Lot Sizing, Distribution, and the Bullwhip

That is what an MRP system does when nobody has told it otherwise.

Every rule from the dynamic lot sizing chapter can be used instead, applied to the net requirement row of whichever record is being planned. None of them is new.

By the explosion equation

\[ G_{jt} = \sum_{i \in \text{parents}(j)} q_{ij}\,\mathit{Rel}_{it} \]

it decides when and in what sizes the components are asked for.

Nothing below level 0 decides anything.

So whatever moves is the end item’s doing, and nothing else.

So the components see the schedule itself, and \(VC = 0.6191\) is the schedule’s own figure.

Every rule that batches raises it, as far as 1.5463 under part-period balancing.

The relation is exact, and the reason is the explosion equation and nothing else.

Every release a parent makes is a requirement its components have to meet, and meeting a requirement costs a setup.

Lot-for-lot releases eleven times, and the components below it place their own orders eleven times each.

It costs $4,860 where the adjusted economic order quantity costs $5,588.

And it is $872 worse over the structure as a whole.

Part-period balancing produces much the lumpiest pattern and is not the most expensive plan.

Wagner-Whitin produces nearly the smoothest and is the second most expensive.

The threshold was 0.2, and every row of that table clears it comfortably.

It leaves the level beneath it alone, and in a structure several levels deep that matters more at each level down.

It produces the smallest projected balances, which is what a planner wants when the requirements above are going to be revised anyway.

It needs no cost parameters. A bill of material with ten thousand items has ten thousand order costs that nobody has ever measured.

The defensible position: batch where the setup is large and genuinely known, usually the end item and the major subassemblies. Below that, the information does not exist.

A distributor holds belts at three regional warehouses, each serving its own dealers, and replenishes all three from a central warehouse.

Nothing is built anywhere.

The arrows point the way a requirement travels, which is the direction they pointed in the bill of material.

That is the explosion equation with every \(q_{ij} = 1\).

Transit time plays the part of lead time, the regions are the level-0 items, the warehouse is their component, and the algorithm runs unchanged.

The relationship reads backwards. In a bill of material the parent is what the child goes into. In a network the parent is the customer and the child is the supplier.

The arrow points the way the requirement travels, upstream in both cases, and that is why the same code carries them.

The regions sell a pattern whose variability coefficient is 0.6191. The center’s is measured over periods 3 to 15, the periods in which it has a requirement under lot-for-lot.

And the regions’ customers did nothing to cause it.

Three locations ordering on different transit times spread the same 1,840 belts over thirteen periods instead of twelve, and that spreading is the whole of the difference.

So amplification is caused by batching, and not by the network.

And every batching row is cheaper than lot-for-lot, at the regions and at the center both.

That is why this chapter can report the amplification without reporting a cost for it.

In a product structure the disagreement propagates, and the propagation is the problem.

A change to the master schedule in a distant period moves the deck assembly’s releases. Those are the belt’s requirements, so the belt replans. With a two-month lead time the belt’s releases move into nearer periods.

Lead times concentrate it. A change far out arrives at the bottom of the structure much sooner, because each level’s lead time pulls it earlier.

Low-level codes spread it. An item with several parents is replanned when any of them moves.

A time fence does the same for a span.

Safety lead time is this chapter’s addition. Instead of holding extra stock, the item is planned to arrive a period early.

It buffers a late delivery in a way safety stock does not, and costs a period of carrying on everything rather than a permanent balance on one item.

Which to use depends on whether the uncertainty is in the quantity or the timing, and requirements planning gives you no way to tell.

And it has no way, from inside the model, to justify the safety stock it offers you.

Cost below a level tracks how often the level above orders, exactly.

The locally optimal rule is not the globally optimal rule, and here the gap is 7.59%.

DRP is the same algorithm with every quantity per equal to one.

Batching at one stage amplifies at the next, and the network itself does not.