ACold Inc. Is a frozen-food distributor with 10 warehouses across the country. Ivan Tory, one of the warehouse managers, wants to make sure that the inventory policies used by the warehouse are minimizing inventory while still maintaining quick delivery to ACold's customers. Because the warehouse carries hundreds of different products, Ivan decided to study one. He picked Caruso's Frozen Pizza (CFP). Demand for CFPs averages 400 per day with a standard deviation of 152. Because ACold orders at least one truck from its supplier each day, ACold can essentially order any quantity of CFP it wants each day. In fact, ACold's computer system is designed to implement an order-up-to policy for each product. Ivan notes that any order for CFPs arrives four days after the order.
Suppose it uses an order up to level of 2410. What is its expected on-hand inventory?
Answer:
The expected Inventory on -hand = 429.074
Explanation:
From the given information;
Mean i,e Demand for CFPs averages = 400 per day
standard deviation = 152
Lead TIme = 4 days
period length = ACold Inc. orders at least one truck from its supplier each day,
Let consider the fact that the order is up to level of S = 2410
Then, the expected demand for the lead time is;
[tex]\mu[/tex] = Demand × (Lead time + period length)
[tex]\mu[/tex] = 400 × ( 4 + 1)
[tex]\mu[/tex] = 400 × 5
[tex]\mu[/tex] = 2000
the standard deviation for the lead time as well is :
[tex]\sigma[/tex] = standard deviation sd[tex]\sqrt{lead \ time \times period \ length }[/tex]
[tex]\sigma[/tex] = [tex]152 \sqrt{4+1}[/tex]
[tex]\sigma[/tex] = [tex]152 \sqrt{5}[/tex]
[tex]\sigma[/tex] = 339.88
The z - value for the test statistics can now be computed as:
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z = \dfrac{2410 - 2000}{339.88}[/tex]
[tex]z = \dfrac{410}{339.88}[/tex]
[tex]z = 1.2063[/tex]
z = 1.21
The order upto level = Inventory on -hand + Inventory order - Backorders
The order upto level - Inventory order + Backorders = Inventory on -hand
Inventory on -hand = The order upto level - Inventory order + Backorders
where ;
the backorders = [tex]\sigma L(z)[/tex] and [tex]L(z)[/tex] = standard loss
From the tables of distribution function and inventory function for standard normal distribution function
L(z) = 0.0561
the backorders can now be = 340 × 0.0561
the backorders can now be = 19.074
Recall that :
Inventory on -hand = The order upto level - Inventory order + Backorders
consider the fact that the order is up to level of S = 2410
∴ Inventory on -hand = 2410 - 2000 + 19.074
Inventory on -hand = 410 + 19.074
Inventory on -hand = 429.074
