(12 points) A. Toledo Grocers is planning to hire an expert (like you) to study
ID: 378950 • Letter: #
Question
(12 points) A. Toledo Grocers is planning to hire an expert (like you) to study their inventory and make recommendations. You are given the following data for Bulk mixed nut to demonstrate your knowledge and use it as a sample to earn their business. You are asked to compare the two approaches to inventory management: Continuous review and periodic review: Use both approaches to evaluate the cost and recommend a method for Toledo Grocers. Data given below.
Distribution of Daily demand
Normal
Mean
600 pounds per day
Standard Deviation of daily demand
90 pounds
Holding cost
0.003 per pound per day
Ordering cost
360
Lead time
4 days
Service level Desired
85%
Review period (when using periodic review)
20 days
Number of days per year
365
On hand Inventory at the time of review
1450
Continuous review system
Formula used (with numbers substituted for variables)
Value obtained
EOQ
Mean lead time demand
s.d. Lead time demand
Z value for a service level of 85%
Safety stock
Reorder Level
Total expected ordering cost per year
Total expected holding cost per year
Total expected total cost per year
New SS, if SS is reduced by 50 units
New reorder level
New Z value
New service level
Periodic review system
Formula used (with numbers substituted for variables)
Value obtained
Mean demand during (lead time + review period )
s.d. of demand during (lead time + review period )
Z value for a service level of 85%
Safety stock
Order up to Level (also called av. Demand during the vulnerable period +safety stock)
Order quantity if on hand inventory as given
Total ordering cost per year
Distribution of Daily demand
Normal
Mean
600 pounds per day
Standard Deviation of daily demand
90 pounds
Holding cost
0.003 per pound per day
Ordering cost
360
Lead time
4 days
Service level Desired
85%
Review period (when using periodic review)
20 days
Number of days per year
365
On hand Inventory at the time of review
1450
Explanation / Answer
CONTINUOUS REVIEW SYSTEM
FORMULA USED ( WITH NUMBERS SUBSTITUTED FOR VARIABLES )
VALUE OBTAINED
EOQ
Square root ( 2 x Ordering cost x daily demand/ Daily unit holding cost ) = Square root ( 2x 360 x 600 / 0.003)
12000 POUNDS
Mean Lead time demand
Mean demand/ day x Lead time ( days) = 600 x 4
2400
Standard deviation of lead time demand
Standard deviation of daily demand x Square root ( Lead time )
= 90 x Square root ( 4 ) = 90 x 2
180
Z value for a service level of 85%
NORMSINV ( 0.85)
1.036
SAFETY STOCK
Zvalue x Standard deviation of lead time demand = 1.036 x 180
186.48
Reorder level
Mean lead time demand + Safety stock = 2400 + 186.48
2586.48
Total expected ordering cost per year
Ordering cost x Annual demand / EOQ
= 360 x 600 x 365 /12000
$6570
Total expected holding cost per year
Daily holding cost x 365 days x EOQ/2
= 0.003 X 365 X 12000/2
$6570
Total expected total cost per year
Total expected ordering cost per year + Total expected holding cost per year = $6570 + $6570
$13140
New SS if SS is reduced by 50 units
Earlier safety stock – 50 = 186.48 – 50
136.48
New reorder level
Mean lead time demand + New SS = 2400 + 136.48
2536.48
New Z value
New SS / Standard deviation of demand during lead time
= 136.48 / 180
0.758
New service level
Derived from standard normal distribution table = 0.7758
77.58%
PERIODIC REVIEW SYSTEM
FORMULA USED ( WITH NUMBERS SUBSTITUTED FOR VARIABLES )
VALUE OBTAINED
Mean demand during ( Lead time +Review period )
Mean demand/ day x( Lead time + Review period ) =
600 x ( 4 + 20)
14400
Standard deviation of demand during ( Lead time + Review period )
Standard deviation of daily demand x Square root ( Lead time + Review period )
= 90 x Square root ( 24 )
440.90
Z value for a service level of 85%
NORMSINV ( 0.85)
1.036
SAFETY STOCK
Zvalue x Standard deviation of demand during ( lead time + review period ) = 1.036 x 440.90
456.77
Order up to Level (also called av. Demand during the vulnerable period +safety stock)
Mean demand during ( Lead time + Review period) + Safety stock
= 14400 + 456.77
14856.77
Order quantity if on hand inventory as given
Order upto level - Inventory
Total ordering cost per year
Ordering cost x annual demand / EOQ = 360 X 600 X 365/12000
6570
CONTINUOUS REVIEW SYSTEM
FORMULA USED ( WITH NUMBERS SUBSTITUTED FOR VARIABLES )
VALUE OBTAINED
EOQ
Square root ( 2 x Ordering cost x daily demand/ Daily unit holding cost ) = Square root ( 2x 360 x 600 / 0.003)
12000 POUNDS
Mean Lead time demand
Mean demand/ day x Lead time ( days) = 600 x 4
2400
Standard deviation of lead time demand
Standard deviation of daily demand x Square root ( Lead time )
= 90 x Square root ( 4 ) = 90 x 2
180
Z value for a service level of 85%
NORMSINV ( 0.85)
1.036
SAFETY STOCK
Zvalue x Standard deviation of lead time demand = 1.036 x 180
186.48
Reorder level
Mean lead time demand + Safety stock = 2400 + 186.48
2586.48
Total expected ordering cost per year
Ordering cost x Annual demand / EOQ
= 360 x 600 x 365 /12000
$6570
Total expected holding cost per year
Daily holding cost x 365 days x EOQ/2
= 0.003 X 365 X 12000/2
$6570
Total expected total cost per year
Total expected ordering cost per year + Total expected holding cost per year = $6570 + $6570
$13140
New SS if SS is reduced by 50 units
Earlier safety stock – 50 = 186.48 – 50
136.48
New reorder level
Mean lead time demand + New SS = 2400 + 136.48
2536.48
New Z value
New SS / Standard deviation of demand during lead time
= 136.48 / 180
0.758
New service level
Derived from standard normal distribution table = 0.7758
77.58%
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