Answer:
a. The Optimal run size is 5,086 hot dogs
b. The Number of runs per year is 18
c. The Run length is 1 day
Explanation:
a. According to the given data we have the following:
Daily production, p = 4500 per day
Daily demand, u = 310 per day
Number of working days in a year, Tyear = 295 days
Annual demand, D = Daily demand x number of working days; D = 310 x 295; D = 91450
Setup cost, S = $60
Annual holding cost, H = $0.45 per hot dog
So, Optimal run-size can be calculated as follows:
Q* = √ 2 x annual demand x Setup cost / holding cost per unit per year x √daily production / daily production - daily demand
Q* = √2DS / H x √p / p-u
Q* = (√ 2 x 91450 x 60 / 0.45) x (√ 4500 / 4500 - 310)
Q* = (√24386667) x (√1.07)
Q* = (4938.29) x (1.03)
Q* = 5086.44 = 5,086
Therefore, Optimal run size is 5,086 hot dogs
b) The Number of runs per year can be calculated as follows:
Cycle time = Q / u
Cycle time = 5086 / 310 = 16 days
Number of runs = Tyear / cycle time
Number of runs = 295 / 16 = 18
The Number of runs per year is 18
c) The Run length or run time can be calculated as follows:
Run time = Q / p
Run time = 5086 / 4500
Run time = 1.13 = 1
Run length is 1 day
