IES 371 Engineering Management Chapter 14: Aggregate Planning

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IES 371 Engineering ManagementChapter 14
Aggregate Planning
Week 13 August 31, 2005

• Learning Objectives
• Understand the concepts and methods of aggregate
  planning
• Formulate and solve capacity planning problem

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Aggregate Plan

• Aggregate Plan A statement of a companys
  production rates, workforce levels, and inventory
  holding based on estimates of customer
  requirements and capacity limitations

• Service Industry
• Staffing Plan
• Regarding staffs and labor related factors

• Manufacturing Industry
• Production Plan
• Regarding production rates and inventory

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Aggregate Production Planning (APP)

• Determines resource capacity to meet demand
• For intermediate time horizon, 6-12 months
• Not feasible to build new facility
• May be feasible to hire/lay off workers,
  overtime, or subcontract
• Adjusting capacity OR managing demand

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How should an aggregate plan fit with other plans?
Figure 14.1
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Aggregate Plan Managerial Inputs
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Aggregate Plan Outputs
Aggressive Alternatives
Complementary Products
Competitive Pricing
Reactive Alternatives
Units or dollars Of Backlogs, backorders , or
stockout
Size of Workforce and Workforce Adjustment
Inventory Levels
Units or dollars subcontracted
Production per month (in units or )
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Aggregate Planning Objectives

• Minimize Costs/Maximize Profits
• Maximize Customer Service
• Minimize Inventory Investment
• Minimize Changes in Production Rates
• Minimize Changes in Workforce Levels
• Maximize Utilization of Plant and Equipment

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Examples of Capacity Adjustment to Meet Demand

1. Producing at a constant rate and using inventory
   to absorb fluctuations in demand
2. Hiring and firing workers to match demand
3. Maintaining resources for high demand levels
4. Increase or decrease working hours (overtime and
   undertime)
5. Subcontracting work to other firms
6. Using part-time workers
7. Providing the service or product at a later time
   period (backordering)

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Planning Strategies

• Chase Strategies
• Match demand during the planning horizon by
  either
• Vary workforce or vary output rate
• Level Strategies
• Maintain a constant workforce level or constant
  output rate during the planning horizon
• Constant workforce or constant output rate
• Mixed Strategies
• Combined several strategies

PURE STRATEGIES
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Pure Strategy
What are pros / cons of these strategies?
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1. Chase 1 vary workforce Layoffs Hiringlevel
to match demand
2. Chase 2 vary output Layoffs,
undertime, Hiring, overtime,rate to match
demand vacations subcontracting
3. Level 1 constant No layoffs, building No
hiring, depletingworkforce level anticipation
inventory, anticipation inventory,
undertime, vacations overtime,
subcontracting, backorders, stockouts
4. Level 2 constant Layoffs, building
antici- Hiring, depleting antici-output rate
pation inventory, pation inventory, over-
undertime, vacations time, subcontracting,
backorders, stockouts
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Aggregate Planning Costs

• Regular-Time Costs
• Overtime Costs
• Hiring and Layoff Costs
• Inventory Holding Costs
• Backorder and Stockout Costs

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Ex 1 Candy Company

• Given the following costs and quarterly sales
  forecasts of a candy company, compare the two
  strategies
• Strategy 1 Level production with constant
  workforce level
• Strategy 2 Chase production by varying workforce
  level

Quarter Sale Forecast (LB)
Spring Summer Fall Winter 80,000 50,000 120,000 150,000
Hiring cost Firing cost Inventory carrying cost Production rate per employee Beginning workforce 100 per worker 500 per worker 0.50 per pound per quarter 1000 pounds per quarter 100 workers
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Transportation Method

• A method of LP
• Gather all cost info into one matrix
• Try to obtain the lowest cost alternative

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Notations

• It inventory at the end of period t (I0
  beginning inventory)
• h holding cost per unit per period,
• r regular production cost per unit,
• o overtime cost per unit,
• u undertime cost per unit
• s subcontracting cost per unit,
• b backordering cost per unit per period
• Rt regular-time capacity in period t
• Ot overtime capacity in period t
• St subcontracting capacity in period t
• Dt forecasted demand for period t
• U total unused capacities

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Tableau Method

• Step 1 Put all capacities from the total
  capacity column into the unused capacity column.
  Next, put unit costs in each of the small boxes
• Step 2 In column 1 (period 1), allocate as much
  production as you can to the cell with the lowest
  cost but do not exceed the unused capacity in
  that row or the demand in that column.
• Step 3 Subtract your allocation from the unused
  capacity for the row. This quantity must never be
  negative.

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Tableau Method (Contd)

• Step 4 If there is still some demand left,
  repeat step 2, allocating as much production as
  possible to the cell with the next-to-lowest
  cost. Repeat until the demand is satisfied.
• Step 5 Repeat steps 2 through 4 for periods 2
  and beyond. Take each column separately before
  proceeding to the next. Be sure to check all
  cells with unused capacity for the cell with the
  lowest cost in a column.

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Ex 2 Transportation Method

• Given the following costs and quarterly sales
  forecasts, use the transportation method to
  design a production plan.
• What is the total cost of the plan?

Inventory carrying cost 3 per unit per quarter Production/worker 1000 units/quarter Regular workforce 50 workers Overtime capacity 50,000 units Subcontracting capacity 40,000 units Regular production cost 50/unit Overtime production cost 75/unit Subcontracting cost 85/unit
Quarter Sale Forecast (unit)
1 2 3 4 50,000 150,000 200,000 52,000
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Linear Programming Model (LP)

• Pure/Mixed Strategy not guarantee optimal
  solution
• LP can get optimal solution
• LP Excel, LINGO, CPLEX,
• LP Formulation
• Objective function
• Constraints
• Ex 2 Formulate LP model for Ex 1 Candy Company
  and Ex 2