with the poblem listed below how do we know that it is more economical to order more than $1000$ units @ $4\mathrm{.}75$ nventory management is a critical aspect of supply chain operations, and adopting an efficient continuous review system is essential for maintaining optimal stock levels. In this scenario, we will explore the key parameters and calculations required to make informed decisions regarding the optimal order quantity, reorder point, safety stock, and average inventory.

a$.$ Optimal Order Quantity:

The Economic Order Quantity $($EOQ$)$ is a fundamental metric in continuous review inventory systems. It represents the ideal order quantity that minimizes the total cost of inventory, considering both ordering and carrying costs. The EOQ formula is given by:

EOQ $=(2$DS$/$H$)$

Where:

D is the demand per day,

S is the ordering cost, and

H is the holding cost per unit per year.

Given the information in the scenario:

D$=20*300$ units per day,

S $=$ $$10,$

H $=0\mathrm{.}2\backslash$times $$4\mathrm{.}75,$ as the holding cost is $20$ percent of the unit price.

Calculate EOQ using the formula.

EOQ $=(2*20*300*10/(0\mathrm{.}2*4\mathrm{.}75)=355\mathrm{.}4356$

b$.$ Reorder Point:

The reorder point is the inventory level at which a new order should be placed to avoid stockouts during the lead time. It is calculated as the product of the average demand during lead time and the lead time in days. The formula is:

ReorderPoint$=$D$\backslash$times LT $+$ safety stock

Where:

D is the demand per day, and

LT is the lead time in days.

Given D$=20$ units per day and LT$=6$ days, calculate the reorder point.

ROP $=20*6+78\mathrm{.}4=198\mathrm{.}4199$

c$.$ Safety Stock:

Safety stock acts as a buffer to account for variability in demand and lead time. It ensures that the desired service level is achieved even in the presence of uncertainties. The formula for safety stock is:

z $\backslash$times $\backslash$sigma $\backslash$times Demand per day $=1\mathrm{.}96\backslash$times $2\backslash$times $20=78\mathrm{.}479$

d$.$ Average Inventory:

The average inventory is the mean level of inventory over time and can be calculated as half of the order quantity plus the safety stock. The formula is:

AverageInventory $=$ EOQ$/2+$ SafetyStock

$=356/2+79=257$

Explanation:

Optimizing inventory management requires a thorough understanding of demand patterns, lead times, and cost structures. By calculating the EOQ, reorder point, safety stock, and average inventory, businesses can strike a balance between the costs associated with ordering and holding inventory.