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Chapter 4

MSCI432 Chapter Notes - Chapter 4: Toilet Paper, Uptime, Fixed Cost

Management Sciences
Course Code
Binyamin Mantin

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Nahmias Chapter 4.
4.2. Discuss the cost penalties incurred by a firm that holds too much inventory and one that holds too
little inventory.
4.2 Too much:
a) Money that is tied up in inventories could be invested elsewhere.
b) Costs of supporting inventory could be high, including cost of storage (such as refrigeration
costs), taxes, insurance, etc.
c) Production/distribution inefficiencies could arise.
d) Stock can become obsolete.
Too little:
a) Insufficient stock to meet customer demand.
b) Production inefficiencies could arise. For example, in a sequential production process, a lack
of sufficient buffer inventory could cause production to come to a halt.
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4.8 a) Month Ending Inventory
Jan. 160
Feb. -1305
March -1225
April -700
May -480
June 1020
b) The total number of excess demands = 1305 incurred in February only. Hence the cost =
(1305)(10) = $13,050. If backorders are filled on a LIFO basis then the cost is the same
whether excess demands are lost or backordered. However, if backorders are filled on a FIFO
basis the cost in the backorder case will be larger.
c) From part (a): cumulative backorders = 3710 which gives the cost = (3710)(10) = $37,100.
d) The criterion used in part (b) would be appropriate in a competitive retail environment where
the customer would normally go elsewhere if demand cannot be filled immediately. The
criterion used in part (c) would be appropriate if the customer must wait for the item, or if the
demand is for a part that causes a production process to be delayed.
4.10. A speciality coffeehouse sells Colombian coffee at a fairly steady rate of 280 pounds annually. The
beans are purchased from a local supplier for $2.40 per pound. The coffeehouse estimates that it cots $45
in paperwork and labour to place an order for the coffee, and holding costs are based on a 20 percent
annual interest rate.
a. Determine the optimal order quantity for Colombian coffee.
b. What is the time between placements of orders?
c. What is the average annual cost of holding and setup due to this item?
d. If replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory.
4.10 λ = 280
c = 2.40
K = 45
I = .20
a) Q* =
(.2)(2.40) =229
b) T = Q*/λ = 229/280 = .8179 yrs. (= 9.81 months)
c) G* =
= $109.98
9.82 mos.
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