Kenichi Kaneko is the manager of a production depart- ment which uses 400 boxes
ID: 372393 • Letter: K
Question
Kenichi Kaneko is the manager of a production depart-
ment which uses 400 boxes of rivets per year. To hold down his
inventory level, Kenichi has been ordering only 50 boxes each
time. However, the supplier of rivets now is offering a discount
for higher-quantity orders according to the following price
schedule, where the price for each category applies to every box
purchased.
Discount Price
Category Quantity (per Box)
1 1 to 99 $8.50
2 100 to 999 8.00
3 1,000 or more 7.50
The company uses an annual holding cost rate of 20 percent
of the price of the item. The total cost associated with placing an
order is $80 per order.
Kenichi has decided to use the EOQ model with quantity dis-
counts to determine his optimal inventory policy for rivets.
(a) For each discount category, write an expression for the total
cost per year (TC) as a function of the order quantity Q.
T (b) For each discount category, use the EOQ formula for the
basic EOQ model to calculate the value of Q (feasible or
infeasible) that gives the minimum value of TC. (You may
use the analytical version of the Excel template for the ba-
sic EOQ model to perform this calculation if you wish.)
(c) For each discount category, use the results from parts (a)
and (b) to determine the feasible value of Q that gives the
feasible minimum value of TC and to calculate this value
of TC.
Explanation / Answer
Economic Order Quantity (EOQ) model uses the formula EOQ=SQRT(2AD/h) where A is ordering cost per order, D is fixed demand for a fixed period, a year. h represents unit holding cost for the fixed period.
Please note EOQ for category1 and category3 are not feasible as per the range mentioned, therefore to make comparison order quantities are tasken as 99 and 1000 respectively.
Minimum total annual cost is as per EOQ=200 units for category2 Total Cost annual (minimum) is $3,520
TC(Q) = AD/Q (Ordering cost) + Qh/2 (Holding cost) + QC (purchase cost)
Catgry-1 Catgry-2 Catgry-3 Annual Demand-D 400.00 400.00 400.00 Ordering cost-A 80.00 80.00 80.00 Holding cost-h (20%) 1.70 1.60 1.50 Price per unit-C 8.50 8.00 7.50 2AD/h 37647.06 40000.00 42666.67 EOQ=SQRT(2AD/h) 194.03 200.00 206.56 Ordering size 99.00 200.00 1000.00 AverageInventory=Q/2 49.50 100.00 500.00 Ordering cost-Annual 323.23 160.00 32.00 Holding cost-annual 84.15 160.00 750.00 Purchase cost-annual 3400.00 3200.00 3000.00 Total cost-annual 3807.38 3520.00 3782.00Related Questions
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