1. IES 371 Engineering Management Chapter 14: Aggregate Planning
Week 13
August 31, 2005
Learning Objectives:
Understand the concepts and methods of aggregate planning
Formulate and solve capacity planning problem

2. Aggregate Plan
Aggregate Plan: A statement of a company’s 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

3. 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

4. How should an aggregate plan fit with other plans?
Business
or annual
plan
Production
or staffing
Plan (Aggregate Plan)
MPS or
workforce
schedule
Figure 14.1

5. Aggregate Plan – Managerial Inputs
Current machine capacities
Plans for future capacities
Workforce capacities
Current staffing level
Operations
Customer needs
Demand forecasts
Competition behavior
Distribution and marketing
Aggregate
plan
Supplier capabilities
Storage capacity
Materials availability
Materials
Cost data
Financial condition
of firm
Accounting and finance
New products
Product design changes
Machine standards
Engineering
Labor-market conditions
Training capacity
Human resources

6. Aggregate Plan – Outputs
Aggressive Alternatives
Complementary
Products
Competitive Pricing
Reactive Alternatives
Aggregate
plan
Size of
Workforce and
Workforce Adjustment
Units or dollars
Of Backlogs, backorders , or stockout
Inventory
Levels
Production
per month
(in units or $)
Units or dollars
subcontracted

7. 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

8. Examples of Capacity Adjustment to Meet Demand
Units
Time
Producing at a constant rate and using inventory to absorb fluctuations in demand
Hiring and firing workers to match 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)

9. Planning Strategies Chase Strategies Level Strategies Mixed 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

10. Pure Strategy Level Production Chase Demand
Units
Time
Chase Demand
Production
Demand
Units
Time
What are pros / cons of these strategies?

11. TABLE 14.1 PLANNING STRATEGIES FOR AGGREGATE PLANS
Possible Alternatives Possible Alternatives
Strategy during Slack Season during Peak Season
1. Chase #1: vary workforce Layoffs Hiring level 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, depleting workforce 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

12. Aggregate Planning Costs
Regular-Time Costs
Overtime Costs
Hiring and Layoff Costs
Inventory Holding Costs
Backorder and Stockout Costs

13. 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

14. Transportation Method
A method of LP
Gather all cost info into one matrix
Try to obtain the lowest cost alternative

15. 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

16. 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.

17. Tableau Method (Cont’d)
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.

18. 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

19. 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