A Shop That Makes Candles Offers A Scented Candle

A Shop That Makes Candles Offers A Scented Candle Which Has a Monthly

A shop that makes candles offers a scented candle, which has a monthly demand of 360 boxes. Candles can be produced at a rate of 36 boxes per day. The shop operates 20 days a month. Assume that demand is uniform throughout the month. Setup cost is $60 for a production run, and holding cost is $2 per box per month. Determine the following: A) the economic run size B) the maximum inventory (I-max) C) the run time in days ALL WORK SHOWN

Paper For Above instruction

This report aims to determine the optimal production and inventory management strategies for a candle manufacturing shop producing scented candles with specific demand and operational parameters. The analysis focuses on calculating the Economic Production Quantity (EPQ), maximum inventory level, and the duration of each production run, given the demand rate, production rate, setup costs, and holding costs.

Introduction

Effective inventory management is essential for manufacturing operations to reduce costs and meet customer demand efficiently. In this context, the manufacturer seeks to find the optimal order quantity, called the Economic Production Quantity (EPQ), which minimizes total inventory costs considering setup and holding costs. This analysis employs the EPQ model, a variation of the Economic Order Quantity (EOQ) model, adapted for continuous production systems (Heizer, Render, & Munson, 2020). Key parameters include monthly demand, production rate, setup costs, and monthly holding costs, which influence the determination of optimal production runs.

Data and Assumptions

  • Monthly demand (D): 360 boxes
  • Production rate (p): 36 boxes per day
  • Number of operational days per month: 20 days
  • Setup cost (S): $60 per production run
  • Holding cost per box per month (H): $2

Because demand is uniformly distributed, the daily demand rate (d) can be calculated as:

d = D / operating days = 360 / 20 = 18 boxes per day.

Calculation of Economic Production Quantity (EPQ)

The EPQ formula is given by:

EPQ = sqrt( (2 D S) / (H * (1 - d/p)) )

where:

- D is the total monthly demand,

- S is the setup cost,

- H is the holding cost per unit per month,

- d is the daily demand,

- p is the production rate.

Using the provided values:

EPQ = sqrt( (2 360 60) / (2 * (1 - 18/36)) )

Calculate the denominator:

1 - 18/36 = 1 - 0.5 = 0.5

Now, plug into the formula:

EPQ = sqrt( (2 360 60) / (2 * 0.5) ) = sqrt( (43,200) / 1 ) = sqrt(43,200)

Therefore, the Economic Production Quantity (EPQ):

EPQ ≈ 208.08 boxes

Maximum Inventory (I-max)

The maximum inventory, which occurs immediately after a production run and before demand reduces it, can be calculated as:

I_max = EPQ * (1 - d/p)

Substituting the values:

I_max = 208.08 (1 - 18/36) = 208.08 0.5 = 104.04 boxes

Run Time in Days

The run time, representing the duration of a production cycle, is:

Run time = EPQ / p

Using the production rate:

Run time = 208.08 / 36 ≈ 5.78 days

Since the shop operates 20 days per month, the production run lasts approximately 5.78 days, and multiple runs are needed per month to meet the demand.

Conclusion

The analysis indicates that the optimal production batch size for the scented candles is approximately 208 boxes per run, with a maximum inventory of about 104 boxes. Each production cycle lasts around 5.78 days, which fits comfortably within the operational calendar of 20 days per month. Implementing this EPQ-based approach can help the shop minimize total inventory costs while ensuring sufficient stock to meet the uniform demand pattern.

References

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