Respuesta :
Answer:
a. Reorder point is 1,164 units to provide a 98 percent service probability.
b. the new service probability will be 79% if production manager reduces the safety stock by 100 units.
Explanation:
a. To provide a 98 percent service probability, what must the reorder point be?
This can be calculated as follows:
Step 1: Calculation of optimal order quantity
The optimal order quantity also known as economic order quantity (EOQ) using the following formula:
[tex]EOQ = \sqrt{\frac{2 *D*O}{C} }[/tex] ........................................... (1)
Where,
EOQ = Optimal order quantity = ?
D = Annual demands = 13,000
O = Ordering cost = $100
C = Carrying cost of annual inventory = $0.65 per unit
Substituting the values into equation (1), we have:
[tex]EOQ = \sqrt{\frac{2*13,000*100}{0.65} }[/tex]
[tex]EOQ = \sqrt{\frac{2,600,000}{0.65} }[/tex]
[tex]EOQ = \sqrt{4,000,000}[/tex]
EOQ = 2,000 units
Step 2: Calculation of standard deviation during the lead time
This can be calculated using the following formula:
[tex]SL = \sqrt{L*(S)^{2} }[/tex] ................................................. (2)
Where;
SL = Standard deviation during the lead time = ?
L = Lead time = 4
S = Standard deviation = 40
Substituting the values into equation (2), we have:
[tex]SL = \sqrt{4 *(40)^{2} }[/tex]
[tex]SL = \sqrt{4*1,600}[/tex]
[tex]SL =\sqrt{6.400}[/tex]
SL = 80
Also, z = 2.05 from the standard normal distribution
Step 3: Calculation of reorder point
Total calculate reorder point, we use the following formula:
R = (d * L) + (z * SL) ............................................ (3)
Where;
R = Reorder point = ?
d = Weekly demand = 250
L = Lead time = 4
z = 2.05
SL = Standard deviation during the lead time = 80
Substituting the values into equation (3), we have:
R = (250 * 4) + (2.05 * 80)
R = 1,000 + 164
R = 1,164 units
Therefore, reorder point is 1,164 units to provide a 98 percent service probability.
b. Suppose the production manager is told to reduce the safety stock of this item by 100 units. If this is done, what will the new service probability be?
ISS = Initial safety stock = z * SL = 2.05 * 80 = 164
If the safety stock is reduced by 100 units, we have:
NSS = New safety stock = ISS - 100 = 164 - 100 = 64
The new z (nz) can be obtained as follows:
NSS = nz * SL ................................................. (4)
Where;
NSS = 64
nz = new z = ?
SL = Standard deviation during the lead time = 80
Substituting the values into equation (4) and solve for nz, we have:
64 = nz * 80
nz = 64 / 80
nz = 0.80
For the new z, nz = 0.80, from Standard Normal distribution, the new service probability is 79%.
Therefore, the new service probability will be 79% if production manager reduces the safety stock by 100 units.
