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436 CHAPTER 10 INVENTORY MODELS

MANAGEMENT SCIENCE IN ACTION

Lowering Inventory Cost at Dutch Companies
n the Netherlands, companies such as Philips, the lead-time demand distribution is approximated
I Rank Xerox and Fokker have followed the trend directly, taking into account both the probabilistic
of developing closer relations between the firm and demand and the probabilistic length of the lead-time
its suppliers. As teamwork, coordination and infor- period.
mation sharing improve, opportunities are available The supplier’s information concerning scheduled
for better cost control in the operation of inventory production runs provides the warehouser with a bet-
systems. ter understanding of the lead time involved for a
One Dutch public warehouser has a contract with product and the resulting lead-time demand distribu-
its supplier under which the supplier routinely pro- tion. With this information, the warehouse can modify
vides information regarding the status and schedule the reorder point accordingly. Information sharing by
of upcoming production runs. The warehouser’s the supplier thus enables the order-quantity, reorder
inventory system operates as an order-quantity, reor- point system to operate with a lower inventory
der point system with probabilistic demand. When holding cost.
the order quantity Q has been determined, the ware-
Based on F.A. van der Duyn Schouten, M.J.G. van Eijs and R.M.J.
houser selects the desired reorder point for the prod-
Heuts, ‘The Value of Supplier Information to Improve Management of a
uct. The distribution of the lead-time demand is Retailer’s Inventory’, Decision Sciences 25, no. 1 (January/February
essential in determining the reorder point. Usually, 1994): 1–14.

assumed normal distribution for lead-time demand with ¼ 154 and s ¼ 25, the
reorder point r is:

r ¼ 154 þ 1:645ð25Þ¼ 195
If a normal distribution is used for lead-time demand, the general equation for r is:

r ¼ þ z (10:37)

where z is the number of standard deviations necessary to obtain the acceptable
stock-out probability.
So, the recommended inventory decision is to order 400 units whenever the
inventory reaches the reorder point of 195. Because the mean or expected demand
during the lead time is 154 units, the 195 154 ¼ 41 units serve as a safety stock,
which absorbs higher-than-usual demand during the lead time. Roughly 95 per cent
of the time, the 195 units will be able to satisfy demand during the lead time. The
anticipated annual cost for this system is as follows:
Holding cost; normal inventory ðQ=2ÞC h ¼ð400=2Þð1:20Þ¼ E240
Holding cost; safety stock ð41ÞC h ¼ 41ð1:20Þ ¼ E 49
Ordering cost ðD=QÞC o ¼ð8008=400Þ12 ¼ E240
Total E529

If Dabco could assume that a known, constant demand rate of 8008 units per year existed
for the lightbulbs, then Q* ¼ 400, r ¼ 154 and a total annual cost of E240 + E240 ¼
E480 would be optimal. When demand is uncertain and can only be expressed in
probabilistic terms, a larger total cost can be expected. The larger cost occurs in the form
of larger holding costs because more inventory must be maintained to limit the number

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