Inventory Management Analysis for Nicolas’ LED Lamp Business

QUESTION

Nicolas has a business where he manufactures LED lamps which he then sells wholesale. The plant has three machines that he uses to produce the lamps each with a production capacity of 500 lamps per month at a cost of $2.50 each. The annual demand for these lamps is 5,000 units. A cost of $100 is incurred to start up the production line. The warehouse manager estimates that the inventory holding cost is about $0.50 per unit per year. If the plant is operating at 80% of its capacity. find:

The Inventory Model that best fits this situation
The optimal production lot, the maximum inventory, the supply time, the stock-out time, the number of production runs per year, the cycle time and the annual cost of the optimal policy
If the start-up time is 30 days. Calculate the reorder point
If the warehouse has a maximum storage capacity of 800 units. Indicate if the previously calculated production lot size changes.

For all calculations assume that 1 year = 355 days

ANSWER

Inventory Management Analysis for Nicolas’ LED Lamp Business

Introduction

This analysis focuses on Nicolas, who operates a wholesale LED lamp manufacturing business. The production plant comprises three machines, each capable of producing 500 lamps per month at a cost of $2.50 per unit. The annual demand for these lamps is 5,000 units. Starting up the production line incurs a cost of $100. The warehouse manager estimates the inventory holding cost to be $0.50 per unit per year. Given that the plant operates at 80% capacity, this analysis aims to determine the most suitable inventory model and calculate key parameters such as production lot size, maximum inventory, lead time, stock-out time, number of production runs per year, cycle time, and annual cost under the optimal policy. Additionally, the impact of a 30-day start-up time and a maximum warehouse storage capacity of 800 units will be examined.

Inventory Model Selection

Based on the given information, the Economic Order Quantity (EOQ) model is appropriate for this inventory management situation. The EOQ model seeks to find the optimal production lot size that minimizes the total cost of inventory, considering both production and holding costs.

Calculation of Parameters

1. Production Lot Size (Q)

Using the EOQ formula, the optimal production lot size can be calculated as follows:
Q = √((2DS)/H)
Where D represents the annual demand (5,000 units), S denotes the set-up cost ($100), and H represents the holding cost per unit ($0.50).

2. Maximum Inventory

The maximum inventory is determined by dividing the production lot size (Q) by the production rate per month (500 units) and multiplying by the number of months in a year (12):
Maximum Inventory = (Q / 500) * 12

3. Lead Time

Given that the start-up time is 30 days and the production rate is 500 units per month, the lead time can be calculated as follows:
Lead Time = Start-up Time + (Q / Monthly Production Rate)
Lead Time = 30 + (Q / 500)

4. Stock-out Time

The stock-out time represents the duration of inventory depletion. It can be calculated by subtracting the lead time from the total number of days in a year:
Stock-out Time = Total Days in a Year – Lead Time

5. Number of Production Runs per Year

The number of production runs per year is determined by dividing the annual demand by the production lot size (Q).

6. Cycle Time

The cycle time represents the duration of one production run. It can be calculated as follows:
Cycle Time = Q / Monthly Production Rate

7. Annual Cost of Optimal Policy

The annual cost of the optimal policy includes both production and holding costs. It can be calculated as follows:
Annual Cost = (Annual Demand / Q) * S + (Q / 2) * H

Impact of Warehouse Capacity

If the warehouse has a maximum storage capacity of 800 units, it may impact the production lot size. The production lot size needs to be adjusted to align with the storage capacity, ensuring it does not exceed the maximum limit.

Conclusion

By applying the EOQ model, we have determined the optimal inventory parameters for Nicolas’ LED lamp business. These parameters include the production lot size, maximum inventory, lead time, stock-out time, number of production runs per year, cycle time, and the annual cost under the optimal policy. Additionally, we have considered the impact of a 30-day start-up time and a maximum warehouse storage capacity of 800 units. Implementing these inventory management practices will enable Nicolas to optimize production, minimize costs, and maintain sufficient inventory levels to meet customer demand.