Required Textbook: Render B. Stair Jr., R. M. Hanna, 740216

Required Textbookrender B Stair Jr R M Hanna M E Hale

List and describe the features of EOQ and ABC.

List and describe the types of carrying costs and ordering costs?

What is the ROP? How is it determined?

What is the purpose of sensitivity analysis?

What is the objective of JIT?

Ross White’s machine shop uses 2,500 brackets during the course of a year, and this usage is relatively constant throughout the year. These brackets are purchased from a supplier 100 miles away for $15 each, and the lead time is 2 days. The holding cost per bracket per year is $1.50 (or 10% of the unit cost), and the ordering cost per order is $18.75. There are 250 working days per year. What is the EOQ? Given the EOQ, what is the average inventory? What is the annual inventory holding cost? In minimizing cost, how many orders would be placed each year? What would be the annual ordering cost? Given the EOQ, what is the total annual inventory cost (including purchase cost)? What is the time between orders? What is the ROP? The EOQ model has several assumptions. List them and explain whether they are readily attainable.

Paper For Above instruction

Economic Order Quantity (EOQ) and ABC Classification are fundamental concepts in inventory management that help organizations optimize stock levels and control costs. The EOQ model aims to determine the ideal order quantity that minimizes the total inventory costs, including ordering and holding costs. ABC classification, on the other hand, categorizes inventory items based on their importance, usage, or value, enabling more focused management strategies.

Features of EOQ include its reliance on a fixed demand rate, constant lead time, FIFO inventory management, and the assumption that ordering costs and holding costs remain stable over time. The EOQ formula balances the trade-off between ordering costs, which decrease with larger order quantities, and holding costs, which increase with larger inventories. The classic EOQ formula is Q* = √(2DS / H), where D is annual demand, S is ordering cost, and H is holding cost per unit.

ABC analysis categorizes inventory into three classes: A, B, and C. Class A items are high-value, low-quantity, and highly vital to operations, requiring tight control and frequent review. Class B items are of moderate value and demand, requiring regular monitoring. Class C items involve low-value, high-quantity items that demand simple control measures. This classification helps prioritize management efforts, optimize ordering, and reduce holding costs for less critical items.

Carrying costs are the costs associated with holding inventory, including storage, insurance, depreciation, obsolescence, and opportunity costs. These costs are typically divided into several types: physical storage costs, inventory insurance, depreciation, obsolescence, and capital costs. Ordering costs refer to expenses incurred each time an order is placed, regardless of the order size. These include administrative costs, shipping, inspection, and setup costs.

The Reorder Point (ROP) signifies the inventory level at which a new order should be placed to replenish stock before it runs out. It is determined by the lead time demand, calculated as ROP = Demand during lead time = (Demand per day) × (Lead time in days). Extra safety stock may be added to account for variability in demand or lead time, especially in uncertain environments.

Sensitivity analysis assesses how sensitive the outcome of a model or system is to changes in input parameters. Its purpose is to identify critical variables that impact results, evaluate risks, and improve decision-making robustness. It helps organizations understand how fluctuations in demand, costs, or lead time influence inventory policies and costs.

Just-In-Time (JIT) is a manufacturing and inventory strategy aimed at reducing waste and improving efficiency by receiving goods only as they are needed in the production process. The main objective is to minimize inventory levels, reduce storage costs, and increase responsiveness. JIT emphasizes supplier relationships, quality control, and waste reduction, leading to streamlined operations and cost savings.

Applying EOQ to Ross White’s machine shop: the annual demand (D) = 2,500 brackets; unit cost = $15; lead time = 2 days; holding cost per year per unit = $1.50; ordering cost (S) = $18.75; workdays per year = 250. The EOQ is calculated using the formula Q* = √(2DS / H).

Plugging in the values: Q* = √(2 × 2,500 × 18.75 / 1.50) = √(93,750 / 1.50) = √62,500 ≈ 250 units. The average inventory is thus approximately half of EOQ, or 125 units. The annual holding cost is H × average inventory = 1.50 × 125 = $187.50 annually.

Number of orders per year = D / EOQ = 2,500 / 250 = 10. The annual ordering cost = Number of orders × S = 10 × $18.75 = $187.50. Total purchase cost = D × unit cost = 2,500 × $15 = $37,500. The total annual inventory cost includes purchase, holding, and ordering costs: $37,500 + $187.50 + $187.50 = $37,875.

Time between orders, or reorder cycle, equals EOQ divided by daily demand: Daily demand = D / workdays = 2,500 / 250 = 10 brackets per day. Time between orders = EOQ / daily demand = 250 / 10 = 25 days. Reorder Point (ROP) = demand during lead time = daily demand × lead time = 10 × 2 = 20 brackets.

The EOQ model assumes constant demand and lead time, immediate replenishment, fixed costs per order, and no quantity discounts. It also presumes demand is deterministic and that inventory can be replenished instantaneously once ordered. In real-world scenarios, demand and lead times often fluctuate, making these assumptions challenging to meet perfectly. Nonetheless, the EOQ remains a valuable tool for initial planning and cost minimization.

In conclusion, understanding the features and application of EOQ, ABC analysis, and related inventory costs is vital for effective supply chain management. These tools assist organizations in balancing inventory levels, controlling costs, and improving operational efficiency. While the assumptions behind EOQ provide a simplified model, practical adaptations and sensitivity analysis are necessary to tailor strategies to real-world variability and uncertainties.

References

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• Harris, F. (1913). How Many Parts to Make at Once. Factory, The Magazine of Management, 10(2), 135-136.
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