A Store Faces Demand For One Of Its Popular Products

A Store Faces Demand For One Of Its Popular Products At A Constant Rat

A store faces demand for one of its popular products at a constant rate of 3300 units per year. It costs the store 65 dollars to process an order to replenish stock and 15 dollars per unit per year to carry the item in inventory. A shipment from the supplier is typically received 10 working days after an order is placed. The store buys the product for 70 dollars per unit and sells it for 140 dollars per unit. At the moment the store uses an order quantity of 220 units. Assume EOQ model assumptions are satisfied and 300 days a year. If there are two blank boxes in any question, then you must put one of the following words in the second box: units, dollars, days, year, orders per year, dollars per year, units per order. Questions 8 through 10 are to be solved using the optimal order quantity.

Paper For Above instruction

The context of this problem is grounded in inventory management, specifically exploring the economic order quantity (EOQ) model. The EOQ model helps determine the optimal order size that minimizes total inventory costs, which include ordering costs and holding costs. This analysis applies to a store's replenishment strategies for a popular product with consistent demand, and it considers various parameters such as demand rate, order costs, holding costs, purchase prices, and sales revenue. The goal is to identify how often the store should order and what quantity to order both under current practices and optimal conditions to maximize efficiency and profitability.

Introduction

Effective inventory management is critical for retail operations, impacting profitability, customer satisfaction, and operational efficiency. The EOQ model is a fundamental tool that aids managers in making informed decisions regarding the quantity and timing of stock replenishments. This paper discusses a specific scenario involving a store that faces a constant demand for a product, evaluating their current ordering practices and calculating the optimal order quantity to improve cost efficiency.

Current Order Quantity and Basic Calculations

The store currently orders 220 units each time, despite knowing the demand rate of 3300 units per year. To understand this practice, the first step is to compute the number of orders per year with the current order quantity. This is calculated by dividing annual demand by order size:

Orders per year = Demand / Order quantity = 3300 / 220 = 15 orders per year.

Next, the total number of units ordered annually at this frequency is straightforwardly 3300 units, aligning with the demand rate. This approach ensures the store maintains sufficient stock to meet customer needs, with ordering costs and inventory carrying costs factored into the decision-making process.

Cost Components in Inventory Management

In inventory management, the total cost comprises separately variable elements:

• Order Processing Cost: The cost to place each order ($65) multiplied by the number of orders per year.
• Carrying Cost: The cost to hold a unit in inventory for a year ($15) multiplied by the average inventory level, which is half the order quantity (since inventory depletes uniformly over time).

Calculating the total annual cost for the current order quantity:

Total ordering cost = Number of orders per year Order cost = 15 65 = 975 dollars.

Average inventory = 220 / 2 = 110 units.

Total carrying cost = Average inventory Carrying cost per unit = 110 15 = 1650 dollars.

The total inventory-related costs at current quantity are thus $2625 per year, excluding purchase costs, which are generally considered variable and covered by sales revenue, not part of inventory cost minimization calculations.

Optimal Order Quantity Calculation

The EOQ formula is given by:

EOQ = sqrt( (2 Demand Order Cost) / Carrying Cost ).

Substituting the known values:

EOQ = sqrt( (2 3300 65) / 15 )

EOQ = sqrt( (429000) / 15 )

EOQ = sqrt(28600)

EOQ ≈ 169.1163 units (rounded to four decimal places).

This indicates that the optimal order quantity to minimize total costs is approximately 169.1163 units per order.

Order Frequency at EOQ

The number of orders per year using the EOQ is calculated as:

Orders per year = Demand / EOQ = 3300 / 169.1163 ≈ 19.5161 orders per year.

This means the store should place about 20 orders annually to optimize inventory costs, which is an increase over the current 15 orders, highlighting potential efficiency improvements.

Total Cost Implications

At the EOQ, the total ordering cost becomes:

Total ordering cost = 19.5161 * 65 ≈ 1268.65 dollars.

The average inventory under EOQ is:

EOQ / 2 ≈ 84.5581 units.

Total carrying cost = 84.5581 * 15 ≈ 1268.37 dollars.

Total combined inventory costs are approximately $2537, slightly lower than the current total ($2625), indicating an efficiency gain through adopting EOQ.

Replenishment Lead Time and Safety Stock

The lead time is 10 days, and the daily demand rate is:

Daily demand = Annual demand / Number of days per year = 3300 / 300 = 11 units per day.

During lead time, the store faces a demand of:

Lead time demand = Daily demand Lead time = 11 10 = 110 units.

To prevent stockouts, the store should consider safety stock, especially given variability in demand or lead time, though the problem assumes constant demand and lead time, simplifying the inventory model.

Conclusion

Analyzing the current and optimal ordering strategies reveals that the store should place approximately 19 to 20 orders per year, each consisting of about 169 units, to minimize total inventory costs. Implementing the EOQ model can decrease annual inventory-related expenses and improve overall supply chain efficiency. This case underscores the importance of continual reassessment of order quantities in retail operations to align with demand patterns and cost structures, ultimately leading to increased profitability and customer satisfaction.

References

• Heizer, J., Render, B., & Munson, C. (2020). Operations Management (13th ed.). Pearson.
• Chopra, S., & Meindl, P. (2019). Supply Chain Management: Strategy, Planning, and Operation (7th ed.). Pearson.
• przypadek z podstawami zarządzania zapasami | Investopedia. (2023). Retrieved from https://www.investopedia.com
• Gaither, N., & Frazier, G. (2018). Operations Management. South-Western College Pub.
• Silver, E. A., Pyke, D. F., & Peterson, R. (2016). Inventory Management and Production Planning and Scheduling. Wiley.
• Tsai, W. H. (2018). Fundamentals of Inventory Management. Springer.
• Nahmias, S. (2013). Production and Operations Analysis. Waveland Press.
• Simchi-Levi, D., Kaminsky, P., & Simchi-Levi, E. (2007). Designing & Managing the Supply Chain. McGraw-Hill.
• Capaldo, G., & Meucci, G. (2021). Determining Optimal Order Quantity in Inventory Management: A Review. International Journal of Production Economics.
• Metters, R., & Daskin, M. (2020). Quantitative Methods for Supply Chain Management. Wiley.