Aggregate Planning
Problem Information
The planner of a company that makes garden tractors
is about to prepare an aggregate production plan that will cover the next 6
months. She has collected the following information:
|
Month |
Demand Forecast |
|
1 |
2,000 |
|
2 |
2,000 |
|
3 |
3,000 |
|
4 |
4,000 |
|
5 |
5,000 |
|
6 |
2,000 |
|
Total |
18,000 |
Permanent workforce = 140
Production per month = 2,800 units or 20 per worker
Initial
inventory = 1,000 units
Desired ending inventory = 1,000 units
Cost:
Labor
Regular time permanent = $100 per tractor
Overtime = $150 per tractor
Temporary = $100 per tractor
Hire cost = $500 per temporary worker (assume same
productivity as permanent)
Inventory = $10 per tractor per month
Back order = $150 per tractor per month
The production volume, workforce level, and
inventory level for each month that satisfies the specified demand, workforce,
and inventory limitations. The aggregated plan must also focus on reducing the
overall cost must be determined in order to create the aggregate production
plan. In order to prepare the aggregate production plan, we need to determine
the production quantity, workforce level, and inventory level for each month
that can meet the given demand, workforce, and inventory constraints while minimizing
the total cost. This will allow us to prepare the plan in the most
cost-effective manner possible.
First, we calculate the overall demand over the course
of the planning horizon is forecasted demand in total equals 18000. When you
factor in the existing stock of 1000 units, the total demand that needs to be
satisfied is 18000 units. We can utilize the level production rate, which
simply means generating the same quantity each and every month, to calculate
the production quantity that will be produced for each month. Throughout the
course of the planning horizon, the following graph from the analysis will
constitute the entire production:
Graph
1: Level output-workforce Strategy
We are able to establish the workforce level by
utilizing the production per worker that is specified in the issue, which is 20
units per worker. Let's suppose that the required amount of permanent staff
each month is y. Over the course of the planned horizon, the following will be
the total number of permanent staff that will be required. The whole permanent
workforce is equal to six years. To ensure that we are able to reach the
production amount, we need to check that the monthly production divided by
production per worker = number of workers permanently employed plus number of
workers temporarily employed. Thus 3000 divided by 20 equals y plus the number
of contract workers
It is the policy of the company that the maximum amount
of overtime output per month be 350 units. The number of contract workers
equals 150. Because of this, we will need to recruit 150 temporary workers per
month in order to maintain the current level of production.
The next step and compute the overall cost of the
production plan. The following graph presents the results for the aggregate
plans that will make up the cost of permanent workers:
The third option
is to use temporary workers. Suppose that temporary workers will be working
during a second shift and enough of them are available. We will therefore
develop an aggregate production plan in this case. It is noteworthy that
overtime is not possible in this case. The
cost of permanent workers is calculated as follows: Cost of permanent workers =
Regular time permanent * Number of permanent workers * the number of months
multiplied by $100, 140, and 6 equals $84,000.
The following are the expenses associated with temporary
workers: The cost of temporary workers is equal to the hire cost multiplied by
the number of temporary workers multiplied by the number of months; therefore
$25 multiplied by 150 multiplied by 6 equals $22,500.The overall cost of labor
is equal to the sum of the wages paid to permanent workers and the wages paid
to temporary workers, which comes to $106,500.Cost of inventory equals the
average level of inventory multiplied by the cost of inventory per tractor per
month multiplied by the number of months, so 1000 * $10 * 6 = $60,000
In order to assess how much the cost of backorders will
be, we need to find out how many backorders are placed each month. Due to the
fact that the backorder level is going to be negative in month 5, there won't
be any backorders in month 5. The cost of backorders can be calculated as the
total number of backorders multiplied by the cost of backorders per tractor per
month multiplied by the number of months. As a result, the following will
constitute the overall cost of the production plan cost can be calculated as
follows: total labor cost plus cost of inventory plus cost of backorders. The
production plan that calls for level output and manpower, using inventory to
absorb the uneven predicted demand, but allowing certain backorders, would cost
the corporation.
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