. 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”, “citrus” and “tea tree”. Demand for the four scents are 150, 120, 75 and 50 kgs per hour respectively. Sarah’s production process can produce any soap at the rate of 450 kgs 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.

a /How many kgs of “regular” should Sarah produce before switching over to another scent? (Hint: the Process Capacity = Demand)

b/ Sarah needs to purchase organic Palm Oil to make the soaps. She needs 1,000 kgs of palm oil per day on average. The supplier charges a $60 delivery fee per order (independent of the order size)and $4.75 per kg. Sarah’s annual holding cost equals 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much palm oil should she purchase with each order (in kgs)? (Hint: use the EOQ formula)

Explanation / Answer

(a) Let X be the number of hours of cycle time, during which atleast one batch production of all the four scents takes place.

So, Production Capacity = 450*(x-6) . 6 hours is the total setup time required for 4 setups required to switchover from one scent to the other. So actual production time is (x-6)

Demand of all the four scents in X hours = (150+120+75+50)*x = 395*x

For demand-production equilibrium state, Production Capacity = Demand

450*(x-6) = 395*x

X = (450*6/(450-395) = 49.09 hours .

Production time for Regular scent before switchover = (49.09-6)*150/395 = 16.36 hours

Qty of Regular scent produced before switchover = 7364 kgs

(b) Annual Demand of Palm Oil = 1000*5*52 = 260,000

Ordering cost = $ 60

Annual holding cost per unit = 25%*4.75 = 1.1875

To minimize Annual holding cost and ordering cost, use EOQ model,

EOQ = (2*Annual Demand*Ordering cost/Holding cost)^0.5 = (2*260000*60/1.1875)^0.5 = 5126 kgs

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