Case study: the SOCA
SOCA, a television manufacturing company, produces its own speakers for assembly into
its television sets. To maintain its production schedule for television sets, the company needs to
have 1,000 speakers available for assembly per day. Each time an order is placed to produce more
speakers, the rate of production is 3,000 speakers per day until the order is filled, after which the
production facilities are used for other purposes until another production run for speakers is
needed. Since this production rate is three times the rate at which the speakers are needed, speakers
are being produced only one-third of the time.
The current policy for managing SOCA’s inventory of speakers is summarized below.
Current Inventory Policy of SOCA
a. Daily demand rate = 1,000 speakers per day.
b. Daily production rate = 3,000 speakers per day (when producing).
c. The production facilities get set up to start a production run each time the inventory level
is scheduled to drop to 0.
d. Each production run produces 30,000 speakers over a period of 10 working days, so
another 20 working days elapse before the next production run is needed.
This policy leads to the pattern of inventory levels over time shown in Figure 5.10. Thus,
the inventory level fluctuates between 0 and a maximum inventory level that is somewhat under
30,000 speakers. The reason for not reaching 30,000 is that speakers also are being withdrawn
from inventory for assembly into television sets while a production run is under way.
Consequently,
Maximum inventory level = production lot size minus demand during production run
= 30,000 speakers – (10 days) (1,000 speakers/day)
= 30,000 speakers – 10,000 speakers
= 20,000 speakers
Therefore,
Average inventory level = (maximum inventory level)/2
= 10,000 speakers
SOCA’s costs associated with this inventory policy are summarized below.
c = unit production cost = $12 per speaker produced,
K = setup cost for a production run = $12,000,
h = unit holding cost = $3.60 per speaker in inventory per year.
With 250 working days per year, the number of speakers needed per year is
D = annual demand rate
= (1,000 speakers/day) (250 days)
= 250,000 speakers.
Excluding setup costs, the annual cost of producing these speakers is fixed at
($12/speaker) (250,000 speakers) = $3 million, regardless of the choice of the production lot
size.
One cost that does depend on this lot size is
𝐷
Annual setup cost = 𝐴𝑛𝑛𝑢𝑎𝑙 𝑠𝑒𝑡𝑢𝑝 𝑐𝑜𝑠𝑡 = 𝐾 𝑄
$12,000 250,000 𝑠𝑝𝑒𝑎𝑘𝑒𝑟𝑠
=(
)
= $100,000
𝑠𝑒𝑡𝑢𝑝 30,000(𝑠𝑝𝑒𝑎𝑘𝑒𝑟𝑠)
𝑠𝑒𝑡𝑢𝑝
The other variable cost is
Annual holding cost = h (average inventory level)
= ($3.60/speaker)(10,000 speakers)
= $36,000
Therefore, SOCA’s total variable inventory cost per year is
TVC = annual setup cost + annual holding cost
= $136,000
SOCA management now wants to determine whether this total cost can be decreased by
adjusting the production lot size appropriately.