Betapharm Operation

Question 3

1. Betapharm is able to identify specifically all its aspect with certainty including its daily demand (70kg with SD=15kg); constant percentage of annual holding cost and constant lead time of each suppliers. Thus the appropriate inventory management model for this cost for this company is Fix-Order Quantity Model.
2. No matter what supplier Betapharm would choose, it has the same service level, set up cost and demand. The differences between those two suppliers comprise of procurement price and the lead time.

Chun Wu has procurement price per unit is  €59 which is much lower than Tao ($145). Thus, the holding rate (80%* price of each supplier) of Chun Wu would be much lower than one of Tao.

The optimal order quantity for Betapharm is estimated by formula

QOPT = [pic 1]

The higher holding rate of Tao would lead to the lower quantity ordered of Betapharm when it works with this supplier. On the contrary, the quantity ordered would be higher for Betapharm when working with Chun Wu.

In terms of safety stock (SS), Betapharm would get higher level of SS when working with Chun Wu instead of working with Tao because of Chun Wu’s higher lead time.

Hence, the reorder point (ROP= demand *leadtime+SS) and the average inventory (QOTP/2+SS) of Betapharm working with Chun Wu would be much higher than those when working with Tao.

Finally, the annual holding cost of Betapharm when working with Chun Wu is higher than those when working with Tao even though the price per unit of Chun Wu is lower than Tao.

The COD policy of Tao helps Betapharm eliminate safety stock because it can modify the amount of stock using for unpredictable variability until the day it has to pay (3 days of lead time) rather than pay when placing order with Chun Wu although its lead time is 7 days.

1. Procurement cost for each supplier:

• Calculation for Tao

Price/kg= €145

Service Level=0.999 therefore Z=3.09

(ref: http://www.inventoryops.com/safety_stock.htm)

Set up Cost=€80 Demand=70±15 kg

Holding cost=0.8*145=€116

Total working days=300 Total Demand/Year= 70*300 21000 kg

Lead time=3 days

Order Quantity= Sq. rt(2*21000*80/116)= 170.19 kg

• Safety Stock for 99.999% service level.

σL= 15√3 therefore =25.98

SS=Z σL=25.98*3.09= 80.28kg

• Reorder Point = d*Lead time+SS

= 70*3+ 80.28= 290.28kg

Since Tao is Cash on Delivery, Total average inventory owned by firm is Q/2+SS

= 170.19/2+80.28 =165.38 kg

• Total Annual Procurement Cost of Betapharm with Tao = 145*165.38 =  €23,979.38

• Calculations for Chun Wu

Price/kg= €59

Service Level=0.999 therefore Z=3.09

Set up Cost=€80

Demand=70±15 kg,

Holding cost=0.8*59= €47.2

Total working days=300

Total Demand/Year=21000 kg,

Lead time=7 days

• Order Quantity= Sq. rt(2*21000*80/47.2) =266.80 kg

• Safety Stock for 99.999% service level.

σL= 15√7 therefore =39.68

SS=Z σL=39.68*3.09=122.61 kg

• Reorder Point = d*Lead time+ SS

= 70*7+122.61= 612.61kg

• Since Chun Wu has pay on ordering, Total Inventory Owned = Q/2+SS+dL =746.01 kg
• Total Annual Procurement Cost of Betapharm with Chun Wu = 746.01*59 =  €44,014.59

1. Holding cost for each supplier:

• Calculation for Tao

• Total Annual Holding Cost        = Holding cost/unit x Average inventory

                                = (80/100x145) x 218.5

                                = €25,436

• Calculation for Chun Wu

• Total Annual Holding Cost        = Holding cost/unit x Average inventory

                                = (80/100x59) x 825.6

                                = €38,968.32

Hence, if switching to Chun Wu, the increase in the annual inventory holding cost would be €13,622.32 (equals €38,968.32 - €25,346).

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