Formulae Aggregate Planning



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Formula Sheet
Little’s Law
Little’s Law: WIP = R x T
Throughput (R): is the average number of entities/items completed per unit time, the output rate from a process.
Flow time or Cycle time (T): is the average time it takes to complete one cycle of a process.
Cycle time = Processing time + Delay time
Work in Progress (WIP): is defined as products (or people) which the organisation has partially processed and are not completed.
Throughput Time: is the average time required to complete a batch or job.
Work Content: is the average time to process one item.
Server: is the person or machine doing the work
Throughput Time = WIP x Cycle Time
WIP = Throughput Time
Cycle Time
Cycle Time = Throughput Time
Work in progress
Servers Required = Work Content
Cycle Time
Efficiency = Amount of product produced x 100 %
Amount of raw material used.
Utilisation (U) = Resources Used
Resources Available
Utilisation (U) = Demand Rate
(Service Rate x Number of Servers)

Cycle time = Process time (for a batch)


Number processed
Throughput efficiency = Work content
Throughput time
Value Added Throughput Efficiency (VATE):
VATE = Value-added work content
Throughput time


Balancing Loss
Idle Time on each stage = Bottleneck time – processing time for that stage
Total Idle time for a process = ∑(Idle Time on each stage)
Balancing Loss = Total Idle time for a process
Cycle Time x No of Stages
Where:
Idle Time is when a machine is not processing an item and is waiting for work to be passed from the previous machine in a process.
The Cycle Time is governed by the bottleneck in the process. The cycle time will include some idle time on some machines or processes but not the bottleneck.
The Number of Stages is the number of separate processes (e.g. number of machines) in the overall production process.


Productivity
Productivity = Quantity of Output
Quantity of Input
Productivity = Output from the operation
Input to the operation
Single factor productivity = Output from the operation
One input to the operation
Multifactor productivity = Output from the operation
All inputs to the operation
Actual Productivity = Actual Output
Resources actually consumed
Total Productivity = Total Output
Total Input
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