a. How many JJ39877 filters should Filter Systems produce in each production run
ID: 372877 • Letter: A
Question
a. How many JJ39877 filters should Filter Systems produce in each production run of this particular part in order to minimize its annual holding plus set-up cost?
Total demand of filters per year D = 200 * 12 = 2400 units per year
Total production capacity of filters per year P = 50 * 6 *20 *12 = 72,000 per year (ignoring set-up time)
Now calculate modified holding cost in following manner
H’ = H* (1-D/P)
Where,
H’ is the modified holding rate
H is the holding cost = 22% of $2.50 or 0.22 *$2.50
Total demand of filters D = 2400 units per year
Total production capacity of filters P = 72,000 per year
Therefore
H’ = 0.22 * $2.50 (1- 2400/72,000) = 0.55 * 0.9667 = 0.5317 per unit per year
For minimum cost, we have to calculate Optimum Order quantity per order Q
Q = (2 * D* S/ H’)
Where average annual demand, D = 2400 units per year
Production run started costs or Set-up cost, S= (100 +55) * 1.5 = $232.5
Annual holding cost, H’ = 0.5317 per unit per year
Therefore
Q = (2 * 2400* 232.5 / 0.5317) = 1448.77 or 1449 (rounding off to nearest whole number)
Therefore 1449 filters should be produced in each production run to minimize its annual holding plus set-up cost.
b. Assuming that it produces the optimal number of filters in each run, what is the maximum level of on-hand inventory of these filters that the firm has at any point in time?
The maximum level of on-hand inventory of these filters that the firm has at any point in time
H = Q * (1 –D/P) = 1449 * (1- 2400/72,000) = 1400.7 or 1401 units
c. What percentage of the working time does the company produce these particular filters, assuming that the policy in part (a) is used?
Percentage of the working time does the company produce these particular filters = T1 / T
Where T = Q/D = 1449 /2400 = 0.60375 years
And T1 = Q/P = 1449 /72000 = 0.0201 years
Therefore
Percentage of the working time does the company produce these particular filters
= T1 / T
= 0.0201/0.60375
= 0.033 or 3.3%
Therefore 3.3% of each cycle time is set-up time.
Explanation / Answer
Exercise Problem #20 from Nahmias (2013) on p. 220 20. Filter Systems produces air filters for domestic and foreign cars. One filter, part number JJ39877, is supplied on an exclusive contract basis to Oil Changers at a constant 200 units monthly. Filter Systems can produce this filter at a rate of 50 per hour. Setup time to change the settings on the equipment is 1.5 hours. Worker time (including overhead) is charged at the rate of $55 per hour, and plant idle time during setups is estimated to cost the firm S100 per hour in lost profit. Filter Systems has established a 22 percent annual interest charge for determining holding cost. Each filter costs the company $2.50 to produce; they are sold for S5.50 each to Oil Changers. Assume 6-hour days, 20 working days per month, and 12 months per year for your cal culations. a. How many JJ39877 filters should Filter Systems produce in each production run of this particular part to minimize annual holding and setup costs? b. Assuming that it produces the optimal number of filters in each run, what is the maximum level of on-hand inventory of these filters that the firm has at any point in time? c. What percentage of the working time does the company produce these partic- ular filters, assuming that the policy in part (a) is used?
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.