Aggregate
Production
Planning
THE AGGREGATE PLANNING PROBLEM
The
objective of the aggregate plan is to satisfy demand in a way that
maximizes profit for the firm.
“Given the demand forecast for each period in the planning
horizon, determine the production level, inventory level,
capacity level (internal and outsourced), and any backlogs
(unmet demand) for each period that maximize the firm’s
profit over the planning horizon.”
Inputs for Aggregate Planning Problem
demand forecast 𝐅𝐭 for each Period t in a planning horizon that
extends over T periods
Aggregate
Production costs
Labor costs, regular
time ($/hour), and overtime costs ($/hour)
Cost of subcontracting production ($/unit or $/hour)
Cost
of changing capacity; specifically, cost of hiring/laying off workforce
($/worker) and cost of adding or reducing machine capacity ($/machine)
Labor/machine hours required per unit
Inventory holding cost ($/unit/period)
Stockout or backlog cost ($/unit/period)
Constraints
Limits on overtime
Limits on layoffs
Limits on capital available
Limits on stockouts and backlogs
Constraints from suppliers to the enterprise
Outputs
Production
Quantity from Regular Time, Overtime, and Subcontracted Time:
used to determine number of workers and supplier purchase levels
Inventory
Held: used to determine the warehouse space and working capital
required
Backlog/Stockout Quantity: used to determine customer service levels
Workforce
Hired/Laid Off: used to determine any labor issues likely to be
encountered
Machine
Capacity Increase/Decrease: used to determine if new production
equipment should be purchased or available equipment idled
Identifying Aggregate Units of Production
An important first step in aggregate planning is the identification of a suitable
aggregate unit of production.
While
planning is done at the aggregate level, it is important that the
aggregate unit be identified in a way that when the final production schedule
is built (this has to be at the disaggregate product level), the results of the
aggregate plan reflect approximately what can be accomplished in practice.
Given
that the bottleneck is likely to be the most constraining area in any
manufacturing facility, it is important to focus on the bottleneck when
selecting the aggregate unit and identifying capacity as well as production
times.
Determining Aggregate Unit
A
simple approach to defining the aggregate unit is based on the
weighted average of the percentage of sales represented by each
family.
Such
an approach is meaningful if management is relatively
confident of the mix of sales and all the product families use
roughly the same set of resources at a plant.
Determining Aggregate Unit
the material cost per
aggregate unit is obtained as (15 * 0.10) + (7 * 0.25) + (9
* 0.20) + (12 * 0.10) + (9 * 0.20) + (13 * 0.15) = $10.
Using
a similar evaluation, we obtain that the revenue per aggregate unit =
$40 and the net production time per aggregate unit = 4.00 hours.
Formulation of Linear Programming
Formulation of Linear Programming…..
Red
Tomato sells each tool through retailers for $40. The company has a
starting inventory in January of 1,000 tools. At the beginning of January, the
company has a workforce of 80 employees.
The
plant has a total of 20 working days in each month, and each employee
earns $4 per hour regular time. Each employee works eight hours per day on
straight time and the rest on overtime.
The
capacity of the production operation is determined primarily by the total
labor hours worked. Therefore, machine capacity does not limit the capacity
of the production operation.
Because
of labor rules, no employee works more than 10 hours of overtime
per month.
Variable Costs
Formulation of Linear Programming…..
Currently,
Red Tomato has no limits on subcontracting, inventories, and
stockouts/backlog.
All
stockouts are backlogged and supplied from the following months’
production.
Inventory costs are incurred on the ending inventory in the month.
The
supply chain manager’s goal is to obtain the optimal aggregate plan that
allows Red Tomato to end June with at least 500 units (i.e., no stockouts at
the end of June and at least 500 units in inventory).
Decision Variables
Objective Function
Regular Time Labor Cost
Overtime Cost
Costs of Hiring and Layoffs
Cost of Inventory and Stockout
Cost of Materials and Subcontracting
Objective Function
Constraints
Constraints
Constraints
Constraints
Solutions
We
can easily add constraints that limit the amount purchased from
subcontractors each month or the maximum number of employees to be
hired or laid off.
Any
other constraints limiting backlogs or inventories can also be
accommodated.
Ideally,
the number of employees hired or laid off should be integer
variables.
Fractional
variables may be justified if some employees work for only part of
a month.
Such a linear program can be solved using the tool Solver in Excel.
Average Inventory and Average Time in Inventory
Solutions
Cost = $422660
Impact on Inventory Parameters
Impact of Higher Demand Variability
All the data are exactly the same as in our previous discussion of Red Tomato,
except for the demand forecast.
Assume
that the same overall demand (16,000 units) is distributed over the
six months in such a way that the seasonal fluctuation of demand is higher, as
shown in Table 8-5.
Impact of Higher Demand Variability
Solution
Cost = $433,080
Impact on Inventory Parameters
Impact of Lower Cost of Hiring and Layoffs
Assume
that demand at Red Tomato is as shown in Table 8-2, and all other
data are the same except that the costs of hiring and layoff are now $50 each.
Solution
Cost = $412,780
Impact on Inventory Parameters
BUILDING A ROUGH MASTER PRODUCTION SCHEDULE
From
an aggregate plan, a planner must disaggregate the available
information and build a rough master production schedule (MPS) that
identifies the batches produced in each period at the level of each product
family.
We
return to the Red Tomato example to illustrate a simple approach to
disaggregate an aggregate plan.
While
this approach is not necessarily optimal, it is simple to implement and
allows for a feasibility check.
Aggregate Plan
BUILDING A ROUGH MASTER PRODUCTION SCHEDULE
•
Consider the aggregate plan in Table 8-4.
•
The plan calls for a workforce of 64 and a production of 2,560 aggregate units
in Period 1.
•
We know that the production constraint is feasible at the aggregate level, but
we will need to check feasibility at the disaggregate level.
•
The first step is to divide the production quantity of 2,560 across the six
families. We do so in the ratio of expected sales as shown in Table 8-8.
Master Production Schedule
BUILDING A ROUGH MASTER PRODUCTION SCHEDULE
•
Thus, the plan is to produce 256 units of Family A in Period 1 because it
represents 10 percent of sales.
•
The next step is to identify the number of planned batches for each family.
•
To get feasibility of the plan, we divide the planned production quantity by
the average batch size and the round the answer down.
•
For Family A, the planned number of setups (batches) is thus 256/50 = 5.12
rounded down, which equals 5.
•
As a result, the average batch size of Family A produced in this period will be
larger than 50 (about 51).
BUILDING A ROUGH MASTER PRODUCTION SCHEDULE
•
We similarly obtain the planned number of setups (batches) for each of the other
families in Period 1 as shown in Table 8-8.
•
To check the feasibility of the planned schedule, we calculate the setup time and
the production time for the planned number of batches and units of each product
family.
•
From Table 8-8, the total planned production and setup time is 10,231.4 hours (209
for setup + 10,022.4 for production).
•
Given the 64 people planned, the available production time in the period is 64 *
160 = 10,240 hours.
•
The planned schedule thus seems feasible.
IMPLEMENTING AGGREGATE PLANNING IN PRACTICE
1.
Think beyond the enterprise to the entire supply chain:
 Most aggregate planning today takes only the enterprise as its breadth of scope.
 However, many factors outside the enterprise and throughout the supply chain can affect
the optimal aggregate plan dramatically.
 Therefore, avoid the trap of thinking only about your enterprise when planning.
 Work with downstream partners to produce forecasts, with upstream partners to
determine constraints, and with any other supply chain entities that can improve the
quality of the inputs into the aggregate plan.
IMPLEMENTING AGGREGATE PLANNING IN PRACTICE
2.
Make plans flexible, because forecasts are always inaccurate:
 Aggregate plans are based on forecasts
of future demand.
 Given that these forecasts
are always inaccurate to some degree, the aggregate plan needs to have
some flexibility built into it if it is to be useful.
 By building flexibility into the plan, when future demand changes, or other
changes occur such as
increases in costs, the plan can adjust appropriately to handle the new situation.
 To increase a manager can perform
sensitivity analysis on the inputs into an aggregate plan.
 For example, if the plan recommends expanding expensive capacity while facing uncertain
demand, examine the outcome of a new aggregate plan when demand is higher and lower than
expected.
 If this examination
reveals a small savings from expanding capacity when demand is high but a
large increase in cost when demand is lower than expected, deciding to postpone the capacity
investment decision is a potentially attractive option.
IMPLEMENTING AGGREGATE PLANNING IN PRACTICE
3.
Rerun the aggregate plan as new data emerge:
 As we have mentioned, aggregate plans provide a map for the next 3 to 18 months.
 This does not mean that a firm should run aggregate plans only once every 3 to 18 months.
 As inputs such as demand forecasts change, managers should use the latest values of
these inputs and rerun the aggregate plan.
 By using the latest inputs, the plan will avoid sub-optimization based on old data and will
produce a better solution.
IMPLEMENTING AGGREGATE PLANNING IN PRACTICE
Use aggregate planning as capacity utilization increases:
4.
 Surprisingly,
many companies do not create aggregate plans and instead rely solely on
orders from their distributors or warehouses to determine their production schedules.
 These
orders are driven either by actual demand or through inventory management
algorithms.
 If
a company has no trouble meeting demand efficiently this way, then the lack of
aggregate planning may not harm the company significantly.
 However,
when utilization becomes high and capacity is an issue, relying on orders to set
the production schedule can lead to capacity problems.
 When utilization is high, the likelihood of producing for all the orders as they arrive is low.
 Planning needs to be done to best utilize the capacity to meet the forecasted demand.
 Therefore,
as capacity utilization increases, it becomes more important to perform
aggregate planning.
Example 1
Skycell, a major European cell phone manufacturer, is making production plans for the coming year.
Skycell has worked with its customers (the service providers) to come up with forecasts of monthly
requirements (in thousands of phones) as shown in Table 8-9. Manufacturing is primarily an
assembly operation, and capacity is governed by the number of people on the production line. The
plant operates for 22 days in the months of January, March, May, July, August, October, and
December, 19 days in the months of February, April, and November, and 20 days in the months of
June and September eight hours each day. One person can assemble a phone every 10 minutes.
Workers are paid 20 euros per hour and a 50 percent premium for overtime. The plant currently
employs 1,250 workers. Component costs for each cell phone total 20 euros. Given the rapid decline
in component and finished-product prices, carrying inventory from one month to the next incurs a
cost of 3 euros per phone per month. Skycell currently has a no-layoff policy in place. Overtime is
limited to a maximum of 20 hours per month per employee. Assume that Skycell has a starting
inventory of 50,000 units and wants to end the year with the same level of inventory.
Example 1
a.
Assuming no backlogs, no subcontracting, and no new hires, what is the optimum production
schedule? What is the annual cost of this schedule?
b.
Is there any value for management to negotiate an increase of allowed overtime per employee
per month from 20 hours to 40?
c.
Reconsider parts (a) and (b) if Skycell starts with only 1,200 employees. Reconsider parts (a) and
(b) if Skycell starts with 1,300 employees. What happens to the value of additional overtime as
the workforce size decreases?
d.
Consider part (a) for the case in which Skycell aims for a level production schedule such that the
quantity produced each month does not exceed the average demand over the next 12 months
(1,241,667) by 50,000 units. Thus, monthly production including overtime should be no more
than 1,291,667. What would be the cost of this level production schedule? What is the value of
overtime flexibility?
Example 2
Reconsider the Skycell data in Exercise 1. Assume that the plant has 1,250 employees and a no-layoff
policy. Overtime is limited to 20 hours per employee per month. A third party has offered to produce
cell phones as needed at a cost of $26 per unit (this includes component costs of $20 per unit).
a.
What is the average per unit of in-house production (including inventory holding and overtime
cost) if the third party is not used?
b.
How should Skycell use the third party? How does your answer change if the third party offers a
price of $25 per unit?
c.
Should Skycell use the third party if the per unit cost is $28?
d.
Why would Skycell use the third party even when the per-unit cost of the third party is higher
than the average per-unit cost (including inventory holding and overtime) for in-house
production?