Answer :
(a) The economic batch size is 547 parts.
(b) The total annual inventory cost is $1047.36.
(c) The batch quantity represents 1.09 weeks of demand.
(a) Economic batch size:
First, let's calculate the changeover cost per batch. The changeover time is 2.5 hours, and the cost of downtime is $180 per hour, so the changeover cost per batch is 2.5 hours × $180/hour = $450.
Next, let's calculate the production cost per batch. The daily requirement is 100 parts, and the supplier delivers 5 days a week for 52 weeks. So the annual requirement is 100 parts/day × 5 days/week × 52 weeks/year = 26,000 parts.
To minimize the total cost, we need to find the batch size that balances the changeover cost and the holding cost. Using the economic order quantity (EOQ) formula, we can calculate it as:
EOQ = √[(2 × annual requirement × changeover cost) / holding cost]
Substituting the values, we have:
EOQ = √[(2 × 26,000 × $450) / (0.24 × $16)]
≈ √(23,400,000 / 77.76)
≈ √300,000
≈ 547 parts (approximately)
Therefore, the economic batch size is approximately 547 parts.
(b) Total annual inventory cost:
To find the total annual inventory cost, we need to calculate the carrying cost, which is the holding cost multiplied by the average inventory level.
Average inventory level = Economic batch size / 2 = 547 / 2 = 273.5 parts
Carrying cost = Holding cost × Average inventory level
= 0.24 × $16 × 273.5
≈ $1047.36
Thus, the total annual inventory cost is approximately $1047.36.
(c) Number of weeks of demand represented by the batch quantity:
The batch size is 547 parts, and the daily requirement is 100 parts. Therefore, the batch quantity represents 547 parts / 100 parts/day = 5.47 days of demand.
Since there are 5 working days in a week, the batch quantity represents approximately 5.47 / 5 ≈ 1.09 weeks of demand.
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