Question

Sam’s Cat Hotel operates 52 weeks per year, 7 days per week, and uses a continuous review inventory system. It purchases Kitty Litter for $16.38 per bag. The following information is available about these bags: Demand: 125 bags/week, Order Cost: $75.00 per order, Annual Holding Cost: 27% of cost, Desired Cycle-Service Level: 80%, Lead Time: 3 weeks (21 working days), Standard Deviation of weekly demand: 21 bags, Current on Hand Inventory: 450 bags, Open Orders or Backorders: 0. SHOW YOUR CALCULATIONS: A. What is the Economic Order Quantity (EOQ) for Kitty Litter? B. What would be the average time between orders (in weeks)? C. What would the Re-order Point (R)) be? D. An inventory withdrawal of 50 bags was just made... Is it time to re-order? E. The store currently uses a lot size of 700 bags (Q = 700). What would be the annual cost saved by shifting from the 700-bag lot size to the EOQ?

Answer 1

Sam's Cat Hotel can save $165.15 annually by shifting from the 700-bag lot size to the EOQ (470 bags).

Sam's Cat Hotel Inventory Management Calculations:

A. Economic Order Quantity (EOQ):

1. Annual Demand (D): 125 bags/week × 52 weeks/year = 6500 bags/year

2. Annual Holding Cost (H): 27% of $16.38 = $4.4226/bag

3. Order Cost (S): $75.00 per order

4. EOQ = √(2DS)/H

5. EOQ = √(2 × 75 × 6500) / 4.4226

6. EOQ = 469.53 bags (round to 470 bags)

B. Average Time Between Orders:

1. Number of Orders (N) = D/EOQ = 6500 bags/year / 470 bags/order = 13.83 orders/year

2. Average Time Between Orders (T) = 1 year / N = 1 year / 13.83 orders/year = 3.76 weeks

C. Re-order Point (R):

1. Safety Stock = Standard Deviation × Safety Factor

2. Safety Factor for 80% Service Level = 0.84 (based on service level charts)

3. Safety Stock = 21 bags × 0.84 = 17.64 bags

4. R = (Demand × Lead Time) + Safety Stock + Standard Deviation

5. R = (125 bags/week × 3 weeks) + 17.64 bags + 21 bags = 413.64 bags (round to 414 bags)

D. Re-order Decision:

After the withdrawal of 50 bags, the current on-hand inventory is 450 bags - 50 bags = 400 bags.

This is below the re-order point (414 bags).

Therefore, it is time to re-order.

E. Annual Cost Saving:

1. Annual Ordering Cost at Q = 700: D/Q × S =

6500 bags/year / 700 bags/order × $75.00/order

= $1038.57

2. Annual Holding Cost at Q = 700: (Q/2) × H =

(700 bags/2) × $4.4226/bag = $1547.86

3. Total Annual Inventory Cost at Q = 700:

$1038.57 + $1547.86 = $2586.43

4. Annual Ordering Cost at EOQ: D/EOQ × S =

6500 bags/year / 470 bags/order × $75.00/order

= $1383.00

5. Annual Holding Cost at EOQ:

(EOQ/2) × H = (470 bags / 2) × $4.4226/bag = $1038.28

6. Total Annual Inventory Cost at EOQ:

$1383.00 + $1038.28 = $2421.28

7. Annual Cost Saving:

$2586.43 - $2421.28 = $165.15

Therefore, Sam's Cat Hotel can save $165.15 annually by shifting from the 700-bag lot size to the EOQ (470 bags).