### A Simple Controller

There are many ways to design a PAL model. The design that comes naturally to our minds is the one that splits the available quantity over a number of buckets (markets, plants, customers, etc).

This design is simple to understand, but from the point of view of automatic control it faces serious challenges. A control system would have to compute where to deallocate and where to allocate quantity. It becomes an optimization problem.

But let's see a different design (that was also part of this discussion). It checks first the capacity on the main buckets and then checks on a second level a capacity that is available for all orders (sequence of procedures).

Let's suppose we use monthly buckets and that at the start of the month the first procedure has 100% of total capacity and the second procedure has zero capacity. This is exactly as having just one level. Then as time passes the control system can read each bucket and compare the available capacity to some expected target value. If there is more free capacity than the target the system can reduce the bucket capacity and allocate the remaining to the second procedure.

The target open quantity can be one of many functions that return a profile of consumption over time. For example it could just be linear, linear within an internal interval or exponential as shown bellow.

This will make a control algorithm that is simple to understand and implement. And for many practical purposes it does what business expects (if a market is not consuming the quota, then it becomes available for the other markets).

This design is simple to understand, but from the point of view of automatic control it faces serious challenges. A control system would have to compute where to deallocate and where to allocate quantity. It becomes an optimization problem.

But let's see a different design (that was also part of this discussion). It checks first the capacity on the main buckets and then checks on a second level a capacity that is available for all orders (sequence of procedures).

Let's suppose we use monthly buckets and that at the start of the month the first procedure has 100% of total capacity and the second procedure has zero capacity. This is exactly as having just one level. Then as time passes the control system can read each bucket and compare the available capacity to some expected target value. If there is more free capacity than the target the system can reduce the bucket capacity and allocate the remaining to the second procedure.

The target open quantity can be one of many functions that return a profile of consumption over time. For example it could just be linear, linear within an internal interval or exponential as shown bellow.

This will make a control algorithm that is simple to understand and implement. And for many practical purposes it does what business expects (if a market is not consuming the quota, then it becomes available for the other markets).

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