Question

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.

Answer 1

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;

$\mu$ = Demand × (Lead time + period length)

$\mu$ =  400 × ( 4 + 1)

$\mu$ =  400 × 5

$\mu$ =  2000

the standard deviation for the lead time as well is :

$\sigma$ = standard deviation sd$\sqrt{lead \ time \times period \ length }$

$\sigma$ = $152 \sqrt{4+1}$

$\sigma$ = $152 \sqrt{5}$

$\sigma$ = 339.88

The z - value for the test statistics can now be computed as:

$z = \dfrac{X - \mu}{\sigma}$

$z = \dfrac{2410 - 2000}{339.88}$

$z = \dfrac{410}{339.88}$

$z = 1.2063$

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 = $\sigma L(z)$ and $L(z)$ = 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