Question

In: Operations Management

Your firm uses a continuous review system and operates 52 weeks per year. One of the...

Your firm uses a continuous review system and operates 52 weeks per year. One of the SKUs has the following characteristics. Refer to the Z values.

>Demand (D) = 20,600units / (year)

>Ordering cost (S) = $45.00/order

>Holding cost (H)=$3.00/unit/year

> Lead (L) = 1 weeks

>Cycle-service |evel=96%

>Demand is normally distributed, with a standard deviation of weekly demand of 103 units.

>Current on-hand inventory is 1,040 units, with no scheduled receipts and no backorders.

The item's economic order quantity is ___ units.

The average time between orders is ___ weeks

To provide a 96 percent cycle-service level the safety stock for this item is _____ units.

To provide a 96 percent cycle-service level, the reorder point for this item is ______.

For these policies the annual cost of holding the cycle inventory is _______ and annual cost of placing orders is______.

Solutions

Expert Solution

(A)

Annual demand (D) = 20,600 units

Ordering cost per order (S) = $ 45

Annual Holding cost per unit (H) = $ 3

EOQ = 786.13 units

EOQ = 786 Units (rounded off to nearest whole number)

EOQ = 786 units

(B)

Given number of weeks = 52

Average time between orders = (Q/D) × Number of weeks

Average time between ordere = (786/20,600) × 52

Average time between orders = 1.98 weeks (rounded off to 2 decimals)

(C)

Given Standard Deviation () = 103 units

Lead time (L) = 1 week

Service level = 96%

Value of Z corresponding to service level of 96% = 1.75

Safety Stock = 1.75 × 103 × 1

Safety Stock = 180.25 units

Safety Stock = 180 (rounded off to nearest whole number)

Safety Stock = 180 units

(C)

Annual demand (D) = 20,600

Number of weeks = 52

Daily demand (d) = 20,600/52

Daily demand (d) = 396.154 units

Re-Order Point = (d × L) + Safety Stock

Re-Order Point = (396.154 × 1) + 180

Re-Order Point = 576.154 units

Re-Order Point = 576 units (rounded off to next whole number)

Re-Order Point = 576 units

(D)

Annual Holding cost = (Q/2) × H

Annual Holding cost = (786/2) × 3

Annual Holding cost = $ 1,179

Annual cost of placing order = (D/Q) × S

Annual cost of placing order = (20,600/786) × 45

Annual cost of placing order = $ 1,179.389

Annual cost of placing order = $ 1,179.39 (rounded off to 2 decimals)

keosha answered 1 year ago

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