MGT 303 Operations Management Homework 3 Total 5 Points Due

Mgt 303 Operations Managementhomework 3 Total 5 Pointsdue Time Be

Analyze inventory management problems involving economic order quantity, reorder points, and safety stock for different scenarios. Calculate optimal order sizes, time between orders, cycle stock, annual holding costs, safety stock, reorder points, and order-up-to levels based on demand data, lead times, and service level targets. Compare safety stock levels between continuous and periodic review policies and explain the reasons for differences.

Paper For Above instruction

Introduction

Inventory management is a critical component of operations management that directly influences a company's efficiency, customer satisfaction, and overall profitability. Effective inventory control involves balancing various costs such as ordering costs, holding costs, and stockout costs while meeting customer demand with minimal delays. This paper dives into practical inventory management calculations through two detailed scenarios, emphasizing the derivation of optimal order quantities, safety stock levels, and reorder points, and culminates in a comparative analysis of different inventory policies.

Scenario 1: Carpet Inventory Management

In the first scenario, a carpet wholesaler faces a steady demand of 10,000 square feet per month, which translates to a monthly demand (D) of 10,000 sqft. The annual demand (D_annual) is calculated by multiplying monthly demand by 12, resulting in 120,000 sqft per year. The ordering cost (S) is $100 per order, and the cost per square foot (C) is $3. The annual holding cost rate (h) is 20% of the unit cost, which translates to an annual holding cost per unit (H) of $0.60 ($3 * 0.20).

A. Optimal Order Quantity (EOQ)

The Economic Order Quantity (EOQ) formula is defined as:

EOQ = √(2DS / H)

Substituting the known values:

EOQ = √(2 120,000 100 / 0.60) = √(24,000,000 / 0.60) = √40,000,000 ≈ 6324.56 sqft

Thus, the optimal order size is approximately 6324.56 square feet, rounded to two decimal places.

B. Time Between Orders

The reorder interval (T) in days is computed by dividing the total demand per year by the number of orders placed annually and multiplying by days per year (assuming 365 days):

Number of orders per year = D_annual / EOQ = 120,000 / 6324.56 ≈ 18.97

Time between orders (T) in days = 365 / 18.97 ≈ 19.22 days, rounded to 19 days.

C. Average Cycle Stock

The average stock during an order cycle is half the EOQ:

Cycle stock = EOQ / 2 = 6324.56 / 2 ≈ 3162.28 sqft

D. Annual Holding Cost

The annual holding cost is calculated by multiplying the average stock by the holding cost per unit:

Annual holding cost = Cycle stock H = 3162.28 0.60 ≈ $1897.37

Scenario 2: Motorola Cell Phones

The weekly demand for Motorola cell phones is normally distributed with a mean (μ) of 300 units and a standard deviation (σ) of 200 units. The lead time (L) for supply is two weeks, so the demand during lead time (D_LT) and its variability (σ_LT) are vital for inventory control.

A. Safety Stock and Reorder Point with Continuous Monitoring

To maintain a 95% service level (Z-score ≈ 1.645), the safety stock (SS) during the lead time is:

SS = Z * σ_LT

σ_LT = σ √L = 200 √2 ≈ 200 * 1.414 ≈ 282.84 units

SS = 1.645 * 282.84 ≈ 465.31 units, rounded to 465 units.

The reorder point (R) considers average demand during lead time plus safety stock:

R = D L + SS = (300 units/week 2 weeks) + 465 ≈ 600 + 465 = 1065 units

B. Periodic Review Policy and Safety Stock

For a review period (T_p) of three weeks, the demand during T_p is:

D_Tp = 300 units/week * 3 = 900 units

The variability of demand during three weeks is:

σ_Tp = σ √T_p = 200 √3 ≈ 200 * 1.732 ≈ 346.41 units

The safety stock for this policy is: SS = Z σ_Tp ≈ 1.645 346.41 ≈ 569.10 units, rounded to 569 units.

The order-up-to level (T) is determined by adding the targeted demand during T_p plus safety stock:

T = D * T_p + SS = 900 + 569 = 1469 units.

Comparison and Analysis of Safety Stocks

The safety stock in the continuous review policy (465 units) is lower than in the periodic review policy (569 units). This difference stems from the nature of the inventory control policies. Continuous review systems monitor inventory levels constantly, allowing for more precise responses and smaller safety stocks aligned closely with actual demand variability. In contrast, periodic review policies evaluate inventory at fixed intervals, leading to increased safety stock to buffer against demand fluctuations during the review period, thus ensuring the desired service level.

Additionally, the periodic review approach necessitates larger safety stocks because the system cannot respond immediately to demand surges during the three-week review period. This buffer helps prevent stockouts but also increases holding costs and tied-up capital. The choice between these policies depends on factors such as the cost of stockouts, ordering costs, and the capacity for real-time inventory monitoring.

Conclusion

This analysis showcases essential inventory management techniques, highlighting the importance of calculating EOQ, safety stock, and reorder points for efficient operations. The differentiation between continuous and periodic review systems illustrates how monitoring frequency influences safety stock levels and overall inventory costs. Properly balancing these parameters ensures high service levels while minimizing the costs associated with inventory. Incorporating demand variability and lead-time considerations into planning is vital for maintaining an optimal inventory system that aligns with the company's operational capabilities and customer service objectives.

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