Question

MySchool Notebook Company produces custom 3-ring binders with school logos for high schools in the Midwest. They mold binders in four standard colors and then imprint the school’s logo on a to-order basis. The average daily demand for the base color notebooks is as follows: Green: 200 notebooks/day Blue: 255 notebooks/day Red: 185 notebooks/day Black: 525 notebooks/day MySchool can produce 1,620 notebooks per 24-hour day. It takes 8 hours to setup production for another color at a cost of $460. Each notebook costs $0.50 to manufacture prior to printing the logos, and MySchool assumes that the annual holding cost for notebooks is 15% of this cost. Calculate the minimum cost cycle time in days.

Answer 1

Total demand rate = 200+255+185+525

=1165 notebooks /day

Annual demand = 1165*365

=426225 notebooks

Production rate = 1620 notebooks per day

Unit cost = $0.5

Holding cost = 0.5*15/100

= 0.075

Setup cost = $460* 4 colour

=$1840

Optimal production lot size = sqrt(2*annual demand* setup cost/ holding cost*(1 - total demand rate/ production rate)

= sqrt ( 2* 426225*1840 / 0.075 (1 - 1165 / 1620 )

= sqrt (1568508000 / 0.021 )

= 273296 notebooks

Cycle time = optimal production lot size / total demand rate

= 273296 / 1165

Minimum cost cycle time = 234.5 days

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