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: 240 notebooks/day

Blue: 295 notebooks/day

Red: 170 notebooks/day

Black: 575 notebooks/day

MySchool can produce 1,520 notebooks per 24-hour day. It takes 8 hours to setup production for another color at a cost of $440. Each notebook costs $0.50 to manufacture prior to printing the logos, and MySchool assumes that the annual holding cost for notebooks is 14% of this cost. Calculate the minimum cost cycle time in days.

Answer 1

Total demand rate, d = 240+295+170+575 = 1280 notebooks/day

Annual demand, D = 1280*365 = 467200 notebooks

Production rate, p = 1520 notebooks/day

Unit cost = $ 0.5

Holding cost, h = 0.5*14% = $ 0.07

Setup cost, k = $ 440 per color * 4 colors = $ 1760

Optimal production lot size, Q = sqrt(2Dk/(h*(1-d/p)))

= sqrt(2*467200*1760/(0.07*(1-1280/1520))) = 385736 notebooks (combined all 4 colors)

Cycle time = Q/d = 301.4 days

Minimum cost cycle time = 301.4 days ANSWER