A supplier of parts to an assembly plant in the household appliance industry is required to make deliveries on a just-in-time basis (daily). For one of the parts that must be delivered, the daily requirement is 100 parts, five days per week, 52 weeks per year. However, the supplier cannot afford to make just 100 parts each day due to the high cost of changing over the production machine. Instead, it must produce in larger batch sizes and maintain an inventory of the parts from which 100 units are withdrawn for shipment each day.

Cost per piece: $16
Holding cost: 24% of piece cost
Changeover time for the production machine: 2.5 hours
Cost of downtime on this machine: $180/hour

Determine:
(a) The economic batch size.
(b) The total annual inventory cost for the data.
(c) How many weeks of demand does this batch quantity represent?

(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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