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(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%