Rough Draft: MATH $1324$ Signature Assignment:

In today$$s world of retail, inventory management is key to success. As someone who wants to be in business management, I know how important it is to order the right amount to meet customer demand without storing extra. This write$-$up will go through a scenario where I, as a store manager, need to determine the optimal order quantity for a hot running shoe. We$$ll apply concepts from my math class to calculate the economic order quantity $($EOQ$)$ to make a smart business decision.

The Problem

My store $$Stride Strong$$ carries the popular brand of running shoes $$Trailblazers$.$ We currently have $20$ pairs of Trailblazers in stock, with a daily average demand of $3$ pairs. The supplier charges $$50$ per shoe and there$$s a fixed ordering cost of $$25$ per order. Our storage cost is $$1$ per shoe per month.The question: How many pairs of Trailblazers should I order at once to minimize total inventory cost $($ordering cost $+$ storage cost$)?$ My solution: To calculate the optimal order quantity $($EOQ$),$ we can use the EOQ formula: EOQ $=(2$DS $/$ H$),$ where D $=$ Daily average demand $(3$ pairs$)$S $=$ Ordering cost per order $($$$25)$H $=$ Holding cost per unit per year $($We need to convert monthly storage cost to annual cost$)$ Calculating Holding Cost $($H$)$:First, we need to convert the monthly storage cost of $$1$ per shoe to an annual cost: Annual holding cost per shoe $($H$)=$ Monthly storage cost per shoe $*$ Number of months in a year: H $=$ $$1/$shoe $*12$ months$/$year $=$ $$12/$shoe$/$year$.$ Applying the EOQ Formula: Now, let$$s plug in the values: EOQ $=(23$ pairs$/$day $$25/$order $/$ $$12/$shoe$/$year$)$EOQ $(150)12\mathrm{.}25($We can$$t order part of a shoe, so we round up$)$Optimal Order Quantity: So the optimal order quantity for Trailblazers is $13$ pairs. This way we order enough shoes to meet customer demand without incurring too much ordering and storage cost. Benefits of EOQ Calculating: EOQ helps in reducing ordering costs: By ordering in bulk less often, we reduce the number of orders and the ordering cost. Minimizing Storage Costs: Ordering too many shoes means excess inventory and high storage cost. EOQ helps us strike a balance between having enough stock and overstocking. Higher Customer Satisfaction: By having enough inventory, we ensure our customers can find the shoes they need and thus higher customer satisfaction.

Conclusion

Math $1324$ in action! We can run the business better.