Question:
. Sarah’s Organic Soap Company makes four kinds of organic liquid soap: “regular,”
“lavender,” “citrus,” and “tea tree.” Demands 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.
How many kgs of “regular” should Sarah produce before switching over to another scent?
Answer:
Step 1
Sarah should produce 7363.636kgs of “regular” soap scent before switching over to another scent .
Step 2
Within a production cycle, Sarah produces all four types of soaps with total setup time = 1.5 x 4 = 6 hours
Total demand for all four scents of soaps per hour = 150+120+75+50 =395 kg/hour
Per-unit processing time = 1/ 450 hr/kg
With the optimal batch size of B, The process capacity should equal the demand, which is 395 kg /hr, which gives the following equation.
B / (6 + 1/450 x B) = 395 kg/hour
B =(395 * 6) / (1- 395/450)= 19390.91 kg.
the proportion of regular soap among all soaps is 150/395.
Therefore, in each batch, 150/395*19390.91 =7363.636 kg of "regular" soap scent should be produced.
