The University Of Alabama Culverhouse College Of Business ✓ Solved

The University Of Alabama Culverhouse College Of Business Om 423 I

The assignment involves developing inventory management strategies for different scenarios, including order quantity determination with discounts, managing storage space limitations in ordering policies, and calculating economic order quantities and backorders for multiple items with specific parameters. It requires analyzing economic order quantity (EOQ), total costs, reorder levels, and the impact of space constraints and backordering policies on inventory management efficiency.

Sample Paper For Above instruction

Introduction

Effective inventory management is critical for optimizing operational efficiency and minimizing costs in manufacturing and retail industries. This paper explores three distinct scenarios related to inventory control—calculating optimal order quantities with discounts, establishing ordering policies under storage space constraints, and determining EOQ and backordering strategies for multiple items. Each scenario involves analyzing cost factors, demand rates, lead times, and storage limitations to develop practical inventory policies that balance service levels and cost efficiency.

Scenario 1: Order Quantity and Total Cost with All-Units Discount Scheme

The first scenario requires determining the optimal order quantity, total annual costs, and reorder level for a product managed by Company Z. The demand is 1,575 units per week over 45 operational weeks per year, with per-unit costs decreasing based on quantity discounts. The key factors include the ordering cost ($400), the demand rate, unit costs at various quantity levels, and holding costs (30% of unit cost annually).

To find the economic order quantity considering quantity discounts, we analyze the two primary elements: ordering cost and holding cost, and how they interplay with discounts. The classic EOQ formula is modified to account for different unit prices at various order quantities, to select the most cost-effective ordering point. For example, lower unit costs at higher quantities reduce overall costs but increase order size, affecting holding costs.

The calculation involves:

- Evaluating the EOQ for each price level.

- Checking whether the EOQ aligns with the quantity discounts' bounds.

- Selecting the order quantity that yields the lowest total annual cost, combining ordering, holding, and purchase costs.

The total annual cost includes:

- Purchase cost = unit cost * demand volume.

- Ordering cost = number of orders per year * order cost.

- Holding cost = average inventory * unit holding cost.

For the reorder level, considering a six-week lead time, it's calculated by demand during lead time, i.e., 1,575 units/week * 6 weeks = 9,450 units.

By calculating these precisely, the optimal order quantity might lean toward the largest quantity discount that minimizes total costs, subject to the demand and cost structure.

Scenario 2: Inventory Policy Under Space Constraints

The second scenario emphasizes the development of ordering policies constrained by a total storage space of 4,500 square feet and specific space allocations for items 1 and 2. The weekly demands, costs, and space per unit are specified, with the company operating 50 weeks annually.

A key aspect involves calculating the EOQ for each item without constraints and then adjusting it using a space reduction factor, denoted as C=2, which moderates order size to respect storage limitations. The decision involves:

- Computing the standard EOQ for each item:

EOQ = √(2 Demand Setup Cost / Holding Cost Rate).

- Adjusting EOQ based on the space constraint:

Adjusted EOQ = EOQ / C, if necessary, to ensure the total space used, i.e., sum of (EOQ/2 * space per unit), does not exceed 4,500 sqft.

Analyzing whether C=2 is reasonable involves assessing if this factor yields feasible order quantities that respect the storage constraints. Justification is based on cost efficiency and the practicality of the reduced order sizes.

The comparison of total relevant cost (TRC)—which includes purchase, ordering, and holding costs—under the adjusted policy versus the unconstrained EOQ approach illustrates the impact of space limitations on inventory costs.

Scenario 3: Inventory Policy with Backorders

The third scenario involves managing two items with specific demand, cost, and lead time parameters, while allowing backorders. For each item, the EOQ with backordering, total relevant costs, and reorder level are calculated based on economic order quantity models that incorporate backorder costs.

- The EOQ with backorders is derived considering:

EOQ_b = √(2 Demand Setup Cost / (Holding Cost + Backorder Cost))

- Planned backorders are evaluated to minimize total costs, balancing ordering, holding, and backorder penalties.

- The reorder level includes demand during lead time plus safety stock or backorder considerations, which depend on the critical ratio (calculated from costs).

These calculations aid in determining optimal stock levels while permitting backordering, reducing excess inventory, and improving service levels during supply shortages. The analysis demonstrates the trade-offs between carrying costs, stockouts, and backorder costs in developing effective policies.

Conclusion

Effective inventory management requires a comprehensive balancing of costs, storage limitations, and supply chain variables. By analyzing economic order quantities, adjusting for space constraints, and incorporating backorders, firms can develop sophisticated policies to minimize costs while maintaining desired service levels. Each scenario illustrates the importance of tailoring inventory strategies to specific operational contexts, highlighting the value of quantitative tools like EOQ models and constraint-based adjustments.

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