Nahmias Chapter 4.
4.2. Discuss the cost penalties incurred by a firm that holds too much inventory and one that holds too
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.
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. 4.8 a) Month Ending Inventory
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* = = = 229
b) T = Q*/λ = 229/280 = .8179 yrs. (= 9.81 months)
c) G* = 2Kλh = (2)(45)(280)(.2)(2.40= $109.98
9.82 mos. r = λγ = (280)(3/52) = 16.15
r = 16 units
4.11. For the question described in Problem 10, draw a graph of the amount of inventory on order. Using
your graph, determine the average amount of inventory on order. Also compute the demand during the
replenishment lead time. How to these quantities differ?
3 wks 3 wks
42.53 wks 42.53 wks
Avg = (229 x 3)/42.53 = 16.1538
Demand during lead time = λγ = (280/52)(3) = 16.1538 (exactly the same).
4.13.Consider the coffeehouse discussed in Problem 10. Suppose that its setup cost for ordering was
really $15. Determine the error made in calculating the annual cost of holding and setup incurred as a
result of its using the wrong value of K. (Note that this implies that its current order policy is suboptimal.)
4.13 True optimal Q = (2)(15)(280= 132