Question

Case analysis (state all calculations and analysis processes required for analysis)

Example 4. Ajou Hospital uses 1000 boxes of medical bands a week. A box of medical bands costs 35 won. The hospital operates 52 weeks a year. A fixed order cost of 15 won is incurred for a single order. The annual inventory cost is 15 per cent of the cost.

(a) Currently, the hospital orders 900 boxes of medical bands once. Determine the difference between economic orders that minimize costs and then determine the amount of savings that can be caused by ordering economic orders.

(b) Demand follows the normal distribution (average = 1000 boxes per week, standard deviation = 100 boxes), and order lead time = 2 weeks. Determine the hospital reorder point under the assumption that the service level is 97%.

  

Answer 1

(a)

Annual Demand = 1000 x 52 = 52000 boxes

Unit cost = 35

Ordering cost = 15 per order

Annual Inventory cost per unit = 15% of Unit cost = 0.15 x 35 = 5.25

For current order quantity of 900 boxes:

Annual Ordering cost = ( Annual Demand / Order Quantity) x Order cost per order

= ( 52000 / 900) x 15 = 866.67

Annual Inventory cost = (Order Quantity / 2) x Annual Inventory cost per unit

= ( 900 / 2) x 5.25 = 2362.5

Total Annual cost = Annual Ordering cost + Annual Inventory cost = 866.67 + 2362.5 = 3229.17 won

For Economic Order Quantity(EOQ):

EOQ = √ (( 2 x Annual Demand x Ordering Cost) / Annual Inventory cost per unit)

= √ (( 2 x 52000 x 15) / 5.25)

= 545.108 = 545 (Rounding off)

Annual Ordering cost = ( 52000 / 545) x 15 = 1431.19

Annual Inventory cost = ( 545 / 2) x 5.25 = 1430.625

Total Annual Cost = 1431.19 + 1430.625 = 2861.815 won

Therefore,

The difference between original order quantity and economic orders that minimize costs = 900 - 545 = 355

The amount of savings that can be caused by ordering economic orders = 3229.17 - 2861.815 = 367.355 won

(b)

Average demand = 1000 boxes per week

Standard deviation of demand = 100 boxes

Lead time = 2 weeks

Service level = 97%

Z value for Service level of 97% is 1.881. (From Z table or NORM.S.INV function in MS Excel)

Re-order point = (Average demand x Lead time) + ( Z value x Standard Deviation of Demand x √ Lead time)

= ( 1000 x 2) + ( 1.881 x 100 x √ 2)

= 2000 + ( 1.881 x 100 x 1.414)

= 2000 + 265.973

= 2265.973