Question

In: Operations Management

Sarah’s Organic Soap Company makes four kinds of organic liquid soap: regular, lavender, citrus, and tea...

Sarah’s Organic Soap Company makes four kinds of organic liquid soap: regular, lavender, citrus, and tea tree. The demand for the four scents are 150, 120, 75, and 50 kg per hour respectively. Sarah’s production process can produce any soap at the rate of 450 kg per hour, but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn’t produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held.

How many kg of regular soap should Sarah produce before switching over to another scent? (Round the answer to 3 decimal places.)

Number of Regular Soap in kg?

Sarah uses 1,000 kg of organic palm oil per day on average. The supplier charges a $60 delivery fee per order (which is independent of the order size) and $4.75 per kg. Sarah's annual holding cost is 25%. Assume 52 weeks per year and 5 days per week.

Sarah’s supplier is willing to sell her palm oil at a 5% discount if she purchases 10,000 kg at a time. If she were to purchase 10,000 kg per order, what would be her average inventory holding and delivery fees per day (in $)? (Round both answers to 2 decimal places.)

(Note: Do not include her purchasing costs per day, which would be 1,000 × 4.75 × 95%.)

Inventory Costs per Day ?

Delivery Feeds per Day ?

Solutions

Expert Solution

In one production cycle of producing all 4 soaps, total setup time = 1.5 x 4 = 6 hours

Total demand = 150+120+75+50 =395 kgs/hour

Per-unit processing time = 1/ 450 hr/kg

Let the batch-size be Z

Total Processing time = (1/450) * Z

Total Batch time = Total processing time + Total Set-up time = (1/450)*Z + 6

Process capacity = Total output / Total time = Z / ((1/450)*Z + 6)

Capacity required = Total Demand = 395 kgs/hour

Hence, Z / ((1/450)*Z + 6) = 395

Z = 395 * ((Z / 450 ) + 6)

Z * 450 = 395Z + 395 * 6 * 450

Z = 19,390.91 kg

Total batch size = 19,390.91 kg

Proportion of Regular soap = (150 / 395) * 19,390.91 = 7,363.636 kg

Number of Regular Soap in kg = 7363.636 kg

Daily use = 1000 kg

Annual Usage = D = 1000 * 52 * 5 days per week = 260,000‬ kg

Delivery fee = S = $60

Cost per kg = $4.75

Holding cost = H = 25% = 25% * 4.75 = $1.1875‬

Economic Order quantity = EOQ = = = 5,125.786 kg

Now, Order quantity Q = 10000 kg

Cost per kg = 4.75 - 5% = $4.5125

New holding cost = 25% = 25% * 4.5125 = 1.128125

Average Annual Inventory cost = (Q / 2) * H = (10000 / 2) * 1.128125 = $5,640.625

Daily fees = 5640.625 / (52 weeks * 5 days per week) = 5640.625 / 260 = $21.695

Inventory Holding Costs per Day = $21.695

Annual Ordering cost = (D / Q)*S = (260,000 / 10000) * 60 = $1560

Daily fess = 1560 / (52 * 5) = $6

Delivery Fees per Day = $6

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