# Current Ordering Model Problems

November 24, 2016

Question
Current Ordering Model
A wholesale distributor stocks and sells low flow toilets to contractors for use in commercial
office buildings. The estimated annual demand for the toilets is 5,475 units. The estimated
average demand per day is 15 units. The purchase cost from the toilet manufacturer is \$125.00
per unit. The lead time for a new order is 3 days. The ordering cost is \$100.00 per order. The
average holding cost per unit per year is \$2.50. The distributor has traditionally ordered 250
units each time they placed an order. Answer questions 1-5 based upon the preceding
information regarding the distributors current ordering model.
1. What is the average number of units in inventory based upon ordering 250 units each time an
order is placed?
o 250
o 125
o 75
o 140
2. How many orders per year will be necessary based upon ordering 250 units each time an
order is placed?
o 40
o 67
o 22
o 357
3. What is the average dollar value of inventory based upon ordering 250 units each time an
order is placed?
o \$31,250.00
o \$9,375.25
o \$17,500.50
o \$15,625.00
4. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon
ordering 250 units each time an order is placed?
o \$626,125.00
o \$578,900.00
o \$721,345.25
o \$686,877.50
5. What is the optimal reorder point based upon ordering 250 units each time an order is
placed?
o 30
o 45
o 60
o 15
1

Economic Order Quantity (EOQ) Model
The president of the wholesale distributor has recently heard about the EOQ model and is
interested in learning whether or not using this model would allow the company to reduce its
annual costs by optimizing the number of orders placed each year and the number of toilets
purchased in each order. The estimated annual demand for the toilets, estimated average demand
per day, purchase cost from the toilet manufacturer per unit, lead time for a new order, ordering
cost per order and average holding cost per unit per year remain the same as stated in the
scenario for the current ordering model. Answer questions 6-11 based upon using the EOQ
model.
6. What is the economic order quantity (EOQ) that will minimize inventory costs?
o 661.8
o 456.5
o 371.7
o 278.3
7. What is the average number of units in inventory based upon ordering using the EOQ?
o 343.6
o 228.3
o 330.9
o 139.2
8. What is the average dollar value of inventory based upon ordering using the EOQ?
o \$48,135.10
o \$21,750.01
o \$35,735.76
o \$41,363.48
9. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon
using the EOQ?
o \$721,100.42
o \$686,029.54
o \$578,900.29
o \$652,380.39
10. What is the optimal reorder point based upon using the EOQ?
o 30
o 45
o 60
o 75
11. How many orders per year will be necessary based upon using the EOQ?
o 20.5
o 15.9
2

o 23.4
o 29.1
EOQ Without Instantaneous Receipt Model (a.k.a., Production Run Model)
The wholesale distributor has traditionally relied upon an instantaneous receipt model in which
the material associated with each order is received in a single batch. The toilet manufacturer has
suggested to the president of the wholesale distributor that he might want to consider agreeing to
accept receipt of ordered material incrementally over a period of time rather than in a single
batch as a means for reducing total annual costs. The toilet manufacturer has advised that his
factorys daily production rate is 20 toilets and the set-up cost for each production run is \$250.
The estimated annual demand for the toilets, estimated average demand per day, purchase cost
from the toilet manufacturer per unit, lead time for a new order, ordering cost per order and
average holding cost per unit per year remain the same as stated in the scenario for the current
ordering model. Answer questions 12-18 using the EOQ without instantaneous receipt model
(production run model) in which goods are incrementally delivered at the same they are being
still being produced.
12. What is the optimal order quantity without instantaneous receipt (material is accepted over
time)?
o 2,092.84
o 980.65
o 580.38
o 350.78
13. What is the maximum number of units in inventory without instantaneous receipt (material is
accepted over time)?
o 265.98
o 416.33
o 326.87
o 523.21
14. What is the average number of units in inventory without instantaneous receipt (material is
accepted over time)?
o 132.99
o 132.59
o 261.61
o 208.17
15. What is the average dollar value of inventory without instantaneous receipt (material is
accepted over time)?
o \$20,430.00
o \$32,700.70
o \$26,020.82
o \$10,373.75
3

16. What is the total annual cost (i.e., Purchase Cost + Ordering Cost + Holding Cost) without
instantaneous receipt (material is accepted over time)?
o \$685,683.03
o \$627,081.67
o \$578,893.72
o \$652,480.15
17. What is the optimal reorder point without instantaneous receipt (material is accepted over
time)?
o 30
o 45
o 50
o 57
18. How many set-ups per year will be necessary without instantaneous receipt (material is
accepted over time)?
o 1.65
o 7.89
o 4.41
o 2.62
Quantity Discount Model
The toilet manufacturer has proposed a quantity discount schedule for toilets as reflected in the
following table for consideration by the president of the wholesale distributor as a means to
potentially reduce his total annual costs.
Discount Number
1
2
3

Quantity Ordered
0 to 1,000
1,001 to 2,000
2,001 and over

Unit Cost Discount
0%
10%
15%

The estimated annual demand for the toilets, estimated average demand per day, purchase cost
from the toilet manufacturer per unit, lead time for a new order, ordering cost per order and
average holding cost per unit per year remain the same as stated in the scenario for the current
ordering model. Answer questions 19 and 20 based upon using the quantity discount model.
19. What order quantity will allow the wholesale distributor to minimize their total annual
inventory costs (Purchase Cost + Ordering Cost + Holding Cost) by taking advantage of the
proposed discount pricing?
o 250
o 751
o 2,001
o 662
4

20. What is the total annual cost (Purchase Cost + Ordering Cost + Holding Cost) based upon
taking advantage of the proposed discount pricing?
o \$626,128.89
o \$601,698.43
o \$584,118.43
o \$487,998.00
Minimizing Total Annual Costs
21. Which ordering model is least effective with regard to minimizing total annual cost (i.e.,
results in the highest total annual cost)?
o Current ordering model
o EOQ model
o Production run model
o Quantity discount model
22. Which ordering model is most effective with regard to minimizing total annual cost (i.e.,
results in the lowest total annual cost)?
o Current ordering model
o EOQ model
o Production run model
o Quantity discount model
Safety Stock
The president of the wholesale distributor is concerned about the possibility of stockouts causing
a loss of customer confidence and loyalty and is interested in maintaining safety stock in
inventory to prevent potential stockouts. Answer questions 23 through 25 based upon using the
safety stock models.
23. Assuming demand is normally distributed with a mean of 15 units and a standard deviation
of 3 units, and a constant lead time of 3 days, what is the reorder point necessary to provide a
97% level of service?
o 54.77
o 45.14
o 34.41
o 60.49
24. Assuming demand is constant at 15 units per day, and lead time is normally distributed with
a mean of 3 days and a standard deviation of 1 day, what is the reorder point necessary to
provide a 97% level of service?
o 80.48
o 64.87
o 73.21
5

o 53.18
25. Assuming that demand is normally distributed with a mean of 15 units and a standard
deviation of 3 units, and lead time is normally with a mean of 3 days and a standard deviation
of 1 day, what is the reorder point necessary to provide a 97% level of service?
o 59.69
o 81.20
o 66.46
o 74.86

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