Sarah\'s organic Soap Company makes four kinds of organic liquid soap- \"regular

Question

Sarah's organic Soap Company makes four kinds of organic liquid soap- "regular, " lavender, " "lea tree." Demand for the four scents are 175, 100, 90, and 25 kgs per hour respectively. Sarah's production process can produce any soap at the rate 500 kgs per hour, but 1.4 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 cycles repeatedly through the four scent s, meets the required demand and minimizes the amount of inventory held. How many kgs of "regular" should Sarah produce before switching over to another scent kgs

Explanation / Answer

Sol:

Recommended Batch Size = Flow rate x Set up time/ [1 – (Flowrate*Processing time)]

Flow Rate = 175 + 100 + 90 + 25 = 390 kgs per hour

Set up time = 4 different scents x 1.4 hour for each switch to a newscent = 5.6 hours

and

Processing time = 500 kgs per hour

Recommended batch size = (390) x (5.6) / [(1 – (390/500)] = 2184 / (0.22) =9927.2727 kgs

Regular Recommended batch = (175/390) x 9927.2727 =4454.55kgs

should be produced before Sarah switches to another scent

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