Aggregate Planning Ash Soni ODT Department Kelley School of Business

Aggregate Planning
Ash Soni
ODT Department
Kelley School of Business
What is Aggregate Planning
Aggregate planning is a process by
which a company determines levels of
capacity, production, subcontracting,
inventory, stock-outs and pricing over a
specified time horizon. The objective is
to satisfy demand in a way that
maximizes profit or minimizes costs for
the firm
Process Planning
Long-range
Strategic Capacity Planning
Intermediaterange
Manufacturing
Aggregate Planning
Master Production Scheduling
Services
Material Requirements Planning
Order Scheduling
Short-range
Weekly Workforce &
Customer Scheduling
Daily Workforce &
Customer Scheduling
Variables to be Determined Over
the Planning Horizon
Production Rate – No of units completed per time unit
(such as week or per month)
Workforce – No of workers/units needed for production
Overtime – The amount of overtime production
planned
Machine Capacity Level
Subcontracting – The subcontracted capacity required
Backlog – Demand not satisfied but carried over to
future periods beyond the planning horizon
Inventory on Hand – Inventory carried over the various
periods in the planning horizon
Formal Definition
Given the demand forecasts for each
period in the planning horizon,
determine the production level,
inventory level, and the capacity level
for each period that maximizes the
firm’s profit over the planning horizon
Information Required for an
Aggregate Plan
Demand Forecasts for each period in the
planning period
Production Costs



Labor costs – Regular Time and Overtime ($/Hr)
Cost of subcontracting production ($/Unit or $/Hr)
Cost of changing production – cost of hiring/laying
off workforce ($/Worker) and cost of adding or
reducing machine capacity ($/Machine)
Labor/Machine Hours required per unit
Information Required for an
Aggregate Plan Cont’d
Inventory holding cost ($/Unit/Period)
Stockout or Backlog Cost ($/Unit/Period)
Constraints




Limits
Limits
Limits
Limits
on
on
on
on
Overtime
Layoffs
Capital Available
Stockouts and Backlogs
Some Key Determinations from
Aggregate Planning
Production quantity from regular time, overtime, and
subcontracted time allows determination of number
of workers and supplier purchase levels
Inventory Held – Used to determine warehouse space
required
Backlogs/Stock-outs – Used to determine customer
service levels
Workers Hired/Laid Off – Used to determine labor
issues
Machine Capacity increase/decrease – Used to
determine if new production equipment needs to be
purchased
Aggregate Planning Strategies
Trade-offs between three costs – capacity,
inventory and backlogs
Decrease in one cost usually results in an
increase in the other two costs
For example, to lower inventory costs, a
planner must increase either capacity or
backlogs or both
This leads to trade-offs between capacity,
inventory and backlogs.
Aggregate Planning Strategies
Chase Strategy – Uses capacity as a
lever. Production rate is synchronized
with the demand rate by varying
machine capacity or hiring and laying
off workers. It can be used when the
carrying cost of inventory is very high
and costs to change levels of capacity
and workforce are low.
Aggregate Planning Strategies
Level Strategy – Using Inventory as a
Lever. A stable machine capacity and
workforce are used to maintain a
constant output. Inventories or
backlogs play a big role. It can used
when inventory carrying costs and
backlog costs are low.
Aggregate Planning Strategies
Time Flexibility from Workforce or
Capacity Strategy – Using utilization as
a lever. May be used if there is excess
machine capacity. Then workforce
capacity can be kept stable but no. of
hours worked is varied to synchronize
production with demand. Results in
lower inventory levels but the average
utilization is lower
Example

Redwood Furniture Weekly Production
Resource Table Chair Available
Wood
30
20
300
Labor
5
10
110
Profit
$6
$8
Mathematical Formulation
XT - Number Of Tables
XC - Number of Chairs
Objective : Max 6 XT + 9 XC
Subject to (Constraints)
30 XT + 20 XC <= 300 (Wood)
5 XT + 10 XC <= 110 (Labor)
XT, XC >= 0 (Non-Negativity)
Red Tomato Inc.
Month
January
February
March
April
May
June
Demand Forecast
1,600
3,000
3,200
3,800
2,200
2,200
Red Tomato Inc.
Item
Material Cost
Cost
$10/Unit
Inventory Holding Cost
Marginal Cost of Stock-out/Backlog
Hiring and Training Costs
Layoff Cost
Labor hours Required
Regular Time Cost
Overtime Cost
Cost of Subcontracting
$2/Unit/Month
$5/Unit/Month
$300/Worker
$500/Worker
4 Hours/Unit
$4/Hour
$6/Hour
$30/Hour
Red Tomato – LP Formulation
Wt=Workforce size for month t, t=1,2 …..6
Ht=No of employees hired at the beginning of month t,
t=1,2 …..6
Lt=No of employees laid off at the beginning of month t,
t=1,2 …..6
Pt=No of units produced in month t, t=1,2 …..6
It=Inventory at the end of month t, t=1,2 …..6
St=No of units stocked out/backlogged at the end of
month t, t=1,2 …..6
Ct= No of units subcontracted for month t, t=1,2 …..6
Ot= No of overtime worked in month t, t=1,2 …..6
Red Tomato – LP Formulation
Objective Function
Regular time labor cost
Overtime labor cost
Cost of hiring and layoffs
Cost of holding inventory
Cost of stocking out
Cost of subcontracting
Material cost