## DRP and Deployment: an interesting 2-tier problem

I lent a hand yesterday at a workshop run with a client to aid configuration of an upgrade to their ERP system. The workshop, which focussed on DRP (Distribution Resource Planning) and Deployment (how we turn DRP plans into purchase orders and stock transfers), threw up the following problem.

## Manufacturer to Packer to Distribution Centre

The supply chain consists of Manufacturers, a Packing Plant, and a number of Distribution Centres (DCs). The DCs hold stock for the local market. The Packer does some final processing on the products, but holds no stock – product arriving at the Packer is immediately processed and distributed to the DCs. For some of the DCs this takes only a couple of days – for others that are further away that final shipping leg can be over a month. Manufacturing lead times are 1-6 months. Many products are held at each of the DCs.

At the moment DRP doesn’t cope with this very well – multiple schedules are provided to the Manufacturers for the same product held at different DCs.

## Deployment opportunities

The upgrade of DRP will help by presenting a consolidated schedule for the same part to its Manufacturer. But the more important benefit comes from the Deployment process. This is difficult to describe in abstract terms so I will give an example.

Suppose we have two DCs only and for a particular product DRP suggests we will need a quantity of 70 for one DC and 30 for the other. We raise the order on the Manufacturer for 100. By the time that 100 arrives at the Packer, things may have changed. Sales from the second DC might have been higher than expected. It makes no sense to keep us tied to the original split of the 100. The Deployment logic will reassess the requirements (rerunning DRP) and send, perhaps, 55 to the first DC and 45 to the other.

(Deployment will also distribute fair shares to second tier stock-holding points where there is a shortage at the parent stocking point. In fact, this is the normal usage of this process and where it typically allows an improvement on classical DRP.)

## The safety stock question

So that sounds great – we have greater flexibility, and we should get better availability to the customer from the same stock level. But by how much? And what if we would prefer to maintain availability but take the benefit in reduced stock?

This comes down to the question of what the safety stock should be for the DCs, and this is where I am scratching my head somewhat. What should be a straightforward problem turns out to be pretty subtle. You can get an insight into what the answer might be by thinking about the extreme cases when either the lead time into the Packer, or from the Packer to the DCs, is zero.

In the former case, you have no flexibility. It is as if the DCs are ordering independently on the Manufacturer. In the latter case, all of the stock for each of the DCs is pooled. There is total flexibility of stock.

## Here come the statistics…

For a given desired availability level, the safety stock for a SKU is proportional to the standard deviation of its demand over the lead time. And, if we pool demand from several sources, the standard deviation we use is the square root of the summed variances.

So the extra safety stock we require without pooling is the pooled safety stock multiplied by the square root of the number of locations (simplifying horribly – the “square root rule” deserves a proper write-up). So if we had 4 DCs, their total safety stock would be twice as much as if we pooled all their demand and satisified it from a single DC.

## Back to Deployment

The two extreme cases differ from each other in the same way as this square root rule relationship. If the two links in the supply chain have non-zero lead times, we get something in between. But exactly what is very difficult to work out. Clearly relative demands and lead times for different DCs are part of the equation, as is order interval (as in the standard safety stock problem). We’ll probably end up interpolating between the soluble extreme cases to come up with an approximation, but it would be nice to know if someone had solved this problem. The ERP supplier certainly hasn’t…

Categories: Thought Pieces.

Tags: DRP, Inventory Management

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