1' Types of Inventories

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INVENTORY MODEL ANALYSIS
Class Work Home Work 1 of 2
By Prof. Y. Peter Chiu 2007 / 09 / 01
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N4.1
What are the two questions that inventory control
addresses?
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N4.9
HAL Ltd. produces a line of high-capacity disk
drives for mainframe computers. The housing for
drives are produced in Hamilton, Ontario, and
shipped to the main plant in Toronto. HAL uses
the drive housings at a fairly steady rate of 720
per Year. Suppose that the housings are shipped
in trucks that can hold 40 housings at one time.
It is estimated that the fixed cost of loading
the housings onto the truck and unloading them
on the other end is 300 for shipments of 120 or
fewer housings (i.e. three or fewer truckloads.)
Each trip made by a single truck cost the
company 160 in driver time, gasoline, oil,
insurance, and wear and tear on the
truck. Compute the annual costs of
transportation and loading and unloading the
housings for the following policies
(1) shipping one truck per week,
(2) shipping one full truckload as often as
needed, and (3) shipping three full
truckloads as often as needed.
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S 5.1
a. For the item used as an illustration in
Section 5.2, suppose that A was changed
to 12.80. Now find 1. EOQ in units
2. EOQ in dollars 3. EOQ as a months
supply Does the effect of the change in A
make sense ? b. For the same item suppose
that A was still 3.20 but r was
increased from 0.24/yr to 0.30/yr. Find
the same quantities requested in part (a).
Does the effect of the change in r make sense ?
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(No Transcript)
6
C.1 Given
  in sensitivity analysis, please show

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C.2 In sensitivity analysis, given
Please show
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N4.12

• A large automobile repair shop installs 1,250
  mufflers per year.
• 18 percent of which are for imported cars. All
  of the imported-
• car mufflers are purchased from a single local
  supplier at a cost
• of 18.50 each. The shop uses a holding cost
  based on a 25
• Percent annual interest rate. The setup cost for
  placing an order
• is estimated to be 28.
• Determine the optimal number of imported-car
  mufflers the
• shop should purchase each time an order is
  placed , and the
• time between replacement of orders.
• (b) If the replenishment lead time is six weeks ,
  what is the
• reorder point based on the level of on-hand
  inventory?
• (c) The current reorder policy is to buy
  imported-car mufflers
• only once a year . What are the additional
  holding and setup
• cost incurred by this policy?

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N4.14

• A local machine shop buys hex nuts and molly
  screws form the same supplier. The hex nuts cost
  15 cents each and the molly screws cost 38 cents
  each. A setup cost of 100 is assumed for all
  orders. This includes the cost of tracking and
  receiving the orders. Holding costs are based on
  a 25 percent annual interest rate. The shop uses
  an average of 20,000 hex nuts and 14,000 molly
  screws, annually.
• Determine the optimal size of the orders of hex
  nuts and
• molly screws, and the optimal time between
  placement
• of orders of these two items.
• (b) If both items are ordered and received
  simultaneously , the
• setup cost of 100 applies to the combined
  order. Compare the average annual cost of
  holding and setup if these items are ordered
  separately if they are both ordered when the
  hex nuts would normally be ordered and if they
  are both ordered when the molly screws would
  normally be ordered.

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C.3 Given that
Please show
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C.3.5

• A company purchases a product from an outside
  supplier. This item has experienced a relatively
  flat demand of 4,000 units per year. The
  accounting department has estimated that it costs
  450 to initiate an order, each unit costs the
  company 2, the cost of holding is based on an
  annual interest rate of 30, and shortages are
  backordered at 0.2 per item short per year. The
  company would like to know
• (a) The optimal order quantity.
• (b) The maximum backorder level.
• (c) How often to order.
• The maximum on-hand inventory level.
• (e) Length of time that shortages occur.

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N4.17

• The Wod Chemical Company produces a chemical
  compound that is used as a lawn fertilizer. The
  compound can be produced at rate of 10,000 pounds
  per day. Annual demand for the compound is 0.6
  million pounds per year. The fixed cost of
  setting up for a production run of the chemical
  is 1,500, and the variable cost of production is
  3.50 per pound. The company uses an interest
  rate of 22 to account for the cost of capital,
  and the costs of storage and handling of the
  chemical amount to 12 of the value. Assume that
  there are 250 working days in a year.
• What is the optimal size of the production run
  for this particular compound.
• What proportion of each production cycle consists
  of uptime and what proportion consists of
  downtime?
• What is the average annual cost of holding and
  setup attributed to this item? If the compound
  sells for 3.90 per pound, what is the annual
  profit the company is realizing from this item?

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N4.20

• Filter System produces air filters for domestic
  and foreign cars.
• One filter, part number JJ39877, is supplied on
  an exclusive
• contract basis to Oil Changers at a constant 200
  units monthly.
• Filter Systems can produce this filter at a rate
  of 50 per hour.
• Setup time to change the settings on the
  equipment is 1.5 hours.
• Worker time (including overhead) is charged at
  the rate of 55
• per hour and plant idle time during setups is
  estimated to cost
• the firm 100 per hours in lost profit.
• Filter Systems has established a 22 percent
  annual interest
• charge for determining holding cost. Each filter
  costs the
• company 2.50 to produce they are sold for 5.50
  each to Oil
• Changers. Assume 6-hour days, 20 working days
  per month,
• and 12 months per year for your calculations.
• How many JJ39877 filters should Filter Systems
  produce
• in each production run of this particular
  part to minimize
• annual holding and setup costs ?

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N4.20
(b) Assuming that it produces the optimal number
of filters in each run, what is the
maximum level of on-hand inventory of these
filters that the firm has at any point in time
? (c) What percentage of the working time does
the company produce these particular
filters, assuming that the policy in part
(a) is used ?
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C.3.8
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C.3.9
A company produces a product for several
industrial clients. It has experienced a
relatively flat demand of 4,000 units per year.
This item is produced at a rate of 10,000 units
per year. The accounting department has estimated
that it costs 450 to initiate a production run,
each unit costs the company 2 to manufacture,
the cost of holding is based on an annual
interest rate of 30, and shortages are
backordered at 0.2 per item short per year. The
company would like to know (a) The optimal order
quantity. (b) The maximum backorder level. (c)
How often to order. (d) The maximum on-hand
inventory level. (e) Length of time that
shortages occur.
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S5.3
A firm can load and package their own brand
of 35-mm slide film, or buy prepacked rolls of
Discount brand film. If they load their own
film, there is a production setup cost of 20.
The finished product is valued at 1.23 a roll,
and the production rate is 500 rolls /day.
Discount film costs the firm 1.26 per roll and
the fixed ordering charge is 3/order. In either
case, an inventory carrying charge of 0.24//yr
would be used by the company. Demand for this
item is 10,000 rolls per year. From the
standpoint of replenishment and carrying costs,
what should the company do? What other
considerations might affect the decision?
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S5.4
A manufacturing firm located in Calgary
produces an item in a three-month time supply. An
analyst, attempting to introduce a more logical
approach to selecting run quantities, has
obtained the following estimates of
characteristics of the items
D 4000 units /yr A 5 v 4 per 100
units r 0.25 //yr

• Note Assume that the production rate is much
  larger than D.
• What is the EOQ of the item?
• What is the time b/w consecutive replenishments
  of the item when the EOQ is used?
• The production manager insists that the A 5 is
  only a guess. Therefore, he insists on using his
  3-month supply rule. Indicate how you would find
  the range of A values for which the EOQ (based on
  A5) would be preferable to the 3-month supply.

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S5.7
U.R. Sick Labs manufactures penicillin.
Briefly discuss special considerations required
in establishing the run quantity of such an item.
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N4.22
A silicon wafer purchasing agent must
decide among three wafer suppliers. Source A will
sell the silicon wafers for 2.50 per wafer
independent of the number of wafers ordered.
Source B will sell the wafers for 2.40 each but
will not consider an order for less than 3,000
wafers, and Source C will sell the wafers for
2.30 each but will not accept an order for less
than 4,000 wafers. Assume an order setup cost of
100 and an annual requirement of 20,000 wafers.
Assume a 20 annual interest rate for holding
cost calculations. (a) Which source should
be used, and what is the size of the
standing order? (b) What is the optimal
value of the holding and setup costs
for wafers when the optimal source is used?
(c) If the replenishment lead time for wafers is
3 months, determine the reorder point
based on the on-hand level of
inventory of wafers.
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N4.24
In the calculation of an optimal policy for an
all-units discount schedule, you first compute
the EOQ values for each of the three order cost,
and you obtain The all-units discount schedule
has breakpoints at 750 and 900. Based on this
information only, can you determine what the
optimal order quantity is ? Explain your
answer.
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S5.9
A mining company routinely replaces
a specific part on a certain type of equipment.
The usage rate is forty per week, and there is no
significant seasonality. The supplier of the part
offers the following all-units discount
structure. Range of Q
Unit Cost 0 lt Q lt 300 units
10.00 300 ? Q
9.70 The fixed cost of a
replenishment is estimated to be 25, and a
carrying charge of 0.26//yr is used by the
company. (a) What replenishment size should
be used? (b) If the supplier was interested
in having the mining company acquire
at least 500 units at a time, what is the largest
unit price they could charge for an order of 500
units?
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N4.23
Assume that two years have passed, and
the purchasing agent mentioned in HW4.22 must
recompute the optimal number of wafers to
purchase and from which source to purchase them.
Source B has decided to accept any size offer,
but sells the wafers for 2.55 each for orders of
up to 3,000 wafers and 2.25 each for the
incremental amount ordered over 3,000 wafers.
Source A still has the same price schedule, and
Source C went out of business. Now which source
should be used?
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N4.35
A large producer of household products purchases
a glyceride used in one of its deodorant soaps
from outside of the company. It uses the
glyceride at a fairly steady rate of 40 pounds
per month, and the company uses a 23 percent
annual interest rate to compute holding costs.
The chemical can be purchased from two suppliers
, A and B. A offers the following all units
discount schedule
Order Size Price
per Pound
0 ? Q lt500
1.30 500 ? Q lt1,000
1.20 1,000 ? Q
1.10
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N4.35
whereas B offers the following incremental
discount schedule 1.25 per pound for all orders
less than or equal to 700 pounds, and 1.05 per
pound for all incremental amounts over 700
pounds. Assume that the cost of order processing
for each case is 150. Which supplier should be
used ?
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S5.14
The Dartmouth Bookstore sells 300
notebooks per term. Each notebook carries a
variable cost of 0.50, while the fixed cost to
restock the shelves amounts to 4.00. The
carrying charge of one notebook tied in inventory
is 0.08 per /term. (a) Calculate the EOQ
(b) Calculate the TRC associated with EOQ
calculated in (a) (c) If the Dartmouth
Bookstore chooses to order 300 notebooks
instead of the EOQ, calculate the percentage cost
penalty of this order size. (d) Calculate
the best order quantity now, considering a 40
percent discount on orders greater than 300.
(e) Calculate the optimal order quantity if the
bookstore decides to incorporate an inflation
rate of 2 in the decision. (f) Assume that
this particular notebook occupies 0.10 cubic foot
of space, for which the bookstore figures it
costs them 2 per term per cubic foot. Calculate
the best replenishment quantity under these
circumstances. (g) Now assume that unit cost
of the same notebook increases from 0.50 to
0.60. Calculate the new EOQ.
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The End Problems 1 of 2