The lead-time for a replenishment item at a local grocery store is 3 weeks. Mana
ID: 374429 • Letter: T
Question
The lead-time for a replenishment item at a local grocery store is 3 weeks. Management would like to tolerate only one stockout each year. The ordering cost is $110, the holding cost is $4.50/unit/year. The weekly demand is normally distributed with a mean of 100 and a standard deviation (sigma) of 12. Assume the company operates 50 weeks in a year. Determine:
The economic order quantity. (3 pts)
The service level (2 pts)
The safety stock for the desired customer service level. (2 pts)
The reorder point. (2 pts)
The average inventory. (2 pts)
Suppose the lead time changes to 2 weeks, what will be the new safety stock? (2 pts)
Service Level (%)
Safety Factor
85
1.04
86
1.08
87
1.13
88
1.18
89
1.23
90
1.28
91
1.34
92
1.40
93
1.48
94
1.56
95
1.65
96
1.75
97
1.88
98
2.05
99
2.33
99.99
4.00
Service Level (%)
Safety Factor
85
1.04
86
1.08
87
1.13
88
1.18
89
1.23
90
1.28
91
1.34
92
1.40
93
1.48
94
1.56
95
1.65
96
1.75
97
1.88
98
2.05
99
2.33
99.99
4.00
Explanation / Answer
Annual demand at the grocery store = 100/weeks x 52 weeks = 5200
Economic order quantity ( EOQ ) will be defined as :
EOQ = Square root ( 2 x Co x D/Ch)
Where,
Co = Ordering cost = $110
D = Annual demand = 5200
Ch = Annual unit holding cost = $ 4.5
Therefore, Economic Order quantity ( EOQ )
= Square root ( 2 x 110 x 5200 / 4.5)
= 504.20 ( 504 rounded to nearest whole number )
Hence, Number of orders in a year = annual demand / EOQ = 5200/504 = 10.317
Permissible number of stockout in a year = 1
Hence, proportion of stockout = 1 / 10.317 = 0.0969
Hence, Service level = 1 – 0.0969 = 0.9031
Corresponding Z value for service level of 0.9031 = NORMSINV ( 0.9031) = 1.2994
Standard deviation of demand during lead time
= standard deviation of weekly demand x Square root ( Lead time in weeks )
= 50 x Square root ( 3 )
= 50 x 1.732
= 86.6
Hence, safety stock
= Z Value x standard deviation of demand during lead time= 1.2994x86.6= 112.53 ( 113 rounding to next higher whole number )
Reorder point
= Weekly demand x Lead time ( weeks ) + safety stock
= 100 x 3 + 113
= 300 + 113
= 413
Average inventory = EOQ/2 + Safety stock = 504/2 + 113 = 252 + 113 = 365
ECONOMIC ORDER QUANTITY = 504
SERVICE LEVEL = 0.9031 ( 90.31 %)
SAFETY STOCK = 113
REORDER POINT = 413
AVERAGE INVENTORY = 365
ECONOMIC ORDER QUANTITY = 504
SERVICE LEVEL = 0.9031 ( 90.31 %)
SAFETY STOCK = 113
REORDER POINT = 413
AVERAGE INVENTORY = 365
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