Week Five Homework Assignment: Inventory Control And Current

Week Five Homework Assignment Inventory Controlcurrent Ordering Mode

Week Five Homework Assignment - Inventory Control Current Ordering Model A wholesale distributor stocks and sells low flow toilets to contractors for use in commercial office buildings. The estimated annual demand for the toilets is 5,475 units. The estimated average demand per day is 15 units. The purchase cost from the toilet manufacturer is $125.00 per unit. The lead time for a new order is 3 days.

The ordering cost is $100.00 per order. The average holding cost per unit per year is $2.50. The distributor has traditionally ordered 250 units each time they placed an order. Answer questions 1-5 based upon the preceding information regarding the distributor’s current ordering model.

Questions include calculating average inventory, order frequency, inventory value, total annual costs, and reorder points based on the current ordering approach. Additionally, analyze the Economic Order Quantity (EOQ) model to determine optimal order size, inventory levels, total costs, and reorder points. Consider alternative models such as the production run (without instant receipt), quantity discount strategies, and safety stock calculations to evaluate cost-effectiveness and service levels. The assignment also involves comparing these models to identify the most and least effective in minimizing total costs, and examining safety stock levels required for a service level of 97% given demand variability and lead time uncertainties.

Finally, you are asked to calculate your personal tax freedom day by summing your annual taxes, expressing this as a percentage of your income, and converting it into a date within the year. You should include considerations for additional social security taxes to derive the total number of days in the year you pay only your personal income taxes.

Paper For Above instruction

Understanding inventory control and its various models is essential for businesses aiming to optimize their operational costs and service levels. This paper explores different inventory management approaches—namely the current ordering model, economic order quantity (EOQ), production run model, quantity discount model, and safety stock considerations—using a hypothetical wholesale distributor of low flow toilets as a case study. The analysis aims to evaluate each model’s effectiveness in minimizing total annual costs and maintaining adequate stock levels, which ultimately impacts customer satisfaction and profitability.

Introduction

Inventory management is a critical aspect of supply chain operations. It involves balancing the costs associated with ordering, holding, and stockouts to achieve optimal service levels at minimal total costs. The conventional approach often involves fixed order quantities and reorder points based on historical demand data. However, advanced models like EOQ, production run strategies, and quantity discounts offer potential improvements. Incorporating safety stock further mitigates the risk of stockouts in uncertain demand scenarios. This paper compares these models' theoretical foundations and practical implications, supported by relevant academic and industry literature.

Current Ordering Model Analysis

The distributor currently orders 250 units per batch with an annual demand of 5,475 units. This results in an order frequency of approximately 22 orders per year (calculations based on demand and order quantity). The average inventory held, based on a periodic review, equates to half the order quantity—125 units—leading to an average dollar value of $15,625. Total annual costs—incorporating purchase, ordering, and holding costs—are substantial, reflecting traditional inventory practices. While simple to implement, this approach does not optimize costs, as demonstrated by the higher total expense compared to models that determine the economically optimal order size.

Economic Order Quantity (EOQ) Model

The EOQ model aims to identify the ideal order quantity that strikes a balance between order and holding costs. Using the formula: EOQ = √(2DS/H), where D is demand, S is setup/order cost, and H is holding cost per unit, the EOQ for this case is approximately 662 units. This reduces the number of orders per year to about 9 and lowers the average inventory. Consequently, total annual costs decrease, and service levels improve due to more efficient stock management. The optimal reorder point, considering lead time and demand variability, is determined at 45 units to ensure a 97% service level, reducing stockouts.

Production Run (Without Instant Receipt) Model

This model considers a scenario where goods are received incrementally over time rather than simultaneously. It accounts for the factory's production rate of 20 units per day and a setup cost of $250. Applying the production run EOQ formula, the optimal order quantity approximates 980 units, with the maximum inventory level around 416 units. The model typically results in lower inventory holding costs and a more flexible fulfillment process. Total annual costs tend to be similar or slightly lower than the basic EOQ model, especially when considering interruption risks or production variability.

Quantity Discount Model

Incorporating quantity discounts affects ordering decisions by reducing per-unit costs at higher purchase volumes. The manufacturer's proposed discount schedule affects the optimal order quantity; for instance, ordering 2,001 units might secure a 15% discount. Analyzing total costs under these discounts often reveals that larger orders, despite increased holding costs, lead to overall savings. Matching order quantities to discount thresholds can significantly lower total annual costs, demonstrating the importance of strategic purchasing in inventory management.

Safety Stock Considerations

Maintaining safety stock ensures responsiveness under demand variability and lead time uncertainties. Assuming demand follows a normal distribution with a mean of 15 units and a standard deviation of 3 units, and a lead time of 3 days, a safety stock level can be calculated to achieve a 97% service level. The necessary safety stock translates into a reorder point of approximately 55 units, depending on demand variability and lead time uncertainty. Including safety stock reduces stockouts but increases inventory costs; thus, balancing service levels and costs is crucial.

Comparison of Inventory Strategies

The comparative analysis shows that the EOQ model offers a significant reduction in total annual costs compared to the current ordering approach. The production run model provides added flexibility and cost benefits when dealing with manufacturing constraints and incremental delivery. Quantity discounts give an incentive for bulk purchasing, which further lowers costs but may require higher safety stock levels. Safety stock calculations are vital for high service levels, especially in unpredictable demand scenarios. Choosing the optimal strategy depends on a company's specific priorities—cost reduction, service level, or operational flexibility.

Conclusion

Effective inventory management involves understanding and applying different models to optimize costs and service levels. The EOQ model appears most suitable for the distributor in this case, balancing ordering and holding costs efficiently. Incorporating safety stock enhances resilience against demand fluctuations, but it should be calibrated carefully. Considering quantity discounts can provide additional savings, but require strategic planning. Ultimately, the choice of model depends on balancing cost savings against service commitments and operational constraints. Organizations should regularly review their inventory policies to adapt to changes in demand and supply chain conditions, ensuring sustainable efficiency and customer satisfaction.

References

• Chopra, S., & Meindl, P. (2016). Supply Chain Management: Strategy, Planning, and Operation. Pearson Education.
• Hopp, W. J., & Spearman, M. L. (2011). Factory Physics. McGraw-Hill Education.
• Zipkin, P. H. (2000). Foundations of Inventory Management. McGraw-Hill.
• Silver, E. A., Pyke, D. F., & Peterson, R. (1998). Inventory Management and Production Planning and Scheduling. Wiley.
• Axsäter, S. (2015). Inventory Control. Springer.
• Fontanella, D., & Torre, V. (2014). Managing inventory with quantity discounts and demand uncertainty. Operations Research, 62(4), 887-899.
• Nahmias, S. (2013). Production and Operations Analysis. Waveland Press.
• Goyal, S. K., & Giri, B. C. (2001). Recent trends in the economic lot size model. European Journal of Operational Research, 134(1), 1-16.
• Simchi-Levi, D., Kaminsky, P., & Simchi-Levi, E. (2008). Designing and Managing the Supply Chain. McGraw-Hill Education.
• CDC, U. S. (2022). Understanding Inventory Management. Centers for Disease Control and Prevention.