The first letter he opened was from Faucet Masters, a long$-$time

supplier of a specialty faucet. This was a unique faucet that did not

sell at a large volume but was steadily ordered by Jefferson$$s loyal

customers at the rate of $100$ units annually. The salespeople often

commented that having the faucet available in stock was crucial to

retaining some customers. The letter started with Faucet Masters

expressing its gratitude for the long$-$term business relationship with

Jefferson Plumbing. The letter also announced that lately the company had adopted a new minimum$-$order$-$size policy. Consequently,

faucet number $36543$ should be ordered at a minimum of $130$ units.

This new requirement caught Alex by a surprise as it was about three

times the amount he has been ordering. Through a quick rough calculation: $(3+1$

$/3)/2,$ Alex figured out that tripling the order quantity will

raise the management cost associated with this faucet by nearly $67\%.$

Alex was very uncomfortable with such a cost increase. Furthermore,

given the current low inventory level of this item, Alex knew that a

new order would have to be placed soon, and he was determined to

find a resolution even sooner.

Jefferson Plumbing sells a variety of plumbing supplies at its store

in Richmond, Virginia. Because space is a premium in its city location,

Jefferson tends to keep only small inventories and replenish them

often. With an annual holding cost of $$10$ per unit for faucet $36543,$

Alex knew that increasing the order quantity to $130$ will have a drastic

cost impact. At the same time, he hoped that ordering a large quantity

would reduce the number of orders. At an ordering cost rate of $$100$

per order, that may help a little. However, he was still concerned with

his $67\%$ increase estimate. Alex asked himself,

QUESTION

$$Should Alex place large orders of faucet $36543,$ keep them in our warehouse at an annual holding rate of $$1$ per unit, and ship small batches to the store?$$ However, when Alex recalled that each time the store

places an order from the warehouse there is a charge of $$50,$ he was

not as sure about the advantage of this approach.