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Michigan State Figurine Inc. (MSF) sells crystal figurines to Spartan fans. MSF buys the figurines from a manufacturer for $10 per unit. They send orders electronically to the manufacturer, costing $20 per order and they experience an average lead time of 8 days for each order to arrive from the manufacturer. Their inventory carrying cost is 20%. The average daily demand for the figurines is 2 units per day. They are open for business 250 days a year. Answer the following questions:

Required:
a. How many units should the firm order each time? Assume there is no uncertainty at all about the demand or the lead time.
b. How many orders will it place in a year?
c. What is the average inventory?
d. What is the annual ordering cost?
e. What is the annual inventory carrying cost?

Sagot :

Answer:

Follows are the solution to the given points:

Explanation:

Given:

[tex]cost= \$10 / \ unit \\\\s= \$20 / \ order \\\\Lt= 8 / days \\\\H= 20 \% \ of \ cost \\\\[/tex]

    [tex]= \frac{20}{100} \times 10\\\\= \frac{200}{100}\\\\= 2 \ \frac{unit}{year}[/tex]

[tex]d= 2 \ \frac{units}{day}\\\\n= 250 \ \frac{days}{year}\\\\D=d\times n \\\\[/tex]

   [tex]=2 \times 250\\\\=500 \ \frac{units}{day}[/tex]

For point a:

[tex]\to EOQ=\sqrt{\frac{2DS}{H}}[/tex]

             [tex]=\sqrt{\frac{ 2 \times 500 \times 20 }{2}} \\\\=\sqrt{500 \times 20}\\\\=\sqrt{1,000}\\\\=100 \ units[/tex]

For point b:

[tex]\to N=\frac{D}{Q} =\frac{500}{100} =5 \ orders[/tex]

For point c:

Calculating the average inventory:

[tex]\to \frac{Q}{2} =\frac{100}{2} =50 \ units[/tex]

For point d:

Calculating the annual ordering cost:

[tex]\to \frac{D}{Q} \times S\\\\[/tex]

[tex]=\frac{500}{100} \times 20\\\\ = 5\times 20 \\\\= \$100[/tex]

For point e:

Calculating the annual inventory carrying cost:

[tex]\to \frac{Q}{2} \times H =\frac{100}{2} \times 2=\$ 100[/tex]

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