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Simulating Inventory Control with Orders that Cross during Lead Time
Johnson Graduate School of Management
Ithaca NY 14853
This workbook is intended for teaching or research.
You are welcome
to use it in any manner,
and change it as you see fit.
It comes without any guarantee whatsoever, and is distributed
Most inventory control systems use a formula for lead-time demand to set safety stock levels.
Research has uncovered situations where that method leads to large and expensive errors.*
In particular, if replenishment orders might not arrive in the same order in which they are placed, then
the above method will leave you with too much inventory if your objective is a high level of protection,
and too little inventory if you are aiming to run out of stock frequently. That is, the variance of the
inventory level is smaller than the variance of lead-time demand.
*See Robinson, L.R, J.R. Bradley and L.J. Thomas, "Consequences of Order Crossover under
Volume 3, No. 3 (2001), pp.175-188.
This workbook contains a macro, written in Visual Basic, that allows you to simulate the inventory control
system known variously as the Min-Max system, the (s,S) system, or the reorder-level, order-up-to system.
Two versions are available in the simulation:
> Periodic review: orders may be placed only at specific points of time, such as daily or weekly.
> Continuous review: orders are placed instantly, as soon as inventory reaches the reorder level.
In both cases, the state of the system is tracked at all times, so that accurate costs may be calculated.
The word "order" refers to an action taken to replenish the supply of an item that is stocked in inventory
and sold to customers. The word "demand" refers to a customer wanting to buy one unit of the item.
A "backorder" is an unsatisfied demand for which the customer will take delivery at a later time.
The simulation assumes that all customers are willing to wait if their demand is backordered.
The simulation allows orders to cross. It assumes that the lead time of one order is independent of
that for any other order, and therefore crossing occurs whenever the lead time for an order is longer
than the interval between orders plus the lead time for the next order.
Please note that the independence assumption is not true in some real circumstances. For example,
if both orders are shipped by rail, and if one freight car cannot pass another, the orders cannot cross.
However, in that case lead times are also not independent, but rather are positively correlated, so
models that assume independence (i.e. most inventory models) are also incorrect.
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Changes are frequent, so check back frequently for a new version.