Fossett_HW3

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Katelyn Fossett 02/28/2024 IE 427 IE 427 HW # 3 Chapters 5 & 6 Chapter 5 1. How does the batch size affect the average inventory? The Economic Order Quantity (EOQ) model helps us find the optimal batch size, minimizing total inventory costs like holding and ordering costs. Smaller batches may increase ordering costs but reduce holding costs, while larger batches may lower ordering costs but raise holding costs. In manufacturing, larger production batches may lead to higher average inventory levels if demand doesn't align. Batch size influences reorder points and lead times, with larger batches potentially extending lead times. Smaller batches can increase inventory turnover, while larger ones may require more storage space, impacting holding costs. The relationship depends on ordering policies, production processes, demand patterns, and costs, as organizations seek a balance for cost efficiency using the EOQ model. 2. Explain the tradeoff between setup cost and carrying cost. The tradeoff between setup costs and carrying costs is a critical aspect of inventory management, particularly in the Economic Order Quantity (EOQ) model. Setup costs, incurred with each order or production batch, decrease as batch sizes increase but can rise due to infrequent orders. On the other hand, carrying costs, associated with holding inventory, increase with larger batch sizes due to higher inventory levels but decrease with smaller batches. The challenge lies in finding the optimal balance, known as EOQ, where the total costs of setup and carrying costs are minimized. This equilibrium ensures efficient and cost-effective inventory control by determining the right order or production batch size. 3. Discuss the effects of reducing the size of process batches. Reducing the size of process batches in manufacturing offers advantages such as increased flexibility, lower inventory levels, and quicker response times to market changes. Smaller batches can lead to improved quality control, more efficient resource utilization, and a reduction in environmental impact through minimized waste. However, this approach may result in higher per-unit production costs due to increased setup expenses, and careful consideration is needed to strike a balance between batch size and cost-effectiveness. While smaller batches enhance

adaptability and reduce lead times, managing potential challenges like setup costs and scalability is crucial for optimizing operational efficiency and achieving overall success. 4. A manufacturer buys cardboard boxes from a supplier. The annual demand is 36,000 boxes and is uniformly distributed. The boxes cost $4 each. The estimated order cost is $6, and the carrying cost rate is 30% per year. A. What is the EOQ and what is the annual order and carrying cost? H = 0.3*4 = 1.2 EOQ = sqrt(2DS/H) EOQ = sqrt((2*36,000*6)/1.2) EOQ = 600 OC = D/EOQ * S OC = 36,000/600 * 6 = 60 * 6 = 360 CC = EOQ/2 * H = 600/2 * 1.2 = 360 TC = 360 + 360 = 720 B. How many times a year are orders placed, and what is the average time, in weeks, between orders? N = D/EOQ = 36,000/60 = 60 T = 1/N * 52 = 1/60 * 52 = 0.867 C. Using the answer from (b), if you round the average time between orders to the nearest week, what should the order quantity be? Would you recommend using this order quantity and time interval? If we round the average time between orders to the nearest week, resulting in an interval of 1 week, the recommended order quantity is approximately 692 boxes. However, it's essential to note that this recommendation is based on rounding for simplicity and may deviate from the Economic Order Quantity (EOQ) calculated earlier, which was approximately 600 boxes. The EOQ is a formula that minimizes total inventory costs, and while rounding the time interval provides a straightforward approach, it may not

necessarily lead to the most cost-effective order quantity. Therefore, in practical inventory management, it is generally recommended to use the calculated EOQ to ensure optimal balance between order and carrying costs. 5. Suppose the actual demand turns out to be 72,000 boxes instead of 36,000 boxes. If you had used the EOQ from the previous problem, what would the annual order and carrying cost be? What percent larger is this cost than the cost estimated in (a)? What can you conclude about the cost of an incorrect demand estimate? H = 0.3*4 = 1.2 EOQ = sqrt(2DS/H) EOQ = sqrt((2*72,000*6)/1.2) EOQ = 849 OC = D/EOQ * S OC = 72,000/849 * 6 = 51 * 6 = $306 CC = EOQ/2 * H = 849/2 * 1.2 = $509.4 TC = 306 + 509.4 = $815.4 Percent Increase = ((AC - EC)/EC) * 100 = ((815.4 - 720)/720) * 100 = 13.25% In conclusion, an inaccurate demand estimate can significantly inflate costs. In this case, where the actual demand was twice the initial estimate, it led to a cost increase of around 13.25%. This underscores the crucial role of precise demand forecasting in effective inventory management, emphasizing the need for minimizing costs and optimizing order quantities through accurate predictions. Chapter 6 1. Discuss the cost, quality, time, and flexibility ramifications of reducing setup times. Reducing setup times in manufacturing has multifaceted benefits. It leads to cost savings by minimizing downtime and lowering labor costs associated with setups. The improved consistency in production processes results in higher product quality and reliability, reducing the likelihood of defects. Additionally, shorter setup times increase production throughput, enabling a faster response to changes in demand or product specifications. This enhanced agility

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