Aggregate Planning

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Aggregate Planning
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9/19 Agenda

• 600 715 Discuss cases (7-11, Guinness) and
  Ch. 4
• 715 730 Crash course on Linear Programming
• 730 815 Aggregate Production Planning
  example
• 830 930 Using Excels LP Solver for
  Aggregate Planning
• 930 1000 Aggregate Planning
  investigation/experimentation
• Due next class (10/1)
• Case readings World Co. Wal-Mart
• Group Project Specialty Packaging Corporation,
  Parts AB

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Linear ProgrammingA Simple Example
Jack makes Xylophones and Yo-yos out of string
and wood (and time). The following table
provides per-unit resource and profit data for X
and Y, and resource availability this week.
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Linear ProgrammingA Simple Example (cont)
Let X and Y represent the number of xylophones
and yo-yos Jack will make this week. Because of
resource constraints (and common sense), X and Y
must obey
50
Time
String
32
25
Feasible Region
Wood
30
32
60
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Linear ProgrammingA Simple Example (cont)
All points inside the 5-vertex polygonal feasible
region represent possible production plans for
the week. But profit 2x3y, so the vector
(2,3) points in the direction of more
profitability.
50
Time
String
3
32
25
2
Feasible Region
Wood
30
32
60
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Linear ProgrammingA Simple Example (cont)
Which point is most profitable? The intersection
of constraints Time and Wood is furthest in the
profitable direction.
50
String
Time
32
25
Feasible Region
Wood
30
32
60
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Linear ProgrammingA Simple Example (cont)
Formulated as a Linear Program, the whole problem
looks like

• Commercial software exists to solve very large
  problems of this form very quickly, and MANY
  business problems take this form.
• Permissible variations include
• Max or Min
• Constraints lt, , or gt
• Free variables (allowed to be negative)
• Other variations can be optimized using other
  techniques
• Variables forced to be integer or binary (0,1)
• Nonlinear Objective function and/or constraints
• Constraints satisfied with a specified
  probability
• Etc!

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Aggregate Planning at Red Tomato Tools
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Fundamental tradeoffs in Aggregate Planning

• Capacity (regular time, over time, subcontract)
• Inventory
• Backlog / lost sales

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Basic Production Planning Strategies

• Chase strategy
• Manipulate production capacity to meet changes in
  demand
• Hire/layoff workforce
• Buy/sell machinery/facilities
• Low inventory/stockout cost
• High workforce/capital cost

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Basic Production Planning Strategies

• Time flexibility from workforce or capacity
• Maintain high capacity, and manipulate
  utilization
• Alternate tasking for workforce/machinery in
  periods of low demand
• Low inventory/stockout cost
• High overhead due to lower average utilization
• Need flexible/skilled workforce

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Basic Production Planning Strategies

• Level Strategy
• Maintain capacity and high utilization
• Manipulate Inventory/Stockout levels to meet
  changing demand
• High inventory/stockout cost
• Low operating costs due to efficiency (high
  utilization)

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Aggregate PlanningSpecify Data
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Aggregate Planning Define Decision Variables

• Wt Workforce size during month t
• Ht Number of employees hired at the beginning
  of month t
• Lt Number of employees laid off at the
  beginning of month t
• Pt Production in month t
• It Inventory at the end of month t
• St Number of units stocked out at the end of
  month t
• Ct Number of units subcontracted for month t
• Ot Number of overtime hours worked in month t
• All for t 16

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Aggregate PlanningDefine Objective Function
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Aggregate Planning Define Variable
Relationships (Constraints)

• Workforce size for each month is based on hiring
  and layoffs

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Aggregate Planning (Constraints)

• Production for each month cannot exceed capacity

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Aggregate Planning (Constraints)

• Inventory balance for each month

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Aggregate Planning (Constraints)

• Overtime for each month

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Scenarios

• Increase in holding cost (from 2 to 6)
• Overtime cost drops to 4.1 per hour
• Increased demand fluctuation

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Increased Demand Fluctuation
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Managing Predictable Variability

• Manage Supply
• Manage capacity
• Time flexibility from workforce (OT and
  otherwise)
• Use of seasonal workforce
• Use of subcontracting
• Flexible processes
• Counter cyclical products
• Manage inventory
• Component commonality
• Seasonal inventory of predictable products

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Managing Predictable Variability

• Manage demand with pricing
• Original pricing Cost 422,275, Revenue
  640,000
• Demand increase from discounting
• Market growth
• Stealing market share
• Forward buying
• Discount of 1 increases period demand by 10 and
  moves 20 of next two months demand forward

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Off-Peak (January) Discount from 40 to 39
Cost 421,915, Revenue 643,400, Profit
221,485
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Peak (April) Discount from 40 to 39
Cost 438,857, Revenue 650,140, Profit
211,283
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Demand Management

• Pricing and Aggregate Planning must be done
  jointly
• Factors affecting discount timing
• Product Margin Impact of higher margin (40
  instead of 31)
• Consumption Changing fraction of increase coming
  from forward buy (100 increase in consumption
  instead of 10 increase)
• Forward buy

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Performance Under Different Scenarios
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Factors Affecting Promotion Timing
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Summary of Learning Objectives

• Forecasting
• Aggregate planning
• Supply and demand management during aggregate
  planning with predictable demand variation
• Supply management levers
• Demand management levers

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Factors Influencing Discount Timing

• Impact of discount on consumption
• Impact of discount on forward buy
• Product margin

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Inventory/Capacity tradeoff

• Leveling capacity forces inventory to build up in
  anticipation of seasonal variation in demand
• Carrying low levels of inventory requires
  capacity to vary with seasonal variation in
  demand or enough capacity to cover peak demand
  during season

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January Discount 100 increase in consumption,
sale price 40 (39)
Off peak discount Cost 456,750, Revenue
699,560
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Peak (April) Discount 100 increase in
consumption, sale price 40 (39)
Peak discount Cost 536,200, Revenue
783,520