I need a detailed assistance to solve this problem in: Operations Analysis.
3) A chemical manufacturer produces a compound at the rate of 10,000 pounds a day over 250 days each year. Annual demand for that compound is 600,000 pounds per year, and each pound sells for $3.90. There is a fixed setup cost of $1,500 for each production run, and a variable cost of $3.50 for each pound produced. The following costs are incurred:
a)- What is the optimal production lot for the compound (write down the model name, its parameters and formula)?
Step1: Calculating the value of optimal production lot for the compound. We have,
Model Name: Economic production Quantity (EPQ)
The formula of EPQ is as follow:
EPQ = Square Root of [2 x D x S / h (1- D/P)]
D = Annual Demand = 600,000 pounds per year
S = Set-up Cost per production run = $ 1,500
P = Total production = 10,000 x 250 = 2,500,000
h =Holding cost = (Cost of capital + Storage and handling cost) Variable cost per pound
h = (0.22 + 0.12) $ 3.50 = 0.32 x $ 3.50 = $ 1.12 per pound, per year
Substituting these value in the above formula. We get;
EPQ = Square Root of [2 x 600,000 x $1,500 / $ 1.12 (1- 600,000/2,500,000)]
EPQ = Square Root of [$1,800,000,000 / $ 1.12(1 – 0.24)]
EPQ = 45,985.45 units
Step2: Calculating the value of uptime, downtime and cycle time in days, cycle fraction of uptime and the cycle fraction of downtime. We have,
(a) Cycle time between production run = EQP / Total Demand
Time between production run = 45,985.45 / 600,000
Time between production run = 0.07664
(b) Value of uptime = EPQ / Total production
Value of uptime = 45,985.45 / 2,500,000
Value of uptime = 0.01839
(c) Value of downtime = Cycle time between production run – Value of uptime
Value of downtime = 0.07664 – 0.01839
Value of downtime = 0.05825
(d) Cycle fraction of uptime = Value of uptime / Cycle time between production run
Cycle fraction of uptime = 0.01839 / 0.07664
Cycle fraction of uptime = 0.2399
(e) Cycle fraction of downtime = Value of downtime / Cycle time between production run
Cycle fraction of downtime = 0.05825 / 0.07664
Cycle fraction of downtime = 0.760
Step3: Calculating the value of average annual holding and setup costs for the compound. We have,
The average annual cost of holding and setup = D*S/Q + h (1- D/P) Q/2
D = Total Demand = 600,000 pounds
P = Total production = 2,500,000
S = Set-up cost = $ 1,500
Q = EPQ = 45,985.45 pounds
h = Carrying cost = = (0.22 + 0.12) $ 3.50 = 0.32 x $ 3.50 = $ 1.12 per pound, pe...
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