Question

Daily demand of the carpet d = 28000/350 = 80

Daily production capability p =400

a. Optimum production run quantity = [ 2x demand per annum x set up cost / cost of holding a unit ( 1-d/p)]1/2

= [ 2 x28000 x800 / 5 x ( 1-0.2)]1/2

= 3346.64 =3347

b. Min total inventory cost per year = (1/2) x avg quantity per set up x cost of holding a unit per year x ( 1-d/p)

= 1/2 x3347 x 5 x0.8 = 6694

c.Optimum length of a production run = order size / daily production = 3347/400 = 8.36 days.

d. Number of production runs per year

annual demand / optimum production quantity = 28000/3347 =8.36

e

Quantities consumed during production run = 80x8.36 = 668.8

Remaining quantity = 3447-669 =2678

Number of days for which the quantity will be sufficient = 2678/80 = 33.47 days

which will be the cycle time between the runs.

f. Max inventory level will be at the time when production runs just stops = 2678 ( as calculated in e)

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