mix Model (cont.)
Backorders
Overtime
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Workforce Planning Example
Problem Description

• 12 month planning horizon
• 168 hours per month
• 15 workers currently in system
• regular time labor at 35 per hour
• overtime labor at 52.50 per hour
• 2,500 to hire and train new worker
• 2,500/16814.88 ? 15/hour
• 1,500 to lay off worker
• 1,500/1688.93 ? 9/hour
• 12 hours labor per unit
• demand assumed met (Stdt, so St variables are
  unnecessary)

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Workforce Planning Example (cont.)

• Solutions
• Chase Solution infeasible
• LP optimal Solution layoff 9.5 workers
• Add constraint Ft0
• results in 48 hours/worker/week of overtime
• Add constraint Ot ? 0.2Wt
• Reasonable solution?